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Beekman, Matthew K.
Fundamental investigations on open-framework intermetallic materials of group 14
h [electronic resource] /
by Matthew K. Beekman.
[Tampa, Fla.] :
b University of South Florida,
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Dissertation (Ph.D.)--University of South Florida, 2009.
Includes bibliographical references.
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ABSTRACT: Crystalline open-framework intermetallics have long attracted the attention of chemists, physicists, and materials scientists. The intriguing structures such materials exhibit are often intimately related to the unique physical properties they possess. The present work is focused on the preparation and characterization of open-framework intermetallic materials based on group 14 elements, in particular those crystallizing in clathrate and related structures such as the clathrate-II phases. Materials possessing the clathrate-II crystal structure have received increased attention in recent years, as a result of both the unique properties they exhibit as well as potential for use in technologically important applications such as thermoelectrics, photovoltaics, and optoelectronics. However, in comparison with other clathrate structure types, characterization of clathrate-II materials has in general been far less extensive.Moreover, many conceivable compositions have yet to be realized. The purpose of this work is to expand the current knowledge of the structural, chemical, and physical properties of these materials, while simultaneously exploring new compositions and synthetic routes to clathrate-II phases. One of the unique and promising aspects of clathrate-II materials is the ability to vary the guest concentration, which is shown to have significant implications for the structural and physical properties of NaxSi (0< x< 24) materials. It is demonstrated that new compositions can be explored by novel approaches to chemical design. Framework substitution in clathrate-II compounds is explored in an effort to assess possibilities for influencing the physical properties of these materials.A novel zeolite-like framework phase, Na1-xGe3+z, has been discovered, and is shown to be a new low-thermal conductivity crystalline solid, suggesting a new approach to the design of crystalline intermetallic materials with low thermal conductivity. New directions in synthesis of intermetallics are identified, with emphasis on unconventional preparative methods and the opportunities they offer. Processing of reactive precursors by spark plasma sintering is demonstrated as a new preparative tool for crystal growth, identifying the first method for preparation of clathrate-II NaSisingle-crystals since the discovery of these compounds more than four decades ago.
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Advisor: George S. Nolas, Ph.D.
t USF Electronic Theses and Dissertations.
Fundamental Investigations on Open-frame work Intermetallic Materials of Group 14 by Matthew K. Beekman A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics College of Arts and Sciences University of South Florida Major Professor: George S. Nolas, Ph.D. Lilia Woods, Ph.D. Sarath Witanachchi, Ph.D. Garret Matthews, Ph.D. Date of Approval: March 24, 2009 Keywords: clathrates, intermetallics, silic on, germanium, thermoelectrics, photovoltaics Copyright 2009 Matthew K. Beekman
To my parents, Linda and Frank Beekman, who have always given me support and encouragement in all that I have endeavored to do.
Acknowledgements First, and foremost, I must express my deep gratitude and appreciation to my advisor Prof. George Nolas, who has guided me th rough the ups and downs, ins and outs, and joys and frustrations that ar e the process of pursuing a P h.D. in scientific research. Looking back, I can imagine no better lab to ha ve been in, or advisor to have worked with. IÂ’d like to thank all of the many great post-doctoral associates and fellow students, present and past, that IÂ’ve ha d the pleasure to work with in our lab over the years, who have each made the workplace somewhere to look forward to each morning. Special thanks to (Dr.) Joshua Martin for many great discussions and insi ght. My appreciation goes to my committee members for guidance, in particular to Prof. Lilia Woods for continued encouragement. I wish to express my sincere gratitude for the University of South Florida Presidential Doctoral Fellowship, which gave me the freedom to focus on research during my graduate career. Appreciation is given to th e Deutscher Akademischer Austasch Dienst (DAAD) for a graduate research scholarshi p which funded my three month independent research visitation at the Max Planck Institut fr Chemische Physik fester Stoffe (MPICPfS) in Dresden, Germany, where research pr esented in Chapter 5 was carried out. I am grateful to Prof. Dr. Yuri Grin, Director of MPI-CPfS, for accommodating and advising me at the Institute during that time. I would also like to acknowledge funding pr ovide by the U.S. Department of Energy, Office of Basic Energy Sciences, for the res earch presented in the pages that follow. I am indebted to a number of colleagues who have contributed their expertise in various ways to this collective work. Rather than list them here, I have instead indicated the contributions of others at the points in th e text where they are discussed. I would like however to take the opportunity here to thank Dr. Winnie Wong-Ng of NIST for continuing collaboration and assistance, as we ll as Prof. Jan Gryko of JSU for useful
discussions on the synthesis of clathrates. My colleagues Dr Michael Baitinger and Mr. Bodo Bhme are acknowledged for many stimul ating discussions and assistance during my short time at MPI-CPfS. I would like to thank the memb ers of our office staff in the Department of Physics, present and past, for all of th eir support and assistance: Mary Ann Prowant, Daisy Matos, Kimberly Carter, Evelyne Keeton-Williams, and the late Sue Wolfe. The importance of the support and understand ing of my friends and family throughout my time as a graduate student can not be overstated. I especially thank Teresa for all of her support and patience through thick and thin.
i Table of Contents List of Tables................................................................................................................. ..iii List of Figures................................................................................................................ ..vi Abstract....................................................................................................................... ....xii 1 Introduction................................................................................................................. ...1 1.1 Clathrate-I compounds....................................................................................2 1.2 Structure, bonding, and crystal chemistry in clathrate-II materials.....................................................................................3 1.3 Synthetic routes to cl athrate-II materials........................................................9 1.4 Electronic properties of clathrate-II materials..............................................14 1.5 Thermal and vibratio nal properties of clathrate-II materials...................................................................................18 1.6 Remarks on the present work........................................................................21 2 Preparation and physical pr operties of the binary clathrate-I K8Ge44....................................................................................................23 3 Framework substitution in germanium clathrate-II.....................................................33 3.1 Synthesis.......................................................................................................33 3.2 Single crystal X-ray diffraction studies of Cs8Na16AgyGe136y.......................................................................................34 3.3 Structural characterization of Cs8Na16Cu5Ge131: Powder X-ray diffraction and EXAFS........................................................44 3.4 Electrical and thermal transport in Cs8Na16Cu5Ge131.........................................................................................55 3.5 Concluding remarks and future directions....................................................58 4 Synthesis and characterization of NaxSi136 (0 < x < 24)..............................................60 4.1 Synthesis of NaxSi136 (0 < x < 24).................................................................60 4.2 Structural characterization of NaxSi136 (0 < x < 24) clathrates.................................................................................64 4.3 Thermal stability of NaxSi136 clathrates........................................................72 4.4 Transport properties of Na22Si136..................................................................73
ii 5 Single-crystals of intermetallic clathrates by spark plasma sintering: preparation, crystal structure, and transport properties of Na24Si136.............................................................................77 5.1 Preparation of Na24Si136 by spark plasma sintering......................................78 5.2 Single-crystal X-ray diffraction studies on Na24Si136......................................................................................................83 5.3 Transport properties of Na24Si136..................................................................87 5.4 SPS processing as a general preparative tool................................................92 6 Synthesis and characteriza tion of a novel zeolite-like binary phase: Na1xGe3+ z.........................................................................................94 6.1 Synthesis.......................................................................................................94 6.2 Crystal structure solution and refinement.....................................................96 6.3 Crystal structure and crystal chemistry of Na1xGe3+ z...................................98 6.4 Transport properties of Na1xGe3+ z..............................................................105 References..................................................................................................................... 109 Bibliography.................................................................................................................12 5 Appendix....................................................................................................................... 126 About the Author.................................................................................................End Page
iii List of Tables Table 1.1 Clathrate-II com positions, synthesis method, and lattice parameters.............................................................................14 Table 1.2 Vibrational frequenc ies for the guest atoms in Cs8Na16Si136 and Cs8Na16Ge136, as determined from temperature dependent single crystal XRD (ADP data), Raman scattering, and density functional theory calculations.................................................................18 Table 2.1 Examples of known binary type I clathrate compositions with selected references given..........................................24 Table 2.2 Selected data at 300 K for the K8Ge442 specimen of the present work..................................................................................27 Table 3.1 Summary of data collection for the three compositions of Cs8Na16AgxGe136x.....................................................................................35 Table 3.2 Crystal and struct ure refinement data for Cs8Na16AgxGe136x (at 25 C)..................................................................37 Table 3.3 Atomic coordinates for the three Cs8Na16AgyGe136y Compositions ( Fd 3 m No. 227, origin chosen at center.......................................................................................................38
iv Table 3.4 Selected inter-atomic distances () in Cs8Na16AgyGe136y...................................................................................40 Table 3.5 Selected bond angles for Cs8Na16AgyGe136y ( ).....................................42 Table 3.6 Selected crystallographic data and Rietveld refinement details for Cs8Na16Ge136 and Cs8Na16Cu5Ge131............................................................................................................................ .....45 Table 3.7 Atomic coordinates for Cs8Na16Ge136 and Cs8Na16Cu5Ge131.....................................................................................45 Table 3.8 Summary of local struct ure parameters as determined From analysis of XAFS spectra..............................................................51 Table 3.9 Summary of th e static disorder ( static 2 ), thermal disorder ( thermal 2 ), total disorder ( total 2 ), Debye temperature ( D), and Einstein temperature ( E) for the Cu-Ge and Ge-Ge pairs in Cs8Na16Cu5Ge131....................................53 Table 5.1 Crystallographic data for Na24Si136, single-crystal XRD........................84 Table 5.2 Atomic parameters for Na24Si136 (single-site model)..............................85 Table 5.3 Anisotropic disp lacement parameters for Na24Si136 (single site model)...................................................................................85 Table 5.4 Atomic parameters for Na24Si136 (split-site model)................................85 Table 5.5 Anisotropic disp lacement parameters for Na24Si136 (split-site model).....................................................................................85
v Table 5.6 Comparison of the r oom temperature electrical resistivities and residu al resistance ratios RRR = R (300 K)/ R ( T0), for the Na24Si136 specimen of the present work and several intermetallic clathrate specimens from the literat ure showing metallic or Â“metallic-likeÂ” resistivities (i.e. d /dt is positive definite over the entire range of measurement)......................................89 Table 6.1 Refinement results for Specimens I and II..............................................98 Table 6.2 Lattice parameters for Specimens I and II..............................................98 Table 6.3 Crystallographic data for Na1xGe3+ z from Rietveld refinement against sync hrotron X-ray and neutron powder diffraction.................................................................................101
vi List of Figures Figure 1.1 Sixteen pentagonal dodecahedra ( E20) and eight hexacaidecahedra ( E28) share faces to form the clathrate-II crystal structure......................................................................4 Figure 1.2 Free cavity diameter to cage-member diameter ratio versus the square root of coordination number (CN) of the interior (i.e. guest) site, for several cage-like materials....................................................................................................5 Figure 1.3 Temperature dependent isotropic atomic displacement parameters ( Uiso) for the E28 guest as well as framework sites in A8Na16E136 ( A = Rb, Cs; E =Si, Ge)..............................................7 Figure 1.4 Dimer formation betw een the Na guests in the NaxSi136 clathrates...................................................................................................8 Figure 1.5 Polyatomic Zintl anions..........................................................................10 Figure 1.6 High resolution tran smission electron microscope (HRTEM) image of the new germanium allotrope Ge136, taken for the  zone axis........................................................12
vii Figure 1.7 Seebeck coefficient (ro und symbols) and resistivity (triangular symbols) as a function of temperature for polycrystalline Cs8Na16Si136 (open symbols) and Cs8Na16Ge136 (filled symbols).................................................................15 Figure 1.8 Stokes Raman s cattering spectra for Si136 and Cs8Na16Si136............................................................................................19 Figure 1.9 Computed phonon disper sion relations along selected directions in reciprocal space for Cs8Na16Ge136......................................20 Figure 2.1 Partial crystal structure of K8Ge442......................................................24 Figure 2.2 Simple schematic illustrating the presumed local electronic environment of a framework vacancy in K8Ge442, after Ramachandran et al.......................................................25 Figure 2.3 Powder X-ray diffraction patterns for K8Ge442....................................27 Figure 2.4 Differential thermal analysis (DTA) for K8Ge442................................29 Figure 2.5 Electrica l transport in K8Ge442.............................................................30 Figure 2.6 Temperature dependence of the thermal conductivity of K8Ge442............................................................................................31 Figure 3.1 Powder X-ray diffraction patterns for Cs8Na16AgyGe136y clathrates.................................................................................................36
viii Figure 3.2 Local tetrahedral bonding environments of the (a) Ge1 (96 g ), (b) Ge2(32 e ), and (c) Ge3 (8 a ) sites (b) in Cs8Na16Ge136, with bond angles given..........................................42 Figure 3.3 X-ray powder diffractio n plots (observed, calculated, and difference) for (a) Cs8Na16Ge136 and (b) Cs8Na16Cu5Ge136...............................................................................44 Figure 3.4 EXAFS data for Cs8Na16Cu5Ge131 near the Cu and Ge K-edges.......................................................................................48 Figure 3.5 Comparisons of Four ier transforms of the EXAFS spectra for the Cu and Ge K-edges.........................................................50 Figure 3.6 Comparisons of Fourie r transforms of experimental spectra (solid blue lines) and simulation (fit, dashed lines)............................................................................................51 Figure 3.7 Fourier transforms of the theoretical EXAFS spectra simulated using single sca ttering (SS) contributions and multiple scattering (MS) contributions, for each of the Ge sites in Cs8Na16Ge136...............................................................54 Figure 3.8 Temperature dependence of the electrical resistivity (top) and Seebeck coefficient (bottom) for Cs8Na16Ge136 (open symbols) and Cs8Na16Cu5Ge131 (filled symbols)..........................56 Figure 3.9 Temperature dependence of the thermal conductivity for Cs8Na16Ge136 (open symbols) and Cs8Na16Cu5Ge131 (filled symbols).......................................................................................57
ix Figure 3.10 Powder X-ray diffractio n pattern (observed, calculated, and difference) from a Cs8Na16In8Ge128 specimen.................................58 Figure 4.1 Decomposition of Na4Si4 (top) to form the intermetallic clathrates NaxSi136 (bottom left) and Na8Si46 (bottom right)..........................................................................................61 Figure 4.2 Schematic of the apparatus designed for thermal decomposition of Na4Si4 in the synthesis of NaxSi136 clathrates.................................................................................................62 Figure 4.3 Powder X-ray diffraction patterns for several NaxSi136 specimens................................................................................................63 Figure 4.4 ADP plot for Na2 and its surrounding Si28 cage for Na22Si136............................................................................................66 Figure 4.5 Rietveld plots of powder XRD patterns for (a) Na1.2Si136, (b) Na6.5Si136, (c) Na12.2Si136, and (d) Na21.6Si136: observed (crosses), calculated (solid curve) and difference (lower curve) patterns are shown............................................................67 Figure 4.6 Normalized cage occupancies (bottom) and lattice parameters (top) as a function of the total Na content, as determined from Rietveld refinement.................................................69 Figure 4.7 Si28 and Si20 cage volumes as a function of Na content..........................71 Figure 4.8 Differential thermal an alysis data for six selected NaxSi136 compositions.............................................................................73
x Figure 4.9 Transport propert ies of polycrystalline Na22Si136...................................75 Figure 5.1 Preparation of Na24Si136 by SPS.............................................................79 Figure 5.2 Optical microscope image of Na24Si136 crystals grown at 600oC...................................................................................................81 Figure 5.3 Powder X-ray diffraction pattern for a Na24Si136 specimen grown at 600oC after removal of residual Na4Si4...................................83 Figure 5.4 Difference Fourier map calculated with the Na2 atom removed from the structure model..........................................................86 Figure 5.5 Temperature dependent tr ansport properties measurements on Na24Si136 crystal specimens grown by SPS........................................88 Figure 5.6 Preparation of Rb6Si46 by SPS................................................................92 Figure 6.1 Differential thermal analysis (DTA) data (exothermic up) for Na1xGe3+ z (bottom) indicating decomposition near 400oC......................................................................95 Figure 6.2 Observed, calculat ed, and difference patterns (plotted on the same scale) obtained from Rietveld refinement using neutron diffraction data collected at 4 K.......................................................................................................97 Figure 6.3 Crystal structure of Na1xGe3+ z, as viewed down the c -axis....................99
xi Figure 6.4 Structure of Na1xGe3+ z, in the vicinity of the broad channel as viewed along the c -axis at a slight tilt.................................100 Figure 6.5 Perspectives of the two distinct Ge channels in Na1xGe3+ z, viewed perpendicular to the c -axis.....................................102 Figure 6.6 Atomic displacement parameters for Na1xGe3+ z...................................103 Figure 6.7 Magic angle spinning solid state 23Na NMR data for Na1xGe3+ z........................................................................................105 Figure 6.8 (a) Powder XRD pattern for the Na1xGe3+ z specimen collected after hot-press ing. (b) Thermal conductivity of Na1xGe3+ z..........................................................................................106
xii Fundamental Investigations on Open-Framework Intermetallic Materials of Group 14 Matt Beekman ABSTRACT Crystalline open-framework intermetallics have long attracted the attention of chemists, physicists, and materials scientists The intriguing structures such materials exhibit are often intimately related to the uni que physical properties they possess. The present work is focused on the preparation and characterization of open-framework intermetallic materials based on group 14 elements, in particular those crystallizing in clathrate and related structures such as th e clathrate-II phases. Materials possessing the clathrate-II crystal structure have received incr eased attention in rece nt years, as a result of both the unique properties they exhibit as well as potential for use in technologically important applications such as thermoelec trics, photovoltaics, and optoelectronics. However, in comparison with other clathrate st ructure types, characterization of clathrateII materials has in general been far le ss extensive. Moreover, many conceivable compositions have yet to be realized. The purpose of this work is to expand the current knowledge of the structural, chemical, and physical properties of these ma terials, while simulta neously exploring new compositions and synthetic routes to clathrate-II phases. On e of the unique and promising aspects of clathrate-II material s is the ability to vary the guest concentration, which is shown to have significant implications for the structural and phys ical properties of NaxSi136 (0 < x < 24) materials. It is demonstrated that new compositions can be explored by novel approaches to chemical design. Fr amework substitution in clathrate-II compounds is explored in an effort to asse ss possibilities for in fluencing the physical properties of these materials. A nove l zeolite-like framework phase, Na1xGe3+ z, has been
xiii discovered, and is shown to be a new lo w-thermal conductivity crystalline solid, suggesting a new approach to the design of crystalline intermetallic materials with low thermal conductivity. New directions in synthe sis of intermetallics are identified, with emphasis on unconventional preparative met hods and the opportunities they offer. Processing of reactive precursors by spark plas ma sintering is demonstrated as a new preparative tool for crysta l growth, identifying the firs t method for preparation of clathrate-II Na24Si136 single-crystals since the discovery of these compounds more than four decades ago.
1 1 Introduction The chemistry and physics of group 14 elements such as silicon and germanium have been extensively studied, largely due to their fundamental importance in the development of semiconductor electroni cs. In addition to their ground state configurations (e.g. the diamond structure for -Si and -Ge), these elements can also exist as metastable expa nded framework allotropes1,2 as well as highly stable binary,2-6 ternary,8,9 and higher order compounds10,11 known collectively as cl athrates. Prior to the discovery of intermetallic clathrates based upon elements of group 14, the analogous crystal structures had been known in the gas and liquid hydrates, which constitute expanded forms of ice.12-14 The existence and crystal structure of the first intermetallic clathrates were first reported by Kasper et al.3 Systematic investigations were undertaken by Cros et al. soon thereafter.15-18 The common structural feature of all clathrate materials is an open-structured host framework that has the ability to en cage guest atoms or molecules. The relationship between the struct ure of these and related materials, and the properties they display is of scientific and t echnological importance. In the past ten years there has been a surg e in interest in intermetallic clathrates. The impetus behind the increased attention give n to these materials is predominantly twofold. First, from a chemical and physical view point, these materials a llow for the study of the physics of compounds possessing isomorphi c structures but with greatly varying properties, ranging from metals9 to semiconductors19 to superconductors,20,21 and magnetic materials as well. Intriguing a nd unconventional propertie s displayed by these materials, such as gl asslike thermal conductivity19 and heavy atom tunnelling in the crystalline state,26-28 comprise novel physical phenomena in crystalline solids. Second, is the promise they hold for useful appli cations, ranging from thermoelectrics29-32 to photovoltaics and optoelectronics33-36 to potentially ul tra-hard materials.37 It is important to recognize that these two motivations ar e intimately connected, since a fundamental
2 understanding of their chemistry and physics, as motivated by the first point, can be crucial in assessing their potential for use in applications, as given in the second. There are several structural types that constitute the family of intermetallic clathrate materials.38-41 Of these, those with the clathr ate-I crystal structure have been studied extensively and have received the mo st attention of all of the intermetallic clathrate types. As several ex cellent reviews are available,38-43 only a brief discussion of clathrate-I materials will be given in the presen t chapter. More attention will be paid here to a review of previous work on the synthe sis and characterizati on of another emerging class of open-structured ma terials, those crystallizing with the clathrate-II* structure. The focus will be primarily on the experimental re sults, though theoretical work will also be discussed where pertinent. A rich collection of theoretical treatments of clathrate-II materials may be found in the literature.33-36,44-63 1.1 Clathrate-I compounds Two of the most significant findings that ha ve stimulated so much research effort on intermetallic clathrates were the identifica tion of clathrate-I mate rials as candidates for thermoelectric applications29,30 and the related discovery of rather unconventional heat transport for a crystalline solid, observed for a number of semiconducting clathrate-I variants.19 Since the original suggestion29,30 that intermetallic clathrates would be of interest for thermoelectrics, a number of pr omising advances and innovations have been made,41,64-68 further fueling interest in these materials. The very low lattice thermal conductivities that have been observed19 in clathrates such as Sr8Ga16Ge30 and Eu8Ga16Ge30, and which follow a literally glasslike temperature dependence, have resulted in an immense amount of effort being focused on understanding the lattice dynamics in these and related compounds.69-75 Various explanations have been proposed to elucidate the mechanisms behind this unus ual thermal transport behavior, with the current prevailing understanding being in terms of a strong interacti on (i.e. scattering) between localized phonons (i.e. with negligible group velocity), associ ated with the guest *The synonymous terms clathrate-II and type II clathr ate will be used interchangeably throughout this work, as both terms are in common use in the literature.
3 species, and the heat carrying acoustic phonons of the clathrate.19,69-75 This area continues to be an active field of research. The promise these materials hold for thermoelectrics stems from the relatively good electrical properties (reasonably high Seebeck coefficients and electrical conductivities) that a number of semiconducti ng clathrates possess, in addition to their very low thermal conductivities. This fortuit ous combination of prope rties has resulted in thermoelectric figures of merit ZT Â† on the order of unity for several clathrate-I compounds,76 values comparable with current stateof-the-art materials. Considering the diversity in as yet uninvestig ated compositions (cf. Chapter 2), progress toward enhanced thermoelectric properties in th ese compounds can be expected. 1.2 Structure, bonding, and crystal chem istry in clathrate-II materials As with other inorganic clathrates, th e clathrate-II crystal structure can be visualized in terms of facesharing polyhedral cages resembling fullerene-like building blocks of silicon, germanium, or tin. However, an important difference between the clathrate-II structure and other fu llerene solids (e.g. crystallized C60; Ref. 77) is the tetrahedrally coordinated sp3-like bonding found in the clathrat es. This can be viewed as a direct consequence of the preference of silicon and germanium (and sometimes tin) in forming sp3 bonds, whereas carbon readily forms both sp3(e.g. diamond) and sp2-like bonds (e.g. graphite).78,79 The possibility as to whethe r carbon can crystallize in the clathrate-II structure remains an open experimental question.54 The clathrate-II framework can be perceived in terms of the coordination polyhedra for the guest species: eight 28-membered hexacaidecahedra ( E28, point symmetry Td), and sixteen 20-membered pentagonal dodecahedra ( E20, point symmetry Ih) per conventional unit cell, as shown in Fi gure 1.1. The guest atoms reside inside these polyhedra formed by the framework. There are three crystallographic sites (space group Fd 3 m ) in the framework, 96 g 32 e and 8 a in the Wyckoff notation. The guest species Â† For a given material, the dimensionless thermoelectric figure of merit is defined as ZT = S2T/ where Z = S2/ is the thermoelectric figure of merit, S is the Seebeck coefficient, is the electrical resistivity, is the total thermal conductivity, and T is the absolute temperature. The product ZT originates in the thermodynamic analysis of the efficiency for a thermoelectric module, and to maximize efficiency it is desirable to maximize ZT for the device constituent materials.
4 Figure 1.1 Sixteen pentagonal dodecahedra ( E20) and eight hexacaidecahedra ( E28) share faces to form the clathrate-II crystal structur e. The occupancy of the polyhedral cages in the clathrate-II structure may be either completely filled or complete ly empty, or varied between the two extremes. M. Beekman and G.S. Nolas, J. Mater. Chem. 18 842 (2008). Reproduced by permission of The Royal Society of Chemistry. reside at the 8 b and 16 c sites, inside the E28 and E20 cages, respectively. The resulting structure is face-centered cubic (see Figure 1.1) and the general chemical formula can be written as A8B16E136 ( A = guest in E28, B = guest in E20, and E = Si, Ge, Sn or substituents) in the conventional unit cell. Although qualitative similarities exist between the clathrate-II structure and other clathrate types, at least one important difference should be emphasized. This is the ability to fully vary the guest concentration in the clathrate-II materials,4 whereas the guest content is em pirically fixed at full occupation in, for example, clathrate-I compounds, with very few exceptions. As discussed below, this feature has significant im plications for the physical pr operties of these materials. As evident from Figure 1.1, the clathr ate-II framework is composed of 5membered and 6-membered rings, corresponding to the faces of the E20 and E28 polyhedra. This is in contra st to the diamond structured phases of the Group 14 elements, which exhibit exclusively 6-memb ered rings. Indeed, the average number of atoms per ring in the clathrate-II structure is 5.064, and is the smallest for any known
5 structure. Some of the interesting properties of these materials have b een attributed to this large concentration of 5-membered rings.80,81 Structural analogies exist between th e clathrate-II structure and other known compounds and structures. For example, the guest atom positions (8 b sites) inside the larger E28 polyhedra form an enlarg ed Â“diamond lattice.Â” The E28 polyhedra are centered on these sites, with the E20 polyhedra being formed in the space between the E28 cages. The clathrate-II structure may also be considered as dual to the MgCu2 structure, in the sense that the constituent guest atom positions in the clathrate-II structure (centers of the polyhedra) correspond to the positions of the atoms in the MgCu2 structure (i.e., E20 Cu, E28 Mg). The interested reader can find in the literature a number of useful discussions of the various in teresting structural and geom etric relationships found in clathrate materials.38,47,82-84 In Figure 1.2 a plot of the ra tio of the free cavity diameter ( D ) to cage-atom diameter ( d ) for several cage-like materials is shown as a function of the square root of Figure 1.2 Free cavity diameter to cage-member diameter ratio versus the square root of coordination number (CN) of the interior (i.e. guest) site, for several cage-like materials.39 Si24 corresponds to the Â“flattenedÂ” clathrate-I tetrakaidecahedra, which has two characteristic dimensio ns. M. Beekman and G.S. Nolas, J. Mater. Chem. 18 842 (2008). Reproduced by permission of The Royal Society of Chemistry.
