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Synthesis and physical properties investigations of open-framework intermetallic clathrates
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by Stevce Stefanoski.
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Thesis (M.S.)--University of South Florida, 2010.
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ABSTRACT: Intermetallic clathrates have long been of interest for materials science research. The promise these materials hold for useful applications ranges from thermoelectrics to photovoltaics and optoelectronics to potentially ultra-hard materials and magnetic cooling applications. Their unique physical properties are intimately related to their intriguing structural properties. Thus a fundamental understanding of the chemistry and physics of inorganic clathrates offers the possibility to assess their potential for use in the various applications mentioned above. The purpose of the current work is to expand the current knowledge of the synthetic routes for obtaining clathrate materials, their structural, chemical, and physical properties, particularly those that from in the type I, II and VIII crystal structures. New synthesis routes are presented and used for preparation of single crystals of Na8Si46 and Na24Si136. Single-crystal X-ray analysis, and resistivity, Seebeck coefficient and thermal conductivity measurements are presented. In addition, two "inverse" clathrates with compositions Sn24P19.3Br8 and Sn17Zn7P22Br8 have been characterized in terms of their transport properties. Since the magnetic refrigeration based on the magnetocaloric effect is a topic of great interest, type VIII Eu8Ga16Ge30 clathrates are also explored in terms of their application for magnetic cooling.
Advisor: George S. Nolas, Ph.D.
t USF Electronic Theses and Dissertations.
Synthesis and Physical Properties Investigations of Intermetallic Clathrates by Stevce Stefanoski A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Physics College of Arts and Sciences University of South Florida Major Professor: George S. Nolas, Ph.D. Lilia Woods, Ph.D. Martin Muoz, Ph.D. Date of Approval: April 12, 2010 Keywords: single crystal, transport propert ies, silicon, thermoelectrics, Seebeck Copyright 2010, Stevce Stefanoski
Dedication I dedicate this work to my par ents, Angele and Vera Stefanoski for their support and love that gives me a strength to accomplish my goals.
Acknowledgements I would like to express my grat itude and appreciation to Dr. George S. Nolas for allowing me to become a part of his research group. Working with him as one of the best known experts in the thermoelectric field is a pleasur e, and a challenge. I would like to thank all of my lab fellows, current and previous for all the insightful ques tions, suggestions and advices. I wish to express my deep appreciation to Dr. Matt K. Beekman for many insightful discussions, and guiding me through the resear ch process. I also thank him for his cooperation as a post-doctoral fellow at Univ ersity of Oregon. Sincere thanks to Dr. Joshua Martin for the numerous constr uctive suggestions and advices during the beginning days of my graduate school, and for the current fruitful cooperation with him at NIST which resulted in measurin g the heat capacity of the type I Na8Si46crystals. I thank Dr. Winnie Wong-Ng from NIST for doing the single-crys tal diffraction on the Na8Si46 and Na24Si136 single crystals. My gratitude al so goes to Dr. Andrei V. Shevelkov from the Moscow State University for providi ng me the materials for Chapter 4, as well as for the many insights I got during our communication. I thank Dr. Phan and Dr. Hariharan for performing the measurements on the Eu8Ga16Ge30 in Chapter 5 of this work and the constructive discussions on ma gnetic properties of the materials. I would also like to acknowledge the fundi ng from the University of South Florida Functional Multiscale Material s by Design (FMMD) fellowship for giving me freedom to focus on my research during two ye ars of my graduate career.
i Table of Contents List of Tables ................................................................................................................ ... iii List of Figures ............................................................................................................... .... v Abstract ...................................................................................................................... ....... x 1. Introduction ............................................................................................................... .... 1 1.1 Type I, II and VIII Clathrates ......................................................................... 2 1.2 Synthesis and Crystal Structur e of Type I Clathrates ..................................... 3 1.3 Electronic and Thermal Properties of Type I Clathrates ................................ 6 1.4 Synthesis and Crystal Structur e of Type II Clathrates .................................. 12 1.5 Electronic and Thermal Propertie s of Type II Clathrates ............................. 17 1.6 Clathrates for Thermoel ectric Applications .................................................. 20 2.1 Synthesis and Structural Characterization of Na8Si46 ............................................... 23 2.2 Transport Properties of Na8Si46 ................................................................................ 30 3.1 Synthesis and Structural Characterization of Na24Si136 ............................................ 41
ii 3.2 Transport Properties of Na24Si136 Single Crystals .................................................... 49 4. Resistivity, Seebeck Coefficient and Thermal Conductivity of Sn24P19.3Br8 and Sn17Zn7P22Br8 .............................................................................. 54 5. Type VIII Eu8Ga16Ge30 Clathrates For Magnetic Applications .................................. 63 5.1 Magnetocalloric Effect (MCE) ..................................................................... 63 5.2 Crystal Structure of type VIII Eu8Ga16Ge30 Clathrate .................................. 65 5.3 Synthesis of Type VIII Eu8Ga16Ge30 ........................................................... 66 5.4 Type VIII Eu8Ga16Ge30 Clathrate for Magnetocaloric Applications ............ 68 References .................................................................................................................... ... 73
iii List of Tables Table 1.1 Type-II clathrates, synthesi s methods and lattice parameters Â…Â…Â…..Â….16 Table 2.1 Crystal data and structure refinement for Na8Si46 single crystal XRDÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….....28 Table 2.2 Atomic coordina tes and equivalent isotropic atomic displacement parameters (2) for Na8Si46Â…Â…Â…Â….Â…Â…Â…Â…Â…Â…..Â…..29 Table 2.3 Anisotropic atomic displacement parameters (2) for Na8Si46Â…Â…Â….....29 Table 2.4 Bond lengths () for Na8Si46Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….Â…29 Table 2.5 Comparison of th e room temperature resistivities and residual resistance ratios RRR= R (300 K)/ R ( T0) for the Na8Si46 specimen of the present work and several intermetallic clathrate specimens of type I showing me tallic or Â“metallic-likeÂ” resistivities (i.e. d/ dt is positive definite over the entire temperature interval of measurement). T0 is the lowest temperature at which the corresponding resistivity was reported..Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…...Â…Â…Â…Â…Â…..Â…...33 Table 2.6 Fitting parameters for the ( CpCD)/ T 3 curve, according to two different models. The free parameters in each model are shown in brackets. The De bye temperature was fixed to D=590 KÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…...36
iv Table 2.1 Crystal data and structure refinement for Na8Si46 single crystal XRDÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…46 Table 3.2 Atomic coordinates and equivalent* isotropic atomic displacement parameters (2) for Na24Si136Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…...Â…...Â…Â…Â…47 Table 3.3 Anisotropic atomic displacement parameters* (2) for Na24Si136Â…Â….....47 Table 3.4 Bond lengths () for Na24Si136Â…Â…Â…...Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…47 Table 3.5 Comparison of the room temperature resistivities and residual resistance ratios RRR= R (300 K)/ R ( T0) for the Na24Si136 specimen of the present work and several intermetallic clathrate specimens of type II showing metallic or Â“metallic-likeÂ” resistivities (i.e. d/ dt is positive definite over the entire temperature interval of measurement). T0 is the lowest temperatur e at which the corresponding resistivity was reported. Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….51 Table 4.1 Fit Parameters for the Two Polycrystal line Sn-ClathratesÂ…Â…Â…Â…..........62
v List of Figures Figure 1.1 Crystal structure of type I clathrates. The cubic unit cell is composed of two pentagonal dodecahedra ( E20) and six tetrakaidecahedra ( E24)Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…........4 Figure 1.2 a) and b) S versus temperature for three n -type Sr8Ga16Ge30 specimens with different Ga-to-Ge ratios but with same Sr concentr ations resulting in varyin g carrier concentrationsÂ…Â…Â…Â…Â…Â…..6 Figure 1.3 a) L for several representative type I clathrates b) Â“Glass-likeÂ” for Sr8Ga16Ge30Â…Â…Â…Â…Â…Â…Â…Â…..Â…Â…Â…Â…..Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…8 Figure 1.4 Isotropic atomic displ acement parameters (ADPs) for Cs8Zn4Sn42Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….Â…Â…10 Figure 1.5 Stokes Raman scattering spect ra for selected type I clathrates. The vibrational modes of the filler atoms are indicated by arrowsÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….....11 Figure 1.6 Crystal structure of type II clathrates. The cubic unit cell is composed of sixteen pentagonal dodecahedra ( E20) and eight hexacaidecahedra ( E28)Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…...Â…Â….....13 Figure 1.7 S (round symbols) and (triangular symbols) as a function of temperature fo r polycrystalline Cs8Na16Si136 (open symbols) and Cs8Na16Ge136 (filled symbols). Inset: DFT computed