6 the number of atoms in the cage, i.e. th e coordination number (CN). We see that a straight line fits the data quite well indicating an empirical dependence on the coordination number of CN ~ / d D. The figure allows an estimate as to which atoms or molecules might be entrapped in a particul ar host material. From the figure, we can see that the clathrate-II E20 and E28 polyhedra fall in the intermediate range for this ratio, with the smallest and largest values shown being for the tetrahedron and the fullerene C60, respectively. The clathrates can also be considered as expanded forms of silicon, germanium, and tin, and as a result of their cage-like st ructure they can be viewed as Â“naturallyÂ” nano-porous crystalline solids. As a conseque nce of their open structure, the volume per framework atom is as much as 15 to 20% la rger in the cl athrate relative to the diamond structure. However, the average EÂ—E bond lengths for the guest-free Si136 (2.34 )1 and Ge136 (2.45 )2 clathrates are not signif icantly different from th e Â“idealÂ” bond lengths for the corresponding diamond structures.85 In addition, the clathrat e-II bond angles average close to the ideal 109.47o expected for tetrahedral coordination. As such, the free energies for the clathrate structures are found to be only slightly higher in energy than for the corresponding ground-state diam ond structures (e.g. for -Si).33 The incorporation of guests into the empty structure typically results in a small but significant expansion of the structure.9,86-88 Although the clathrate-II allo tropes such as the empty Si136 and Ge136 are energetically metastable w ith respect to the diamond structured phases, the energy difference is apparently quite small33,47,48 and a significant energy and/or kinetic barrier must exist allowing the clathrate stru cture to endure. San-Miguel et al.89 and Ramachandran et al.90 have independently shown that the Si136 framework is stable under pressure up to 11 GPa. Moreover, no transi tion towards the diamond phase is observed, rather the Si136 framework undergoes an irreve rsible transition to the -Sn structure of silicon at 11.5 GPa, accompanied by a large volume reduction of more than 30%.89,90 Further discussion of the high pressure propert ies and stability of cl athrates may be found in the literature.42,43,89-92
7 Figure 1.3 Temperature dependent isotropic atomic displacement parameters (Uiso) for the E28 guest as well as framework sites in A8Na16E136 ( A = Rb, Cs; E = Si, Ge).93 The guest atoms all have significantly larger Uiso with stronger temperature dependence th an those for the framework, with the Uiso increasing with decreasing guest size relative to its cage. M. Beekman and G.S. Nolas, J. Mater. Chem. 18 842 (2008). Reproduced by permission of The Royal Society of Chemistry. Some of the most interesting st ructural aspects of clathrate-II materials are related to the relatively weak bonding between the guest at oms and the host framework. Nolas et al.93 have reported on temperature dependent si ngle crystal X-ray diffraction studies on several clathrate-II silicon and germaniu m compounds. Figure 1.3 shows the temperature dependence of the isotropic atomic displacement parameters (ADP or Uiso) for the framework atoms in these compounds, as well as for the guest atoms inside the larger E28 cage. For all of the guests, the ADPs are consid erably larger than those of the framework sites. Moreover, there is much stronger temperature dependence for the guest ADPs relative to the framework. The magnitude a nd temperature dependence of the guest ADPs is indicative of relatively large amplitude thermal motion, and is a consequence of both the significant Â“spaceÂ” inside the hexacaide cahedra, as well as relatively weak bonding between guest and framework. Bobev and Sevov9 have estimated the relative size of
8 Figure 1.4 Dimer formation between the Na guests in the NaxSi136 clathrates. (a) In the ideal Fd 3 m symmetry the guests occupy the centers of the Si28 polyhedra. (b) EXAFS measurements indicate the formation of a weak dimer between Na guests in adjacent Si28 cages, with the guests moving toward the shared hexagonal face of the polyhedra.95,96 M. Beekman and G.S. Nolas, J. Mater. Chem. 18 842 (2008). Reproduced by permission of The Royal Society of Chemistry. guest and cage by subtracting framework atomic radii from the shortest guest-framework distances, compared to the estimated ionic radii of the guests. It is in teresting to note that in general the larger the difference in size between guest relative to its E28 cage, the larger the ADP, as evidenced in Figur e 1.3. The relationship of the guest thermal motion to the thermal properties of these materials is discussed in more detail below. Assuming the highest symmet ry arrangement within the Fd 3 m space group, the guest atoms in the clathrate-II structure are located at the centers of their respective polyhedral cages. However, in the case of the Na4Si136 clathrate it was originally suggested by Demkov et al.,44 who used quantum molecular dynamics simulations, that the Na guest inside the Si28 cage could in fact move off-center, thus lowering the site symmetry from Td to C3v. This was interpreted in terms of a Jahn-Teller distortion, and accompanying energy-lowering lifting of the degeneracy of the lowest conduction band.44 Electron spin resonance measurements reported94 soon after gave experimental evidence for this guest displacement in Na3Si136. More recently, analysis of extended X-ray absorption fine structure (EXAFS) measurements95,96 and accompanying theoretical studies indicate that the Na guests in the Si28 polyhedra can indeed move off-center in the NaxSi136 clathrates ( x = 8 and ~ 24), toward the shared hexagonal faces by as much as 1
9 . Those results were interpreted in terms of the formation of a dimer between Na guests in adjacent Si28 cages, shown schematically in Figure 1.4. This effect may be akin to the well known Peierls distortion97 associated with the hypothetical one-dimensional monatomic lattice. As suggested by temp erature dependent NMR data, a similar dimerization may also occu r between Cs guests in Cs8Ge136.98 The off-center nature of guest atoms in clathrat e-I compounds such as Sr8Ga16Ge30 and Eu8Ga16Ge30 has been shown70,71,99,100 to be intimately linked to their unique physical prope rties, and such phenomena remain an aspect warranting further study in clathrate-II compounds. 1.3 Synthetic routes to clathrate-II materials There are various synthetic methods that have been used to prepare clathrate-II materials, and some compositions can be produced by more than one method. Arguably the most straightforward method is direct synthesis from the elements. Guided by the observation that stabilization of the clathrate-II structure is facilitated through matching relative sizes of guest and cage, Bobev and Sevov first synthesized9,86 the A8Na16E136 clathrates ( A = Cs, Rb; E = Si, Ge) by reaction of the high purity elements inside sealed niobium capsules. The mixtures were held at 650oC for three weeks, and then slowly cooled to room temperature. Later, Nolas et al.93,101,102 used a similar method to synthesize these compounds for further char acterization. The products were well-formed small crystals (~ 1 to 3 mm in size), typically along with coarse pol ycrystalline powders. An important consideration in the synthesis of these alkali-containing clathrates is the relatively high vapor pressure of the alkali me tals and their ability to react easily with silica ampoules if used, so that reactions must be carried out within sealed, metal vessels. The synthesis of a Sn clathrateII compound has also been reported103 by reaction of a mixture of K:Ba:Ga:Sn in th e ratio 8:16:32:104, with no K incorporated into the end compound Ba16Ga32Sn104. This is the only Sn clathr ate-II compound reported to date. Semiconducting clathrate-II compounds are expe cted to have promising thermoelectric properties. Novel routes to preparing such compositions, some of which will be given in the present work, could provide an important path to the di scovery of new thermoelectric clathrate materials.
10 Figure 1.5 Polyatomic Zintl anions (a) [ E4]4and (b) [ E9]4that act as precursor constituents in the synthesis of clathrates-II materials via thermal decomposition of silicides or ge rmanides, as well as reaction in ionic liquids. M. Beekman and G.S. Nolas, J. Mater. Chem. 18 842 (2008). Reproduced by permission of The Royal Society of Chemistry. Novel compositions may be prepared from those synthesized directly from the elements. This follows from the fact that, in contrast to other clathrate types, the guest concentration in the clathrate-II may be varied while still maintaining the integrity of the structure. In our previous work,98 we have synthesized th e new clathrate composition Cs8Ge136, in which Cs solely occupies the eight larger Ge28 cages in the structure. This was achieved by first starting with stoichiometric Cs8Na16Ge136, prepared from the elements as discussed above. The Na content was then reduced by successively heating Cs8NaxGe136 ( x < 16) under high vacuum, causing the Na to Â“degasÂ” from the clathrate, while Cs remained incorporated in the structur e. Using this procedure, the Na content can be reduced to less than 600 ppm.98 Similarly, Rb8Ge136 can also be prepared in this manner.104 Although direct synthesis may be the most straightforward synt hesis route, this method has to date been unsuccessful for preparation of a number of compositions. Conspicuous examples include the NaxSi136 (0 < x < 24) clathrates. These were of the first inorganic clathrates to be discovered by Kasper et al.,3 followed shortly thereafter by a systematic study originally undertaken by Cros et al.4,15-18 Until the present work (cf. Chapter 5), NaxSi136 have only been prepared via thermal decomposition of the Zintl compound Na4Si4.3,4,15-18,97,98,105 Na4Si4 is prepared from the elements by reaction at 650oC or higher under inert atmo sphere, though the product is extremely air and moisture
11 sensitive and handling must be performed in a N2 or Ar glove-box. NaxSi136 is formed upon heating Na4Si4 under vacuum (< 10-5 torr) to temperatures above ~ 350oC. The structure106-108 of Na4Si4 is monoclinic (space group C 2/ c ) and consists of Na+ and [Si4]4Zintl ions (cf. Figure 1.5a).109 During thermal decomposition, most of the Na+ ions are reduced and are removed as vapor, with the remaining Na acting as a template for the Si136 framework formed by reconstruction of the [Si4]4cluster ions. The sodium content x is controlled by varying both the temperatur e and time for which the specimen is heated, with higher temperatures and longer times lead ing to lower sodium contents. The relative intensities of several reflections from powder X-ray diffraction exhibit a strong dependence upon the Na content,87,88 thus allowing for the determination of the Na content (and therefore co mposition) from Rietveld110,111 structure refinement. The relative occupancy of the cages can also be determined in this way (cf. Â§4.2). In addition to NaxSi136, the clathrate-I Na8Si46 is also commonly present in specimens prepared from decomposition of Na4Si4, constituting as much as 45 wt% in as prepared specimens.87,88 This poses a chal lenge to producing NaxSi136 specimens of high purity for further characteriza tion of their physical propert ies. Ramachandran et al.87 utilized the difference in de nsities between the two phases in order to separate them. However, this technique can be quite difficu lt to employ, as the crys tallites of the two phases are often inter-grown.112 Preparation of phase pure NaxSi136 specimens (i.e. with negligible Na8Si46 fraction) continued to be a challenge until the present work, an aspect that will be discussed in later ch apters (cf. Â§4.1 and Chapter 5). Unlike the case for NaxSi136, thermal decomposition of binary phases under vacuum is not as successful in producing the Ge analogue NaxGe136 from Na4Ge4. Although NaxGe136 can be prepared from Na4Ge4,4 a systematic study has shown that the yield is typically small, and NaxGe136 only forms in a narrow range of synthesis temperatures.104,113 Rather, a novel hexagonal zeolite-like framework phase Na1xGe3+ z (cf. Chapter 6) forms as the majority phase.114 The reason may be linked to the crystal structures of the precursor compounds Na4Si4 and Na4Ge4: although both are monoclinic and are composed of Na+ and [ E4]4Â– Zintl ions, the struct ures are not identical.106,107 Thus
12 Figure 1.6 High resolution transmission electron micros cope (HRTEM) image of the new germanium allotrope Ge136, taken for the  zone axis. A simulated image is shown in the upper right-hand corner. Reprinted by permission from Macmillan Publishers Ltd: A.M. Guloy, R. Ramlau, Z. Tang, W. Schnelle, M. Baitinger, and Yu. Grin, Nature 443 320 (2006), copyright 2006. the subtle morphological differences in Na4Ge4 (space group P 21/ c ) and Na4Si4 (space group C 2/ c ) may promote differing structures for the decomposition products. Other clathrate-II compositions have also been prepared by the thermal decomposition of mixed alkali or alkali/alka line earth silicides. Ramachandran et al.115 synthesized Cs8Na16Si136 by thermal decomposition of CsxNa1xSi, while similarly Latturner et al.116 synthesized Rb8Na16Si136 from RbxNa1xSi. The synthesis of Ba8Na16Si136 via thermal decomposition of Na2BaSi4 has also been reported,117 though the products consisted of a mixture of several phases. It is interest ing to note that all precursors used thus far to prepare inorganic clathrates via thermal decomposition (and also more recently chemical oxidation2,118,119) contain cluster [ En]m ( n m intergers) anions, an aspect clearly linked to their ab ility to promote the clathrate structure upon reaction. One of the original questions concerning clathrate-II materials was the stability of the structure upon complete removal of the guests. Gryko et al.1 showed that the clathrate-II framework is indeed stable wh en emptied (Na content less than 600 ppm Si),
13 and prepared the guest-free silicon clathrate Si136 by means of repeated degassing of NaxSi136 and treatment with concentr ated acids. Ammar et al.120 later also prepared Si136 using a similar technique, but reduced the resi dual Na content even further by reaction of the clathrate with iodine (final residual Na content ~ 35 ppm Si). The crystalline clathrate Si136 in essence constitutes a new allotrope of silicon. Although preparing a guest-free Ge136 clathrate by the above described process of degassing NaxGe136 is not feasible,104,113,114 a new method has recently been developed by Guloy et al.2,121 in order to circumvent this difficu lty. The investigations were motivated by previous studies indica ting ionic liquids are eff ective in polymerizing [Ge9]4(Fig. 1.5b) from solution. The reaction was regarded as a solvation of Na12Ge17 in a 1:1 molar ratio melt of AlCl3 and dodecyltrimethylammonium ch loride (DTAC). Specimens with Ge136 as the major phase could be prepared by heating the reaction mixture at 300oC while sealed under inert atmosphere. This reac tion was explained in terms of the reaction of the [Ge9]4Â– with DTAC according to2 4[CH3(CH2)11N(CH3)3]+ + [Ge9]4Â– 9Ge0 + 4CH3(CH2)9CH=CH2 + 4N(CH3)3 + 2H2 The synthesis of Ge136 was reproduced by the author using Na4Ge4 as a precursor, but solvation of the precursor was not observe d, indicating the reaction may in fact be heterogeneous in nature.122 This new open-structured allo trope of Ge deserves further characterization. Using similar pro cedures, but with the precursor K4Ge9, the authors also have successfully prepared the clathrate-II K8Ge136.2,123 Table 1.1 lists clathrate-II compositions that have been reported to date. By comparison with the extensive number of known intermetallic clathrate-I compounds,38-43 one can quickly conclude that the conceiva ble clathrate-II compos itions still to be investigated is quite signifi cant. The synthesis of new com positions, in addition to those listed in Table 1.1, is important for the study of their physical and chemical properties, and to develop a fundamental understanding of structure-property relationships in openframework and guest-host materi als. Some previous work to ward this understanding is outlined in the remainder of this chapter.
14 1.4 Electronic properties of clathrate-II materials Since the observation of unique opt ical properties in porous silicon,124 lowdensity forms of this tech nologically important semiconduc tor have continued to be investigated for their intere sting electronic properties, in comparison with the bulk crystalline diamond structured state ( -Si). An important discovery regarding the electronic properties of cl athrate-II materials was the theoretical prediction33 and later Table 1.1 Clathrate-II compositions, synthesis method, and lattice parameters. Composition Synthesis Method Lattice Parameter a () Referencea Si136 Degassing of NaxSi136 14.62601(9) 1 NaxSi136 Decomposition of NaSi 14.62601(9) a < 14.70704(1) (0 x < 24) 1,4 Cs7Si136 Decomposition of CsSi 14.64 4 Rb8Na16Si136 Direct reaction of elements 14.7400(4) 9 Cs8Na16Si136 Direct reaction of elements 14.7560(4) 9 Ba8Na16Si136 Decomposition of Na2BaSi4 Not reported 117 Ge136 Reaction of [Ge9]4in DTAC/AlCl315.2115(1) 2 NaxGe136 Decomposition of NaGe 15.4 4 Cs8Ge136 Degassing of Cs8Na16Ge136 15.329 98 Rb8Na16Ge136 Direct reaction of elements 15.4858(6) 9 Cs8Na16Ge136 Direct reaction of elements 15.4805(6) 9 Ba16Ga32Sn104 Direct reaction of elements 17.054(1) 103 a Selected references. experimental verification1 that the band gap of the empty clathrate Si136 is expanded by approximately 0.7 eV relative to that for diamond structured silicon ( Egap of -Si ~ 1.2 eV). Thus the Si136 allotrope constitutes a novel wide-band gap semiconductor. However, whereas the interesting optical properties of materials such as porous silicon have been attributed to quantum confinement ef fects, the widening of the gap in Si136 (relative to diamond structured Si) can be understood in term s of the slight distortion in the clathrate of the ideal tetrah edral bonding found in -Si, as well as the high density of 5-membered rings in the Si136 structure.33 Recent theoretical work36 has discussed the importance of
15 Figure 1.7 Seebeck coefficient (round symbols) and resi stivity (triangular symbols) as a function of temperature for polycrystalline Cs8Na16Si136 (open symbols) and Cs8Na16Ge136 (filled symbols).93 Inset: DFT computed electronic de nsity of states for Cs8Na16Si136 (lower)115 and Cs8Na16Ge136 (upper)98 the dashed line indicates the Fermi level, which is well within the conduction band for both materials. M. Beekman and G.S. Nolas, J. Mater. Chem. 18 842 (2008). Reproduced by permission of The Royal Society of Chemistry. symmetry considerations for the optical proper ties of silicon clathrate-II materials, as well as the potential for intercalation of gue sts with electronegativities that are higher than that of silicon. A promising aspect of these open-fram ework Si and Ge semiconductors is the potential for band-gap engineering with composition. Moriguchi et al.34 have explored the electronic structure of clathrat e-II silicon-germanium alloys, Si136xGex, using density functional techniques. These authors found th at the effect of alloying silicon and germanium on the clathrate framework can not only allow for varying the size of the ~ 2 eV band gap of Si136, but also that Si136xGex clathrates should po ssess a direct band gap for a range of values of x Their results indicate the band gap of Si136xGex alloys could be
16 continuously Â“tunedÂ” from approximately 1.2 to 2 eV, in the visible range of the electromagnetic spectrum. This band-gap depe ndence can be contrasted to that observed in the diamond structured Si1xGex alloys (0.7 to 1.1 eV). Although the synthesis of Si136xGex clathrates has yet to be achieved, such predicted properties make these materials of particular interest for poten tial use in optoelectronic or photovoltaic applications. The electronic properties of the filled group 14 clathrates can be discussed in terms of a rigid band model, in which th e electropositive guests donate their valence electrons to the host framework. Within this model, the Â“emptyÂ” clathrate framework electronic band structure (e.g. that of Si136 or Ge136) is only minimally modified by introduction of the guests into the framewor k cages, and the donated electrons occupy the framework conduction band levels (i.e. stat es with Â“anti-bondingÂ” character). For compounds such as Cs8Na16Si136 and Cs8Na16Ge136, the result is a high density of charge carriers (> 1021 cm-3) in a partially filled ba nd and metallic properties.93,98,115 This is exemplified in Figure 1.7, which shows experi mental results from temperature dependent electrical transport measurements,93 corroborated by theo retical ca lculations98,115 of the electronic density of states (DOS) for these two compounds. For both compounds, the resistivities increase monotonically with temperature (typical metallic behavior), while the Seebeck coefficients remain relatively sm all, the (negative) sign indicating electrons are the majority carriers. It should be noted that the rigid band approximation is, strictly speaking, a simplified model, a nd there is evidence that the introduction of the guests can indeed modify the band structure of these materials.125 Nevertheless, it remains a useful model for the qualitative understa nding of the electron ic properties of these materials. To date, the only semiconducting clat hrate-II phases for which el ectrical trans port properties have been reported are the guest-free Si136 1 and Ge136,2 and the lower Na content NaxSi136.4,126 However, the ability to substitute other species for the framework atoms discussed in Chapter 3 of the present work may allow for the synthesis and characterization of new semic onducting clathrate-II variants. The ability to adjust the guest content in clathrate-II materials offers a unique opportunity to study the effects of guest content and type on the physical properties of
17 inorganic clathrates. It ha s been observed that the electrical properties of NaxSi136 (0 < x < 24) clathrates depend strongly on the Na cont ent, in that increasing the guest content considerably reduces the electrical resistivity.4,126 Moreover, high Na content NaxSi136 specimens exhibit metallic behavior wher eas lower Na content specimens show semiconducting or insulating behaviour.4,126,127 Transport,4,126 NMR,128 and magnetic susceptibility measurements,129 as well as theoretical calculations,44,125 indicate a metal to insulator transition occurs at 7 < x < 12, though the precise value of x at which this occurs has yet to be determined unequivocally and c ould also conceivably depend on the relative occupation of the two different caged Na site s in the structure. In analogy with the superconducting fullerenes130 and also some clathrate-I compounds20,21 the possibility of superconductivity in clathrate-II NaxSi136 129 and Ba8Na16Si136 117 has been explored, but with negative results. Superconductivity has as yet not been obser ved in clathrate-II phases. The electronic structure of several clat hrate-II phases has been studied employing nuclear magnetic resonance techniques.1,98,115,128,131-134 Common to several clathrate-II materials are the relatively large NMR shifts for both the guest and framework species. These shifts have been interpreted as akin to the Knight shifts in metals, originating in the hyperfine interactions between the NMR nuclei and the delocalized conduction electrons.135 Indeed, the Knight shifts for 23Na in the NaxSi136 clathrates (1600 to 2000 ppm as referenced to 1 mol NaCl at 0 ppm) are larger than in metallic sodium (1123 ppm).132,133 Moreover, in contrast to the behavior associated with Knight shifts in metals, which are typically found to be appr oximately temperature independent,135 the Knight shifts in Rb8Na16Si136,116 NaxSi136,132,133 and Cs8Ge136 98 are found to exhibit strong temperature dependences, increasing as the temperature is decreased. As originally suggested by Gryko et al.,132,133 this phenomenon appears to be related to distinct features, such as a sharply peaked structure, in the electronic density of states near the Fermi level in these materials.61
18 1.5 Thermal and vibrational propertie s of clathrateII materials Of the most conspicuous aspects of intermetal lic clathrates (as well as hydrate and other clathrates) are their thermal, lattice dynamical, and vibrationa l properties, which continue to be intensely studied.19,48,49,57,93,136-144 The relatively large number of atoms in the clathrate-II unit cell, as well as the presence or absence of the guests, results in distinctive thermal properties for these materials. As discussed above, the relatively large difference in size and weak bonding between guest and cage in many filled clathrates promotes localized guest vibration modes, a phenomenon wh ich has been termed as Â“rattling.Â” This is reflected in the magnitude and temper ature dependence of the guest atom ADPs determined from single crystal XRD, as discussed above (Figure 1.3).93 Previous studies have shown145-147 that ADPs determined from crystallographic analysis can be used to estimate the frequencies of the localized vibrations undergone by guest atoms such as those in the clathrate-II mate rials, and also to es timate other pertinent physical quantities for the solid. With the a ssumption that the guest acts as a three dimensional Â“EinsteinÂ” oscillator,148 the Â“rattlerÂ” frequency can be estimated from the simple relation Uiso = kBT / m (2 )2, where kB is BoltzmannÂ’s constant, m is the mass of the Â“rattler,Â” and is the frequency of vibration. Vibr ation frequencies determined using this approach for Cs8Na16Si136 and Cs8Na16Ge136 are given in Table 1.2.93 Table 1.2 Vibrational frequencies for the guest atoms in Cs8Na16Si136 and Cs8Na16Ge136, as determined from temperature dependent single crystal XRD (ADP data),93 Raman scattering,101 and density functional theory calculations.57,101 Compound ADP Raman theory Cs Na Cs Na Cs Na Cs8Na16Si136 53.4 141 57 N.A.a 64 120 Cs8Na16Ge136 41.8 117 18 N.A.a 21 89 aN.A. = Not Raman Active
19 The Â“rattlingÂ” motions of the guest atom, or soft phonon modes, in the A8B16E136 clathrates have also been studi ed by Raman scattering experiments.101 From group theoretic analysis, it is found that the guest atoms in the larger E28 hexacaidecahedra contribute a Raman-active optic mode ( T2 g symmetry), while the guest atoms in the smaller E20 dodecahedra do not contribute any Ra man-active modes. Figure 1.8 shows room temperature Raman scattering sp ectra obtained on polycrystalline Si136 and singlecrystal Cs8Na16Si136. The low-frequency Cs Â“rattleÂ” mode at 57 cm-1 is clearly discernable, and this observed Raman shift is in qualitative agreement with the frequency of 64 cm-1 predicted for this mode by density func tional theory computations. A similar Figure 1.8 Stokes Raman scattering spectra for Si136 and Cs8Na16Si136. The Cs Â“rattleÂ” mode at ~ 57 cm-1 is indicated. Reprinted with permission from G.S. Nolas, C.A. Kendziora, J. Gryko, J.J. Dong, C.W. Myles, A. Poddar, and O.F. Sankey, J. Appl. Phys. 2002, 92 7225, Copyright 2002, American Institute of Physics.
20 Figure 1.9 Computed phonon dispersion re lations along selected direc tions in reciprocal space for Cs8Na16Ge136. The Na and Cs Â“rattleÂ” modes are labeled. The frequency of the Cs mode is well within the range of the host Ge136 framework modes. Reproduced with permission from Ref. 57. Cs optic mode was observed for Cs8Na16Ge136, and the majority of the other Ramanactive vibrational modes, largely due to framework optical phonons, for Si136, Cs8Na16Si136, and Cs8Na16Ge136 were also identified.101 A comparison of the guest vibration frequencies determined from th e ADPs, Raman scattering, and theoretical calculations are given in Table 1.2.57,93,101 Further theoretical calculations concerni ng the vibrational properties of filled A8B16E136 clathrates have been reported by Myles et al.,57 who used density functional techniques. Figure 1.9 shows the calculated phonon disper sion curves for one of the compounds studied in that work, Cs8Na16Ge136. For the most part, the phonon dispersion is very similar in character to that calculated for the parent Ge136 clathrate.48 The important difference, however, is the appearance of fl at, nearly dispersionless modes corresponding to the localized motion of the Na and Cs gue sts (labeled in Figure 1.9).In particular, the Cs guest modes are found well within the fr equency range of the host acoustic phonons, which are responsible for the dominant heat carrying contribution to the lattice thermal conductivity. The above results indicate the potential for strong s cattering of these acoustic phonons. Such phenomena have been observed a nd extensively studied in clathrate-I
21 materials (Â§1.1) as well as clathrate hydrates,149 wherein localized guest vibrational modes can efficiently scatter heat-carry ing acoustic phonons resulting in very low thermal conductivities.19 Our preliminary experimental results104,126 from thermal conductivity measurements on polycrystalline NaxSi136 specimens have suggested this resonant scattering effect may indeed be present in some semi conducting clathrate-II variants. We note that although there is clear evidence for the local ized guest mode in materials such as Cs8Na16Ge136 or Cs8Na16Si136,57,101 the thermal conductivity appears to be dominated by the electronic comp onent in these metallic compounds.93,150 The synthesis of new filled semiconducting clathrat e-II variants will allow further study of their expected interesting thermal transport properties. In addition to vibrational phenomenon related to the caged guest motions, the open-structured framework of cl athrate-II phases results in unique thermal properties in its own right. Nolas et al. reported143 on the thermal properties of the empty clathrate Si136, and found that this crysta lline material has a very low thermal conductivity, an order of magnitude lower than that of diamond-structure silicon and comparable in magnitude with amorphous SiO2. This is observed even in the absence of the phonon scattering mechanisms found in filled clathrates.19 The low thermal conductivity of Si136 relative to diamond silicon can be understood in terms of the combined increase in unit cell size and open-framework st ructure of the former with respect to the latter.81,151 The results of theoretical studies81 point to distinct features in the phonon structure which are related to the rela tive increase in unit cell size. These incl ude gaps in the phonon dispersion relations as well as zone-boundary folding, to which the very low thermal conductivity in the Si136 allotrope can be attributed. These results suggest additional approaches to the design of low th ermal conductivity crystalline solids. 1.6 Remarks on the present work As evidenced in this chapter, the unique structural and physical properties of novel intermetallic clathrate materials, in addition to their potential for use in technologically relevant applic ations, form the impetus for the need for a more detailed understanding of these material systems, in particular the clathrat e-II materials. What
22 opportunities in terms of thermoel ectrics still exist in the clathrate-I system? What is the availible composition space for the clathrateII material system, and how can we access new compositions? What opportunities lie in novel synthetic routes to clathrate and related compounds? What are the structure-propert y relationships in clathrate-II systems? What other types of open-framework intermet allics may be of inte rest? The fundamental investigations into th e synthesis, structural, and physic al properties of open framework intermetallic materials of gr oup 14 described in the pages that follow is an attempt to address these questions. This wo rk is also intended to provi de insight and establish the groundwork for future research into these intriguing and technologically promising material systems.
23 2 Preparation and physical properties of the binary clathrate-I K8Ge442 As noted in Chapter 1, phases with the cl athrate-I crystal structure have been the most studied of the intermetallic clathrates. However, the majority of work to date has concentrated on the ternary compounds. With the exception of the unconventional superconductor Ba8Si46 21,152-168 less attention has been paid to the binary type I clathrates, in particular with regard to their ther moelectric properties. Table 2.1 presents a compilation of known binary type I compositi ons, as well as corresponding references from the literature. Of the binary type I cl athrate compositions listed in Table 2.1, several of these compounds have not been well characte rized with respect to their thermoelectric properties, and one can imagine other hither to unrealized compositions are possible. The clathrate-I crystal structure is ch aracterized by face sharing coordination polyhedra, which form a covalently bonded E46 framework through sp3-like bonding of E = Si, Ge, or Sn. There are three crystallographi cally distinct framework sites in this cubic structure (space group Pm 3 n ), 6 c 16 i and 24 k There are two guest atom sites, 2 a and 6 d corresponding to the centers of two dodecah edral and six tetracaidecahdral cages per unit cell. A fragment of the clathrat e-I unit cell is illustrated in Figure 2.1. The crystal chemistry of type I clathrat es has often been discussed within the context of the Zintl-Klemm concepts.109,196,197 Within this descri ption, electropositive guest atoms (e.g. the alkali metals) are treated formally as electron donors, which donate their valence electrons to the host frame work, within a rigid band approximation.174,193, 198,199 Since the sp3 bonding in the clathrate results in an intrinsic semiconductor in the absence of guests, these donated electrons will, in binary clathrates, occupy the framework conduction bands, or remain loca lized at framework vacancies if the formation of such vacancies is energetically favorable.175,189,193 Thus electron-rich
24Table 2.1 Examples of known binary type I clathrate compositions with selected references given. In the chemical formulas, the symbol Â“ Â” represents a framework vacancy. Composition Synthesis Method Lattice Parameter () References Na8Si46 Decomposition of NaSi 10.19648(2)87 3,4,52,87,88,134,169-174 K8Si46 Decomposition of KSi 10.27518(5)175 4,174-177 Rb6Si46 Decomposition of RbSi 10.27188(6)175 4,175 Cs8Si46 HPHTa 10.4176(4)178 178 Ba8Si46 HPHTa 10.328(2)152 21,152-168 I8Si46xIx HPHTa 10.4195(7)179 179-182 K8Ge442 Decomposition of KGe 10.66771(1)175 4,175,183,184 Rb8Ge46 Decomposition of RbGe 10.704 4 Ba8Ge433 From the elements 10.65615(5)185, b 168,185-187 I8Ge46xIx Decomposition of GeI 10.814188 188 Rb8Sn442 From the elements 12.0581(3)189, b 189,190 Cs8Sn442 From the elements 12.1054(4)192, c 191-195 aHigh-pressure/high-temperature synthesis. bThese type I clathrates can be described by larger unit cells of lower symmetry, with a Â’ = 2 a due to the ordering of the framework vacancies. cAt 120 K. Figure 2.1 Partial crystal structure of K8Ge442. The large, red spheres represent the K guests, while the smaller blue spheres represent the Ge framework. The 6c sites are indicated by the smaller, white spheres.
25 Figure 2.2 Simple schematic illustrating the presumed local electronic environment of a framework vacancy in K8Ge442, after Ramachandran et al.175 compositions such as Na8Si46 and K8Si46 exhibit metallic properties.4,152,170,172 The formation of two vacancies per uni t cell in clathrates such as K8Ge442, Rb8Sn442, and Cs8Sn442 ( = framework vacancy) can be rati onalized by the accommodation of the eight electrons per unit cell donated by the guest s. Since each framework vacancy will be surrounded by four framework atoms that ar e only 3-bonded, each of these atoms can accommodate one electron each in a non-bonding orbital; a schematic illustrating this is shown in Figure 2.2. Several de tailed crystallographic studies175,183,189-192 indicate that the vacancies in these clathrates are found at the 6 c sites (indicated in Figure 2.1), which are the most symmetric of the three framework s ites. As a result of the vacancy formation, the composition is charge-balanced, and the chemical formula may be explained as A8E442 ( A = guest, E = framework). A similar rationale can be used in the case of the halogen substituted and filled clathrates although in this case the guests are electronegative and the guesthost polarity is reversed.179,188 This simple electron counting model is useful as a qualitative description of structure and bonding in these vacancy bearing clathrates.175,189-192
26 In the search for novel clathrate mate rials with enhanced thermoelectric properties, the binary type I cl athrates remain a subset that deserves further study. In this chapter, a study on the prepara tion and electrical and ther mal transport properties of polycrystalline binary clathrate-I K8Ge442 is reported. In compar ison with prior work, the importance of specimen preparation in the observed properties of clathrate compounds is emphasized. Thermal conductivity data for this compound, presented for the first time, reveal the binary clathrate-I K8Ge442 is a low thermal conductivity crystalline solid. The binary clathrate K8Ge442 was synthesized using a procedure analogous to that which has been previously reported.4,174 The monosilicide precursor K4Ge4 (cubic, space group n P 3 4) was first synthesized from the high purity elements. This was accomplished by reacting a mixture of K meta l and Ge powder (ground to 325 mesh) at 650oC in tungsten crucibles, sealed under nitr ogen inside a stainless steel reaction vessel. The resulting K4Ge4 compound is extremely air and moistu re sensitive, thus all handling was carried out inside a nitrog en filled glove box. The K4Ge4 compound was then ground by mortar and pestle to fine powder, placed in a quartz tube closed at one end, and the quartz tube attached to a hi gh vacuum apparatus. The K4Ge4 powder was then heated at 440oC under vacuum (10-5 torr) for 24 hours. The specimen was then removed from the vacuum apparatus, vented in a nitrogen atmosphere, and washed with ethanol and distilled water under flowing nitr ogen to remove any unreacted K4Ge4 or residual K metal. Although the precursor K4Ge4 (which exhibits ionic bonding between K+ and [Ge4]4units) is very sensitive to air and moisture, the clathrate K8Ge442 is stable as a result of the strong covalent Ge bonding of the framework, and the encapsulation of K within the framework polyhedra. The speci men was in turn dried by heating under vacuum overnight. The synthesis products were very fine, grayish polycrystalline powders, which were further ground and then compacted into an 83% dense pellet by hot pressing at 380oC under flowing nitrogen. A parall elepiped specimen for transport measurements of approximate dimensions 2 mm 2 mm 5 mm was then cut from the pellet using a wire saw.
27 Figure 2.3 Powder X-ray diffraction patterns for K8Ge442. (a) PXRD pattern calculated for exactly two vacancies per unit cell on the 6c site, with all other s ites fully occupied. (b) Expe rimental, measured pattern using powder ground from the hot-pressed pellet. Table 2.2 Selected data at 300 K for the K8Ge442 specimen of the present work. Compostion (EDS) a () Relative Density (%) (mOhm-cm) S ( V/K) (W/m-K) K8Ge431(9) 10.667(5) 83 30.5 77 1.2 Structure and crystallinity were conf irmed by powder X-ra y diffraction (XRD) using Cu K radiation. Diffraction data were co llected using powder ground from the pellet after hot pressing. Micros tructure and chemical composition were analyzed using a JOEL scanning electron microscope (SEM) and Oxford energy dispersive spectroscopy (EDS). Thermal analysis was performed using a TA Instruments SDT Q600. Four-probe electrical resistivity ( ) and steady state Seebeck coefficient ( S ) and thermal conductivity ( ) were carried out on the same specimen in a radiation shielded cryostat. Voltage contacts were made by solder ing electrical leads to nickel plated dots Degrees 2 203040506070Intensity (arb. units) K 8 Ge 44 Calculated Degrees 2 203040506070Intensity (arb. units) K 8 Ge 44 Experimentala b
28 0.5 mm in diameter, while the temperature difference and specimen temperature were measured by thermocouples attach ed to the specimen by StycastTM epoxy. Figure 2.3 shows a powder XRD pattern colle cted from powder ground from the pellet post-hot pressing, and indicates the phase pur ity of the specimen. Also shown in Figure 2.3 (bottom) is a simulated powder XRD pattern200 for K8Ge442, calculated assuming exactly 2 vacancies per unit cell on the 6 c site. This calculated pattern corroborates the experimental diffraction pattern very well. The cubic lattice parameter a = 10.667(5) was calculated from the positions of high angle reflections using NIST SRM silicon as an internal standard, and is in agreement with the valu e 10.66771(1) previously reported.175 Scanning electron microscopy (SEM) analys is indicated typical grain size in the range of 1 to 10 m, though both larger and smaller grains were observed. Energy dispersive spectroscopy (EDS) measurements taken on 11 separate grains yielded an average chemical composition in reasonable ag reement with the expected composition of K8Ge442, and confirmed the presence of vacancies on the Ge framework (Table 2.2). We have assumed the guest sites to be fully occupied, as is the case in the majority of type I clathrates. Results from differential thermal analysis (DTA) measurements on the K8Ge442 specimen are shown in Figure 2.4. The large endothermic transition at high temperature is the melt of -Ge (diamond structure), which is present after the complete decomposition of the KGe specimen. The cu rve shows at least tw o exothermic events between 400 and 600oC (inset), the first of wh ich occurs just above 480oC. This indicates that K8Ge442 is a meta-stable phase. The presence of multiple exothermic peaks in the curve suggests phase transitions to ot her K-Ge phases. von Schnering et al,184 have studied the thermal decomposition of K4Ge4 underdynamic vacuum, and found evidence for several other binary K-Ge phases, in addition to K8Ge442. Several of these proposed compounds have not yet been further characterized. Figure 2.5 shows the temperature dependence of and S from 12 to 300 K. The sign of S is negative in the entire temperature range shown, and increases in magnitude monotonically with temperature with essentiall y constant slope. Thes e data indicate the
29 Figure 2.4 Differential thermal analysis (DTA) for K8Ge442. An enlargement of the curve in the range 400 to 700oC is shown in the inset, showing the multi-peak nature of the decomposition. M. Beekman and G.S. Nolas, Physical Properties of Hot-pressed K8Ge442, Advances in Electronic Ceramics, Ceram. Eng. Sci. Proc. 28 (8), 233 (2007). Reprinted with permission of The American Ceramic Society, www.ceramics.org (2007). All rights reserved. majority carriers in K8Ge442 are electrons, and S reaches a moderate value of 77 V/K at 300 K. With the exception of very low temperature activated behavior below 40 K, increases monotonically with temperature, behavior typical of a metallic or heavily doped semiconductor material. This result contrast s appreciably with previously reported measurements of Ramachandran et al.,175 who reported the electrical conductivity (replotted as in mOhm-cm in the inset of Figure 2.5) of a cold-pressed pellet of K8Ge442 (synthesized at a temperature between 350 and 380oC) exhibiting an activated temperature dependence. As both the synthe sis and consolidation procedures (hotpressing vs. cold-pressing) differed between th ese two works, we suggest that specimen preparation can have a significant effect on th e measured transport properties of this material. In particular, although the specimens studied in Ref. 175 were reported to be 85-90% of the theoretical density, we emphasi ze that electrical measurements will be more reliable when obtained on hot-pressed rath er than cold-pressed materials, since the former better ensures good elec trical contact between the pol ycrystalline grains, which Temperature ( o C) 020040060080010001200 Temperature Difference ( o C) -14 -12 -10 -8 -6 -4 -2 0 Temperature ( o C) 400450500550600650700 Temperature Difference ( o C) -18 -16 -1.4 -12 -10 -08 -06 d-Ge melt exotherm = up
30 Temperature (K) 050100150200250300350 Electrical Resistivity (mOhm-cm) 26 27 28 29 30 Seebeck Coefficient ( V/K) -80 -60 -40 -20 0 0200400600 400 800 1200 a b Figure 2.5 Electrical transport for K8Ge442. (a) Temperature dependence of the Seebeck coefficient for K8Ge442. (b) Temperature dependent electrical resistivity of K8Ge442. Inset to (b): Resistivity data from Ramachandran et al., re-plotted from Ref. 175 in mOhm-cm vs. T (K) for comparison (same units as main plot). cannot be guaranteed with the latter. Th e metallic-like temperature dependence of shown in Figure 2.5 suggests that K8Ge442 might be included in the class of metallic Zintl phases,201,202 but may also indicate significant contributi ons to conduction from impurity levels, as observed previously for the Cs8Sn442 analogue.194 Figure 2.6 shows of K8Ge442 in the range 12 to 300 K. For comparison, the thermal conductivities of two other type I clathrates, Cs8Sn442 192,194 and Sr8Ga16Ge30 19,30 are also shown. Our measurements reveal that K8Ge442 is a very low thermal conductivity crystall ine solid, with ~ 1 W/m-K at room te mperature. Although the thermal conductivities of the th ree clathrates are all compar able at room temperature,
31 Temperature (K) 10100 Thermal Conductivity (Wm -1 K -1 ) 1 10 Sr8Ga16Ge30 Cs8Sn44 K8Ge44 Figure 2.6 Temperature dependence of th e thermal conductivity of K8Ge442. Also shown are data for two other type I clathrates, Cs8Sn442 192,194 and Sr8Ga16Ge30.19,30 they differ somewhat in both magnitude and temperature dependence at lower temperatures. It has been shown previously192,194 that for Cs8Sn442 the guest atom vibrations have a much smalle r significance in the scattering of the heat carrying acoustic phonons than for Sr8Ga16Ge30, and the latter exhibits a much lower attributed to strong phonon scattering via a resonant interaction with the localized Sr vibrations.19,30 Below 200 K, K8Ge442 displays a thermal conductivity in termediate between that of Cs8Sn442 and Sr8Ga16Ge30, with a relatively flat temperature dependence as compared to the other two clathrates, over entire rang e of measurement. Although we expect that there will be point defect scattering of phonons present in K8Ge442 due to the presence of vacancies on the Ge framework, it is unlikely that th is alone explains the very low thermal conductivity. Therefore we suggest that K vi brations inside the Ge cages of the
32 framework are able to scatter phonons in K8Ge442 as is the case with other type I clathrates. However, it is clear from Figure 2.6 that this effect is not as prominent as in Sr8Ga16Ge30. Theoretical calculations by Dong et al.203 have predicted a much stronger interaction between alkaline earth guests (e.g., Sr or Ba) and the framework acoustic modes in germanium clathrates as compared to alkali guests (e.g., K). This is in agreement with the results shown in Figure 2. 6. More detailed crystallographic study, in combination with inelastic scattering experime nts (e.g. Raman scattering) should help to elucidate the extent of the effects of the K guest vibrations on the vibrational properties of K8Ge442. To summarize, we have presented here th e results from a study of the temperature dependent transport properties of the binary clathrate-I K8Ge442. This intermetallic clathrate exhibits a metallic-like and a relatively high S eebeck coefficient of Â–77 V/K at room temperature. A comparison of the el ectrical properties with previous work indicates the dependence of specimen propert ies on preparation, and we emphasize the importance of specimen preparation as key in the proper evaluation of thermoelectric materials. In particular, of interest for futu re work is a comprehensive investigation into the possible influence of synthesis conditions on the composition and physical properties in this K-Ge clathrate-I syst em. The thermal conductivity of K8Ge442, presented for the first time, is shown to be very low, comparab le in magnitude to ot her type I clathrates. The resistivity of K8Ge442 is relatively high, but the moderate room temperature Seebeck coefficient and very low thermal c onductivity suggests that the binary type I clathrates are a class of materials which dese rve further evaluation in the search for new thermoelectric materials.
33 3 Framework substitution in germanium clathrate-II An important aspect regarding the clathrate-II intermetallics pertains to the diversity in compositions that are in principl e possible within this material system (cf. Â§1.3). To date, only a small subset of these conceivable compositions has been experimentally realized. This raises the question, what approaches are promising to explore novel compositions, while simultaneous ly allowing for the study of the influence of composition on physical properties? Subs titution on the group 14 framework by other atomic species provides such an opportunity, and may also facilitate preparation of semiconducting clathrate-II compositions, wh ich are expected to possess favourable thermoelectric properties (cf. Â§1.5). As su ch, we have initiate d the first study of framework substitution in clathrate-II materials through the synthesis and characterization of novel germanium-based compositions. Since it is known that noble metals substitute on the group 14 fr ameworks in clathrate-I compounds,8 the substitution of Ag and Cu for Ge in Cs8Na16Ge136 was investigated, throu gh synthetic study, singlecrystal and powder X-ray diffr action, energy dispersive sp ectroscopy (EDS), extended Xray absorption fine structure (EXAFS) analys is, and transport properties measurements. 3.1 Synthesis The synthesis104 of Cs8Na16MyGe136y (M = Ag and Cu) specimens studied in this work was performed as follows. High purity Cs metal (99.98%), Na metal (99.95%), Ag or Cu powder (99.9%), and Ge powder (gr ound to 325 mesh from intrinsic crystalline Ge), were combined in tungsten crucibles, after thoroughly premixing the Ag (or Cu) and Ge powders. The crucibles and mixtures were then sealed under nitrogen inside steel canisters, which were in turn sealed in qua rtz ampoules. The mixtures were held at 800oC for two days, then at 650oC for seven days. Specimens w ith nominal transition metal contents of y = 5, 8, and 10 were prepared. The products consisted of small (~ 0.5 mm in
34 size) crystals possessing a metallic lustre th at are stable toward both air and water. Portions of the entire sample were ground for powder X-ray diffraction. The compositions of the small crystals were also analyzed using energy dispersive spectroscopy (EDS). EDS an alysis on hot-pressed Cs8Na16Cu5Ge131 showed a uniform Cu:Ge ratio of 4.7:131.3 within the polycrystalline grains, very close to the nominal ratio 5:131. For optimal comparison, specimens of the parent compound Cs8Na16Ge136 (i.e. non-substituted) were also prepared, acco rding to the same procedure as for Cs8Na16MyGe136y. The attempt to prepare a specimen with composition Cs8Na16Cu10Ge126 according to the above procedure resulted in a type II clathrate with a lattice parameter only marginally larger than that for Cs8Na16Cu5Ge131, and the appearance of a small amount of the additional Cu3Ge phase, as detected by X-ray powde r diffraction. This suggests the solubility limit for Cu in the structure ha s been exceeded. Similar results were observed for Ag substitution as discussed below. 3.2 Single crystal X-ray diffraction studies of Cs8Na16AgyGe136-y Three Cs8Na16AgyGe136y specimens were studied by single crystal XRD, and are denoted according to their nominal compositions as I ( y = 0), II ( y = 5), and III ( y = 8). Single crystal X-ray diffraction measurements a nd structural refinements were carried out by Dr. Winnie Wong-Ng of the Na tional Institute of Standard s and Technology. Small (< 0.1 mm in size) single crystals were cut from the larger aggregates for single crystal Xray diffraction (XRD) measuremen ts. The structures of the Cs8Na16AgxGe136x crystals were determined using single crystals mounted on Lindemann t ype glass fibres in random orientations. Data collection wa s performed at 298 K with Mo K radiation on a computer-controlled -axis diffractometer equipped with a graphite crystal incident beam monochromator. Mo K radiation (0.71073 ) and a Zr f ilter were used. Preliminary cell constants and orientation matrices for data collection were obtained from least-squares refinements using setting angl es of 25 reflections (18 < < 25). The final lattice parameters of the three Cs8Na16AgyGe136y samples were obtained from X-ray powder diffraction using the Rietveld refinement me thod (see Appendix A). The GSAS software
35Table 3.1 Summary of data collection for the three compositions of Cs8Na16AgyGe136y y = 0 y = 5.9 y = 6.7 Color gray (metallic) gr ay (metallic) gray (metallic) Radiation, graphite Monochromator Mo, 0.7107 Mo, 0.7107 Mo, 0.7107 Data collection Standard reflections Intensity monitor 8 8 8 Â–3 Â–13 Â–3 Â–3 Â–13 Â–3 10 10 0 8 8 Â–8 8 8 8 10 6 0 10 10 0 Â–10 0 Â–10 Orientation monitor 8 8 8 10 10 0 4 0 16 16 4 0 4 0 16 11 11 5 10 6 0 5 15 5 5 15 5 # Reflections measured Total 1627 2252 2409 Independent 352 474 505 Refinement 311 (> 4 ) 403 (> 4 ) 397 (> 4 ) 2 range ( ) 2 64 2 72 2 72 Range of h k 0 < h k, l < 23 0 < h k, l < 25 0 < h k, l < 26 Range of transmission factors 0.15 0.23 0.11 0.25 0.14 0.30 was used for anaylsis of the powder XRD data.205,206 The reported9 structure of Cs8Na16Ge136 was employed as a starting model. Table 3.1 gives details of the experiment al and structural solution for the three crystals. The /2 scan method was used for data co llection. During th e data collection process, 3 reflections were used to monitor the stability of the crystal, and another three to monitor the orientation. A ll three crystals were found to be stable chemically and mechanically with respect to X-ray. Lo rentz and polarization corrections (CAD4 manual207) were applied. At the end of da ta collection, 3 reflections with angles near 90 were measured as a function of the angle in order to obtain the empirical absorption correction curve.
36 Fig. 3.1 Powder X-ray diffraction patterns for Cs8Na16AgyGe136y clathrates. Reprinte d from M. Beekman, et al ., Â“Synthesis and single-crystal X-ray diffraction studies of ne w framework substituted type II clathrates, Cs8Na16AgxGe136x ( x < 7),Â” J. Solid State Chem. 180 1076-1082, Copyright 2007, with permission from Elsevier. The data were reduced and the structures were refined using the PC version of SHELXTL.208 The initial model used for leastsquares refinements was that of Cs8Na16Ge136.9 The cell parameters obtained from the powder diffraction data were then used during structure refinements. Full matr ix least-squares refinements on structure factors ( F2) were carried out. Atomic scattering fact ors were taken from the International Tables of Crystallography.209 A summary of data collection details is given in Table 3.1. X-ray powder diffraction pa tterns for the three Cs8Na16AgyGe136y samples are presented in Figure 3.1. All pa tterns exhibit reflections char acteristic of the type II clathrate crystal structure, and indicate the ph ase purity of the samples. As shown in the
37Table 3.2 Crystal data and structure refinement for Cs8Na16AgyGe136y (at 25 C) Sample I ( y = 0) Sample II ( y = 5.9) Sample III ( y = 6.7) Crystal data Space group Fd 3 m (No. 227) Fd 3 m (No. 227) Fd 3 m (No. 227) Cell constant a (powder) 15.49262(9) 15.51605(6) 15.51618(9) V 3718.56(4) 3 3735.46(2) 3 3735.55(3) 3 Z 1 1 1 Least-squares refinements wR ( F2) 0.0571 0.070 0.064 R 1 0.024 (311 refl.) 0.027 (403 refl.) 0.029 (397 refl.) R 2 0.031 (352 refl.) 0.036 (474 refl.) 0.044 (505 refl.) Goodness of Fit 1.159 1.060 1.130 inset of Figure 3.1, a very small amount of elemental Ag was found to be present in Sample III. This is consistent with singlecrystal XRD and EDS measurements discussed below, which found the value of y for Sample III to be less than the target value of 8. This indicates the solubility limit for Ag in the structure has likely been exceeded. As confirmed by single crystal and powder XRD measurements, all three samples crystallized with the cu bic type II clathrate crystal structure (space group Fd 3 m ). Summaries of the single crystal XRD data coll ection and refinement results are given in Tables 3.1 and 3.2. The refined atomic posi tions, occupancies, and thermal parameters are given in Table 3.3. The Na atoms were found to exclusively occupy the smaller Ge20 dodecahedra, while the Cs atoms occupy the larger Ge28 hexacaidecahedra. No mixing of the cation guests was observed at these sites, both of which were also found to be fully occupied from the single crystal structural refinement. As was originally observed by Bobev and Sevov,9 stabilization of the clathrate stru cture appears to be facilitated by Â“matchingÂ” cation and cage sizes, thus the smal ler Na and larger Cs reside in the smaller Ge20 and larger Ge28 polyhedra, respectively.