vi EDOS for Cs8Na16Si136 (lower) and Cs8Na16Ge136 (upper). The dashed line indicates the Fermi level, which is well within the conduction band for both materialsÂ…Â…Â…Â…...Â…Â…Â…Â…Â…Â…Â…..Â….18 Figure 1.8 Temperature dependent isotropic atomic displacement parameters (Uiso) for the E28 guest as well as framework sites in A8Na16E136 (A = Rb, Cs; E = Si, Ge)Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….....19 Figure 1.9 as a function of temperat ure for polycrystalline Si136 and a -SiO2. The solid line indicates a temperature dependence of T 3Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….20 Figure 1.10 ZT as a function of temper ature for three type-I clathratesÂ…Â…Â…Â…...Â…22 Figure 2.1 a) The structure of the Zintl precursor Na4Si4 b) An SEM image of a Na8Si46 single crysta l synthesized by the Novel technique Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….Â…....24 Figure 2.2 X-ray diffraction pattern for the type I Na8Si46 clathrateÂ…Â…Â…Â…..Â…....25 Figure 2.3 Schematic diagram of th e two building polyhedral cages in the Na8Si46 structure. The four Si-Si distances and the eight non-equivalent bonding angles are indicated. The numbers 1-3 indicate the three dis tinct crystallographic sites 24 k 6 c and 16 i at which the framework atoms resideÂ…Â…Â…Â…Â…Â…......26 Figure 2.4 Measuring the transport prope rties of a type-I single crystalÂ…Â…Â…Â…....30 Figure 2.5 and S for a single crystal of Na8Si46Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…...32
vii Figure 2.6 Thermal conductivity for Na8Si46 single crystals (filled circles) and microcrystalline powder (empty circles)Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…35 Figure 2.7 Heat capacity for single crystal Na8Si46. The inset shows Cp ( T ) versus T 2 below T =7 KÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…..36 Figure 2.8 Temperature depende nce of the lattice contribution to the specific heat Cph plotted as Cph/ T 3 vs T The inset shows l for a single crystal Na8Si46Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…....38 Figure 2.9 Temperature depe ndence of the lattice contribution to the specific heat Cph plotted as Cph/ T 3 vs T b) Temperature de pendence of the mean free path for single crystal Na8Si46Â…Â….Â…Â….40 Figure 3.1 X-ray diffraction pattern for the type I Na8Si46 clathrate Miller indices are assign ed to every reflection Â…Â…Â…Â…Â…..Â…Â…Â…Â…...42 Figure 3.2 SEM image of Na24Si136 single crystals obtained by the Novel methodÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…..Â…...43 Figure 3.3 Formation of different phases at different temperatures starting from a same precursor Na4Si4Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…...44 Figure 3.4 Schematic diagram of the two building polyhedral cages in the Na24Si136 structure. The four Si-Si distances and the seven non-equivale nt bonding angles are indicatedÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…....45 Figure 3.5 A photograph of a mounted single crystal Na24Si136 for transport properties measurementsÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…49
viii Figure 3.6 (empty circles) and S (filled circles) for a single crystal of Na24Si136Â…Â…Â…Â….................................................................................50 Figure 3.7 Thermal conductivity of Na24Si136 single crystals in comparison with polycryst alline clathrate materialsÂ…Â…Â…Â…Â…Â…Â…..Â…52 Figure 4.1 Crystal structur e of type I clathrate. The open circles represent th e guest Br atoms occupying the polyhedra formed by Sn, P, and Zn. The filled circles are the 6 c and 16 i crystallographic positions and th e gray circles represent the 24 k crystallographic positionÂ…................................Â…Â…Â…Â…Â…Â…Â…Â…........55 Figure 4.2 Coordination of the metal atoms in Sn24P19.3Br8. The Sn(32)Â–Sn(32) bonding is shown in grayÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…...56 Figure 4.3 Coordination of the atoms in Sn17Zn7P22Br8Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….....56 Figure 4.4 Electrical conductivity for (a) Sn24P19.3Br8 and (b) Sn17Zn7P22Br8Â…Â…..58 Figure 4.5 S for Sn24P19.3Br8 (black circles) and Sn17Zn7P22Br8 (open squares)Â…Â….59 Figure 4.6 L for Sn24P19.3Br8 (filled circles) and Sn17Zn7P22Br8 (open squares). The straight lines are fits to the data employing Eqs. 1 and 2Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…..61 Figure 5.1 Schematic representation of a magnetic refrigeration cycleÂ…Â…Â…Â…Â…..64 Figure 5.2 Crystal structure of type VIII Eu8Ga16Ge30Â…Â…Â…..Â…Â…Â…Â…Â…Â…Â…Â….65
ix Figure 5.3 XRD patterns for type I (a) and type VIII (b) phasesÂ…Â…Â…Â…Â…Â…Â…....67 Figure 5.4 Magnetization curves ta ken at 0.01 mT with increasing (heating) and decreasing (cooling) temperature. The corresponding dM / dT curve for the heating branch is also overlaid to mark the transition temperature. The inset shows the magnetization cu rves taken at applied fields of 1, 2, and 3 TÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…...68 Figure 5.5 a) Magnetization isothe rms measured at different temperatures between 5 and 53 K with 3 K interval. b) The H / M vs M 2 plots for represen tative temperatures around the TCÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….Â…....69 Figure 5.6 Magnetic entropy change SM as a function of temperature ( T) extracted from M H T curves via the Maxwell relation. The inset shows the hyste resis loop measured at 5 KÂ…Â…Â…Â…Â…Â…Â…....71
x Synthesis and Physical Pr operties Investigations of Intermetallic Clathrates Stevce Stefanoski ABSTRACT Intermetallic clathrates have long been of interest for materi als science research. The promise these materials hold for useful a pplications ranges from thermoelectrics to photovoltaics and optoelectronics to potentially ultra-hard ma terials and magnetic cooling applications. Their unique physical properties are intimately related to their intriguing structural properties. Thus a fundamental understanding of the ch emistry and physics of inorganic clathrates offers the possibility to assess their potential for use in the various applications mentioned above. The purpose of the current work is to expand the current knowledge of the synthetic routes for obtaining cl athrate materials, their stru ctural, chemical, and physical properties, particularly those that from in the type I, II and VIII crystal structures. New synthesis routes are presented and used fo r preparation of sing le crystals of Na8Si46 and Na24Si136. Single-crystal X-ray analysis, and resi stivity, Seebeck coefficient and thermal conductivity measurements are presented. In addition, two "inverse" clathrates with compositions Sn24P19.3Br8 and Sn17Zn7P22Br8 have been characterized in terms of their transport properties. Since the magnetic refrig eration based on the ma gnetocaloric effect is a topic of great in terest, type VIII Eu8Ga16Ge30 clathrates are also explored in terms of their application for magnetic cooling.
1 1. Introduction The term clathrate is derived from the Latin word Â“clathratusÂ” meaning Â“furnished with a latticeÂ”. Clathrates are compounds formed by inclusion of atoms or molecules of one type into cavities of a seque stering crystal lattice of another. The first known clathrate compound, the chlorine-wat er molecule, was di scovered by Humphry Davy in 18111 and, together with the analogous compounds discovered later, were termed Â“gas hydratesÂ” because they entrap ga s molecules in ice. Research undertaken by Kasper et al.2 reported the existence of the clathrate phase Na8Si46 which was isomorphic with that of the gas hydrates. Furt her investigations by Cross et al.3 and Gallmeier et al.4 revealed new structures with frameworks co mposed of Ge, Si or Sn atoms encapsulating alkaline atoms. Einsmann et al.4 synthesized the ternary compounds A8B16E30 (A=alkaline metal; B=Ga, Al; E=Si, Ge, Sn). In the early 1990s, the U.S. Department of Defense (DoD) initiated a program to sear ch for new materials with potential for thermoelectric applications. One approach ta ken by the scientific community was to discover novel bulk-materials that comply with the Â“Phonon-Glass Electron-Single CrystalÂ” (PGEC) concept introduced by Slack.5 According to this concept, a good thermoelectric material would possess a low (Â“glasslikeÂ”) thermal conductivity, typical of amorphous materials, hi gh electrical conductivity, similar to metals, and high Seebeck coefficient, S akin to semiconductors. Certai n clathrates are materials that exhibit such properties.6-8 They possess atomic-sizes voids that can encapsulate heavyions that undergo large anharmonic vibr ations (Â“rattlingÂ”) and scatter phonons effectively, while their electrica l properties vary with doping. The first transport characterization on Si and Ge clathrate compounds was made by Nolas et al.6. They reported on these materials to have temperature dependences and amplitudes similar to amorphous materials, pure amorphous Ge in particular. Besides having a low these materials possess other interesting properties9 that are of interest for a range of applications. Most of the known clathrates to date are composed of group 14 elements.6,8 In addition to their ground state conf iguration, there is a variety of highly stable binary,2,10,11 ternary,4,12,13 and quaternary clathrates.14,15
2 From a chemical and physical viewpoint, clathrate materials allow for the study of compounds possessing isomorphic structures w ith greatly varying properties, ranging from metals13 to semiconductors16 to superconductors,17,18 while other compositions have been studied for their magnetic properties19,20 (cf. Chapter 5). The unconventional properties displayed by these materials, such as the aforementioned glass-like 16 and the heavy atom tunneling in the crystalline state,21-23 comprise novel physical phenomena in crystalline solids. The promise these material s hold for useful applications ranges from thermoelectrics24,25 to photovoltaics and optoelectronics26-29 to potentially ultra-hard materials30 and magnetic coo ling applications.19,20 All of these unique physical properties are intimately related to thei r intriguing structural prope rties. Thus a fundamental understanding of the chemistry and physics of inorganic clathrates offers the possibility to assess their potential for use in th e various applications mentioned above. 1.1 Type I, II and VIII clathrates The term Â“clathrateÂ” refers to inclusi on compounds in general, though there is a variety of crystal structure types amongst the known clathrate materials. There exist nine distinctive types of clathrate structure types,9 of which types I, II a nd VIII are considered in this work. Clathrates generally consist of a covalently-bonded framework composed of a group-14 elements (Si, Ge and Sn)6,31-33 encapsulating alkaline metals (Na, K, Rb. Cs)34,35, alkaline earth metals (Ba, Sr)36 or Lanthanides (Eu).19,20 The framework of the various types of clathrates can be thought of being built by different polyhedral Â“cagesÂ”. Type I clathrates form in the Pm 3 n space group and consist of two types of polyhedra, dodecahedra ( E20) and tetrakaidecahedra ( E24).9 The frameworks of the type II clathrates are comprised of dodecahedra ( E20) and hexacaidecahedra ( E28),38 and their crystal structure is Fd 3 m Type VIII clathrates form only one (distorted) pentagonal dodecahedra with the space group I 43 m .14