38Table 3.3 Atomic coordinates of the three Cs8Na16AgyGe136y compositions ( Fd 3 m No. 227; origin chosen at center (3 m )). Atom Site Symm. Occupancy x y z Uiso (2) Sample I, y = 0 Cs 8 b 4 3 m 1.0 3/8 3/8 3/8 0.0352(3) Na 16 c 3 m 1.0 0 0 0 0.036(1) Ge1 96 g m 1.0 0.06783(2) 0.06783(2) 0.37033(2) 0.0116(2) Ge2 32 e 3 m 1.0 0.21761(2) 0.21761(2) 0.21761(2) 0.0110(1) Ge3 8 a 4 3 m 1.0 1/8 1/8 1/8 0.0103(3) Sample II, y = 5.9(1.0) Cs 8 b 4 3 m 1.0 3/8 3/8 3/8 0.0402(4) Na 16 c 3 m 1.0 0 0 0 0.041(1) Ge1/ 96 g m 0.94(1)/ 0.06771(2) 0.06771(2) 0.37045(2) 0.0095(1) Ag1 0.06(1) Ge2 32 e 3 m 1.0 0.21755(2) 0.21755(2) 0.21755(2) 0.0092(2) Ge3 8 a 4 3 m 1.0 1/8 1/8 1/8 0.0092(3) Sample III, y = 6.7(1.1) Cs 8 b 4 3 m 1.0 3/8 3/8 3/8 0.0335(4) Na 16 c 3 m 1.0 0 0 0 0.035(2) Ge1/ 96 g m 0.952(8)/ 0.06767(2) 0.06767(2) 0.37043(2) 0.0029(2) Ag1 0.048(8) Ge2/ 32 e 3 m 0.94(1)/ 0.21751(3) 0.21751(3) 0.21751(3) 0.0037(2) Ag2 0.06(1) Ge3 8 a 4 3 m 1.0 1/8 1/8 1/8 0.0021(3) Empirically, in type I clathrates, trans ition metals have only been observed to occupy framework positions.8 For completeness, the possibility of Ag substitution at the guest positions of the type II clathrates in the present study was syst ematically ruled out during preliminary structural refinements, and the single crystal X-ray diffraction data indicate Ag substitutes exclusively for Ge on the Ge framework. All Ge/Ag sites in the present study of the Cs8Na16AgyGe136y clathrates were refined with a total occupancy constrained to unity. As indicated by the si te occupancies in Table 3.3, Ag shows a
39 preference for substitution on the 96 g site. For Sample II ( y = 5.9(1.0)), substitution is found exclusively on the E1 (96 g ) site. For Sample III ( y = 6.7(1.1)), the majority of the Ag again substitutes on this site ( 70% of the total Ag cont ent), though 4.8% and 6.5% of the 96 g and 32 e sites, respectively, are occupied by Ag. Preferential occupation of substituting species has also been observed in type I clathrates, a nd several structural studies have revealed a preference for the 6 c site (space group Pm 3 n ) in these compounds.7,8,210 In particular, transition metals substituting for silicon and germanium were found to preferentially occupy the 6 c site,8 which is the most symmetric of the type I clathrate framework sites. The 6 c sites in the type I clathr ates are located on hexagonal six-member rings of framework atoms. The E1 (96 g ) sites in the type II clathrate structure, which the Ag atoms are found to prefer entially occupy, in f act constitute all of the hexagonal six-member sites (cf. Figure 1.1), whereas the clathrate-I 6 c sites comprise one third of the hexagonal ring sites. In contrast to the 6 c sites of the type I clathrates, the 96 g sites are the least symmetric site of the fr amework in the clathrate-II structure, but they also bear the most strain of all of the sites in the struct ure, as with the 6 c site in clathrate-I. We next offer a qualitative discussion of the cage environments of the alkali guests in the Cs8Na16AgyGe136y samples. The relevant bond distances in Cs8Na16AgyGe136y are given in Table 3.4. In Cs8Na16AgyGe136y, Na resides in the smaller 20-membered cage with Na-Ge distances rang ing from 3.3543(0) to 3.5419(2) for Sample I; from 3.3593(0) to 3.5492(2) fo r Sample II; and from 3.3594(0) to 3.5493(3) for Sample III. The larger Cs were found to reside inside the larger 28membered cage, with Cs-G e distances ranging from 4.1395(4) to 4.2255(11) for Sample I; 4.1448(3) to 4.2315(6) for Samp le II; and 4.1454(4) to 4.2326(7) for Sample III. The shortest Cs-Ge and Na-G e distances in the three compounds are 4.1395(4) and 3.3543(0) , respectively, a nd both were found in the non-substituted Cs8Na16Ge136 sample. Subtracting from these dist ances the single-bond radius of Ge (1.225 ),211 the difference values become 2.915 and 2.129 for Cs-Ge and Na-Ge, respectively. This provides a rough measur e of the amount of Â“spaceÂ” inside the respective cages. If we instead subtract the single-bond radius for Ag (1.412 )211 from
40 these guest-framework distances, we obtain 2.728 and 1.942 for Cs-Ag and Na-Ag, respectively. Assuming the alka li guests to be singly ionized9 (i.e. Na+ and Cs+), we may take the approximate ionic radii for Cs a nd Na to be 1.70 and 1.3 , respectively.212 Using this simple estimate of the available space inside the framework polyhedra, these alkali metals can Â“fitÂ” into the type II cavit ies quite easily, with some excess space. As shown in Table 3.3, the refined atomic displacement parameters (Uiso) for the Cs and Na guests in the Cs8Na16AgyGe136y specimens are both significantly larger than those for the Table 3.4 Selected inter-atomic distances () in Cs8Na16AgyGe136y x Atoms Distance Atoms Distance Sample I 0.0 Cs-Ge1 4.1395(4) 12 Ge1-Ge1 2.5006(4) 2 Cs-Ge1 4.226(1) 12 Ge1-Ge1 2.5051(9) Cs-Ge2 4.224(1) 4 Ge1-Ge2 2.4902(4) Na-Ge1 3.5419(2) 12 Ge2-Ge1 2.4903(4) 3 Na-Ge2 3.4452(3) 6 Ge2-Ge3 2.4850(6) Na-Ge3 3.3543(0) 2 Ge3-Ge2 2.4850(5) 4 Sample II 5.9(1.0) Cs-Ge1/Ag1 4.1448(3) 12 Ge/Ag1-Ge/Ag1 12.5013(4) 2 Ge1/Ag1-Cs 4.2293(4) 12 GeAg1-Ge/Ag1 2.5142(8) Ge2-Cs 4.2315(6) 4 Ge/Ag1-Ge2 2.4955(4) Na-Ge1/Ag1 3.5492(2) 12 Ge2-Ge/Ag1 2.4955(4) 3 Na-Ge2 3.4497(2) 6 Ge2-Ge3 2.4871(6) Na-Ge3 3.3593(0) 2 Ge3-Ge2 2.4871(6) 4 Sample III 6.7(1.1) Cs-Ge1/Ag1 4.1454(4) 12 Ge1/Ag1 2.5010(4) 2 Ge1/Ag1-Cs 4.2285(5) 12 Ge1/Ag1 2.516(1) Ge2/Ag2-Cs 4.2326(7) 4 Ge/Ag1-Ge/Ag2 2.4952(5) Ge1/Ag1-Na 3.5493(3) 12 Ge/Ag2-Ge/Ag1 2.4952(5) 3 Na-Ge2/Ag2 3.4494(3) 6 Ge/Ag2-Ge3 2.4861(7) Na-Ge3 3.3594(0) 2 Ge3-Ge/Ag2 2.4861(7) 4
41 framework Ge/Ag atoms, in agreement with those previously reported for Cs8Na16Ge136.93 The larger Uiso for Cs and Na can be attributed to the weaker bonding between guest and framework, allowing for re latively large thermal motion of the guest atoms inside their framework cages (cf. Â§1.2 and 1.4). Indeed, the thermal motion associated with Cs in the larger cage of these clathrates corresponds to an optic phonon mode.101 The presence of such loosely bound guest atoms in type I clathrate materials results in the very low lattice therma l conductivities some clathrates possess,19 which can be attributed to the scattering of the h eat carrying acoustic pho nons by the localized, incoherent guest vibration modes. Recent experimental104,126 and theoretical57 results suggest a similar effect may occur in t ype II clathrates, and from the large Uiso values for the alkali guests we postulate that the lattice thermal conductivities of Cs8Na16AgyGe136y clathrates should be quite low. The Ge-Ge distances in the three Cs8Na16AgyGe136y compounds (in the range of 2.4850(4) to 2.5159(10) ) are somewh at longer than that in elemental -Ge (2.445 ), where strong tetrahedral bonds are expe cted. As one compares the corresponding bond lengths in the three Cs8Na16AgyGe136y compositions (Table 3.4), one observes that in general the compositions with Ag substi tution give rise to longer bond lengths as compared to those of Cs8Na16Ge136. However, the corresponding bond distances in compositions II and III are not significantly di fferent (consistent with their somewhat similar lattice parameters). Table 3.5 gives the selected bond angl es surrounding the Ge/Ag sites. In Cs8Na16Ge136, each Ge is bonded to four other Ge atoms; schematics showing the local bonding environments of the Ge1 (96 g ), Ge2 (32 e ), and Ge3 (8 a ) sites are given in Figure 3.2. The Ge3 (8 a ) site has four equal bonds and six equal bond angles and therefore it is the most symmetric site (a nd also has the strongest Ge-Ge bond among the three Ge sites). The Ge2 (32 e ) site has two different sets of angles, and by comparison with the Ge3 (8 a ) site it is relatively more dist orted (or more strained). Around Ge1 (96 g ), the angles show the most pronounced de viation from ideal tetrahedral symmetry, with an angle of 120 corresponding to the internal a ngle of the hexagona l face of the E28
42Table 3.5 Selected bond angles for Cs8Na16AgyGe136y ( ) _____________________________________________________________________________ Central atom Angles ( ) _______________________________________________________________ Sample I (y = 0) Sample II (y = 5.9(1.0)) Sample III (y = 6.7(1.1)) _____________________________________________________________________________ Ge1 105.26(2) 2 105.34(2) 2 105.40(2) 2 108.17(2) 1 108.06(2) 1 108.02(2) 1 108.87(2) 2 108.83(1) 2 108.80(2) 2 119.82(0) 1 119.83(0) 1 119.83(0) 2 Ge2 107.10(2) 3 107.20(2) 3 107.24(2) 3 111.74(2) 3 111.64(1) 3 111.60(2) 3 Ge3 109.47(2) 6 109.47(0) 6 109.47(0) 6 _____________________________________________________________________________ Figure 3.2 Local tetrahedral bonding environments of the (a) Ge1 (96 g ), (b) Ge2(32 e ), and (c) Ge3 (8 a ) sites in Cs8Na16Ge136, with bond angles given. The Ge1 site in (a ) is the least symmetric, and is the center for the ~ 120o interior angle of the hexagonal face of the he xacaidecahedra. Ag subs titutes preferentially at this site. Reprinted from A.N. Mansour, et al. Â“Local Structure of Cu in Cs8Na16Cu5Ge131 Type II Clathrate,Â” J. Solid State Chem. 182 107-114, Copyright 2009, with permission from Elsevier.
43 cage. (Recall six Ge1 link together to form the hexagonal face of the polyhedra in the Cs8Na16Ge136 structure.) Therefore the local bonding environment around the Ge1 (96 g ) site is the most Â“distortedÂ” of the three fram ework sites, and is expected to be the most susceptible for substitution. Our single cr ystal XRD refinement results support this conclusion, as preference is found for substitution at the Ge1 (96 g ) site. Also, from Table 3.4, we note that the bond distances surrounding the Ge1 site are slight ly larger that the others in the structure, in dicating slightly weaker bonding around this site. Although the presence of the d -orbitals of Ag may also affect the bonding geometry, our results indicate that the substitution of Ag does not have a signifi cant effect on the geometry around the Ge/Ag sites (Table 2.5). Results of SEM/EDS analysis also conf irmed the presence of Ag within the clathrate crystals. Severe overlap of th e Na K (1.041 KeV) and Ge L (1.096 KeV) excitations makes accurate measurements of the Na composition extremely difficult, thus it has been assumed that the Na contribution to the compositions is ~ 10 atomic % in all compounds, an assumption that is supported by the structure determin ation results that there are no vacancies observed for any site in the structure. The composition of Sample II as determined from EDS was Cs7.0Na15.7Ag4.4Ge131.6, in reasonable ag reement with the expected value for Sample II, whereas the Ag content y was determined from single crystal X-ray refinement to be 5.9(1.0). Fo r sample III the composition was determined from EDS to be Cs7.4Na15.7Ag4.8Ge131.2, whereas the Ag content y was determined to be 6.7(1.1) from XRD structure re finements, notably less than the nominal value of y = 8. As determined from both X-ray diffraction and EDS measurements, the Ag content in Samples II and III are only marginally different, and both less than y = 8. These results suggest that the value of y for the solid solubility of Ag in the Cs8Na16AgyGe136y compounds is approximately 7. The small diffe rence in the Ag content between Samples II and III is consistent with the fact that the lattice parameter of Sample III is only marginally larger than that of Sample II.
44 3.3 Structural characterization of Cs8Na16Cu5Ge131: Powder X-ray diffraction and EXAFS Powder X-ray diffraction patterns we re collected by Dr. James Kaduk of Innovene on a Bruker D8 Advance using Cu K radiation, with Rietveld structure refinements carried out using the GSAS suite.205,206 Rietveld refinements ( vide infra ) indicated the 8 b and 16 c sites to be fully occupied by Cs and Na, respectively, with no mixing on the two sites. Due to the lack of X-ray scattering contrast between Cu and Ge, determination of Cu/Ge relative occupancies using either single cr ystal or powder X-ray diffraction for the Cu substituted samples is exceedingly difficult. This aspect is further addressed by EXAFS studies below. Figure 3.3 shows Rietveld refine ment powder XRD plots for both Cs8Na16Ge136 and Cs8Na16Cu5Ge131. Details of the refinement results are given in Table 3.6. The type II clathrate crystal structure was confirmed fo r both specimens. As shown in Figure 3.3b, a trace amount (~ 1 wt%) of elemen tal Ge was detected in the Cs8Na16Cu5Ge131 specimen. As noted from Table 3.6, the unit cell constant a shrinks Figure 3.3 Rietveld X-ray powder diffraction plots (observed, calculated, and difference) for (a) Cs8Na16Ge136 and (b) Cs8Na16Cu5Ge136. The vertical scale for data above 50o 2 has been multiplied by a factor of 5 for clarity. The upper tic k marks in (b) indicate reflections due to ~ 1 wt% impurity of elemental Ge detected in the Cs8Na16Cu5Ge136 specimen. Reprin ted from M. Beekman et al. Â“Synthesis and characterization of framework-substituted Cs8Na16Cu5Ge131,Â” J. of Alloys and Comp. 470 365-368, Copyright 2009, with permission from Elsevier. (a) (b)
45 Table 3.6 Selected crystallographic data and Rietveld refinement results for Cs8Na16Ge136 and Cs8Na16Cu5Ge131 Specimen Cs8Na16Ge136 Cs8Na16Cu5Ge131 Crystal system Cubic Cubic Space group m Fd 3 m Fd 3 Cell constant a () 15.49263(10) 15.42000(9) Cell Volume 3718.56(7) 3666.52(6) Z 1 1 Radiation Cu K Cu K Impurity phases (wt %) None Elemental Ge (1.4 %) Rp 0.0663 0.0476 wRp 0.0863 0.0620 Rexp 0.0517 0.0449 R(F2) 0.08610 0.05399 2 1.67 1.38 Table 3.7 Atomic coordinates for Cs8Na16Ge136 and Cs8Na16Cu5Ge131 Atom Site x y z Frac. Uiso (2) Cs8Na16Ge136 Cs 8 b 0.375 0.375 0.375 1.0 0.0505(5) Na 16 c 0 0 0 1.0 0.0453(20) Ge3 8 a 0.125 0.125 0.125 1.0 0.0223(2) Ge2 32 e 0.21825(6) 0.21825(6) 0.21825(6) 1.0 0.0223(2) Ge1 96 g 0.067284(27) 0.067284(27) 0.37126(5) 1.0 0.0223(2) Cs8Na16Cu5Ge131 Cs 8 b 0.375 0.375 0.375 1.0 0.0564(5) Na 16 c 0 0 0 1.0 0.0596(20) Ge3/ Cu3 8 a 0.125 0.125 0.125 0.9893(24)/ 0.011(1) 0.0214(1) Ge2 32 e 0.21830(5) 0.21830(5) 0.21830(5) 1.0 0.0214(1) Ge1/ Cu1 96 g 0.067298(23) 0.067298(23) 0.37163(4) 0.9264(10)/ 0.074(1) 0.0214(1)
46 slightly but significantly from 15.49263(10) for Cs8Na16Ge136 to 15.42000(9) for Cs8Na16Cu5Ge131, due to substitution of Cu for Ge on the framework. Analogous behaviour was observed in Ba8CuxGe46x type I clathrates.213,214 Table 3.7 gives site occupancies, atomic positions, and isotropic atomic displacement parameters (Uiso) for both specimens as determined from Rietveld refinement. The stru ctural refinements indicate all crystallographic sites are fully occupied in both specimens. During the structural refinements the Cu content was allowed to refine, though it is not possible to determine the Cu cont ent accurately usi ng conventional X-ray diffraction, since the X-ray scattering pow ers of Cu and Ge are very similar as notedabove. As such, the accurate determinati on of any site occupation preference for Cu in Cs8Na16Cu5Ge131 is also unattainable from the pow der X-ray diffraction data. In the single crystal XRD work discu ssed above, it was found that Ag substitutes preferentially for Ge at the 96 g framework site, which is the most di storted or Â“straine dÂ” site of the framework. Presumably Cu is likely to subs titute preferentially at this site in Cs8Na16Cu5Ge131 as well. In order to gain insight into the local structure and site preference for Cu in Cs8Na16Cu5Ge131, EXAFS experiments were performed. EXAFS data collection and analysis were carried out by Dr. Azzam Mansour of the Naval Surface Warfare Center, West Beth esda, MD. Experiments were conducted at room temperature (RT) and liquid nitroge n temperature (LNT) on the bending magnet station X-11A of the National Synchrotr on Light Source. A brief summary of the principles and analysis underl ying EXAFS are given in the A ppendix; further details of the data collection, experimental procedure, and methods of analysis can be found in Ref. 215. All fits were made using the curve fitting code FEFFIT (version 2.984) of the University of Washington XAFS (UWXAFS) software package.216 The data were fitted using theoretical standards cal culated based on the curved-wav e scattering formalism of the FEFF Code (version 8.2).217,218 The FEFF calculations were performed us ing established structural models for elemental Ge220 and the Cs8Na16Ge136.9 The local structure parameters for the first few coordination spheres around Ge in Cs8Na16Ge136 are listed in Table 3.8. In accordance with the convention used above, the three nonequivalent sites are labeled as Ge1 (96 g ),
47 Ge2 (32 e ), and Ge3 (8 a ); the nearest neighbor coordi nation environments and site symmetries for the three sites can be recalled from Figure 3.2. Due to the high degree of symmetry of the Ge3 site, it was used in the FEFF code to calculate the backscattering amplitudes and phase shifts for Ge-Ge interactions. The phase shift for the central Cu atom was calculated using the same cluster data for the Ge3 site while placing a Cu atom at the origin of the cluster. For comparison purposes, local structure parameters for the first two coordination spheres of elemental Ge can be found in Ref. 215. A comparison of the raw and normalized Cu and Ge K-edge XAFS spectra collected near the liquid n itrogen temperature for Cs8Na16Cu5Ge131 are displayed in Figure 3.4. As noted from the raw data, the Ge K-edge jump is significantly larger than the Cu K-edge jump due to the higher Ge c oncentration relative to the Cu concentration in the specimen. The absorption edge jumps are 0.092 and 3.18 for Cu and Ge respectively. Taking into account the theoretical edge jump s for Cu and Ge of 26485 and 20068 Barns/atom,220 respectively, the atomic ratio of Ge to Cu in the specimen is determined to be 26.19. This value compares very well with the nominal value of 26.20, which is calculated on the basis of the nom inal composition of the specimen. Once the spectra are normalized per Cu or Ge atom, the EXAFS oscillations are clearly prominent in the XAFS spectra for both Cu and Ge. Th ese oscillations extend several hundred eV above the edge energy for both Cu and Ge. Shown in Figure 3.4 are comparisons of the RT and near LNT Ge K-edge EXAFS spectra and the corresponding k-weighted Fourier transforms. It is important to note that the EXAFS spectra and Fourier transforms re present an ensemble average of the local structure of three non-equivalent sites of Ge namely, Ge1, Ge2 and Ge3. Furthermore, the distances of various coordi nation spheres in the Fourier transforms are shifted lower by about 0.2-0.3 relative to real distances du e to the phase shifts of the central and back scattering atoms. The apparent contractions in the Fourier transforms distances are accounted for during the quantitat ive analysis of the EXAFS spectra. As anticipated, the amplitude of the EXAFS oscillations as well as the amplitude of th e Fourier transforms increased when the specimen temperature d ecreased from RT to the LNT due to the quenching of the thermal motion of the atoms. The Fourier transforms display a major
48 Figure 3.4 EXAFS data for Cs8Na16Cu5Ge131 near the Cu and Ge K-edges. (a) Raw Cu and Ge K-edge XAS data near liquid nitrogen temperature (LNT). (b) Normalized LN Cu and Ge K-edge XAS data. (c) Room temperature (RT) and LNT EXAFS spectra for Ge. (d) Fourier transformed EXAFS spectra at RT and LNT for Ge. (e) RT and LNT EXAFS spectra for Cu. (f) Fourier transformed EXAFS spectra at RT and LNT for Cu. Reprinted from A.N. Mansour, et al. Local Structure of Cu in Cs8Na16Cu5Ge131 Type II Clathrate, J. Solid State Chem. 182, 107-114, Copyright 2009, with permission from Elsevier. PhotonEnergy(KeV) 9 10 11 12 X(RawData) 210 1 2 3 4 5 6 CuK-edge GeK-edge PhotonEnergy(KeV) 9 10 11 12 X(RawData) 210 1 2 3 4 5 6 PhotonEnergy(KeV) 9 10 11 12 X(RawData) 210 1 2 3 4 5 6 CuK-edge GeK-edge PhotonEnergy(KeV) 9 10 11 12 N o r m al iz edX 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 CuK-edge GeK-edge PhotonEnergy(KeV) 9 10 11 12 N o r m al iz edX 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 PhotonEnergy(KeV) 9 10 11 12 N o r m al iz edX 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 CuK-edge GeK-edge WaveNumber(-1) 2 4 6 8 10 12 14 16 18 (k) 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 Ge-RT Ge-LN Cs8Na16Cu5Ge131 WaveNumber(-1) 2 4 6 8 10 12 14 16 18 (k) 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 WaveNumber(-1) 2 4 6 8 10 12 14 16 18 (k) 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 Ge-RT Ge-LN Cs8Na16Cu5Ge131 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Ge-RT Ge-LN Cs8Na16Cu5Ge131 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Ge-RT Ge-LN Cs8Na16Cu5Ge131 WaveNumber(-1) 2 4 6 8 10 12 14 16 18 (k) 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 Cu-RT Cu-LN Cs8Na16Cu5Ge131 WaveNumber(-1) 2 4 6 8 10 12 14 16 18 (k) 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 WaveNumber(-1) 2 4 6 8 10 12 14 16 18 (k) 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 Cu-RT Cu-LN Cs8Na Cu-RT Cu-LN Cs8Na16Cu5Ge131 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Cu-RT Cu-LN Cs8Na16Cu5Ge131 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Cu-RT Cu-LN Cs8Na16Cu5Ge131a b c d e f
49 peak centered around 2.2 , which corresponds to the first coordina tion sphere of the tetrahedral coordination of framework Ge at oms, while the peak centered near 3.7 corresponds to the more distan t Ge-Ge coordination spheres. Due to the rattling behavior of the Cs and Na atoms (c.f Â§1.4), these guest atoms possess high degrees of thermal disorder and, therefore, the contributions of the Ge-Na and Ge-Cs interactions are very small and can effectively be ignored. As show n below, the total disorder for each of the Ge-Na and Ge-Cs pair interactions was estimated to be greater than 0.02 2. The high degree of disorders for Ge-Na and Ge-Cs we re necessary in order for the simulated Fourier transforms derived on th e basis of local structure pa rameters from XRD data to closely resemble the Fourier transforms of th e experimentally measured EXAFS spectra. A comparison of the RT and the near LNT Cu K-edge EXAFS spectra and the corresponding k-weighted Fourie r transforms are also shown in Figure 3.4. Again, as anticipated, the amplitude of the EXAFS osc illations as well as the amplitude of the Fourier transforms increased when the speci men temperature decreased from RT to the LNT due to the quenching of the thermal moti on of the atoms. Thes e Fourier transforms display a major peak centered around 2.1 , which corresponds to the first coordination sphere of Cu-Ge interactions and a minor p eak centered around 3.7 , which corresponds to more distant Cu-Ge interactions. A comparison of the Fourier transforms of RT Cu and Ge EXAFS spectra and the LNT Cu and Ge EXAFS spectra are shown in Figure 3.5. The high degree of similarity between the features of the Fourier transforms for Cu and Ge at each particular temperature is clear. As discussed earlier, bot h sets of Fourier tran sforms display a major and a minor peak corresponding to the first and second coordination spheres, respectively. This confirms that Cu substitutes for the framework Ge atoms in the structure. However, the position of the first peak in the Fourier transforms for Cu is shifted to a lower distance relative to that in the Fourier transforms for Ge. As confirmed from quantitative analysis of th e spectra, the Cu-Ge distance is significantly shorter than the Ge-Ge distance.