3 1.2 Synthesis and crystal stru cture of type I clathrates The type I clathrate structure is represented by the general formula A8E46, where A are alkali metals or alkaliearth atoms, and E are the grou p 14 elements Si, Ge or Sn.9 Type I ternary compounds with general formula A8B16E30 where B is Zn, Cd, Al, Ga, In, As, Sb or Bi4,12,13 also exist. For these compounds, th e bonding is analogous to that of Zintl-phases38, where the more electropositive gu est atoms donates their valence electrons to the more electronegative host at oms resulting in a cl osed-valence shell. These valence electrons form the covalent ly bonded face-sharing host framework. The type I clathrate crystal structure compri ses two 20-membered pentagonal dodecahedra E20, each formed by twelve pentagonal faces (Figure 1.1) creating a void with 3m symmetry, and six 24-membered tetrakaidecahedra E24, formed by twelve pentagonal and two hexagonal faces, each creating a void with 4 m 2 symmetry.4,31 The corresponding unit cell is cubic with space group Pm 3 n The group 14 framework at oms reside at three distinctive sites, 6 c 16 i and 24 k while the Â“guestÂ” atoms are encapsulated at 2 a and 6 d sites inside the E20 and E24, respectively. Analogous to their diamond structured compounds,39 the E-E-E bonds range from 105 to 126, averaging the ideal sp3 hybridization angle9 of 109.5. The clathrate structure deviates from the diamond structured counterpart in th eir larger average interatomi c distances and larger (~15%) volume per group 14 atom, demonstrating th e Â“opennessÂ” of the clathrate crystal structure.9
4 Figure 1.1 Crystal structure of type I clathrates The cubic unit cell is composed of two pentagonal dodecahedra ( E20) and six tetrakaidecahedra ( E24). Reprinted with permission from Ref. 9 Copyri ght , American Institute of Physics. Type I clathrates have been the most st udied clathrate type to date. There are a few excellent reviews on the structure and the properties of these materials.9,40-42 In this work we are going to outline some of the most conspicuous aspects of the type I clathrates, regarding their st ructure, their relevance for thermoelectric applications24,25 and the related discovery of the rather unconve ntional heat transport, for a crystalline solid.16 Cross et al.2 first reported the synthesis of type I clathrates with a structure similar to that of the gas hydrates. They synthesized Na8Si46 by thermal decomposition of alkali silicides under high va cuum. Einsmann et al.4 first synthesized ternary compounds A8B16E30 (A=alkaline metal; B=Ga, Al; E=Si, Ge, Sn) by mixing stoichiometric quantities of the pure elements in alumina cr ucibles. The mixtures were slowly heated under argon atmosphere at a rate 2C/min up to a maximum temperature of 1150C for
5 Si, 1050C for Ge and 850C for Sn mixtures and kept there for an hour before slow cooling to room temperature. Some stoichiometric mixtures melt congrue ntly at certain temp eratures. This was used in the direct synthesis of certa in type I clathrates. Phan et al.19 synthesized type I Eu8Ga16Ge30 by reacting stoichiometric ratios of the high purity elements in boron nitride (BN) crucible, sealed under nitrogen in a quartz tube, in an induction furnace at 1100 0C followed by rapid water quenchi ng. Single crystals of the halogen-filled clathrate I8As8Ge38 were grown by Chu et al43 by vapor deposition in a two-zone furnace. The stoichiometric mixtures were enclosed in a sealed fused silica tube. Ge was kept at a temperature between 720 and 730C, and As at a temperature between 600 and 610C. Nolas et al.36,45 grew single crystals of Sr8Ga16Ge30 and Eu8Ga16Ge30 by mixing and reacting stoichiometric quantities of the high purity elements and holding them for 3 days at 950C inside a BN crucible that was itself s ealed in a fused quartz ampoule that was evacuated and back filled with argon. The ampoule was then slowly cooled to 700C where it was left for 4 days. It was then slowly cooled to room temperature. The crystals of various Sn clathrates were synthesized by Nolas et al.46 by mixing and reacting the constituent elements for 2 weeks at 550C inside a tungsten crucible that was itself sealed inside a stainless steel canist er, after the canister was evacuat ed and backfilled with highpurity argon. The resulting Sn clathrates cons isted of small octahedr al shaped crystals with a shiny, somewhat blackish, me tallic luster. Chakoumakos et al.47 grew single crystals of Sr8Ga16Ge30 by first arc-melting high purity Sr and Ge together in an argon atmosphere to form SrGe2. Then they loaded stoichiometric amounts of SrGe2, Ga shot and Ge in a helium dry box into a carbonized silica tube. The constituents were then heated to 1050C at 2C/min, held at 1050C for 20 hours, and then slowly cooled to 650C, where they were held for several days, and finally cooled down to room temperature. Single crystals 5-10 mm in length were obtained. Reny et al.48 synthesized the type I clathrate I8Si46xIx, the first clathrate to be filled with an electronegative element. Another interesting as pect of this material is th at the iodine can be found both on the framework site and as the interstitial atom.
6 1.3 Electronic and thermal prope rties of type I clathrates Inorganic clathrates show a rich varia tion in their electric properties. In a simplified model, the valen ce electrons from the guest atoms are donated to the framework conduction bands. If charge comp ensation is not accomplished by substitution on the framework sites, metallic transport is expected.49,50 Maudryk et al.50 has characterized a series of Ba and Eu substitute d type I clathrates, including Cu-stabilized variants, with various framework substitutions. These include Al, Ga or In atoms occupying Si or Ge host sites. The temperatur e dependence of the electrical resistivity, is typical for metallic materials. The negative S throughout the entire temperature range may be an indication that the majority carriers in these compounds are electrons. A number of type I clathrates ha ve been found to have semiconducting properties.6,9,40,51 Nolas et al.6 measured (Figure 1.2a) and S (Figure 1.2b) of Sr8Ga16+ xGe30x, where x is varied slightly.
7 Figure 1.2 a) and b) S versus temperature for three n -type Sr8Ga16Ge30 specimens with different Ga-to-Ge ratios but with same Sr concentrati ons resulting in varying carrier concentrations.6 Reprinted with permission from Ref. 6 Copyri ght , American Institute of Physics. The ability to vary the d oping level of these semiconduc tor compounds by varying the chemical composition is one reason why th ey are of interest for thermoelectric applications. Ga shows a strong preference for the 6 c site and a weaker preference for the 24 k site.52 The observed Ga distribution has implications for the bonding in these materials, suggesting some Ga(6 c )-Ga(24 k ) bonds. The doping level of this series of specimens was varied by changing the Ga-t o-Ge ratio while maintaining a fixed Sr concentration. S decreases with increasi ng the carrier concentra tion, as shown in Figure 1.3b, and also decreases with decreasing te mperature as expected in heavily doped semiconductors with negligible phonon drag. This form of substitution didnÂ’t produce p type conduction, however subst ituting Zn for Ge does produce p -type semiconductors.9,53 The mobility in these specimens is relatively high, ranging from 730 to 2200 cm2/V. Blake et al.52 estimated the bang gaps for Sr8Ga16Ge30 and Ba8Ga16Ge30 to be 0.3 eV and 0.6 eV, respectively, and the larger band gap for Ba8Ga16Ge30 resulting in and better thermoelectric performance.54 a) b)
8 The guest-host interaction in clathrate materials directly determines the unique properties in these material s. The guest atom is weakly bonded to the framework9 and can Â“rattleÂ” creating a strong phonon scattering center, which has a dramatic effect on the thermal conductivity of the clat hrate materials. Figure 1.3a de monstrates the difference in temperature dependent la ttice thermal conductivity, L for several type I clathrates.9 Figure 1.3 a) L for several representative type I clathrates9 b) Â“Glass-likeÂ” for Sr8Ga16Ge30 9 Reprinted with permission from Ref. 9 Copyri ght , American Institute of Physics. A comparison of guest atomÂ’s radii (1.17 for Eu2+ and 1.18 for Sr2+)56 with polyhedra size suggest that smaller ions may Â“r attleÂ” more effectively within their cages and thus scatter phonons and s uppress the thermal conductivit y. It is apparent from Figure 1.3a that Eu8Ga16Ge30 possesses an amorphous-like L lower than Sr8Ga16Ge30, due to the smaller atomic radius for Eu2+ and the larger mass (almost twice as massive). The difference in L of Eu8Ga16Ge30 and Cs8Sn44 is even more pronounced due to the much larger atomic radius of Cs1+ (1.70 ).56 L for Cs8Sn44 varies as T -1 and is typical of a crystalline semiconductor dominated by umklapp-scattering. Additional bonding is introduced between Cs and Sn atoms neighboring the vacancies in Cs8Sn44 such that it a) b)
9 constrains the Cs atoms. In the case of Sr4Eu4Ga16Ge30 there are two different atoms enclosed inside the polyhedra that introduce six different sca ttering frequencies, three for each atom. This compound exhibits the lowest L in the temperature range shown, tracking the temperature dependence of a-SiO2 very closely. L of Ba8Ga16Si30 is relatively low, however with temperature de pendence different from the one of the Geclathrates. Even though Ba2+ is more massive than Ga and Si, it is similar in size with Si20 and Si24 cages, whereas Sr2+ and Eu2+ are smaller than the Ge cages. Thus the temperature dependence is similar to that of a crystalline so lid, exhibiting a massfluctuation scattering.9 One of the most interesting and important discoveries in terms of thermoelectrics was the magnitude and the temperature dependence of L of Ge clathrates. Figure 1.3b shows the temperature dependence of for Sr8Ga16Ge30.57 The magnitude and temperature dependence are similar to that of amorphous material. The low temperature (<1 K) data indicates a T 2 temperature dependence, as s hown by the straight-line fit to the data in Figure 1.4b. Although the values exceed those of amorphous Ge ( a -Ge) at room temperature, they are sm aller than amorphous quartz ( a -SiO2) above 100 K. The low-frequency acoustic phonons ha ve the highest group velocity54 and contribute most to Temperature dependent single crystal a nd powder neutron diffraction experiments have been used by Nolas et al.46 and Chakoumakos et al.47 and the isotropic atomic displacement parameters (ADPs) were reported (Figure 1.4).