50 Figure 3.5 Comparisons of Fourier transforms of the EXAFS spectra for the Cu and Ge K-edges. (a) RT and (b) LNT. The data indicate s horter Cu-Ce contacts than those for Ge-Ge. Reprinted from A.N. Mansour, et al. Â“Local Structure of Cu in Cs8Na16Cu5Ge131 Type II Clathrate,Â” J. Solid State Chem. 182 107-114, Copyright 2009, with permission from Elsevier. The local structure parameters of Cu and Ge in Cs8Na16Cu5Ge131 are summarized in Table 3.8. Also included in this table are the local structure parameters of elemental Ge for comparison purposes. Comparisons of Fourie r transforms of expe rimental spectra and simulation (fit data) are shown in Figure 3.6. Within the uncertainty in the data, the many body amplitude reduction factor, S0 2, for Cu is similar to that for Ge in the clathrate specimen. The value of S0 2 for elemental Ge is slightly outside the range obtained for Ge in the clathrate specimen but this is likely due to the higher degree of correlation between S0 2 and the disorder in the case of elem ental Ge since, in this case, the XAFS measurements were made only at RT. Our analysis for elemental -Ge reveals a RT first sh ell Ge-Ge distance of 2.444 , which is in excellent agreement with the well-established value of 2.450 .219 The RT first shell Ge-Ge distance of 2.486 for the cl athrate is also in excellent agreement with the weighted average distance of the three Ge sites, which is calcula ted to be also 2.486 . The RT Cu-Ge distance of 2.354 , however, is significantly smaller than the RT GeGe distance of 2.486 . The Cu-Ge distance is also significantly sm aller than the well Distance() 0 1 2 3 4 5FTMagnitude 0.0 0.1 0.2 0.3 Cu-RT Ge-RT Cs8Na16Cu5Ge131 Distance() 0 1 2 3 4 5FTMagnitude 0.0 0.1 0.2 0.3 Distance() 0 1 2 3 4 5FTMagnitude 0.0 0.1 0.2 0.3 Cu-RT Ge-RT Cs8Na16Cu5Ge131 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Cu-LN Ge-LN Cs8Na16Cu5Ge131 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Distance() 0 1 2 3 4 5F TM agnitu d e 0.0 0.1 0.2 0.3 0.4 Cu-LN Ge-LN Cs8Na16Cu5Ge131a b
51Table 3.8 Summary of local structure parameters as determined from analysis of XAFS spectra. S0 2 is the many body amplitude reduction factor which account s for inelastic losses within the central absorbing atom, R is the coordination distance, 2 mean square relative displacement for the given X-Y pair of atoms, which includes both thermal and static disorder, and th e R-factor is the measure of the goodness of fit for the model used to fit the experimental data. Figure 3.6 Comparisons of Fourier transforms of experimental spectra (solid blue lines) and simulation (fit, dashed lines). (a) RT data for Ge K-edge for elemental -Ge. (b) LNT data for Ge K-edge for Cs8Na16Cu5Ge131. (c) LNT data for the Cu K-edge for Cs8Na16Cu5Ge131. Reprinted from A.N. Mansour, et al. Local Structure of Cu in Cs8Na16Cu5Ge131 Type II Clathrate, J. Solid State Chem. 182, 107-114, Copyright 2009, with permission from Elsevier. Specimen T X-Y pair S0 2 R, 2, 10-32 R-factor RT Cu-Ge 0.740.03 2.3540.004 4.340.46 0.005 LN Cu-Ge 0.740.03 2.3490.003 2.320.29 0.006 RT Ge-Ge/Cu 0.800.05 2.4860.007 4.730.61 0.020 Cs8Na16Cu5Ge131 LN Ge-Ge/Cu 0.800.05 2.481.005 2.820.42 0.015 Ge Powder RT Ge-Ge 0.700.04 2.444.003 3.460.37 0.004 RadialDistance() 1 2 3FTMagnitude 0.0 0.1 0.2 0.3 0.4 Ge-LN-Exp Ge-LN-Fit Cs8Na16Cu5Ge131 RadialDistance() 1 2 3FTMagnitude 0.0 0.1 0.2 0.3 0.4 Ge-LN-Exp Ge-LN-Fit Cs8Na16Cu5 RadialDistance() 1 2 3FTMagnitude 0.0 0.1 0.2 0.3 0.4 Ge-LN-Exp Ge-LN-Fit Cs8Na16Cu5Ge131 RadialDistance() 1 2 3FTMagnitude 0.0 0.1 0.2 0.3 Ge-RT-Exp Ge-RT-Fit Ge RadialDistance() 1 2 3FTMagnitude 0.0 0.1 0.2 0.3 Ge-RT-Exp Ge-RT-Fit Ge RadialDistance() 1 2 3FTMagnitude 0.0 0.1 0.2 0.3 0.4 Cu-LN-Exp Cu-LN-Fit Cs8Na16Cu5Ge131 RadialDistance() 1 2 3FTMagnitude 0.0 0.1 0.2 0.3 0.4 Cu-LN-Exp Cu-LN-Fit Cs RadialDistance() 1 2 3FTMagnitude 0.0 0.1 0.2 0.3 0.4 Cu-LN-Exp Cu-LN-Fit Cs8Na16Cu5Ge131a b c
52 established elemental Cu-Cu fi rst shell distance of 2.556 .219 The Cu-Ge distance is smaller by 0.132 from the Ge-Ge distance in Cs8Na16Cu5Ge131 and by 0.202 from the elemental Cu-Cu distance. This shorter Cu -Ge distance is consistent with the small reduction in the lattice parameter for Cs8Na16Cu5Ge131 ( a = 15.42000 ) relative to the parent compound Cs8Na16Ge136 ( a = 15.49263 ) as discussed above. On the basis of these results, we conclude that a local distor tion in the Ge framework of the clathrate is created in the proximity of the Cu atoms. In spite of such a local distortion, the RT as well as the LNT disorders for th e Cu-Ge pair are essentially th e same as those for the GeGe pair within the uncertainty in our results. The total disorder consists of a temperature independent static term and a temperatur e dependent thermal term, which can be extracted separately by appropriately anal yzing the temperature dependence of XAFS spectra. The microscopic Debye and Einstein temperatures for the Cu-Ge and Ge-Ge interactions are determined by modeling the temperature dependence of the thermal term using the Debye and Einstein models for lattice vibrations, respectively.221 Accordingly, our results for the static disorder, thermal di sorder, and total disorder for the Cu-Ge and Ge-Ge pairs are summarized in Table 3.9. The large uncertainties in the Debye and Einstein temperatures are due to the lim ited number of temperature dependent EXAFS data sets (RT and LNT) we used in modeling the thermal disorder. The Debye temperatures for both Cu and Ge are sim ilar to those observed for Ge and Ga in Eu8Ga16Ge30 and Sr8Ga16Ge30 and are characteristic of a stiff lattice.100 The similarities in the degree of static disorder, Debye temperat ure, and Einstein temperature for the Cu-Ge and Ge-Ge pairs indicate that the local bonding environment for Cu is very similar to that for Ge. To address the issue of site preference for Cu substitution noted above, theoretical EXAFS spectra and Fourier transf orms for each of the three Ge sites were calculated. In addition, we calculated the theoretical EXA FS spectra and Fourier transforms of the weighted average for the three Ge sites. These calculations were made using all of the local structure parameters given in Ref. 215, in which further details concerning the calculations may also be found. In these calculations, the many body amplitude reduction factor, S0 2, was set to the experimentally determin ed value of 0.80 for Ge. The disorders
53 were set to 0.005 2 for the first shell of tetrahedrally coordinated Ge-Ge interactions, 0.010 2 for the more distant second she ll of Ge-Ge interactions, and 0.020 2 for both the Ge-Na and Ge-Cs interactions. The diso rders were primarily selected to bring qualitative resemblance with the Fourier tr ansforms of the experimentally measured EXAFS spectra. The higher degree of disord er for the Ge-Na and Ge-Cs interactions relative to the Ge-Ge interactions is consistent with the rattling behavi or of the Na and Cs guest atoms inside the framewo rk polyhedral cages. Such a high degree of disorder was also observed for the rattling Eu and Sr atoms in Eu8Ga16Ge30 and Sr8Ga16Ge30, respectively.100 Comparisons of the Fourier transforms of the theoretical EXAFS spectra simulated using single scattering (SS) contribu tions for each of the Ge sites with those simulated including multiple contributions (MS) are shown in Figure 3.7. It is clear from the figure that the relative tre nds observed in the amplitudes of the first and second shells in the case of the single scattering simulation are similar to those observed in the case of the simulation which also included the MS contributions. As evident from Fourier Table 3.9 Summary of the static disorder ( static 2 ), thermal disorder ( thermal 2 ), total disorder ( total 2 ), Debye temperature ( D), and Einstein temperature ( E) for the Cu-Ge and Ge-Ge pairs in Cs8Na16Cu5Ge131. Model X-Y pair static 2 (10-3 2) thermal 2 (10-3 2) total 2 (10-3 2) D or E (K) Debye model Cu-Ge (RT) Cu-Ge (LN) 0.360.35 3.99 1.97 4.35 2.33 42732 Debye model Ge-Ge (RT) Ge-Ge (LN) 0.800.47 3.74 1.84 4.54 2.65 42840 Einstein model Cu-Ge (RT) Cu-Ge (LN) 0.110.35 4.23 2.21 4.34 2.32 33324 Einstein model Ge-Ge (RT) Ge-Ge (LN) 0.600.47 3.94 2.06 4.54 2.65 33430
54 transformed data, it is extremely difficult to distinguish between the three Ge sites on the basis of the first peak in the Fourier transfor ms due the high degree of similarity in local structure parameters of the tetrahedral coordination of the three Ge sites. However, it is possible to qualitatively differentiate betw een the three Ge sites on the basis of the amplitude of the second peak in the Fourier tran sforms and its relative magnitute in comparison to the first peak. The amplitude of this peak increases upon going from the Ge1 site, to the Ge2 site, to the Ge3 site, due to a gradual decrease in the degree of effective static disorder resulting from an increase in site symmetry for the three Ge sites in the same respective order (i.e., Ge1, to Ge2, to Ge3, as indicated in Figure 3.2). Due to the significantly higher multiplicity of the Ge1 site and its large contribution to the weighted average EXAFS signal, the amplitude of the second peak in the Fourier transform for the weighted average of the three Ge sites is closer to that of the Ge1 site than that of the Ge2 or Ge3 site. Figure 3.7 Fourier transforms of the theoretical EXAFS sp ectra simulated using (a) single scattering (SS) contributions and (b) multiple scattering (MS) contributions, for each of the Ge sites in Cs8Na16Ge136. Reprinted from A.N. Mansour, et al. Local Structure of Cu in Cs8Na16Cu5Ge131 Type II Clathrate, J. Solid State Chem. 182, 107-114, Copyright 2009, with permission from Elsevier. a b
55 On the basis of the experimentally measur ed spectra (Figure 3.4), the amplitude of the second peak in the Fourier tr ansform for Cu is qualitatively quite similar to that of the second peak in the Fourier transform for Ge, which again is a weighted average dominated by the contribution from the 96 g site. This qualitatively suggests that Cu is either (i) randomly substituting for Ge or (ii) preferentially substituting in the Ge1 site. In other words, preferential subs titution of Cu in the Ge2 site or the Ge3 site can be excluded from consideration. These results ar e consistent with the single crystal X-ray diffraction results presented above that show ed preference for Ag and substitution on the 96g (Ge1) site in Cs8Na16AgyGe136y. 3.4 Electrical and thermal transport in Cs8Na16Cu5Ge131 Polycrystalline Cs8Na16Cu5Ge131 and Cs8Na16Ge136 specimens were prepared for transport measurements as follows. The specimens were ground and sieved to 325 mesh inside a nitrogen-filled glove box, and then consolidated by hot-pressing at 400oC. From the consolidated pellets, parallelepipeds of approximate dimensions 2 mm 2 mm 5 mm were cut for transport measurements usi ng a wire saw. Details on the measurement of electrical and thermal transport properties are given in Appendix B. The temperature dependence of S and from 12 to 300 K are shown in Figures 3.8 and 3.9. The transport data for the Cs8Na16Ge136 specimen in the present study agree well in both magnitude and temperature de pendence with those reported previously.93 As shown in Figure 3.9, for both specimens increases m onotonically with temperature, indicative of behavior typical for a metal lic or heavily doped semiconductor material. This can be qualitatively unde rstood in terms of a simplifie d Â“rigid bandÂ” picture, in which the alkali guests (Cs and Na) donate el ectrons to the Ge and Ge-Cu framework conduction bands resulting in a relatively high concentration of carriers (cf. Â§1.3). The sign of S is negative for both specimen s, indicating electrons are the majority carriers. For Cs8Na16Cu5Ge131, we see that (300 K) is significantly larger than for Cs8Na16Ge136. As shown in the bottom of Figure 3.8, S also increased significan tly in magnitude (by a factor of ~ 2) for Cs8Na16Cu5Ge131 relative to Cs8Na16Ge136, and displays somewhat different temperature dependence. The fou r-coordinated covalent bonding in the Ge136
56 Temperature (K) 050100150200250300 Seebeck Coefficient ( V/K) -16 -14 -12 -10 -8 -6 -4 -2 Cs 8 Na 16 Cu 5 Ge 131 Cs 8 Na 16 Ge 136 Resistivity (mOhm-cm) 0.0 0.1 0.2 1.5 2.0 2.5 Cs 8 Na 16 Cu 5 Ge 131 Cs 8 Na 16 Ge 136 Figure 3.8 Temperature dependence of the electrical resistiv ity (top) and Seebeck co efficient (bottom) for Cs8Na16Ge136 (open symbols) and Cs8Na16Cu5Ge131 (filled symbols). Reprinted from M. Beekman et al. Â“Synthesis and characterizatio n of framework-substituted Cs8Na16Cu5Ge131,Â” J. of Alloys and Comp. 470 365-368, Copyright 2009, with permission from Elsevier. framework is analogous to the sp3 bonding found in elemental diamond structure Ge, in which substitutional Cu has been shown to behave as an electronic acceptor.222 The observed increased magnitudes of both and S for Cs8Na16Cu5Ge131 relative to Cs8Na16Ge136 are consistent with a decrease in the available number of electrons participating in the conduction processes, indicating partial charge compensation as a result of Cu substitution on the Ge framework.
57 Temperature (K) 10100 Thermal Conductivity (W/mK) 1 10 Cs 8 Na 16 Cu 5 Ge 131 Cs 8 Na 16 Ge 136 Figure 3.9 Temperature dependence of th e thermal conductivity for Cs8Na16Ge136 (open symbols) and Cs8Na16Cu5Ge131 (filled symbols). Reprinted from M. Beekman et al. Â“Synthesis and characterization of framework-substituted Cs8Na16Cu5Ge131,Â” J. of Alloys and Comp. 470 365-368, Copyright 2009, with permission from Elsevier. The thermal conductivities of the two speci mens show very similar temperature dependences as presented in Figure 3.9. Since both Cs8Na16Ge136 and Cs8Na16Cu5Ge131 exhibit metallic-like electri cal conductivities (F igure 3.8), a consid erable electronic contribution to the thermal conductivities show n in Figure 3.9 is expected. As the mass difference between Cu and Ge is relatively sm all (along with the concentration of Cu), significant mass fluctuation eff ects with respect to the la ttice thermal conductivity are unlikely. From the EXAFS modeling presented above, similarities in the degree of static disorder, Debye temperature, and Einstein temperature for the Cu-Ge and Ge-Ge pairs indicate that the local bonding environment for Cu is very similar to that for Ge. Thus significant strain field effect s on the lattice thermal conductiv ity are also not expected. Indeed, upon correction of the measured thermal conductivities for porosity,223 and subtracting the estimate d electronic contribution e = L0T/ ( L0 = 2.45 10-8 V2K-2, obtained from the data of Figure 3.8), L for the two specimens are the same within experimental uncertainties ( L(300 K) = 2.7 Wm-1K-1 and 2.6 Wm-1K-1 for Cs8Na16Ge136 and Cs8Na16Cu5Ge131, respectively). Thus reduction in for Cs8Na16Cu5Ge131 relative to
58 Cs8Na16Ge136 is most likely due to a decrease in the electronic contribution to in the former, consistent with the increas e in electrical resistivity for Cs8Na16Cu5Ge131. We note that semiconducting filled type II clathrates are in general ex pected to possess relatively low lattice thermal conductivities, due to their enlarged unit cell and potential phonon scattering as a result of large amplitude anharmonic guest atom vibrations. 3.5 Concluding remarks and future directions The synthesis and characterization of framework-substituted clathrate-II intermetallics was reported for the first time in this chapter. The Cu and Ag substituted compositions studied show response to fram ework substitution in both structure and physical properties. It should in principle be possible to substitute other species as well, thus the approach demonstrated herein can a llow a variety of clathrate-II compositions to be explored. A preliminary investigation into group 13 substitution was also initiated as a part of the present work. Figure 3.10 show s an X-ray powder diffraction pattern for Cs8Na16In8Ge128 (Rietveld refine d composition of the specimen is Cs8Na16In7.8Ge128.2). The pattern shows no discernable impurities or secondary phases. Re finement of the unit cell parameter a yielded the value 15.6263(2) , which is significantly larger (by almost Figure 3.10 Powder X-ray diffraction pattern (observed, calculated, and difference) for a Cs8Na16In8Ge128 specimen. No impurity phases are discernable. Cs8Na16In8Ge128 a = 15.6263(2)
59 1 %) than 15.4926(1) for non-substituted Cs8Na16Ge136, also corroborating that the larger In has substituted for Ge on the type II framework. The ability to vary the guest concentrati on in type II clathrates also offers the opportunity to synthesize a dditional new compositions. For example, we have shown previously98,104 that compositions such as Cs8Ge136 and Rb8Ge136 can be prepared by degassing Na from the stoichiometric compounds Cs8Na16Ge136 and Rb8Na16Ge136. The possibility of degassing framework substituted type II clathrates, to produce compositions such as Cs8In8Ge128 from Cs8Na16In8Ge128 above is an area of future interest. Very recent electronic structur e calculations by Biswas and Myles62 indicated that the clathrate-II composition Rb8Ga8Si128 should be a semiconductor with an indirect gap, thus this synthetic route has the potential to produce filled, semiconducting type II clathrates, of interest as potential thermoelectric materials.
60 4 Synthesis and Characterization of NaxSi136 (0 < x < 24) As noted in Chapter 1, one of the most conspicuous aspects of the clathrate-II phases is the ability to vary the guest c ontent in these materials. The prototypical examples are the NaxSi136 clathrates, where the guest concentration may be varied between empty1 ( x 0 for the Si136 allotrope) and fully filled ( x = 24, cf. Chapter 5). Although some structural and physical properties for the NaxSi136 clathrates have been studied for selected compositions (cf. Chapter 1), a comprehensive understanding of these properties has yet to be established for th is system, in particular with regard to the influence of guest content. This is in larg e part due to the chal lenges inherent in the preparation of NaxSi136 specimens of high phase purity needed for such study. This problem was addressed in the present work. A series of NaxSi136 clathrates was prepared covering a comprehensive range of Na contents. The crystal structures for the entire range of compositions were refined against powder X-ray diffraction. A non-monotonic structural response to filling was discovered, wh ich can be attributed to the preferentially occupation of the distinct polyhedral cages by Na. Transport propert ies are presented for polycrystalline Na22Si136, for which consolidation by spark plasma sintering was found to be effective in achieving improved electrica l contact between the polycrystalline grains. 4.1 Synthesis of NaxSi136 (0 < x < 24) The NaxSi136 specimens were synthesized by th ermal decomposition of the binary monosilicide Na4Si4.106-108 The crystal structure of the Na4Si4 precursor is composed of Si4 4Â– polyanions and Na+ cations arranged in a monoclinic unit cell, as shown in Figure 4.1. Presumably, the Si4 4Â– polyanions are oxidized and Na+ reduced during decomposition: 34[Na+]4[Si4]4 Â– (s) [Na+]x[Si136]x Â– (s) + (136 Â– x )Na (g)
61 Figure 4.1 Decomposition of Na4Si4 (top) to form the intermerallic clathrates NaxSi136 (bottom left) and Na8Si46 (bottom right). Na and Si atoms are colored blue and green, respectively. The synthesis of NaxSi136 by thermal decomposition of Na4Si4 is complicated by the simultaneous formation of the clathrate-I Na8Si46 which can be present as an impurity phase inasmuch as 50 wt% in as-synthesized specimens.87,89 In order for the physical properties of the NaxSi136 clathrates to be thoroughly ch aracterized, a reproducible and higher yield synthesis method is needed. For example, specimens for transport measurements should (i) contain no more than a few wt% impurity phases and (ii) ideally be obtainable in a single synthesis, as opposed to the mixing of several smaller samples from several syntheses which can lead to specimen inhomogeneity. One of the goals of the present work was to optimize the synthe sis by thermal decomposition in order to minimize the Na8Si46 impurity fraction. A schematic of the apparatus used for thermal decomposition of silicides and germinides is shown in Figure 4.2. The de sign and construction of the apparatus is
62 Figure 4.2 Schematic of the apparatus designed for thermal decomposition of Na4Si4 in the synthesis of NaxSi136 clathrates. described by the author in Ref. 104. This apparatus employs a high vacuum system equipped with a turbomolecular pump, to wh ich fused quartz ampoules can be attached. As the Na4Si4 precursor is extremely air and mo isture sensitive, all handling was performed in a nitrogen-filled glove box. A vacuum valve and coupling was employed for transfer of the ampoule containing the sp ecimen from the glove box to the apparatus. The ampoule containing the specimen, once evacua ted, can then be inse rted into a tubular furnace to initiate the reaction. We have used a modified version of the procedure of Â“flash degassingÂ” originally developed by Gryko,105 in which Na4Si4 is rapidly heated through the decomposition temperature (~ 360oC) at the rate of several hundred oC/min. This is achieved by inserting the quartz ampoule containing the sample into a tube furnace preheated to 800oC (see Fig. 4.2), but then removing the sample befo re decomposition of the clathrate ensues (at ~ 450oC under vacuum). Though the exact local temperature of the specimen is not measured, the monitored temperature direc tly outside of the ampoule was calibrated using a Â“trial and errorÂ” procedure. The result from this modified Â“flash decompositionÂ”
63 Figure 4.3 Powder X-ray diffraction patterns for several NaxSi136 specimens. The red arrow indicates the most intense reflection contributed by the Na8Si46 impurity phase. step is a NaxSi136 clathrate with x ~ 24. The Na content is then varied by further heating under vacuum at 360oC to 425oC, with the time and temperature controlling the final composition (higher temperatures and longer h eating times leading to specimens with a lower Na content). Using the above described procedure, NaxSi136 clathrates typically containing less than 3 wt% Na8Si46 are reproducibly synthesized. In a ddition, by scaling up to larger crucible and ampoule sizes, as much as 500 mg of high quality NaxSi136 (as opposed to ~ 100 mg previously104) is produced in a single synthesi s run. Figure 4.3 shows powder Xray diffraction (PXRD) patte rns for representative NaxSi136 specimens prepared using the above described method. The most intense reflection contributed by Na8Si46 is indicated by an arrow in the figure. The effectiveness of this flash decomposition technique to Degrees 2 20 30 40 50 60 Intensity (arb. units) ~ wt.% Na 8 Si 46 x = 1 x = 22 x = 20 x = 17 x = 8 x = 4 2
64 minimize the Na8Si46 fraction suggests the reactio n kinetics and/or formation temperatures for the two clathrate phases may be slightly different, allowing preferential formation of one phase over the othe r depending on the synthesis conditions. The products obtained from the thermal decomposition are fine polycrystalline powders, dark in color with a bluish pigment. In order to remove any residual Na4Si4 and/or elemental Na, the specimens were vented from vacuum in a nitrogen filled glove bag, and then washed with ethanol and then distilled water to hydrolyze the remaining residues. The specimen was then sonicated, decanted, and dried. 4.2 Structural characterization of NaxSi136 (0 < x < 24) clathrates As the products from thermal deco mposition are microcrystalline powders, structural characterization was performed using Rietveld110,111 analysis. An overview of the basic principles and application of the Rietveld method are outlined in the Appendix. pXRD patterns were collected using a Br uker D8 diffractometer in Bragg-Brentano geometry. Sample preparation and data colle ction are two important considerations for obtaining an accurate Rietveld structure refinement.224 A custom-made specimen holder was used, allowing back loading of the powder which results in a flat, planar specimen surface. The orifice of the specimen holder wa s constructed to be large enough to achieve a constant specimen illumination condition with no X-ray beam spill-over onto the holder. This aspect is crucia l for obtaining correct intensities at low angles when beam divergence is significant.224 Overnight data collection was performed at 0.02o steps in 2 for 8 seconds per step, in the range 7 to 145o 2 Rietveld structure refinements were carried out using the GSAS software package.205 The EXPGUI graphical user interface to GSAS was also used.206 The initial model used for Rietveld refi nement was taken assuming the framework Si atoms at the 96 g 32 e and 8 a sites, and the Na atoms at the centers of the Si20 and Si28 cages at the 16 c and 8 b sites, respectively.4,87,88 However, the isotropic atomic displacement parameters ( Uiso) for Na at the 8 b site (fractional coordinates: 3/8, 3/8, 3/8) were found to be unreasonably large: greater than 0.1 2, several times larger than any other site in the structur e. The ADP is interpreted145,224 as the mean square atomic
65 displacement of an atom about its assigned crys tallographic site, and can be attributed to static and/or thermal (i.e. dynamic) displacement. Although strong thermal motion is expected for this caged guest, especially considering the relatively large difference between the size of the Na guest and eff ective free space of the cage interior, the unusually large Uiso suggests, in addition, significant static disorder may be present. Difference Fourier maps computed using the calculated structure factors for the model with Na at the 8 b site completely unoccupied, in dicate significantly non-spherical residual electron density in the vicinity of the 8 b site, and typically with lobes directed toward the hexagonal faces of the Si28 cage. For lower Na content specimens, the maxima in density are observed not on-center at the 8 b site, but rather at four nearby sites within the Si28 cage (3/8 + 3/8 + 3/8 + ). Therefore, further refinement was carried out using a split-site model with Na at the corresponding nearby 32 e site (still space group Fd 3 m ). Stable refinement convergence, with no damping of parameter shifts, was achieved with final simultaneous refinement of Na occupancy, Uiso, and 32 e positional parameter for this site. The refined off-cente r shifts for the sodium atoms were found to be typically near 0.4 . Moreove r, the occupancies for the Na@32 e split site model consistently refined to be of the corresponding single site (i.e., Na@8 b model) occupancies, consistent with the four-fold increase in site multiplicity from 8 a to 32 e and the physical expectation of onl y one Na atom per cage. Thes e results lend support to the interpretation of recent E XAFS experiments (cf. Â§1.2), which indicated significant displacement of Na from the cente r of the hexacaidecahedra in Na8Si136 and Nax ~24Si136.95,96 The value we obtain of ~ 0.4 for the Na off-center shift is similar to that observed for guests in the Ge24 tetracaidecahedra cage in type I clathrates such as Sr8Ga16Ge30 and Eu8Ge16Ge30.71,100 Ellipsoidal depictions225 of the ADPs for Na2 and its surrounding Si28 cage for Na22Si136 are shown in Figure 4.4 for the singleand split-site models. The refined Na@32 e Uiso value is reduced to more physically reasonable values for the split site model, yet still remains relatively large compar ed to the other sites in the structure. As mentioned above, this reflects pronounced therma l disorder for Na in the larger cage.