10 Figure 1.4 Isotropic atomic displacemen t parameters (ADPs) for Cs8Zn4Sn42 46 Reprinted with permission from Ref. 64 Copyri ght , American Institute of Physics. Cs1 and Cs2 represent the filler atoms that occupy the 2 a and 6 d sites. As shown in the figure the Cs2 atoms have much larger ADPs than those of the framework atoms. In addition to this, the temperature dependence of the ADPs for the Cs2 atoms is greater than that of the framework atoms. Nolas et al.58 have also employed Raman scatte ring to study type I clathrates (Figure 1.5). From crystal symmetry consid erations and group theory, the Raman active modes can be determined for both the framewor k and the guest atoms in the clathrates. It was found that the guest atom at the 6 d site contributes two Raman active modes.
11 Figure 1.5 Stokes Raman scattering spectra for selected type I clathrates. The vibrational modes of the filler atoms are indicated by arrows.58 Reprinted with permission from Ref. 58, Copyright , American Physical Society. A theoretical investigation of the Â“rattlingÂ” guest atoms in type I clathrates, offered by Dong et al,59 supports the idea of strong interactio n between the locali zed modes of the guest atoms and the heat-carry ing phonons, resulting in a low in the semiconducting clathrates.
12 1.4 Synthesis and crystal stru cture of type II clathrates The crystal structure of the type II clathr ates is face-centered cubic, with the Fd 3 m space group. Two types of face-sharing polyhedr a participate in the structure of the type II clathrates, sixteen 20-membered pentagonal dodecahedra ( E20, point symmetry Ih) and eight 28-membered hexacaidecahedra ( E28, point symmetry Td) per unit cell (Figure 1.6). The pentagonal dodecahedra contain twelve pentagonal faces, whereas the hexacaidecahedra contain twelve pentagonal and four hexagonal faces. All of the atoms participating in the structure of the type II clathrates are tetrahedrally ( sp3) coordinated. The average number of atoms per ring is 5.064 and is the smallest for any known structure.60 There are five distinct crystallographic sites: 96 g 32 e and 8 a (in the Wyckoff notation) for the framework atoms, and 8 b and 16 c at which the host atoms reside inside the polyhedra. The general formula fo r the type II clathrates is A8B16E136 (A = guest in E28, B = guest in E20, and E = Si, Ge, Sn or substituents). The crystal structure of the type II clathrates can be viewed as dual to the MgCu2 structure, if the 16 c sites in the E20 cages are substituted by Cu atoms, and the 8 b sites in the E28 cages are substituted by Mg atoms.41,61-64 We may think of the type II clathrates as of expanded forms of Si, Ge or Sn. The volume per framework atom is as much as 20% larger in the clathrat e structure relative to the diamond structure, although the bond lengt hs, in both the diamond and the type-II clathrates, are relatively close. This open st ructure is responsible for some of the unique properties of these materials, as de monstrated in the next section.
13 Figure 1.6 Crystal structure of type II clathr ates. The cubic unit cell is composed of sixteen pentagonal dodecahedra ( E20) and eight hexacaidecahedra ( E28).9 Reprinted with permission from Ref. 9 Copyri ght , American Institute of Physics. The first of the inorganic cl athrates discovered by far are NaxSi136 (0 < x < 24). Kasper et al.2 prepared these compositions via thermal decomposition of the Zintl compound Na4Si4. 2,310,65-68 Na4Si4, which is monoclinic with space group C 2 /c was synthesized by direct reaction of the elements mixed in stoichiometric ratio. The final product is grayish polycrystalline material that is extremely air and moisture sensitive, thus the handling must be performed in N2 or Ar-glove box. The sodium content x is controlled by varying both the temperature and time, longer times and higher temperature yielding lower sodium contents. Several refl ections from the X-ray diffraction exhibit strong dependence upon sodium content, thus allowing for determination of the sodium content and the relative cage o ccupancy by the Rietveld method.66,67 Gryko et al.40 showed that after rep eated degassing of the NaxSi136 and treatment with concentrated acids, it is possible to synthesize and Â“empty cageÂ” of Si136, with sodium content less than 600 ppm Si. Further reduction of the sodi um content was achieved by Ammar et al.71 by reaction of the clathrate with iodine, resulting in sodium content less than 35 ppm Si.
14 Experimental observations72,73 have shown that the Si136 framework is stable under pressure up to 11 GPa. No transition to the diamond phase is observed, but an irreversible transition to the -Sn structure of silicon was observed at 11.5 GPa, accompanied by a volume reduction of more than 30%. A challenge in the preparation of phase pure NaxSi136 through degassing is the presence of the type-I Na8Si46 clathrate as an impurity phase with as much as 45 wt% in the prepared type II products.31,74 Efforts have been made to separated the two phases using the difference in densities of the two phases, however the two phases appear to be inter-grown and their physical separation seems to be a rather formidable task. This problem however, has now been resolved (cf. Chapter 3). Cross et al.10 derived NaxGe136 from the Zintl precursor Na4Ge4, but in very small quantities since NaxGe136 forms in a very narrow range of temperatures.75,76 Instead, a novel zeolite-like phase Na1 -xGe3+ z with hexagonal crystal stru cture forms as a majority phase.77 It seems that the subtle structural differences of the two precursors Na4Si4 (space group C 2/ c ) and Na4Ge4 (space group P 21/ c ) promote different structures upon the degassing process. Preparation of a guest free Ge136 allotrope is f easible through a chemical process described by Guloy et al.78 Three-dimensional network of four-bonded Ge atoms forms from the polym erization and oxidation of 4 9Ge anions, followed by soft oxidation at 300 C in eutectic mixture of dodecyltrimethylammonium chloride and aluminium trichloride (1:1 molar ratio). Thermal decomposition of mixed alkali a nd alkali/alkaline ea rth silicides also forms of type-II clathrate compositions. Cs8Na16Ge136 has been synthesized by thermal decomposition of CsxNa1xSi.79 Rb8Na16Ge136 has been synthesized by thermal decomposition of RbxNa1xSi.80 Although the product consist of several different phases, synthesis of Ba8Na16Ge136 via thermal decomposition of Na2BaGe4, has also been reported.81 Probably the most straight -forward way of synthesizi ng clathrates is by direct synthesis of the pure elements mixed in the de sired stoichiometric ratio. Two aspects that have to be taken into consider ation are, first, the final pr oduct does not necessarily reflect the initial stoichiometry, and s econd, due to the high vapor pressure of the alkaline metals
15 and their reaction with quartz glass, reacti ons have to be performed in sealed metal vessels. Noting that the formation of type II clathrates is facilitated when the relative sizes of the guest and the Â“cag eÂ”are matched, Bobev and Sevov13,82 first synthesized A8Na16E136 clathrates (A= Cs, Rb; E = Si,Ge) by reaction of the high purity elements inside sealed niobium capsules. The mixtures were held at 650C for three weeks, and then slowly cooled to room te mperature. Later, Nolas et al.83-85 used similar method to synthesize these compounds for further char acterization. The onl y Sn clathrate-II compound reported to date, Ba16Ga32Sn104, has been synthesized86 by reaction of a mixture of K:Ba:Ga:Sn in th e ratio 8:16:32:104, with no K pr esent in the final compound. The compositions synthesized by the me thod described above can be used as precursors for synthesizing new compositions. For example, Gryko et al.68 synthesized the new clathrate composition Cs8Ge136 by continuous heating of Cs8Na16Ge13 (x < 16) under high vacuum causing sodium to Â“deg asÂ” from the clathr ate, leaving Cs incorporated in the structure. Rb8Ge136 can be prepared in a similar manner.75 Recently Beekman et al.87 reported a novel route for the synthesis of type-II Na24Si136 crystals, using Spark Plasma Sinter ing (SPS) technique. Na4Si4 was used as a precursor in the SPS system, and reacted at 600C for desired amount of time, yi elding bluish crystals with composition Na24Si136. Table 1.1 summarizes the type-II clathrates reported to date. From Table 1.1 it is clear that significant scientific effort remains in order to further investigate type II clathrates, the methods of their synthe sis, and their physi cal and structural characterization.
16 Table 1.1 Type-II clathrates, synthesis methods and lattice parameters Composition Synthesis method Lattice parameter a () Reference Si136 Degassing of NaxSi136 14.62601(9) 39 NaxSi136 Decomposition of NaSi 14.62601(9) a < 14.70704(1) 10,39 (0 x < 24) Na24Si136 SPS 14.7157(2) 87 Ge136 Chemical reaction 15.2115(1) 83 NaxGe136 Decomposition of NaGe 15.4* 10 Rb8Ge136 Degassing of Rb8Na16Ge136 15.3 75 Cs8Ge136 Degassing of Cs8Na16Ge136 15.329 65 Cs7Si136 Decomposition of CsSi 14.64 10 Rb8Na16Si136 Direct reaction of elements 14.7400(4) 13 Cs8Na16Si136 Direct reaction of elements 14.7560(4) 13 Ba8Na16Si136 Decomposition of Na2BaSi4 (Not reported) 76 Rb8Na16Ge136 Direct reaction of elements 15.4858(6) 13 Cs8Na16Ge136 Direct reaction of elements 15.4805(6) 13 Ba16Ga32Sn104 Direct reaction of elements 17.054(1) 81 Note that x for NaxGe136 is not reported in Cross et al.10
17 1.5 Electronic and thermal prope rties of type II clathrates The observation of unique optical properties in porous Si88 initiated further investigations of the electron ic properties of Si clathrat es. Experimental observations42 verified that the band gap of Si136 allotrope is expanded by a pproximately 0.9 eV relative to the diamond structured -Si (band gap of approximately 1.1 eV), promoting this material as a novel wide-band gap semiconduc tor. This widening of the band gap has been attributed26 to a slight distortion of the ideal tetrahedral coordina tion observed in -Si, as well as the high density of 5-me mbered rings in the structure of the Si136 allotrope. Theoretical investigations27 of the type II Si136xGex alloys, that have as yet not been experimentally synthesized, show a direct band gap for a range of x. In addition varying x can also tune this range from 1.2 to 2 eV making them promising materials for optoelectronic and photovo ltaic applications. Figure 1.7 shows experimental da ta from temperature dependent and S measurements83 corroborated by theoretical calculations68,77 for Cs8Na16Si136 and Cs8Na16Ge136. For both compounds increases monotonically with the temperature, as is typical for metals. The high carrier concentration (>1021 cm-3) corresponds to this kind of behavior for The only semiconducting type II clathr ates synthesized so far for which transport properties have been reported are guest free Si136 42 and Ge136,78 and the lower Na content NaxSi136.32,10 It is important to note that the rigid-band model was employed in the calculations, where the electropositive guests atoms donate their electrons to the electronegative host atoms. The donated electrons occupy the framework conduction band levels. The metallic behavior of has been corroborated by Nuclear Magnetic Resonance (NMR) measurements.68,77,90-94 The observed Knight-shifts in these materials originate in the hyperfine inte ractions between the nuclei and the delocalized conduction electrons. In most metallic materials, the Kn ight-shifts are observed to be temperature independent, however for certain type II clathrates, for example NaxSi136,92,93 Cs8Ge136 68 and Rb8Na16Si136,78 these shifts show a significant temperature dependence. The sharp peaks in the electronic density of states (EDOS) near the Fe rmi level are re sponsible for
18 this type of behavior.92 It has been observed that the electrical properties of NaxSi136 are strongly dependent upon the Na content, the bigger the x the lower is. Figure 1.7 S (round symbols) and (triangular symbols) as a function of temperature for polycrystalline Cs8Na16Si136 (open symbols) and Cs8Na16Ge136 (filled symbols).82 Inset: DFT computed EDOS for Cs8Na16Si136 (lower)72 and Cs8Na16Ge136 (upper).68 The dashed line indicates the Fermi level, which is well within the conduction band for both materials. Reprinted with permission from Ref. 82 Copyri ght , American Institute of Physics. Clathrates meet the phonon-glass part of the criterion for the PGEC concept in part because of the oversized cages encapsulating loosely bound atoms. This offers a promising perspective for the thermal prope rties of these materials. Nolas et al.83 have shown the temperature dependence of the isotropic atomic displacement parameters (ADP or Uiso) of the host atoms for A8Na16E136 (A = Rb, Cs; E = Si, Ge). It is evident from Figure 1.8 that the larger the size-di fference between the cage and the guest atoms, the lager the ADP. Bobev and Sevov13 have estimated the relative size of the guest and
19 cage by subtracting framework atomic radii from the shortest guest-framework atom distances, compared to the ionic radii of th e guests. The cages are Â“oversizedÂ” compared to the guest atoms, leaving them a lot of Â“r oomÂ” to Â“rattleÂ”. This rattling combined with the complex structure of these materials co ntributes to the effective scattering of phonons, thus lowering the thermal conductivity and promoting these materials for thermoelectric applications. Figure 1.8 Temperature dependent isotropic atomic displacement parameters ( Uiso) for the E28 guest as well as framework sites in A8Na16E136 (A = Rb, Cs; E = Si, Ge).83 Reprinted with permission from Ref. 83 Copyri ght , American Institute of Physics. Hermann et al.95 proposed a model in which the guest atoms can be considered a 3D-Â“EinsteinÂ” oscillators whose frequency of oscillation can be estimated from the simple relation Uiso=kBT/m(2 v)2, where kB is the BoltzmannÂ’s constant, m is the mass of the Â“rattlerÂ”, T is the absolute temperature and v is the frequency of vibration. Because of the metallic nature of Cs8Na16Si136 and Cs8Na16Ge136 their 83,96 appears to be dominated by the electronic component of the total thermal conductivity, e. Figure 1.9 shows the temperature dependence of for the semiconducting allotrope Si136 from Nolas et al.97 As shown in the figure Si136 has a very low an order of magnitude lower than that of
20 diamond-structure Si and comparable in magnitude with amorphous SiO2. The low of Si136 relative to diamond silicon can be understood in terms of the combined increase in unit cell size and open-framework structure of the former with respect to the latter.98,99 Figure 1.9 as a function of temperature for polycrystalline Si136 and a -SiO2.97 The solid line9 indicates a temperature dependence of T 3 Reprinted with permission from Ref. 97 Copyri ght , American Institute of Physics. 1.6 Clathrates for thermoelectric applications The WorldÂ’s increased energy consumption in the past few decades raises the question of how much longer will fossil fuel sources last? This motivates the scientific community to quest for new, renewable sour ces, such as solar, wind, geothermal, biomass, and thermoelectric. The discovery of new materials is necessary in order to increase the efficiency and decrease the co st associated with our natural sources. Our focus here is on thermoelectric materials. Ther e is an ongoing debate within the scientific community whether thermoelectrics can be cons idered a viable alternative energy source. Although it is clear that thermoelectrics cannot be used for large scale energyproduction100, their perspective for small-scale en ergy production and distributed energy
21 delivery is quite promising. A variety of thermoelectric materials101 is currently under scientific investigation, of which much attention is paid to clathrates. The thermoelectric effect couples ther mal and electrical phenomena, allowing a solid state conversion of energy. An imposed thermal gradient T on a specimen will result in a voltage V across that specimen (Seebeck effect).102-104 The Seebeck Coefficient, S, is defined as S= V / T. This type of power gene ration from heat produced by radioactive plutonium is widely used in deep-space applications.103 On the other hand, an electric current passing through a thermo electric material pr ovides a temperature gradient with heat being absorbed on the cold side of the thermoelectric device and rejected at the heat sink, thus thermoelectr ic devices provide a refrigeration capability (Peltier effect).104,105 The Â“goodnessÂ” of a thermoelectric material is assessed through the dimensionless figure of merit,9,100 ZT= S2T/, where =L+e and T is the absolute temperature. To achieve a maximum efficiency, one needs to optimize ZT by maximizing S and but at the same time reducing Since the most promising materials for thermoelectric applications typically have carrier concentrations of approximately 1019 carriers/cm3, Ioffe106 suggested searching for good thermoelectrics within the mixed semiconductors comprised of heavy atoms. Theoretical models107 suggest that energy gaps of about 10 kBT are desirable for best thermoelec trics. One approach to identify potential thermoelectric material s is the PGEC proposed by Slack.5 One material system that fulfills the PGEC requirements is the clathrate material system. Clathrates posses weakly bonded atoms or molecules encaged in a host framework that can scatter phonons effectively6 resulting in a low thermal conductivity which combined with the possibility of varying the carrier concentration6 and framework substitution108 in these materials, offers a Â“tuningÂ” mechanism fo r optimizing the figure of merit ZT. Due to an accelerated research in the pa st decade there is significant progress in obtaining ZT values higher than the long standing limit of ZT~1. Figure 1.10 shows ZT versus temperature for two type-I clathrates. A Czoc hralski grown Ba8Ga16Ge30 clathrate crystals show ZT of 1.35 at 900 K without passing a maximum100. Sr8Ga16Ge30 shows ZT
22 of 0.2 at room temperature, although theoretical calculations52 suggest that optimized compositions of Ba8In16Sn30 and Sr8Ga16Ge30 could reach ZT of 1.7 at 800 K. Tem p erature ( K ) 2003004005006007008009001000 ZT 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Ba 8 Ga 16 Ge 30 Sr 8 Ga 16 Ge 30 Figure 1.10 ZT as a function of temperature for two type-I clathrates Clathrates are potentially relevant for th e high-temperature a pplications, Bi-based tellurides and sellenides still rema in the best materials in terms of ZT values in the lowtemperature region. Current research on clat hrates is focused on optimizing the power factor, S2, and as Â“tuning knobsÂ” for achieving high ZT-values.