66 Figure 4.4 ADP plot for Na2 and its surrounding Si28 cage for Na22Si136. Left: on-center model. Right: offcenter model. Ellipsoids are drawn for 50% probability. This feature may have important implicati ons regarding the thermal conduction in these materials, also suggested from our thermal conductivity data for a Na8Si136 specimen.104,126 We note that in our refinements str ong correlations exist between the Na Uiso and 32 e position parameter, thus it is difficult to obtain precise values for the position and Uiso from our data. As the refinement qualit y of fit (see Figure 1 and Table) are the same for the on-center and off-center models preference for one model over the other cannot be based on these factors alone. However, the physically more reasonable Uiso are obtained in the off-center model. Similar re sults and conclusions were obtained in structural studies of type I clathrates,71,100,185,226,227 for which single and split site models both result in similar refinement quality. The off-centering of the guest atoms in type I clathrates results in unique phenomena in these compounds.19,27,99 Figure 4.5 shows refinement plots (observe d, calculated, and difference) for four representative specimens with compositions Na1.2Si136, Na6.5Si136, Na12.2Si136, and Na21.6Si136. A small but significant improvement in the fits was achieved by refining terms in the peak shape function corresponding to anisotropic broadening of the peaks. This type of peak broadening has been attr ibuted to the presence of planar defects,228 and indicates such defects ma y be present in our NaxSi136 specimens in small concentrations. Such planar defects have been observed in transmission electr on microscope (TEM) studies on NaxSi136.229 All silicon framework sites were found to be fully occupied for all
Figure 4.5 Rietveld plots of powder XRD patterns for (a) Na12Si136, (b) Na65Si136, (c) Na122Si136, and (d) Na216Si136: observed (crosses), calculated (solid curve) and difference (lower curv e) patterns are shown. Bottom set of tick marks indicate reflection positions for NaxSi136, while upper tick marks indicate those of Na8Si46. A trace amount (< 1 wt %) of -Si was also refined in (c). Refineme nt residuals in each case are also given. 67
68 compositions, in agreement with previous studies87,88 that have shown that framework vacancies are not present in the NaxSi136 clathrates. As shown in Figure 4.5, relatively good fits to the experimental data are achieve d for all compositions, as represented by the difference patterns. An important feature to note from Figure 4.5 is the pronounced influence of the Na content on the relative intensities of a number of reflections in the patterns. This feature allows for accurate dete rmination of the individual occupancies of the two crystallographically independent Na site s in the structure, and therefore also the total Na content in the composition. Refinement of the crystal structures for th e entire range of Na contents revealed an intriguing structural response to Na filling in NaxSi136. The relative occupancies for the two Na sites as well as the lattice parameters as a function of the total Na content are shown in Figure 4.6. The first aspect to note is that as the Na content is increased, Na preferentially occupies the larger Si28 cages first. Not until these sites are almost entirely filled do the smaller Si20 begin to be occupied. This indi cates that Na is preferentially removed from the Si20 cages first during synthesis, in general agreement with previous reports.87,88,129 The preferential occupation of the larger Si28 cages has a pronounced effect on the lattice. As shown in the top portion of Figure 4.6, the lattic e parameter first decreases as Na is incorporated in the Si28 cages, but then increases as the Si20 cages are filled. Thus filling the two distinct cages in the Si136 framework has distinc tly opposite effects on the lattice. This non-monotonic res ponse to filling, predicted qualitatively by Conesa et al.35 who used density functional theory calculatio ns, is observed here experimentally for the first time in a guest-host system. The extent of charge transfer from Na to the Si framework in the NaxSi136 system has not yet been determined unequivocally, but is likely to play an important role in the behavior shown in Figure 4.6. Preliminary re sults from density functional theory (DFT) calculations carried out in collaboration with Mr. Emanue l Nenghabi and Prof. Charles Myles of Texas Tech University offer insight. Initial optimization of the unit cell for x = 0, 4, 8, 12, 16, 20 and 24, filling the Si28 cages first and assuming Na on-center, revealed a trend qualitatively in agreement with that observed in Figure 4.6. The calculations can
69 Total Na Content (x) 04812162024 Cage Occupancy (Normalized) 0.0 0.2 0.4 0.6 0.8 1.0 Si28 cage Si20 cage Lattice Parameter () 14.64 14.66 14.68 14.70 14.72 Figure 4.6 Normalized cage occupancies (bottom) and lattice parameters (top) as a function of the total Na content, as determined from Rietveld refinement. A cage occupancy value of 1 means all cages of this type in the structure are occupied. The 32 e spit-site occupancies for Na in the Si28 cage (where 1/4 corresponds to full occupation of all Si28 cages) were not fixed during refinement which results in the scatter about 1 for x > 8 due to correlations with the the Uiso for this site. The Si28 cage can therefore be considered as fully occupied for x > 8 with high confidence. therefore reproduce the essential features of the phenomenon. An estimate of the charge transfer was made using Bader analysis.230,231 For the seven compos itions investigated, essentially complete transfer of the Na 1 s electron to the Si136 framework is predicted. Such transfer suggests that the conduction band states (either in a rigid band
70 approximation, or due to Si-Na orbital mixing) will be increasingly occupied as the Na content is increased, in agreement with pr evious electronic stru cture calculations.35,44,125 With this in mind, there are several conceivable interactions that could be responsible for the trend observed in Figure 4.6. These include (i) steric (repulsive) interactions resulting from the relative size of guest and cage, (ii) bonding (attractive) interactions resulting from the redistribution of charge and/or transfer from Na to the Si framework, and (iii) the incr easing occupation of the conduction band states as the Na content is increased. The Â“interactionÂ” noted in (iii) would be expected to increase the lattice parameter, since the conduction ba nd states are generally of Â“anti-bondingÂ” character and reduce the Si-Si bond order. While it is likely that to some extent all three of these possibilities are at play in the pr esent case, we infer from the arguments that follow that (ii) is predominant for x < 8 as the Si28 cages are filled, while (i) and/or (iii) are predominant for x > 8 as the Si20 cages are filled. Examination of subtle but significant evol ution in framework atomic coordinates, interatomic distances, and bond angles obtained fr om Rietveld refinement reveal that the framework is not contracting and expanding uniformly. Figure 4.7 shows the interior volumes of the Si28 and Si20 coordination polyhedra, ca lculated using the atomic coordinates and lattice parameters obtained from Rietveld structur e refinements for the series of specimens. A change in the volume of the polyhedra will occur due to either a change in the lattice parameter, a cha nge in the framework atomic coordinates (specifically, the 32 e and 96 g sites which are not fixed by the Fd 3 m symmetry), or a combination of these two factors. The red and blue curves in Figure 4.7 show the Â“expectedÂ” trends if the atomic coordi nates were fixed at the values for Na7.9Si136, i.e. the trend if the volume changes for x < 8 and x > 8 were due solely to the experimentally determined lattice parameter changes. The black lines are linear least squares fits to the actually observed values. These data illustrate that as the Na content increases from x ~ 1 to x ~ 8 (i.e. as the Si28 cages are first filled), the Si28 cage generally shows a more pronounced contraction than expected from th e lattice parameter change alone, while the Si20 cage shows a less pronounced contraction. Conversely as the Na content is increased above x ~ 8 (i.e. as the Si20 cages are filled), the Si28 cages show a less pronounced
71 Si20 Volume ( 3 ) 100.5 101.0 101.5 102.0 102.5 Total Na Content (x) 04812162024 Si28 Volume ( 3 ) 193.5 194.0 194.5 195.0 195.5 196.0 196.5 Figure 4.7 Si28 and Si20 cage volumes as a function of Na content. The volumes where calculated from the refined lattice parameters and atomic coordinates for each corresponding composition. The solid red and blue curves are the trends that would result if the atomic coordinates where fixed at the values for Na79Si136, and thus the volume changes resulted solely fr om the lattice parameter changes. The black lines are linear fits to the actual observed volumes, for x 8 and x 8. expansion than expected from the latti ce parameter change alone, while the Si20 cages show a more pronounced expansion. These trends serve to illustrate th at the contraction of the lattice for x < 8 is driven by the contraction of the Si28 cage as it is filled, while the expansion of the lattice is dr iven by the expansion of the Si20 cage as it is filled. The simplest interpretation of these observations is made in terms of the relative sizes of Na guest and Si cage, and the above mentioned charge transfer. The free space, We note that the crystallographic information obtained in a diffraction experiment is representative of the average structure. Thus as some cages are filled and others not, the local structure will differ. However, the average structure is indicative of the overall st ructural resonse to filling the respective cages.
72 dfree, available in the respective cages can be roughly estimated from the shortest cage center to Si distance, rcage, and the Si covalent radius, rSi = 1.2 ,85 as dfree = rcage Â– rSi. For Na7.9Si136, this results in values for dfree of 2.6 and 2.0 for the Si28 and Si20 cages, respectively. From the estimated values of dfree we can conclude there is up to 70% more available volume (which is proportional to dfree 2) in the Si28 cage relative to Si20. This is reflected in the significantly larger ADP obtained for Na@Si28 as compared to Na@Si20. As tabulated by Shannon,212 the ionic radius of Na+ for coordination number (CN) of nine is approximately 1.3 ; the Na+ ionic radius in NaxSi136 may in principle be larger due to the higher CNs in clathrate-II. Considering also that the average Si radius will effectively increase as more charge is tr ansferred to the framework with increasing Na content, it is apparent that Na does not as readily Â“fitÂ” inside the smaller Si20 as compared to Si28, thus may an expansion of this cage due to steric eff ects, and in turn the lattice as a whole also expands. For Na in Si28, on the other hand, the larg e available volume allows significantly more free space. A bonding interacti on appears to cause the inclusion of Na to Â“pullÂ” this cage in, resulting in the apparent contraction of the lattice in contrast to the expected expansion enduced by occupation of Â“anti-bondingÂ” stat es due to charge transfer from Na. Our results demonstrate th at the clathrate-II NaxSi136 offers a relatively simple system in which the effects of relative guest/ cage size can be studied. In particular, these results demonstrate that the Na-Si guest-fram ework is distinctly different for the two different cage environments, a finding that wa rrants further experime ntal and theoretical investigations. 4.3 Thermal stability of NaxSi136 clathrates The thermal stability of several NaxSi136 compositions was investigated by differential thermal analysis (DTA). DTA curves, collected under flowing N2 in open alumina pans, for temperatures between 250oC and 700oC are shown in Figure 4.8. The NaxSi136 clathrates all decompose exothermically near 600oC, with a slight shift in the decomposition temperature toward lower values observed as the Na content is increased above x ~ 8. -Si is the only phase identified in the post-DTA powder XRD patterns. The
73 Figure 4.8 Differential thermal analysis data for six selected NaxSi136 compositions. exothermic decomposition suggests these clathr ates are metastable with respect to the elements under the above conditions. However, the relatively high decomposition temperatures suggest that the free energy difference is small, in agreement with theoretical calculations for Si136.33 4.4 Transport properties of Na22Si136 Another challenge inherent in a study of the transport pr operties of the NaxSi136 clathrates is preparation of sufficiently dense microcry stalline samples with good intergrain electrical contact. Analogous to silicon in the diamond st ructure, an insulating oxide layer can readily form on the grains of th e polycrystalline specimens. This oxide layer has been directly observed in the NaxSi136 clathrates,134 and can present difficulties in both densification232 and interpretation of the m easured transport properties.4,126,127 Temperature ( o C) 200300400500600700DTA Signal (Arb. Units, exo up) Na12.6Si136Na17.0Si136Na7.0Si136Na10.7Si136Na5.7Si136Na23.1Si136 Exothermic up
74 Although this point will be further addressed by the preparation of NaxSi136 ( x = 24) single crystals in Chapter 5, we have also investigated the feasibility of consolidating microcrystalline NaxSi136 specimens for transport properties investigations. Both conventional hot-pressing as we ll as spark plasma sintering233 (SPS) methods were used. Preliminary investigations into the transport properties of Na1Si136 and Na8Si136 specimens consolidated by hot-pressing we re reported by the author previously.104,126 The measured electrical resistivities revealed a clear influence from the Na content, but suggested large contributions due to the porosity and/or poor inter-grain contact, a result of the low relative densit ies on the order of 70% that are achieved by hot-pressing. Further investigati ons on hot-pressed Na22Si136, which as noted in Â§1.4 is expected to exhibit metallic conduction, revealed room te mperature resistivity of 300 mOhm-cm, and a negative temperature coefficient ( d / dt < 0). These observations confirm the large contribution of Â“extrinsicÂ” specimen-dependent effects, and illustrate the challenges inherent in preparing specimens for transport measurements by conventional hot-pressing techniques. In collaboration with Prof. Yuri Grin and coworkers at Max Planck Institut fr Chemische Physik fester Stoffe (MPI-CPfS) in Dresden, Germany, consolidation of a Na22Si136 specimen by SPS was also investigated. Af ter a systematic study of the effects of heating rate, sintering temp erature, and pressure, a consolidated specimen exhibiting a relative density of 83% was obtai ned. This is a substantial improvement as compared to hot-pressed specimens. The measured S and in the temperature range 60 to 300 K for the Na22Si136 specimen consolidated using SPS are shown in Figure 4.9. increases monotonically with temperature, and remains less than 1 mO hm-cm in the entire temperature range. The value 0.7 mOhm-cm at 300 K is very close to that reported93 for the stoichiometric clathrate Cs8Na16Si136 (cf. Figure 1.7). The values for S remain relatively low, and the magnitude also increases monotonically w ith temperature. The negative sign of S suggests that electrons are the majority carri ers. The observed magnitude and temperature dependence of both and S for Na22Si136 is indicative of metallic or very heavily doped semiconductor behavior.
75 As discussed in Â§1.4, metal-insulator transition has been reported to occur in NaxSi136 near 7 < x < 11, though the precise value of x at which this occurs, as well as the nature of this transition, ha s yet to be determined unequivocally. For the high Na content of Na22Si136, the electronic properties can be qua litatively understood in terms of a simplified rigid-band model, wherein electronic charge is transferred from the Na guests to the framework, therefore resulting in the occupation of the framework conduction bands, and the observed metallic properties. This qualitatively explains the observed behavior in Figure 4.9. Our tr ansport measurements confirm th at inter-grain sintering and relatively good electrical cont act between the grains is achieved for this composition Figure 4.9 Transport properties of polycrystalline Na22Si136. (a) Electrical resistiv ity (filled symbols) and Seebeck coefficient (open symbols). (b ) Total measured thermal conductivity. Temperature (K) 50100150200250300 Thermal Conductivity (W/m-K) 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Temperature (K) 50100150200250300 Resistivity (mOhm-cm) 0.45 0.50 0.55 0.60 0.65 0.70 0.75 Seebeck Coefficient ( V/K) -12 -10 -8 -6 -4 -2 0 a b
76 using the SPS method, indicating the promise of SPS consolidation for future study of the transport properties of these and related materials. The total measured thermal conductivity ( ) for the Na22Si136 specimen is shown in Figure 4.9 (bottom). These data have not b een corrected for the ~ 17% porosity in this specimen, which may have a non-negligible effect on the perceived The temperature dependence of is similar to that reported for Cs8Na16Si136 93 and also the type I Na8Si46.172 achieves a modest value of ~ 5.5 Wm-1K-1 at 300 K. Our previous investigation into the thermal conductivity of hot-pressed NaxSi136 ( x = 0, 1, and 8) clathrates suggests the semiconducting va riants possess relatively low thermal conductivities.104,126
77 5 Single-crystals of intermetallic cl athrates by spark plasma sintering: preparation, crystal structure, and transport properties of Na24Si136 The synthesis of many intermetallic clathrat es presents formidable challenges and a number of clathrate compositi ons have to date only been obtained as microcrystalline powders. In such cases care must be taken in interpretation of measured structural, chemical, and physical properties for which grain boundary effects, surface composition and chemistry, and impurity phases can dire ctly affect the observed properties. The preparation of high-quality si ngle crystals, for structur al and physical properties characterization, can be especially challe nging for materials in which the elemental constituents have greatly differing melting points and/or vapour pressures, when the desired compound is thermodynamically metastab le, or where growth with participation of the melt is generally not possible. This is particularly the case for alkali-silicon clathrates, for which conventional crystal grow th techniques are ge nerally inapplicable. Exploration of novel synthetic routes is n ecessary for realization of new compostitions, but also for the preparation of high-quality si ngle-crystals for these and other materials of interest. Herein we demonstrate the e ffectiveness of spark plasma sintering233-235 (SPS) for redox preparation and crysta l growth of clathrate sili cides of alkali metals, in particular for the clathrate-II Na24Si136 which has evaded single crystal growth for more than four decades since its initial discovery.4 The synthesis by SPS described in this chapter was carried out by the author dur ing a three month independent research visitation at the Max Planck Institut fr Chem ische Physik fester Stoffe (MPI-CPfS), in Dresden, Germany, under the guidance of Inst itute Director, Prof. Yuri Grin. Transport measurements were conducted by the author using our in-house measurement system. These results reveal signif icant opportunities this method offers for preparation and crystal growth of materials. Structural and transport propertie s for bulk crystalline
78 Na24Si136 are presented, constituting the first me asurements of Â“intrinsicÂ” transport for any member of the NaxSi136 system. 5.1 Preparation of Na24Si136 by spark plasma sintering The spark plasma sintering (SPS) technique, a variant of field assisted sintering, has in little more than a decade become an established consolidation method for preparation of dense polycry stalline specimens. The SPS t echnique possesses significant advantages over conventional c onsolidation techniques, in pa rticular for intermetallic compounds.236 The defining characteristic of the SPS process is the pulsed DC electrical current, typically on the order of several hund red Amperes, that is sourced through the powder specimen and die assembly while th ey are simultaneously held under applied uniaxial pressure. Thus the sp ecimen is heated internally, via resistive Joule heating, as opposed to externally as in conventional hot-pressing. The resulting high heating and cooling rates as well as short si ntering times needed have proven233-235 ideal in the consolidation of ceramic, intermetallic, and nanostructured materials, especially where avoidance of grain coarsening is desired. A lthough a complete understanding of the role of the electric field and the beneficial mechan isms involved in this process is developing, and the existence or nature of the inter-grain plasma is still under investigation,233-235 the importance of the SPS method is evidenced by the rapidly growing number of materials investigations utilizing this technique. However, applic ation of SPS as a method for synthesis of materials is still in its infancy, in particular regardi ng bulk crystal growth by this processing technique.235,236 Sodium monosilicide,106-108 Na4Si4, was chosen as the r eaction precursor in our experiments for its known high reactivity in pr omoting the formation of the intermetallic clathrates NaxSi46 (7 < x < 8) and NaxSi136 (0 < x < 24), as evidenced from both thermal decomposition (cf. Chapter 4) and chemical oxidation studies.118 This also comprises an ideal system for our st udy, since although the NaxSi136 variants were the first intermetallic clathrates to be reported more than four decades ago, and they are of considerable interest due to their intriguing structur al and physical properties discussed in Chapter 1, until now
79 Figure 5.1 Preparation of Na24Si136 by SPS. (a) Schematic of the spark plasma sintering (SPS) system used for Na24Si136 crystal growth, with polarity of the applied voltage indicated. (b) Cross-sections of SPSreacted compacts, reacted at 600oC and 100 MPa for 5 minutes, 2 hours, and 3 hours as indicated. The upper portion consists of Na4Si4, while the lower, bluish crystalline fraction is clathrate-II Na24Si136. (c) Scanning electron microscope, secondary electron image of Na24Si136 crystals, after removal of residual Na4Si4 precursor by hydrolysis and dissolution. no method for single-crystal growth has been id entified. As was illustrated in Figure 4.1, the crystal structure of Na4Si4 is composed of Si4 4polyanions and Na+ cations arranged in a monoclinic unit cell.106-108 Upon oxidation of Na4Si4, the silicon clathrate frameworks are formed, while simultaneously encapsulating sodium in the resulting Si20 and Si28 cage-like coordination polyhedr a, as shown in Figure 4.1.
80 Figure 5.1a shows a schematic of the SPS sy stem used in this study. Pulsed DC electrical current (with a possible range of 0 to 1,500 Amperes, depending upon the temperature to be achieved) is sourced through the specimen and die from the bottom (higher potential) electrode to the top (low er potential) electrode, which simultaneously act as the means for application of uniaxi al pressure to the powder specimen. The specimen, die, punches, and electrodes ar e enclosed inside a vacuum chamber and maintained under dynamic vacuum (10-2 torr) throughout the experiment. Alkali metal silicide precursors were pr epared from the high purity elements by reaction at 650oC in tungsten or tantalum crucibles sealed under inert atmosphere for 36 hours, as described in Chapter 4. Improved crystal morphology of the clathrate specimens synthesized by SPS was obtained when a small excess of alkali (10 wt%) was added to the initial precursor reaction mixture. The resulting precursor was ground to fine powder in an Ar filled glove box, and loaded in to graphite dies of inner diameter 10 mm. Tantalum foil was used to surround the pow der specimen on all sides, isolating the specimen from contact with the graphite die and punches during the SPS experiments. SPS experiments were performed using a Sumitomo Dr. Sinter SPS system. The temperature during the SPS experiments was mo nitored by a thermocouple inserted into a small hole drilled into the side of the SPS die (positioned approximately 1 mm from the specimen). It is important to note that the exact local temperature of the specimen is typically not known during the SPS process. In the present experiments we have measured the temperature by the standard technique233-235 and estimate the offset in the actual sample temperature to be less than 50oC during any given stage of the experiment. Polarity of the applied voltage wa s determined in situ during the experiment. The system pulse cycle condition of 12 ON pulse s, 2 OFF, was used for all experiments. Effects of applied uniaxial pressure, temperature, and reaction time were studied. Crystal growth of phase pure Na24Si136 was reproducibly achieved by the following temperature schedule: heating to 450oC at 25oC/min, then to 600oC at 10oC/min, holding at 600oC for 3 hours, and then cooled to room te mperature. Typical el ectrical current and applied voltage (across input leads to SPS apparatus) at 600oC were 267 A and 1.4 V, respectively. Uniaxial applied pressure of 100 MPa produced the best crystalline clathrate
81 Figure 5.2 Optical microscope image of Na24Si136 crystals grown at 600oC. product. Products from reactions at 550oC were found to contain a fraction (estimated to be 5 to 10 wt% from powder X-ray di ffraction (p-XRD)) of the clathrate-I Na8Si46, while those from reactions performed at 700oC were found to contain similar fractions of -Si. A very thin film of Na was observed to condense on the upper electrode (above the punch/die assembly), indicating pr eferential evaporation of Na exiting from the top of the die assembly (illustrated sche matically in Figure 5.1a). The growth of the Na24Si136 crystalline specimens is completely reproducible. Figure 5.1b shows cross-sections of selected fractured compacts after SPS processing at 600oC and 100 MPa for differing reaction times, illustrating that the crystal growth initiates from the bottom electrode and progre sses toward the top. The bluish crystalline Na24Si136 discernable in the lower portion of th e compact increases in fraction as the reaction is allowed to progress for longer durations of time. The remaining Na4Si4 precursor, spatially occupying the top porti on of the SPS compact, is readily removed from the products by careful washing with et hanol and distilled water under flowing 400 m
82 argon,** allowing isolation of single phase Na24Si136 crystalline product, shown in Figure 5.1c and Figure 5.2. As is apparent from Fi gures 5.1c and 5.2, high quality crystalline product is obtained, with sizable (as broad as 500 m along the longest dimension) crystals formed. Energy dispersi ve X-ray analysis detected onl y Na and Si in the crystals, with the inferred composition Na22(1)Si136 in qualitative agreement with Na24Si136 determined from single crystal XRD (vide infra). While a detaile d understanding of the reaction kinetics and mechanisms behind the grow th process has yet to be developed, the observations of Figure 5.1b clearly suggest an influence of the DC electrical current. As such, we propose that the Na24Si136 crystal growth is initiated from oxidation of the Na4Si4 precursor at the anode ( bottom electrode), whereas sodium is reduced at the cathode (top electrode): 34 [Si4]4Â– [Si136]24Â– + 112 eÂ– (anode) 112 Na+ + 112 eÂ– 112 Na (cathode) These processes are driven by the electric fiel d that is present duri ng the SPS experiment and the formation and evaporat ion of Na at the cathode. The PXRD pattern (collected with a STOE STADI P diffractometer (Ge (111) monochromator, zero-background holder, Br agg-Brentano geometry) for a specimen ground from the Na24Si136 product is shown in Figure 5.3, corroborating the phase purity of the specimen. All reflections are indexed with the clathr ate-II crystal structure (space group Fd 3 m ). The demonstrated growth of Na24Si136 by SPS therefore also constitutes a solution to a long standing challe nge in the preparation of NaxSi136 clathrates: the previously known NaxSi136 synthetic routes, such as thermal decomposition87,88 or chemical oxidation118 of Na4Si4, typically produce the Na8Si46 clathrate as well in significant amounts, and this se condary phase is very difficu lt to avoid in the products from these synthetic routes. -Si is a common impurity phase in such specimens as ** Na4Si4 reacts with protic acids such as H2O or alcohols to form SiH4, which can be explosive in air. Thus washing is carried out by slow, controlled addition of ethanol and then distilled water, only under streaming argon. Under argon atmosphere, the specimen should be lo aded in the vessel and sealed, then transferred to the safety hood were washing can be performed. Wearing of protective equipment is strongly recommended.
83 2 (degrees) 102030405060708090Intensity (arb. units) Figure 5.3 Powder X-ray diffraction pattern for a phase pure Na24Si136 specimen grown at 600oC, collected after removal of residual Na4Si4. All reflections correspond to Na24Si136. The most intense reflection corresponding to Na8Si46 which would be found just below 33o 2 is completely unobservable. well.87.88,118 The present work demonstrates that Na24Si136 is reproducibly prepared by SPS free of these impurity phases. DSC measurements were performed on a Na24Si136 specimen using a Netzsch DSC 404 C calorimeter from room te mperature to 1173 K with 5 K minÂ–1 heating rate. 7.5 mg of substance was seal ed in welded Nb ampoules ( 5 mm, 600 mg) under argon atmosphere for measurement. No thermal events were observed on heating until 759oC, whereupon an endothermic event was obser ved corresponding to decomposition of Na24Si136. 5.2 Single-crystal X-ray diffraction studies on Na24Si136 Single crystal X-ray diffraction and i nvestigations were carried out on Na24Si136 by Dr. Horst Bormann, Dr. Michael Baitinger, and Prof. Dr. Yuri Grin of MPI-CPfS. Data collection was performed with a rota ting anode diffractomet er (RIGAKU Spider,
84 Table 5.1 Crystallographic data for Na24Si136, single crystal XRD Formula; molar mass Na24Si136; 4372 g molÂ–1 Crystal system; space group cubic; Fd 3 m (No. 227), 2nd choice of origin a / 14.7157(2); Guiner powder XRD, LaB6 standard Unit cell volume 3186.71(8) 3 Z ; calc/(g cm 3) 1; 2.2779(1) Diffractometer RIGAKU Spider Wave length / ; monochromator 0.71073; multilayer-optics Crystal size 0.2 mm 0.2 mm 0.2 mm T / K 295(2) range 2.77 to 33.53 Indexes ranges 16 h 12, 11 k 22, 10 l 22 / mmÂ–1 1.41 F (000) / e 2168 Absorption correction Multi-scan Reflections collected; independent 4957; 326 [ Rint = 0.018] Refinement method Full-matrix least-squares on F2 Extinction coefficient 0.00035(4) a. Single Site Model Refined parameters 15 Residuals [I > 4 (I)] R 1 = 0.015, wR 2 = 0.024 Residuals (all data) R 1 = 0.016, wR 2 = 0.024 b. Split Site Model Refined parameters 25 Residuals [I > 4 (I)] R 1 = 0.015, wR 2 = 0.024 Residuals (all data) R 1 = 0.017, wR 2 = 0.025
85Table 5.2 Atomic parameters for Na24Si136 (single site model) Atom x / a y / a z / a Ueq* (2) Occ Na1 0 0 0 0.0215(2) 1 Na2 3/8 3/8 3/8 0.119(1) 1 Si3 1/8 1/8 1/8 0.0087(1) 1 Si2 0.21797(1) x x 0.0089(1) 1 Si1 0.06735(1) x 0.37129(1) 0.00876(9) 1 Ueq is defined as one third of the trace of the orthogonalized Uij tensor, appearing in the Debye-Waller factor exp ( 2 2 [ h2a*2U11 + ... + 2 h k a* b* U12]). Table 5.3 Anisotropic displacement parameters for Na24Si136 (single site model) Atom U11 U22 U33 U12 U13 U23 Na1 0.0215(2) U11 U11 Â–0.0018(2) U12 U12 Na2 0.119(1) U11 U11 0 0 0 Si3 0.0087(1) U11 U11 0 0 0 Si2 0.0089(1) U11 U11 0.00021(6) U12 U12 Si1 0.0086(1) U11 0.0090(1) 0.00062(6) 0.00011(5) U13 Table 5.4 Atomic parameters for Na24Si136 (split site model) Atom x / a y / a z / a Ueq (2) Occ Na1 0 0 0 0.0214(2) 1 Na21 3/8 3/8 3/8 0.013(2) 0.19(1) Na22 0.1058(8) 0.1249(5) 0.6363(7) 0.016(4) 0.032(1) Si3 1/8 1/8 1/8 0.0085(2) 1 Si2 0.21798(3) x x 0.0088(1) 1 Si1 0.06735(2) x 0.37134(3) 0.00864(8) 1 Ueq is defined as one third of the trace of the orthogonalized Uij tensor, appearing in the Debye-Waller factor, exp ( 2 2 [ h2a*2U11 + ... + 2 h k a* b* U12]). Table 5.5 Anisotropic displacement parameters for Na24Si136 (split site model) Atom U11 U22 U33 U12 U13 U23 Na1 0.0214(3) U11 U11 Â–0.0016(4) U12 U12 Na21 0.013(2) U11 U11 0 0 0 Na22 0.011(9) 0.019(6) 0.018(7) 0.000(4) 0.002(3) 0.001(4) Si3 0.0085(2) U11 U11 0 0 0 Si2 0.0088(1) U11 U11 0.00013(1) U12 U12 Si1 0.0085(1) U11 0.0089(2) 0.00054(1) 0.00021(8) U13
86 Figure 5.4 Difference Fourier map calculated with the Na2 atom removed from the structure model. Centered at the 8 b site, scaling in fractional coordinates. De spite a large displacement parameter for this site, the difference map shows on average an essentially spherical residual denstity, with a maximum at the center of the cage (3/8, 3/8, 3/8). Varimax optical system, Mo K radiation = 0.710747 ). Absorption correction was performed with a multi-scan procedure and the crystal structure refinement by employing a full-matrix least-squares procedure. St ructure refinements were performed using SHELX.208 Details concerning the data collection and structure refinement are given in Table 5.1. The low residuals (for I > 4 (I): R 1 = 0.014, wR 2 = 0.035, GOF on F2 = 1.241) of the structure refinement (Table 5.1) are indicative of both the qua lity of the acquired data and the crystallinity of the prepared crystal. Unit ce ll parameters were calculated from least squares refinement, using reflection positions obtained by single-profile fit of X-ray Guinier powder diffraction data (Cu K 1 radiation, = 1.540598 , graphite monochromator, Huber 670 camera, 5 2 100, 2 = 0.005; LaB6 NIST standard with a = 4.1569162(97) ). Data analysis was performed with the WinCSD program.237 The cubic unit cell parameter (PXRD) a = 14.716(1) is in general agreement with the previously reported87,88 trend for NaxSi136 extrapolated to x = 24. We note that a direct comparison of lattice parameters is not possible as full occupation of Na ( x = 24) has not been previously achieved. In our single crystal specimens, all silicon framework sites are found to be completely occupied, and both s odium sites show full occupation within the 0.0 0.00.10.2 0.1 0.2 1.4 A  
87 standard deviations, in accordance with the chemical composition Na24Si136. In light of a very large atomic displacement parameter ( Uiso) observed for Na2 at the 8 b site (Table 5.2), and previous EXAFS studies95,96 indicating off-centering of Na in the large oversized Si28 cage, split site models were refined against the single cr ystal data (Table 5.4). However, no improvement in the re siduals was obtained (Table 5.4), and a difference Fourier map calculated with Na in the Si28 cage removed from the model (Figure 5.4) shows only a broadly smeared, e ssentially spherical residual density with a clear maximum at the 8 b site. It is conceivable that freezing out of thermal motion at low temperature95,96 may cause the Na to lock into off-center positions and/or allow offcentering to become more clearly discernable. These possibilities are of interest for future investigations. 5.3 Transport properties of Na24Si136 As noted in Â§1.3, the tran sport properties of the NaxSi136 clathrates are of considerable interest. However, preparation of specimens of sufficient quality for accurate transport properties determination has previously been highly challenging for reasons stated above, but also due to difficu lties in preparation of dense polycrystalline compacts from microcrystalline powders, as di scussed in Chapter 4. Our preparation of Na24Si136 crystals offers the opportunity for the first investigation of the electrical and thermal transport properties of these silic on clathrates, free from interfacial and grain boundary effects associated with consolidated microcrystalline specimens. Due to the small size of the Na24Si136 crystal specimens, it was necessary to modify the standard mounting procedure fo r our transport properties measurement system. A photograph of a Na24Si136 specimen mounted in this manner is shown in Figure 5.5a. Thermal bridges between the heat source (resistive heater, at top) and specimen, and heat sink and specimen, were made by bare Cu wire. Silver filled epoxy was used for thermal contact between the spec imen and Cu wire thermal bridges, as well as electrical contacts for voltage probes. Thermoc ouples were attached with StycastTM epoxy. The transport measurements were then conducted according to the procedures outlined in the Appendix. The difficulty in the determination of the cross-sectional ar ea of the irregularly
88 (mOhm-cm) 0.00 0.01 0.02 0.03 S ( V/K) -4 -2 0 2 4 Temperature (K) 0100200300 (W/m-K) 20 30 40 10 estimated e total measured shaped crystal results in a relatively large uncertainty in the electrical resistivity and thermal conductivity, which we estimate to be on the order of 40%. Regardless of this loss in precision, the obtained values can be interpreted as more accurately representative of the intrinsic properties of the material relative to the same measurements on polycrystalline specimens in this syst em, for which grain boundary effects can dominate.4,104,126,128 Data from temperature dependent electr ical resistivity, Seebeck coefficient ( S ), and thermal conductivity ( ) on as-grown Na24Si136 crystal specimens are shown in Figure 5.5. The temperature dependence and ma gnitude of the resistivity data clearly indicate metallic behaviour for Na24Si136. Indeed, the obser ved magnitude of (29.3 Ohm-cm at room temperature) is, to the best of our knowledg e, lower than for any other intermetallic clathrate reported in the literature to date (with, of course, the exception of Figure 5.5 Temperature dependent transpor t properties measurements on Na24Si136 crystal specimens grown by SPS. (a) Photograph (optical microscope) of a Na24Si136 crystal specimen mounted for transport properties measurements. (b) Electrical resistivity (triangles) and Seebeck coefficient (circles, solid curve to guide the eye). (c) Thermal conductivity of Na24Si136: total measured along with e estimated from the measured electrical resitivity using the Wiedemann-Franz law. a b c 1 mm
89 the superconducting variants belo w their transition temperatures ). This is an indication of both the unequivocal metallic conduction for th is composition and the high quality of the crystals. The quality and crystallinity of the Na24Si136 specimen is also characterized by the calculated Â“residual resistance ra tioÂ” [RRR = R(300 K)/R(12 K)] value of approximately 14. We note that at the lowe st temperature of our measurement (12 K), d / dt > 0, indicating the residual resistance ha s still not yet been reached. A comparison with typical RRR values taken from the litera ture for other intermetallic clathrates is given in Table 5.6. The value for the Na24Si136 specimen of the present work is significantly higher than for a ny other intermetallic clathrate specimen reported in the literature. The magnitude of the Seebeck coe fficient remains very small over the entire temperature range, corroborating the meta llic conduction for this compound. The negative sign of S indicates electrons are the majority carriers. The electronic structures of NaxSi136 (0 < x < 24) have been inve stigated in several density functional theory studies.35,44,125 The inclusion of Na in to the Si coordination polyhedra (Si28 and Si20) has significant effects on th e electronic band structure, indicating a simple rigid band model strictly speaking does not apply to this system. However, as would be expected in a rigid band approximation, as Na is incorporated conduction band states progressi vely become more and more occupied. For the fully filled end member, Na24Si136, pronounced metallic conduction is expected with a relatively high concentration of carriers, which is precisely what is confirmed experimentally for the first time in the data of Figure 5.5. The thermal conductivity of Na24Si136 is shown in Figure 5.5c. The slight increase in just below room temperature is likely due to minor radiation losses. This can be expected in the present case due to the sm all cross-sectional area of the specimen as compared to the surface area of the heater specimen, and copper bridge. The thermal conductivity of Na24Si136 is found to be quite high, which is also consistent with the metallic behavior observed in the electrical transport properties. The thermal conductivity of a solid can typically be expressed as simple sum of a lattice contribution ( L) due to phonon transport and an electronic contribution ( e) due to the charge carriers, so that = L + e. As a first approximation, e can be estimated from
Table 5.6 Comparison of the room temperature electrical resistivities and residual resistance ratios (RRR), R(300 K)/ R( T0), for the Na24Si136 specimen of the present work and several intermetallic clathrate specimens from the literature showing metallic or metallic-like resis tivities (i.e. d /dt is positive definite over the entire range of measurement). T0 is the lowest temperature at which the corresponding resistivity was reported. Composition Structure Type Form Synthesis Method Carrier Type (300 K) (mOhm-cm) T0 (K) RRR Ref. Na24Si136 clathrate-II single crystal SPS n 0.029 12 14 This work Eu8Ga16Ge30 clathrate-VII polycrystalline, as-synthesized direct reaction of stoichiometric mixture n 0.87a 2 3.0b 238 Cs8Na16Si136 clathrate-II polycrystalline, consolidated direct reaction of stoichiometric mixture n 0.68 9 2.4 93 Ba8Ga16Sn30 clathrate-VIII single crystal Ga flux growth p 2.6 6 2.3 239 Ba8Ga16Ge30 clathrate-I single crystal slow cooling of stoichiometric melt n 0.82 2 2.2 139 Sr8Ga16Ge30 clathrate-I polycrystalline, consolidated direct reaction of stoichiometric mixture n 2.0 6 2.1 30 Na8Si46 clathrate-I polycrystalline, consolidated thermal decomposition of Na4Si4 n 9.7 8 1.9 172 Cs8Ge136 clathrate-II polycrystalline, consolidated degassing Na from Cs8Na16Ge136 n 9.2 6 1.8 98 Ba8Al14Si31 clathrate-I single crystal Al flux growth n 0.45 20 1.4 240 aAt 400 K b RRR = R(400 K)/ R (2 K) 89
91 the Wiedemann-Franz relation e = L0T / where L0 = 2.45 10-8 V2/K2 is the (temperature independent) Lorenz number, T is the absolute temperature, and is the electrical resistivity. Also plotte d in Figure 5.5c is the estimated e, calculated from the Wiedemann-Franz relation using the measured shown in Figure 5.5c. It is clear that the Wiedemann-Franz relation overestimates e somewhat, which may signify that this model is not completely valid here, perhaps due to inequality of the electron relaxation times appropriate to thermal and el ectrical conduction; the use of the temperature independent L0 may also contribute. We note however that the two data sets agree over most of the temperature range within the uncertainty of the measurement, and in general the estimation qualitatively reproduces both th e magnitude and temperature dependence of the measured thermal conductivity. This is an indication that the thermal conductivity of Na24Si136 is dominated by the electronic cont ribution in this metallic compound. Although quantitative values for L cannot be calculated from the data of Figure 5.5c, the estimation serves to suggest that the lattice contribution to is small. This is consistent with our previous measurements104,126 on consolidated polycrystalline NaxSi136 ( x = 0, 1, and 8) specimens which all exhi bited very low lattice thermal conductivities. The reasons for the low lattice thermal conduc tivity can made cleare r by consideration of the mechanisms that are expected to signi ficantly impede the heat transport by phonons in in these materials. It is known that the lattice thermal conductivity in solids typically scales with the number of atoms in the primitive unit cell.151 For the relatively large number of 30 atoms per primitive unit cell in Na24Si136, a comparatively low thermal conductivity (compared to -Si, for example, which contains 2 atoms per primitive unit cell and exhibits analogous bonding to the Si136 framework) can be expected. The related increase in the unit cell volum e for the silicon allotrope Si136 results in conspicuous features in the phonon dispersion rela tions (and the corresponding phonon group velocities), which are modified by the relative decrease in the first Brillouin zone boundary (relative to -Si).81 In addition, the strong static and/or dynamic disorder re flected in the large atomic displacement parameter for Na in the Si28 cage also indicates potential mechanisms for impeding thermal transport in Na24Si136. The phenomenon of resona nt scattering of heat
92 carrying acoustic phonons by local modes associ ated with the large amplitude thermal motion of guest atoms in intermetallic clathr ates is well established (cf. Â§1.1). Several studies have suggested that o ff-centering of the guest ion enha nces the effects of resonant scatting in these materials. Though the c ontributions remain to be determined unequivocally, both of these mechanisms are believed to be present in Na24Si136. 5.4 SPS processing as a general preparative tool An important implication of the present work is that the SPS process holds significant promise as a general method for cr ystal growth of materials in cases where reactive precursors can be ut ilized. We have also applie d the SPS method in processing of K4Si4 and Rb4Si4 precursors, using similar conditions to those described above. Single phase crystal growth of the re spective clathrate-I compounds K7.8(1)Si46 ( a = 10.281(1) ) and Rb6.1(1)Si46 ( a = 10.286(1) ) was also successf ully achieved in these cases (see Figure 5.6).We expect the method demons trated herein of crystal growth via SPS processing of appropriate reactive precursors can be applied to the preparation of a Figure 5.6 Preparation of Rb6Si46 by SPS. PXRD (Gunier image plate) shows only reflections from the Rb6Si46 clathrate-I phase. As in Na24Si136, growth initiates from the bottom of the compact (inset), indicating the reaction mechanism is the same.
93 broader range of materials, a nd reveals a new preparative tool for the crystal growth and synthesis of materials where other conve ntional methods are unsuccessful. Analogous behaviour may in principle be common amongst the various AnEm (A = alkali metal, E = group 14 element, n, m integers) Zintl phases, since all contain similar structural and bonding motifs, and suggests direction for future studies.
94 6 Synthesis and characterization of a novel zeolite-like binary phase: Na1xGe3+ z In this chapter, the discovery of a nove l binary phase in the Na-Ge system is reported. Showing qualitative st ructural characteristics analogous to some aluminumsilicate zeolites, the crystal structure of this new phase exhibits an unconventional covalently bonded tunnel-like Ge framewor k, accommodating Na in channels of two different sizes. Specimens were character ized by conventional and synchrotron powder X-ray diffraction, neutron powder diffrac tion, nuclear magneti c resonance (NMR) spectroscopy, and electrical and therma l transport measurements. The thermal conductivity of the new Na1xGe3+ z phase was found to be very low, near 1 Wm-1K-1 near room temperature. 6.1 Synthesis The new Na-Ge phase was prepared in an analogous manner to that described for NaxSi136 above. Na4Ge4 precursor (monoclinic, space group P 21/ c )106,107 was first synthesized by direct reaction of the high purity elements at 650oC. This reaction was carried out in a tungsten crucib le, sealed under ultra high purity nitrogen inside a stainless steel canister, which was in turn sealed insi de a fused quartz ampoule. As with the other alkali-tetrelide precusors, the resulting Na4Ge4 product is highly reactive with moisture and air, thus all handling was performed inside a nitrogen-filled glove box. The Na1xGe3+ z phase is synthesized by thermal decomposition of Na4Ge4 through heating under vacuum ( 1.33 10-4 Pa) at temperatures between 350 to 360oC for several days. Results from a systematic investigati on into the thermal decomposition of Na4Ge4 were presented previously by the author in Ref. 104. The resulting thermal decomposition products are typically fine, grayish microcrystalline powders that, upon removal of any unreacted Na4Ge4 by washing with
95 water and ethanol, are stable in air and moisture. It was eventually found that amorphous fractions typically present in the as-synthesized specimens can be removed by repeated brief sonications in distilled water follo wed by immediate decanting of the resulting impurity-containing suspension, leaving the essentially single phase Na1xGe3+ z product which more quickly settles to the bottom of th e container. After an extensive search of available crystallographic and chemical databa ses and literature, the new phase initially remained unidentifiable. This included refe rence to the available Na-Ge binary phase diagram.241 We note that some of the reporte d Na-Ge phases (including some not represented in phase diagram242) have later been disputed,243 and this system remains to be well-characterized. As such, the crystal structure of the new phase was solved and refined as discussed below. Figure 6.1 Differential thermal analysis (D TA) data (exothermic up) for Na1xGe3+ z (bottom) indicating decomposition near 400oC. The prominent endothermic event at ~ 940oC corresponds to the melting of Ge Upper left: pre-DTA PXRD pattern. Upper ri ght: post-DTA p-XRD pa ttern after DTA to 500oC, indicating decomposition products contain -Ge as the majority phase, with trace amounts of the title phase remaining.
96 Figure 6.1 shows data from differential th ermal analysis on a specimen of the new binary, acquired under flowing nitrogen in open alumina pans. These thermal analysis measurements revealed the new phase decomposes exothermically above 400oC, whereas decomposition begins under vacuum (10-4 Pa) at the lower temperature of 370oC.104 The exothermic nature of the decomposition suggests the phase is thermodynamically metastable with respect to the indivi dual elements under the above conditions. 6.2 Crystal structure solution and refinement As single-crystal specimens were unavailabl e, it was necessary to solve the crystal structure from powder diffraction data. Data collection, structure solution, and initial refinements were carried out by Dr. James Kaduk of INEOS Tec hnologies. Synchrotron X-ray powder diffraction data were collected (Specimen I), with the help of Dr. Peter L. Lee, from 2-43.7o 2 in 0.001o steps on the 32ID beamline of the Advanced Photon Source at Argonne National Laboratory (APS) The wavelength of 0.4958 (25 keV) was used. The pattern was indexed on a prim itive hexagonal unit cell (Figures of merit of M(25) = 270, F(25) = 1503) using DICVOL04.244 A significant fraction of amorphous material in this first specimen under study precluded bulk analysis for experimental determination of the chemical composition. Th erefore, an expected composition (i.e. unit cell contents), based on an empirical relation224 between compositions of the known NaGe phases and their mass densities, and the initial indexed unit cel l parameters of the unknown phases, was derived as a starting point for structure so lution. Attempts to solve the structure by applying singl e crystal techniques to extrac ted structure factors were unsuccessful, as were attempts to solve the st ructure in an orthorhombic sub-cell. Several space groups yielded essentially the same stru cture. The lowest residual was obtained in space group P 6, but eventual analys is of the refined stru cture suggested that P 6/ m (No. 175) was the correct space group. The structur e was solved using Monte Carlo simulated annealing techniques as implemented in th e program Endeavour 1. 3 (Crystal Impact).245 Rietveld refinements were carri ed out using the GSAS suite.205,206 The refined hexagonal unit cell parameters (Table 6.2) for the preliminary structure, as determined from
97 Rietveld refinement against the synchrotron XRD data, are a = 15.05399(5) and c = 3.96845(2) . Neutron powder diffraction intensity data were collected (Specimen II) using the BT-1 high-resolution powder diffractometer at the National Institute for Standards and Technology Center for Neutron Re search. Data collection and structure refinements were carried out by Drs. Winni e Wong-Ng, Qing Huang, and Zhi Yang. A Cu (311) monochromator was employed to produce a mo nochromatic neutron beam of wavelength 1.5403 . Collimators with horizontal divergen ces of 15, 20, and 7 arc were used before and after the monochromator, and after the sample, respectively. The intensities were measured in steps of 0.05 in the 2 range 3-168. Data were collected at 295 K and at 4 K. All data processing and Rietveld structural refinements were carried out using the GSAS suite.205,206 The neutron scattering amplitudes used in the refinements were Figure 6.2 Observed, calculated, and difference patterns (plotte d on the same scale) obtained from Rietveld refinement using neutron diffraction data collected at 4 K. Lower tick marks indicate calculated reflections for Na1xGe3+ z. Upper tick marks indicate calcula ted reflections for elemental Ge, which was present in the sample as a minor impurity. Refinement results are given in Table 6.1. M. Beekman, J.A. Kaduk, Q. Huang, W. Wong-Ng, Z. Yang, D. Wang, and G.S. Nolas, Â“Synthesis and crystal structure of Na1xGe3+ z: A novel zeolite-like framework phase in the Na-Ge system,Â” Chem. Commun. 837 (2007). Reproduced by permission of The Royal Society of Chemistry.
98Table 6.1 Refinement results for Specimens I and II. Specimen I (synchrotron) Specimen II (neutron) 300K 300K 4k R values wRp 0.0445 0.0204 0.0213 Rp 0.0257 0.0171 0.0178 2 2.164 1.195 1.46 No. variables 28 57 57 Total # data points 40699 3119 3120 Impurity phases amorphous Ge (1.2%) Ge (1.2%) Table 6.2 Lattice parameters for Specimens I and II (space group P6/m ). Specimen a () c () V (3) I (synchrotron) 15.05399(5) 3.96845(2) 778.852(5) II (neutron) @ 300K 15.0640(3) 3.9673(1) 779.66(3) @ 4K 15.0052(4) 3.9546(1) 771.10(4) 0.363 and 0.818 ( 10-12 cm) for Na and Ge, respectively. The preliminary structure as determined from synchrotron experiments wa s confirmed and the structural model was refined against neutron diffr action data at 295 and 4 K. The neutron powder diffraction pattern (observed, calculated, and differe nce obtained from Rietvled refinement) collected at 4 K is shown in Figure 6.2. 6.3 Crystal structure and crystal chemistry of Na1-xGe3+z The structure determination revealed that th e new Na-Ge phase crystallizes in a complex zeolite-like structure. Depictions of the crystal structure are shown in Figures 6.3 and 6.4. Atomic coordinates, atomic displacement pa rameters, and site occupancies determined
99 from the structure refinements ag ainst the three data sets are given in Table 6.3. The most conspicuous aspect of the unusual crystal st ructure is a covalently bonded framework of Ge atoms, all of which are arranged in distor ted tetrahedral (i.e. 4bonded; see Figure 6.4) configurations with the excepti on of Ge1, which is only bonded to three other Ge atoms. As illustrated in Figure 6.3, the framework fo rms large and small channels, akin to the channels found in some oxide zeolites (cf. qualitative similarities to the AFI aluminium phosphate zeolite type246). The present structure, howev er,does not correspond to any of the known zeolite structure types.246 The large and small channe ls in the framework both run along the c -direction. The four crystallographical ly independent Ge framework sites (denoted by Ge1, Ge2, Ge3, and Ge4 in Figure 6.4) were all found to be fully occupied in refinements against both synchrotron and neutron diffraction da ta. From neutron Figure 6.3 Crystal structure of Na1xGe3+ z, as viewed down the c -axis. Na atoms are shown in blue, while the framework Ge atoms are shown in turquoise. The Ge7 site, which is partially occupied, is shown in white. The hexagonal unit cell is outlined in the upper right. M. Beekman, J.A. Kaduk, Q. Huang, W. Wong-Ng, Z. Yang, D. Wang, and G.S. Nola s, Â“Synthesis and crystal structure of Na1xGe3+ z: A novel zeolite-like framework phase in the Na-Ge system,Â” Chem. Commun. 837 (2007). Reproduced by permission of The Royal Society of Chemistry.