23 2.1 Synthesis and structural characterization of Na8Si46 Compounds with the type I crys tal structure continue to be of scientific as well as of technological interest due to their broad range of prom ising properties, such as semiconducting behavior,6 superconductivity,24,25 and glass-like thermal conductivity.23 These properties are a direct result of the nature of the structure and bonding in these materials. Na8Si46 was first synthesized by Kasper et al.,2 and was the first reported synthesis of a material with crystal structure similar to that of the gas-hydrates. Thermal decomposition of the Zintl phases MSi (M=N a, K, Rb, Cs) under vacuum or inert atmosphere leads to the formation of clathrates.2,15,17,59 The synthesis of these intermetallic clathrates presents a formidab le challenge, where the final product consists of type I or II clathrate as a majority phase, with the other phase present as an impurity. A number of compositions to date have only been obtained as polycrystalline powders.13 No synthesis attempt to date reports on forma tion of single crystals of the type I Na8Si46 clathrate. In densified polycrystals care must be taken in the interpretation of the explored properties, for which grain-boundary and surface effects, as well as impurity phases, can be of significant importance. The preparation of high-quality single crystals for structural and physical characterization can be especially challenging for compositions in which the elemental constituents have greatly differing melting poi nts and vapor pressures, when the desired compound is thermodynamically unstable, or wh ere the growth from a melt is generally not possible. This is particularly the case with alkali-silicon clathrates, for which conventional crystal growth t echniques are inapplicable. Na8Si46 is perhaps the most studied of all the type I clathrate compounds.9,10, 109-111 Nolas et al.112 has synthesized this clathrate by th ermal decomposition of sodium silicide Na4Si4, 103-105 at 385C under argon at low pressure. Si milarly with other synthesis methods,66 the final product was a polycrystalline pow der that consists mainly of the type I clathrate, and contains a small amount of the type-II NaxSi136 clathrate. Herein we report on the synthesis of single crystals of Na8Si46, grown via a Novel technique113 for which a patent is pending, thus de tails are not going to be disclosed. The Zintl phase Na4Si4 was
24 used as a precursor and it was synthesized by direct reaction of the high purity elements at 650C. The reaction was carried out inside a tungsten crucible, sealed under ultra high purity nitrogen inside a stainless steel canister, which was in turn sealed inside a fused quartz ampoule. The re sulting product was Na4Si4, which is highly reactive with moisture and air, thus all handling was performed inside a nitrogen-filled glove box. Na4Si4 is a Zintl phase which crystal st ructure is composed of Si4polyanions and Na+ cations arranged in a monoclinic unit cell, as shown in Figure 2.1a. After washing with water and ethanol to remove the unreacte d precursor, the final product Na8Si46 consisted of gray truncated cubes with average size of 0.2 mm (Figure 2.1b) and average yield ~5%. The crystals of Na8Si46 are stable in air and water. Figure 2.1 a) The structure of the Zintl precursor Na4Si4 b) An SEM image of a Na8Si46 single crystal synthesized by the Novel technique113 a) b
25 The quality of the sample was confirme d by powder X-ray analysis. All of the peaks were assigned to the type I clathrate structure of Na8Si46 (Figure 2.2). 2 (Degrees) 2030405060 Intensity (Arbitrary Units) 0 2000 4000 6000 8000 (211) (222) (320) (321) (310) (400) (410) (330) (420) (421) (332) (422) (430) (431) (432) (433) (531) (600) (610) (611) (620) (621) Figure 2.2 Powder X-ray diffraction pattern for the type I Na8Si46 clathrate. Miller indices were assigned to every reflection. The silicon host lattice of the type I Na8Si46 clathrate is simple cubic, composed of two pentagonal dodecahedra, Si20, and six tetrakaidecahedra, Si24 (Figure 2.3). The corresponding unit cell is cubi c, with lattice parameter a=10.19 and space group Pm3 n. The Na atoms reside at the 2a and 6d crystallographic positions and the Si(1)-Si(3) atoms forming the framework reside at th ree distinct crystallo graphic positions, 24k, 6c and 16i, respectively. The maximum number of al kali metal atoms in the type I clathrate is eight, two atoms inside the smaller pe ntagonal dodecahedra and six inside the large tetrakaidecahedra. Each Si atom in Si20 forms four bonds of which three are with atoms in the same dodecahedron and the fourth bond may be one of the two types: connecting one Si20 with another or connect to at oms on four different dodecahedrons.26
26 Figure 2.3 Schematic diagram of the two building polyhedral cages in the Na8Si46 structure. Single crystal X-ray crystallographic an alysis was done by Dr. Wong-Ng at the National Institute for Standards and Tec hnologies (NIST). A single crystal of Na8Si46 with approximate dimensions 0.18 0.20 0.20 mm3, was used. The X-ray intensity data were measured at 200(2) K on a three-circle diffractometer system equipped with Bruker Smart Apex II CCD area detector using a graphite monochromator and a MoK finefocus sealed tube (= 0.71073 ). The detector was pl aced at a distance of 5.000 cm from the crystal. A total of 1280 frames were collected with a scan width of 0.30 in and an exposure time of 8 sec/frame us ing Apex2 (Bruker, 2005). The total data collection time was 5.0 hours. The final cell dimensions of a = 10.1973(1) , b = 10.1973(1) , c = 10.1973(1) , = 90, = 90, = 90, V = 1060.366(18) 3, are based upon the refinement of the XYZ-centroi ds of 6336 reflections with 2.8 < < 32.2 using Apex2. Analysis of the data showed 0 % decay during data collection. Data were corrected for absorpti on effects with the Semi-empirical from equivalents method using SADABS (Sheldrick, 1996). The minimum and maximum transmission coefficients were 0.698 and 0.773, respectively. The structure was solved and refined using the SHELXS-97 (Sheldrick, 1990) and SHELXL-97 (Sheldrick, 1997) software in the space group Pm 3n with Z = 2 for the
27 formula unit Na4Si23. The final anisotropic full-matrix least-squares refinement on F2 with 16 variables converged at R1=1.10 % for the observed data and wR2=2.54 % for all data. The goodness-of-fit was 1.000. On the ba sis of the final model, the calculated density was 2.312 g/cm3. The details of the single crys tal refinement are given in Table 2.1. The isotropic atomic displacement parameters Ueq (Table 2.2) for both Na1 and Na2 atoms, positioned at the 2a and 6d sites, respectively, are much larger than those of the atoms constituting the framework, showi ng the relative stiffness of the framework with respect to the more Â“rattlingÂ” beha vior of the guest atoms. The anisotropic displacement parameters (ADPs) for the atoms in the structure of Na8Si46 are listed in Table 2.3, and the bond lengths for the respec tive atoms are listed in Table 2.4. The results for the bond lengths are in agreement with a previous reported data by Cross et al.74
28 Table 2.1 Crystal data and structure refinement for Na8Si46, single crystal XRD ______________________________________________________________________________________ Formula weight 738.03 Temperature 200(2) K Wavelength 0.71073 Crystal size 0.20 0.20 0.18 mm3 Crystal habit gray cube Crystal system Cubic Space group Pm 3 n Unit cell dimension a = 10.1973(1) Volume 1060.366(18) 3 Z 2 (for empirical formula Na4Si23) Density, calc 2.312 g/cm3 Absorption coefficient, 1.432 mm-1 F( 000) 732 e Diffractometer Bruker Smar t Apex II CCD area detector Radiation source fine-focus sealed tube, MoK Detector distance 5.000 cm Detector resolution 11.198 pixels/mm Total frames 1280 Frame size 512 pixels Frame width 0.30 Exposure per frame 8 sec Total measurement time 5.0 hours Data collection method scans range for data collection 2.82 to 29.93 Index ranges -14 h 14, -14 k 14, -14 l 14 Reflections collected 7652 Independent reflections 305 Observed reflection, I >2( I ) 303 Coverage of independent reflections 100.0 % Variation in check reflections 0 % Absorption correction Semi-empirical from equivalents SADABS (Sheldrick, 1996) Max. and min. transmission 0.773 and 0.698 Structure solution technique direct method Structure solution program SHELXS-97 (Sheldrick, 1990) Refinement technique Full-matrix least-squares on F2 Refinement program SHELXL-97 (Sheldrick, 1997) Function minimized w ( Fo 2 Fc 2)2 Data / restraints / parameters 305 / 0 / 16 Goodness-of-fit on F2 1.000 /max 0.000 Final R indices: R1, I >2( I ) 0.0110 wR2, all data 0.0254 Rint 0.0148 Rsig 0.0046 Weighting scheme w = 1/[2( Fo 2)+(0.01 P )2+0.746 P ], P =[max( Fo 2,0)+2 Fo 2]/3 Extinction coefficient 0.0052(5) Largest diff. peak and hole 0.215 and -0.120 e/3 ______________________________________________________________________________________ R1 = || Fo |-| Fc||/ |Fo|, wR 2 = [ w ( Fo 2 Fc 2)2/ w ( Fo 2)2]1/2
29 Table 2.2 Atomic coordinates and equivalent* isotropic atomic displacement parameters (2) for Na8Si46. ______________________________________________________________________________________ Atom Site x/a y/b z/c Ueq ______________________________________________________________________________________ Na1 2 a 0.0000 0.0000 0.0000 0.0145(3) Na2 6 d 0.5000 0.0000 0.2500 0.0296(3) Si1 24 k 0.30782(3) 0.11728(3) 0.0000 0.00637(9) Si2 6 c 0.5000 0.2500 0.0000 0.00621(12) Si3 16 i 0.184101(18) 0.184101(18) 0.184101(18) 0.00638(9) ______________________________________________________________________________________ Ueq is defined as one third of the trace of the orthogonalized Uij tensor. Table 2.3 Anisotropic atomic displacement parameters* (2) for Na8Si46 ______________________________________________________________________________________ Atom U11 U22 U33 U23 U13 U12 ______________________________________________________________________________________ Na1 0.0145(3) 0.0145(3) 0.0145(3) 0.000 0.000 0.000 Na2 0.0346(4) 0.0346(4) 0.0196(6) 0.000 0.000 0.000 Si1 0.00635(13) 0.00613(13) 0.00662(13) 0.000 0.000 -0.00025(9) Si2 0.00603(15) 0.0066(3) 0.00603(15) 0.000 0.000 0.000 Si3 0.00638(9) 0.00638(9) 0.00638(9) -0.00013(6) -0.00013(6) -0.00013(6) ______________________________________________________________________________________ The anisotropic atomic displacement factor exponent takes the form: -2 2 [ h2a *2U11 + ... + 2 hka b U12 ] Table 2.4 Bond lengths () for Na8Si46 ________________________________ Na1-Si1 3.3590(3) 12 Na1-Si3 3.2516(2) 8 Na2-Si1 3.4307(2) 8 Na2-Si1 3.9470(3) 4 Na2-Si2 3.6053(1) 4 Na2-Si3 3.7885(3) 8 Si1-Si1 2.3919(6) Si1-Si2 2.3816(3) Si1-Si3 2.3623(2) 2 Si2-Si1 2.3816(3) 4 Si3-Si1 2.3623(2) 3 Si3-Si3 2.3279(7) _________________________________
30 2.2 Transport properties of Na8Si46 Our preparation of Na8Si46 single crystals offers th e opportunity for the first investigation of the electrical and thermal transport properties on this material, free from grain boundary and interfacial e ffects associated with the co nsolidated polycrystalline specimens. The standard mounting procedure for our transport properties measurement system114 was modified because of the small size of the crystal specimens. The new mounting configuration is depi cted in Figure 2.4. Thermal bridges made by 0.76 mm diameter Cu wire were put across the sample with the voltage leads V+ and Vattached on one side, and the differential thermocouple leads T1 and T2 attached on the other side, respectively. For the thermal contact between the Cu wire and the specimen, as well as electrical contacts for the voltage probes, a Silver filled epoxy was used. The heater and the thermocouples were attached with StycastTM epoxy. Figure 2.4 Measuring the transport properties on a single crystal of Na8Si46 Measurements of S, and were performed on a custom-designed closed cycle refrigerator115 from 12 K to 300 K. is measured by a four-probe method. A small current I=I +=I (Figure 2.4, typically 5mA) is passed through the single crystal
31 specimen, and the voltage difference V=V +-V is measured between two points a distance l apart. is then determined from the OhmÂ’s Law, =lI/VA, where A is the cross-sectional area of the crystal. Fast swit ching of the current direction and measuring the voltage in both directions eliminates possible thermoelectric contributions to V. Temperature gradients for S and measurements are applied by 100 chip resistor attached to the top of the specimen (Figur e 2.4). Using the thermal bridges in the configuration shown in Figure 2.4 allows V and the temperature gradient T=T1-T2 to be measured between the same two points on the specimen, thus reducing the error in the measurement. S is then calculated from the slope of a plot of V versus T, i.e S= V/ T. To measure S, several temperature gradient s are applied and the power P across the heater measured. From the slope of P versus T and the geometry of the specimen, using the Fourier law we can determine the thermal conductivity =(l/A)(P/ T). The relative uncertainties at room temperature for S and are estimated to be 4%, 6% and 8%, respectively.114,115 Figure 2.5 shows the temperature dependence of (empty circles) and S (filled circles) for a single crystal of type-I Na8Si46 clathrate. The positive d/dT and the magnitude clearly indicate a metallic be havior, which should be expected for Na8Si46 due to the excess of electrons coming from th e Na atom. It reaches a value of 0.098 m-cm at 300 K, and is lower than any other type-I clathrate reported in the literature (Table 2.5). A comparison between measured on a consolidated polycrystalline specimen and a single crystal of type-I Na8Si46 clathrate clearly shows that the single crystal exhibits nearly two orders of magnitude lower than the polycrystalline material. This is an indication of the intrinsic metallic trans port in the single crystal, whereas in the polycrystalline material the inter-grain c ontacts, impurities surrounding these contacts, as well as defects that might occur during the densification process,112 affect the measured values.
32 Temperature (K) 050100150200250300 Seebeck Coefficient ( V/K) -7 -6 -5 -4 -3 -2 -1 0 Resistivity (m -cm) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Figure 2.5 and S for a single crystal of Na8Si46 Another indicator of the quality of the si ngle crystals is the Â‘Residual Resistance Ratio (RRR)Â’9, defined as RRR=R(300K)/R(T0), with T0=12 K being the lowest temperature of our measurements. To the best of our knowledge, the single crystals of Na8Si46 have the lowest RRR compared with ot her type-I clathrates reported in the literature (Table 2.5). We note that at the lo west temperature of our measurement (12 K), d/dT>0 which indicates that the residual resi stivity has still not yet been reached.
33 Table 2.5 Comparison of the room temperature re sistivities and residual resistance ratios RRR= R (300 K)/ R ( T0) for the Na8Si46 specimen of the present work and several intermetallic clathrate specimens of type I showing metallic or Â“metallic-likeÂ” resistivities (i.e. d/ dt is positive definite over the entire temperature interval of measurement). T0 is the lowest temperature at which the corresponding resistivity was reported. ____________________________________________________________________________________________________________ Composition Form Synthesis Method Carrier Type (300 K) T0 (K) RRR Ref. (m -cm) ____________________________________________________________________________________________________________ Na8Si46 single crystal novel method n 0.098 12 36 Present Work Na8Si46 polycrystalline th ermal decomposition n 9.7 8 1.9 Nolas of Na4Si4 Eu8Ga16Ge30 a polycrystalline direct reacti on of n 0.87 2 3.0 Bentien stoichiometric mixture Ba8Ga16Sn30 single crystal Ga flux growth p 2.6 6 2.3 Avila Ba8Ga16Ge30 single crystal slow cooling of n 0.82 2 2.2 Sales stoichiometric mixture Sr8Ga16Ge30 polycrystalline direct reac tion of n 2.0 6 2.1 Avila stoichiometric mixture Ba8Al14Si31 single crystal Al flux growth n 0.45 20 1.4 Avila ____________________________________________________________________________________________________________ aType VIII at with (400) K
34 S for the single crystals of Na8Si46 is negative throughout the entire temperature range (filled circles in Figure 2.5), presumably indicating that electrons are the majority carriers, as expected. It reaches a maximum value of nearly -6 V/K at 170 K and remains very small over the entire temp erature range, corroborating the metallic conduction for this compound. S is similar in temperature dependence as that reported on polycrystalline Na8Si46,112 however with a lower magnit udes which coincides with the lower resistivity discussed above. The position of the peak for S at relatively high temperature indicates that phonon-drag effect s may not be causing this temperature dependence behavior, although phonon-electron s cattering could still be the reason why the electrons are excited acro ss the Fermi level and yield higher Seebeck coefficient. Figure 2.6 shows the temperature dependence of for a single crystal of Na8Si46 (filled circles). It increases below 40 K and th en is relatively temperature independent up to room temperature. It reaches a maximu m value of 28 W/m-K at 40 K, and remains relatively high in the entire temperature ra nge, because of the contribution from the electronic thermal conduc tion in crystalline Na8Si46. It is higher compared to a polycrystalline compound112 (empty circles in Figure 2.6) presumably due to the additional phonon scattering from the grain boundaries and higher values in the polycrystalline specimen.
35 Temperature (K) 050100150200250300 Thermal Conductivity (W/m-K) 0 10 20 30 Figure 2.6 Thermal conductivity for Na8Si46 single crystals (filled circles) and microcrystalline powder (empty circles)112 The temperature dependence of the heat capacity Cp is shown in Figure 2.7. The room temperature value is sli ghtly lower than that expect ed from the classical DulongPetit law. The inset in Figure 2.7 illustrates the low-temperature dependence of the heat capacity plotted as Cp/ T versus T 2. The data was fitted with a straight line between 5 K and 7 K according to the formula Cp/ T =+T where is the Somerfield coefficient of the electronic contribution and is the coefficient of the la ttice contribution to the heat capacity.116,117 From this fit we obtain =65 mJ mol-1 K-2 and =1.63 mJ mol-1 K-4.