100 diffraction at 295 K, the GeÂ—Ge distances in the framework range from 2.438(8) to 2.527(6) , as compared to the Â‘idealÂ’ 2.45 for elemental Ge in the diamond structure. The open-framework configuration of Ge in Na1xGe3+ z results in a rather large volume per Ge atom of 32.5 3/atom. This can be compared to 22.6 3/atom for -Ge and 25.8 3/atom for the guest-free clathrate-II Ge136,2 and indicates the pronounced Â“opennessÂ” of the framework in Na1xGe3+ z. As noted above, several crystalline binary compounds have been reported previously in the Na-Ge system.243 Of these, Na4Ge4 and Na12Ge17 have been characterized in the most detail.184,247,248 The crystal chemistry of phases such as Na4Ge4 and Na12Ge17 is understood in terms of Zintl-Klemm concepts.109.196,197 These compounds are composed of [Ge4]4(e.g. Na4Ge4 and Na12Ge17) or [Ge9]4(e.g. Na12Ge17) cluster anions and Na+ cations.184,247,248 In Na4Ge4, for example, the Na atoms formally transfer Figure 6.4 Structure of Na1xGe3+ z, in the vicinity of the broad channel as viewed along the c -axis at a slight tilt. Na atoms in the smaller channels are shown in blue, while the framework Ge atoms are shown in turquoise. The variable occupancy Na6 and Ge7 sites in the larger channel are shown in grey and white, respectively. Tetrahedral coordination of Ge3 is show n, while other tetrahedral arrangements are omitted for clarity. M. Beekman, J.A. Kaduk, Q. Huang, W. Wong-Ng, Z. Yang, D. Wang, and G.S. Nolas, Â“Synthesis and crys tal structure of Na1xGe3+ z: A novel zeolite-like framework phase in the Na-Ge system,Â” Chem. Commun. 837 (2007). Reproduced by permission of The Royal Society of Chemistry.
101 Table 6.3: Crystallographic data for Na1xGe3+ z from Rietveld refinement against synchrotron X-ray and neutron powder diffraction. Atom Wyckoff Position x y z Uiso or Ueq (A2) Occupancy Synchrotron X-ray data Ge1 6 j 0.37332(8) 0.26958(8) 0 .0115(4) 1 Ge2 6 j 0.40826(8) 0.44914(8) 0 .0106(4) 1 Ge3 6 k 0.52012(9) 0.15164(9) 1/2 .0052(3) 1 Ge4 6 k 0.48411(10) 0.30138(7) 1/2 .0071(3) 1 Na5 2 c 2/3 1/3 0 .02 1 Na6 6 k 0.2539(6) 0.0639(7) 1/2 .088(4) .617(9) Ge7 1 b 0 0 1/2 .088 .617(9) Neutron diffraction data at 295 K Ge1 6 j 0.3689(3) 0.2666(3) 0 0.0108(4) 1 Ge2 6 j 0.4069(3) 0.4482(3) 0 0.0108(4) 1 Ge3 6 k 0.5186(3) 0.1518(4) 1/2 0.0108(4) 1 Ge4 6 k 0.4842(4) 0.2996(3) 1/2 0.0108(4) 1 Na5 2 c 2/3 1/3 0 0.038(5) 1 Na6 6 k 0.260(1) 0.068(1) 1/2 0.08534 1 Ge7 12 l 0.108(2) 0.029(3) 0.140(5) 0.052(7) 0.163(4) Neutron diffraction data at 4 K Ge1 6 j 0.3674(3) 0.2652(3) 0 0.0054(4) 1 Ge2 6 j 0.4058(3) 0.4479(3) 0 0.0054(4) 1 Ge3 6 k 0.5180(3) 0.1510(3) 1/2 0.0054(4) 1 Ge4 6 k 0.4842(3) 0.2996(3) 1/2 0.0054(4) 1 Na5 2 c 2/3 1/3 0 0.01956 1 Na6 6 k 0.259(1) 0.0701(9) 1/2 0.07499 1 Ge7 12 l 0.112(2) 0.034(2) 0.141(4) 0.033(5) 0.16667
102 Figure 6.5 Perspectives of the two distinct Ge (green atoms) channels in Na1xGe3+ z, viewed perpendicular to the c -axis. At left is shown the large channel, with th e 24-ring highlighted at the top (Ge7 omitted). At right is shown the smaller channel, where Na (blue atoms) are coordinated in an 18-membered Ge cage. their single s electron to the Ge polyanion clusters, allowing closed shell configurations and an electronically balanced compositi on. The covalent Ge framework of Na1xGe3+ z is in stark contrast to the polyanionic [Ge4]4or [Ge9]4cluster units found in other Na-Ge compounds such as Na4Ge4 and Na12Ge17. Figure 6.5 shows two perspectives of the small and large framework channels in the structure. Na atoms are situated inside the small channels (Na5), as well as in the broad channels (Na6). The broad channel consis ts of alternating Ge and Na, which can be interpreted as connected via NaÂ–Ge bonds. Th e Ge forming this channel may also be described as a 24-ring. Inside the broad ch annel, a maximum of six Na can occupy the Na6 sites that are related to each other by a 6-fold symmetry. The initial synchrotron experiments and corresponding st ructure refinements suggested that additional Ge atoms are disordered in the middle of the broad channe l. The nature of the contents in the larger channel were therefore of particular interest for the neutron diffrac tion investigation. In refinements against neutron diffraction da ta collected at both 295 K and 4 K, the
103 additional nuclear density in the broad cha nnel could be modeled by assigning Ge to additional sites (Ge7 in Figure 6.4) which in fact possess a 6-fold symmetry much like the Na atoms in this channel (Na6), yet reside closer to the center. These Ge sites were not found to be fully occupied, however, in contrast to the connected Ge framework. Rather the Ge7 site was found to have occ upancy of 1/6, so that the Ge atoms are disordered on one Ge7 site per larger channel, per layer progressing along the c -axis. It was observed that the content of both species in the larger channel (Ge7 and Na6) can vary depending on the synthesis conditions In particular, repeated grinding under nitrogen atmosphere and then Â“degassingÂ” (i.e. heating the Na1xGe3+ z specimen under vacuum at 350oC) was found to reduce the Na content in the larger channel. This suggests a significant mobility of Na in the larger ch annel facilitating removal from the structure when heated under vacuum, as also observed in the NaxSi136 clathrates (see Â§4.2). The Ge content inside the broad channel (Ge7 position) can be varied as well. With the Ge Figure 6.6 Atomic displacemen t parameters for Na1xGe3+ z. (a) Ellipsoid representations225 of ADPs in the vicinity of the large channel. (b) ADPs extracted from data collected at 295 K and 4 K (lines are to guide the eye). Temperature (K) 0100200300ADP ( 2 ) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Na6 U 11 Na6 U 33 Na5 Na6 U 22 Ge framework Na6 U iso (synchrotron) Na6 Na5a b
104 framework, Na5, and Na6 sites all fully occupi ed the chemical formula of this new phase is NaGe3. However, since the Na6 and Ge7 occupa ncies inside the larger channel can vary, the general formula for this non-stoichiometric phase is Na1xGe3+ z. Examination of the atomic displacement parameters (ADPs) for Na6 in the larger channel revealed significant disorder. Ellipsoid representations, depicted in the vicinity of the larger channel are shown in Figure 6.6a, while the values for the ADPs at both 295 and 4 K are plotted in Figure 6.6b. The pronounced elongation of the Na6 ellipsoid suggests substantial static disorder for th is site. As shown in Figure 6.7b, the U11 component of the ADP tensor remains very large even at 4 K. At the same time U22 and U33 both exhibit rather large values and stronger temperat ure dependence, indicating significant thermal motion for Na6 as well. The observed static and thermal disorder suggested by the APDs for this site can be understood in terms of the rather poor bonding environment of the large channel, as well as the presence or absence of the nearby Ge7 in its fractionally occupied site. Magic angle spinning solid-state 23Na NMR data were collected at 300 K by Prof. Russell Bowers and co-workers of the Universi ty of Florida in Gainesville, FL, and the National High Magnetic Field Laborat ory in Tallahassee, FL. The 23Na NMR spectrum is shown in Figure 6.7. The NMR shifts are refe renced to 1 M NaCl at 0 ppm. The spectrum reveals two resonances, at approximately 4 ppm and 23 ppm, respectively. The observation of two resonances is consistent with the two distinct crystallographic environments for Na (Na5 and Na6 above) in Na1xGe3+ z. Since the integrated intensity of the NMR peak is proportional to the multiplicity of the site in the crystal structure, we can assign the higher intensity peak at approx imately 23 ppm to Na in the larger channel (multiplicity of 6) and the lower intensity peak at approximately 4 ppm to Na in the smaller channel (multiplicity of 2). The magnitudes of the shifts are relatively small (i.e. close to that for Na+ in NaCl), providing evidence that bo th Na are in an essentially ionic state in this phase. Large 23Na paramagnetic and/or Â“KnightÂ” shifts observed for the NaxSi136 clathrates are not observed in Na1xGe3+ z.
105 Figure 6.7 Magic angle spinning solid state 23Na NMR data for Na1xGe3+ z. The spectrum is referenced to 1 M NaCl at 0 ppm. Na1xGe3+ z constitutes the first example in which an exclusively germanium framework crystallizes in a tunnel configuration, remini scent of those found in the microporous zeolites. A structurally si milar compound, the orthorhombic phase Na5Sn13, has been previously reported249 by Vaughney and Corbett to exist in the Na-Sn system. This compound also exhibits an open-framew ork of covalently bonded Sn atoms, all of which are 4-bonded with the exceptio n of one site on the interior of the larger channel in this structure which is 3-bonded. Na atoms in Na5Sn13 also occupy two different channels in the structure. The existence of these tw o phases exemplifies that novel structural architectures can be obtained in simple bi nary systems between the alkali and group 14 elements. 6.4 Transport properties of Na1-xGe3+z To investigate the transport properties of the new phase, a consolidated specimen was prepared by hot-pressing. Achieving high relative densities in the compact was found to be challenging, due to the metastable nature of the phase (see Â§5.1 above) which precluded the use of high sinter ing temperatures typically need ed to produce a pellet of Na6 Na51 M NaCl
106 Degrees 2 20406080 Intensity (arb. units) Na1-xGe3+zTemperature (K) 100200300400500 Thermal Conductivity (W/mK) 0.1 1 10 100 amorphous Ge Ge crystal polycrystalline Gerelatively high density. A pellet exhibiting 62% of the expected (XRD) density was obtained by hot-pressing at 250oC, and 130 MPa for 1 hour. The powder XRD pattern obtained after hot-pressing, show n in Figure 6.8a, confirmed that the crystallinity of the specimen was maintained and decomposition di d not occur during consolidation. Room temperature Seebeck coefficient and resis tivity, and temperature dependent thermal conductivity were th en investigated. Room temperature Seebeck measur ements yielded the value Â– 330 V/K. This relatively large magnitude for the Seebeck coefficient is typical for an undoped compound semiconductor.250 We were unable to obtain reliable room temperature electrical resistivity data on the specimen due to difficulties in achieving adequate electrical contacts, but our measurements indicate a resistivity on the order of 105 mOhmcm. The large apparent resistivity is consistent with the large magnitude for S (and the difficulty in making good electr ical contacts to the specime n), and also the relatively small 23Na solid state NMR shifts discussed above. Figure 6.8b shows the th ermal conductivity of a Na1xGe3+ z specimen at four temperatures between 150 K and 300 K. We not e that since the crystal structure of Na1xGe3+ z is hexagonal, the transport properties may not be isotropic in this material, and Figure 6.8 (a) Powder XRD pattern for the Na1xGe3+ z specimen collected after hot-pressing. (b) Thermal conductivity of Na1xGe3+ z. Also shown in (b) are the thermal conductivities of bulk single-crystal Ge251 (green curve), as well as polycrystallin e (blue) and amorphous (red) Ge films.252 a b
107 therefore this data should be interpreted as an average of the transport along the different crystallographic directions. Al so shown in Figure 6.8b are the thermal conductivities for single crystal -Ge,251 as well as for polycrystalline and amorphous Ge films.252 As the porosity of the Na1xGe3+ z specimen was considerable (~ 38%), the data shown in Figure 6.8 have been corrected accordingly. It is known that porosity in polycrystalline specimens can significantly reduce the observed thermal conductivity.223,253-255 However, methods have been developed in or der to account for these effects.223,253-255 Particularly useful discussions on the eff ects of porosity on the therma l conductivity of solids have been given by Klemens et al.223,255 As detailed in Ref. 255, the thermal conductivity of the Â“fully denseÂ” material, dense, can be estimated from the observed thermal conductivity of a porous specimen, porous, using the relation porous/ dense = 1 Â– 3 /2, where is the relative porosity in the porous specimen. This approach was shown to be successful in modelling the effects of poros ity on the thermal c onductivity of yttrium stabilized zirconia.255 The data for Na1xGe3+ z in Figure 6.8b are the adjusted data using this approach. The thermal conductivity of Na1xGe3+ z is found to be very low, near 1.4 Wm-1K-1 in the temperature range investigated From the large resistivity discussed above, we can infer that th e electronic contribution to is negligible, and thus the measured thermal conductivity of Na1xGe3+ z can be attributed essentially to the lattice component entirely. As the bonding in the Ge framework of Na1xGe3+ z is akin to that in -Ge, it is useful to compare with the thermal conductivities shown for the other forms of elemental Ge in 6.8. We see that the thermal conductivity of the Na1xGe3+ z phase shows a pronounced reduction as compared to single or polycrystalline Ge, approaching that of amorphous Ge in magnitude. The reasons fo r the low thermal conductivity of this material can be attributed to the unusual features of its unique crystal structure. Low thermal conductivities typically observed256,257 for the structurally analogous oxide zeolites are due to the openness of thei r framework crystal structures, as well contributions (e.g. point-defect and resona nt scattering) from non-framework cations residing in the tunnels and cages in these structures.257 Our observation of very low thermal conductivity for Na1xGe3+ z illustrates that these factors can also play a role in
108 impeding thermal transport in non-oxide, intermetallic materials with similar structural achitectures. The strong static disorder and th ermal motion present in the large channel of the crystal structure may play a significant ro le in the scattering of the heat-carrying acoustic phonons in Na1xGe3+ z. Although the very high electr ical resistivity would pr eclude the use of this material for thermoelectric a pplications, the very large S and very low observed for this novel structure suggests a potential appr oach to the design of open-framework compounds that may show promising ther moelectric properties. Moreover, the nonstoichiometry and phase width implied by the synchrotron X-ray and neutron powder diffraction experiments above sugge sts that the composition of Na1xGe3+ z can be varied. It is therefore of interest fo r future study to determine if the physical properties, and in particular the electrical properties, can in turn be influenced by varying the composition of this intriguing material.
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125Bibliography 1. M. I. Aroyo, J. M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov & H. Wondratschek. "Bilbao Crystallographic Server I: Databases and crystallogr aphic computing programs". Zeitschrift fuer Kristallographie (2006), 221, 1, 15-27. 2. M. I. Aroyo, A. Kirov, C. Capillas, J. M. Perez-Mato & H. Wondratschek. "Bilbao Crystallographic Server II: Representations of crystall ographic point groups and space groups". Acta Cryst. (2006), A62, 115-128. 3. V.K. Percharsky and P.Y. Zavalij, Fundamentals of Powder Diffraction and Structural Characterization of Materials Springer, New York, 2005. 4. R.A. Young, The Rietveld Method Oxford University Press, Oxford, 1995. 5. The Collaborative Computational Project No. 14 (CCP14) in Powder and Small Molecule Single Crystal Diffr action: http://www.ccp14.ac.uk/
127Appendix: Characterization Techniques In this appendix, some basic and br ief introductory comments are made concerning some of the characterization techniques used in this work. The intent is to provide the reader unfamiliar with these techniques with a basic introduction, such that the results presented in the text may perhap s be clearer. No attempt at a comprehensive treatment is made; rather references are gi ven where the reader ma y find more detailed information. A.1 Rietveld crystal structure refinement Many materials of scientific and te chnological interest are obtained as microcrystalline powders, which precludes the use of single-crystal techniques for crystal structure refinement. Moreover, information c ontained in a powder diffraction pattern can in some cases be more representative of a bul k specimen than a selected single-crystal. It was the pioneering work of Hugo Rietveld (R efs. A1 and A2) that showed that powder diffraction data can be systematically empl oyed (in nontrivial cases ) in the solution and refinement of the crystal stru cture of a material. Detailed overviews of the Rietveld methods can be found in Refs. A3 and A4. One of the most important considerations in a powder diffraction experiment is that the 3-dimensional diffraction informati on is projected onto a single dimension (2 ), thus information is inevitably lost due to re flection overlap. Rietveld analysis approaches this problem by fitting the entire observed powder diffraction pattern to a calculated pattern using a structural model. It is impor tant to note that Riet veld refinement is precisely that: a crystal structure refinement technique, and cannot be used for structure solution. Rather, a starting st ructural model is always n eeded before proceeding with Rietveld refinement. The basic principle behind the Rietveld method is that for each step in a powder diffraction experiment, 2 i, the observed diffracted intensity, Ioi, can be fit to a calculated intensity, Ici, which is given by (see Ref. A4, for example)
1282) ( i ci i i II I w S (A1) where the hkl values indicate the Miller indi ces for the Bragg reflection under consideration, 2 hkl indicates the position of the Bragg reflection corresponding to hkl s is the scale factor, Lhkl contains the Lorentz, polarizat ion, and multiplicity factors, is the reflection profile function (due to both instrumental and sample-dependent effects), Phkl is a preferred orientation function, A is an absorption factor, Fhkl is the structure factor, Iib is a contribution from the background, and the su m is over all reflecti ons contributing to Ici at 2 i. During Rietveld refinement, these quanti ties are systematically varied employing a least squares refinement algorithm which minimizes the quantity (A2) where wi = 1/ Ii is a weighting factor. In other words, the algorithm aims to minimize the overall difference between the powder diffractio n pattern calculated from the structural model and the pattern that is experimentally observed. This is achieved by systematically varying the structural aspects from the cr ystal structure model and specimen-related quantities (e.g. lattice parame ters, atomic coordinates, atomic displacement parameters, site occupancies, specimen related peak profile parameters, etc.), as well as instrument/experiment related contributions (e.g., scale factor, specimen displacement, experiment related peak profile parameters etc.), both of which contribute to the calculated intensity given by Eq. A1. In most cases, it is, of course, the information about the crystal structure that is desired. The quality of a Rietveld refinement is judged by the refinement residuals (see Refs. A3 and A4), but more importantly by the graphical display of the fit. The standard practice for displaying this is shown in Figure A.1. The refinement profile plot has four main components: the experimentally observed diffraction pattern, th e calculated pattern from the structural model, the difference pattern (equal to Ioi Â– Ici), and tick marks indicating the positions for the calculated reflections for each refined phase. The hkl hkl hkl hkl i hkl hkl ciI A P F L s I ) 2 2 (2
129 important indicator of the quality of fit is the difference pattern, which in the best case scenario should approach a flat line. In addition to the contribution of his refinement method to the crystallography community, Rietveld also made freely and wi dely available his computer program which implemented the refinement algorithm. This tr adition continues to th e present day, as a number of Rietveld refinement programs and software are available for download via the internet free of Figure A.1 Rietveld profile fit for a Na22Si136 specimen. (a) indicates the different components of the profile plot, while (b) shows a blown-up section from (a), showing the quality of the peak fitting in the region displayed. Difference Pattern Measured (Observed) Data Calculated Pattern Reflection Positions a b
130 charge (Ref. A5). In the present work, the General Structure Analysis System (GSAS) software suite developed (Ref. A6) by A. C. Larson and R. von Dreele and was used, along with the EXPGUI graphical user inte rface to GSAS, developed by Dr. Brian Toby (Ref. A7). A.2 Extended X-ray absorpti on fine structure (EXAFS) EXAFS has in the last several decad es become an increasingly employed technique for gleaning useful information abou t local structure in a material. As opposed to a diffraction experiment, which yields aver aged microscopic structural information, EXAFS is an element selective technique that yields local structural information about the environment of the atomic species whose absorption edge is be ing investigated. An introduction to the principles as well as a pproaches to modeling of EXAFS spectra can be found in Ref. A8. In an X-ray absorption spectroscopy (XAS) experiment, the energy of an incident beam of monochromatic X-rays (e.g. from a synchrotron source) is varied, while the transmission though the specimen is monitored. As an absorption edge for a particular atomic species in the material is transversed, the absorption coefficient of the material containing that species will exhibit a sharp rise, due to electronic ionization (i.e. the photoelectric effect) from the associated core energy level. As the incident photon energy is further increased above the edge, characteri stic oscillations are observed; these are the XAS features of interest, the Â“fine structure.Â” An essential principle behind the mechanisms responsible for the EXAFS oscillations observed in the ab sorption coefficient is the effect of scattering on the excited photoelectron. The excited photoelectron (due to its wave nature) is scattered by neighboring atoms (shown schematically in Figur e A.2), resulting in interference between outgoing and scattered waves at the source (i.e. the absorbing atom). This interference can be constructive or destructive depe nding and the electron wavelength and nearest neighbor distances. Thus the EXAFS signal c ontains information about these distances around the central absorbing atom. As a result of considerable theoretical efforts in recent
131 Figure A.2 Simplified schematic, after Rehr and Albers (R ef. A.8), illustrating multiple scattering events for an excited photoelectron. The darker colored Â“waveÂ” at upper left represents the initial outgoing excitation. decades, a well developed theory of the processes underling EXAFS has emerged (Ref. A8). As such, established computer programs are available which allow for fitting the EXAFS data using structural models, and can in turn allow very useful information concerning the local environment of th e absorbing atom to be obtained. A.3 Transport properties measurements All transport properties measurements re ported in this work were measured on our custom designed measurement system. Th e details of the design and implementation of this system, as well as the typical speci men mounting procedure, are found in Refs. A9 and A10. A closed cycle helium cryostat allo ws measurement of electrical resistivity ( ), Seebeck coefficient ( S ), and thermal conductivity ( ) from 12 K to 320 K, on a single specimen, in a single measurement cycle. The transport system was extensively tested by measurement of several Standard Referen ce Materials (SRM) obtained from the National Institute of Standards and T echnology (NIST), as well as in ter-laboratory verification of measurements through comparison with othe r established measurement systems in industrial and uni versity labs.
132 Schematics illustrating the measurement of the three transport coefficients are given in Figure A.4. Electri cal resistivity is measured by a four-probe method. A small known current (typically ~ 5 mA) is passed through the specimen, and the voltage difference ( V ) measured between two points a known distance apart. is then determined from OhmÂ’s Law and the geometry of the sample as shown in Figure A.4a. To eliminate possible thermoelectric contributions to V data is acquired with current sourced in both directions, with fast switching of the current directi on, and the results are averaged. Temperature gradients for measurement of S and are applied by a small chip resistor attached to one end of the specimen, which acts as a heat source. S is measured by sweeping the temperature gradient, a nd measuring the voltage difference ( V ) and temperature difference ( T ) at two points in a plane perp endicular to the axis of the specimen. S is then determined from the slope of a plot of V vs. T i.e. S = dV / dT as shown in Figure A.4b. For the case of measuring several temperature gradients are applied to the specimen, and the slope of a plot of the power vs. the measured T yields the thermal conductance. is then determined from this conductance and the geometry of Figure A.4 Schematics illustrating the measurement of tran sport properties: (a) Four-probe resistivity, (b) Seebeck coefficient, S and (c) thermal conductivity, a b c A I V R dT dV S T A P
133 the sample. The power ( P ) passing through the specimen is assumed to be equal to the power generated by the heater ( Pheater), which is calculated from Pheater = IheaterVheater. The total measurement relative uncertainty at room temperature for S and are estimated to be 4%, 6%, and 8%, respectively (Ref. A10). Appendix References A1. H.M. Rietveld, Acta Crystallogr. 22, 151 (1967). A2. H.M Rietveld, J. Appl. Crystallogr. 2, 65 (1969). A3. V.K. Percharsky and P.Y. Zavalij, Fundamentals of Powder Diffraction and Structural Characterization of Materials Springer, New York, 2005. A4. R.A. Young, The Rietveld Method Oxford University Press, Oxford, 1995. A5. See http://www.ccp14.ac.uk/ for an extensive repository. A6. A.C. Larson and R.B. Von Dreele, "General Structure Analysis System (GSAS)", Los Alamos National Laborator y Report LAUR 86-748 (2004). A7. B.H. Toby, J. Appl. Cryst. 34, 210 (2001). A8. J.J. Rehr and R.C. Albers, Rev. Mod. Phys. 72, 621 (2000). A9. J. Martin, M.S. Thesis, University of South Florida, 2005. A10. J. Martin, Ph.D. Dissertation, Univ ersity of South Florida, 2008.
About the Author Matt Beekman received his B.S. and M.S. degrees in Physics in 2003 and 2006, respectively, from the University of Sout h Florida. Mr. Beekman entered the Ph.D. program in Applied Physics as a USF Pres idential Fellow in 2003. While in the Ph.D. program at USF, he has authored or co-aut hored more than seve nteen peer reviewed journal publications and twelve confer ence proceedings, and has given several presentations on his research at meetings of the MRS, ITS, ACS, and ACerS. In recognition of his research accomplishm ents, Mr. Beekman has received the 2008 ITS Goldsmid Award for Excellence in Research in Thermoelectrics by a Graduate Student the 2006 USF Outstanding MasterÂ’s Thesis Award and several student presentation awards at international scientific conferences.