36 T (K) 050100150200250300 Cp (J mol-1 K-1) 0 200 400 600 800 1000 1200 T2(K2) 253035404550 Cp/T (J mol-1 K-2) 0.06 0.07 0.08 0.09 0.10 0.11 Figure 2.7 Heat capacity for single crystal Na8Si46. The inset shows Cp ( T ) versus T 2 below T =7 K. From the above value of we have estimated the density of states at the Fermi level for both spin direction N ( EF) using the relation117,118 ) 1 )( ( 32 2 ph e F BE N k (2.1) where e-ph is the electron-phonon coupling constant set to zero as a first approximation, and obtain the value N ( EF)=27.2 states eV-1 per formula unit. This value is comparable to that reported by theoretical calculations119 for Na8Si46, yet slightly hi gher, which is another indicator of the quality of the single crystals presumab ly with no defects present. To get a better in sight into the lattic e dynamics of the Na8Si46 clathrate, we can represent the total Cp as a sum of the three contributions116: the electronic contribution, Cel=T coming from the electrons as heat carriers, the Debye contribution, CD, originating from the cage-like struct ure, and the Einstein contribution, CE, arising from the localized vibrations of the Na at oms inside the oversized cages, i.e.
37 E D el pC C C C (2.2) The Debye term is given as120 T x x D D DDdx e e x T R N C/ 0 2 4 31 9, (2.3) where ND is the number of Debye oscillators per formula unit (ND=46 for Na8Si46), D is the Debye temperature, and x= /kBT, with being the phonon-angular frequency. The Einstein term is given as116 N i T T Ei Ei i EEi Eie e T R N p C1 2 21 (2.4) where pi are the degrees of freedom, NEi are the number of Einstein oscillators ( NEi =2 and NEi =6 for the Na atoms inside the dodecahedra and tetrakaidecahedra, respectively), and Ei are the Einstein temperatures associated with the ith vibrational mode. Figure 2.8 shows the plot ( Cp-CD) / T 3 vs T (filled circles) fitted with a solid line according to the theoretical model represented by E quation (2.2), employing Equations (2.3) and (2.4), respectively. Fitting pa rameters corresponding to two di fferent models are listed in Table 2.6, with the free parameters for each model indicated. The Einstein temperatures for the Na atoms inside the dodecahedra are denoted by E 1, and for those inside the tetrakaidecahedra, E 2, respectively. Furthermore, the Einstein temperatures for the inplane vibrations of the Na atoms insi de the tetrakaidecahedra are denoted by E 2 and for the out-of-plane (along the vertical z -axis) by E 2 Table 2.6 Fitting parameters for the ( CpCD)/ T3 curve, according to two different models. The free parameters in each model are shown in brackets. The Debye temperature was fixed to D=590 K.112 Model (free parameters) (J mol-1 K-2) E 1 (K) E 2 (K) E 2 (K) E 2 (K) ____________________________________________________________________________________________________________ I (, E 1, E 2) 0.0690 143 82 N/A N/A II (, E 1, E 2 E 2 ) 0.0691 164 N/A 163 95
38 For the first model we allowed E 1 and E2 to be free parameters. The value obtained for from the fit is in an excellent agreement with the value calculated from the linear fit to the low-temperature Cp data in Figure 2.7. Temperature (K) 050100150200250300 ( CpCD)/ T3 x 10-4 J mol-1 K-1 0 5 10 15 20 25 Temperature (K) 01020304050 l (W/m-K) 2 4 6 8 10 12 14 Figure 2.8 Temperature dependence of the lattice contribution to the specific heat Cph plotted as Cph/ T 3 vs T The inset shows l for a single crystal Na8Si46. The pronounced peak centered around 25 K come s from the contributio n of the localized vibrations of the Na atoms inside the cages in the structure of Na8Si46. This Â‘rattlingÂ’ behavior appears as a Â‘dipÂ’ in the lattice thermal conductivity (shown in the inset in Fig. 2.8) for a single crystal Na8Si46, which was obtain by subtracting e= L0T / from the total (Figure 2.6), where L0=2.45 10-8 W K-2 is the Lorenz number. Theoretical investigations of the phonon band st ructure and resonant scattering121 and Raman scattering122 in Na8Si46 confirm that the contribution of the localized vibrations to and CP appears near this temperature. Th e higher ADPs for the Na atoms at 6 d site inside the
39 tetrakaidecahedron (Figure 2.3) is consistent with the lower E 2 compared to the E 1 for the Na atom at 2 a position inside the smaller dodecahed ron. This can be corroborated by a different approach to calculating E 1 and E 2. From the isotropic ADPs, Ueq, for Na@2 a and Na@6 d sites, respectively, employing the relations Ueq= kBT / m (2)2 where m is the mass of the Na Â“rattlerÂ” and is the Â“rattlingÂ” frequency, and E= h/ kB, we estimate the respective Einstein temperatures to be E 1 170 K and E 2 120 K. In the second model th e asymmetry of the tetrakaidecahedron requires the vibrational modes of the Na atoms to be de scribed by two-dimensional in-plane motions (characterized by E 2 and p NE 2=2 6) and one-dimensional out-of-plane motions (E 2 p NE =1 6), whereas the more symmetric dodecahedron can still be described with an isotropic E1. The results from the fitting E 2 =162.27 K and E 2 =95.48 K are consistent with the larger in-plane vibrational amplitudes (lower E 2 ). From the simple crystal chemistry formulation [Na+]8 [(4 b )Si0]136, assuming a formal charge of +1 for each Na-ion a nd the room temperature unit cell volume V =1060.366 3 (Table 2.5) we estimate the carrier concentration n for the single crystal Na8Si46 to be n =7.5 1021 cm-3, an indication of the metallic behavior for this compound. In the single band approximation, assuming =( ne)-1, where e is the elementary charge, we estimate the room temperature electron mobility to be =8.5 cm2 V-1 s-1. The inferred electron relaxation time = m /ne2=0.51 10-14 s, where m is the free electron mass is comparable to the room temperature values for metals.123 Figure 2.9 shows the temperature dependence of the mean free path of the heat carriers, estimated from the values (Figure 2.6), the heat capacity (2.7) of single crystal Na8Si46 and the sound velocity estimate d from the elastic constants124 for Na8Si46.
40 Temperature (K) 050100150200250300 Mean Free Path ( m) 1 10 100 1000 10000 Figure 2.9 Temperature dependence of the lattice contribution to the specific heat Cph plotted as Cph/ T 3 vs T b) Temperature dependence of the m ean free path for single crystal Na8Si46 At room temperature the mean free path of the phonons is approximately 3.6 m and increases dramatically as the temperature is lowered. This value is nearly two orders of magnitude higher that that reported112 on a polycrystalline Na8Si46 clathrate which is not surprising taking into consider ation that the inter-grain bound ary scattering of acoustic phonons, which is a dominant effect in the polycrystalline Na8Si46 clathrate at low temperatures, is not present in single crys tals. At the lowest temperature of our measurements (12 K) the mean free path is co mparable to the size of the single crystals, which may be an indication that the Â‘rattlin gÂ’ of the Na atoms Â‘freezes outÂ’ as the temperature is lowered. Since this is the first ti me anyone has investigated the transport properties of single crystal Na8Si46, it is impossible to compare th e results with other respective analyses. However the comparison between th e measurements on a single crystal and a polycrystalline specimen clearly confirms that the single crystals offer a better opportunity to investigate the intrin sic properties of the composition Na8Si46.
41 3.1 Synthesis and structural characterization of Na24Si136 In this chapter structural and physical properties of single crystal type-II Na24Si136 clathrates are investigated. Even though polycrystalline specimens with composition NaxSi136 (0< x <24) have been known for a long time46,77a comprehensive understanding of their physical properties is still needed, mainly due to the fact that it is still a formidable task to obtain phase pure specimens. The first success in synthesizing single crystals of Na24Si136 was made by Beekman et al.87 using the SPS technique. In this work single crystals of Na24Si136 clathrates were grown by the Novel method.113 The final product with an average yield ~5% consisted of bluish-tetrahedral crystals with smooth triangular faces (Figure 3.1) and average size of 0.5 mm. Th e quality of the product mate rial was confirmed by X-ray analysis on powdered specimen, where all peaks were assigned to the type II Na24Si136 structure (Figure 3.1), and SEM analysis on a single crystal, illustrated in Figure 3.2.
42 2 (Degrees) 2030405060 Intensity (Arbitrary Units) 0 2000 4000 6000 (311) (222) (400) (331) (422) (333) (531) (442) (440) (620) (533) (551) (444) (642) (733) (822) (751) (911) (933) (622) (844) Figure 3.1 Powder X-ray diffraction pattern of powdered single crystal of type II Na24Si136 clathrate specimens. Miller indices are assigned to every reflection.
43 Figure 3.2 SEM image of Na24Si136 single crystals obtained by the Novel method The starting material is the Zintl Phase Na4Si4 which was annealed at different temperatures and pressures, for various times.113 Our approach was to hold the pressure constant and vary the annealing temperatur e and time. Figure 3.3 shows details on the dependence of temperature in the fo rmation of single crystals of Na8Si46 and Na24Si136. In all cases the annealing time was 8 hrs. Annealing Na4Si4 at 5850C results in a formation of single crystals of Na8Si46 with the purity of the produc t material confirmed by X-ray analysis on powdered specimens (Figure 3. 1). When the annealing temperature was increased to 6000C, peaks (indicated by in Figure 3.3) of the type-II Na24Si136 phase started appearing. This may indicated that at higher temperatures the type-II phase is the more stable phase. Indeed, at temperatures of 6650C it was found that only crystals of Na24Si136 form. The purity of the product material was confirmed by X-ray analysis on powdered specimens. No peaks due to Na8Si46 were observed in the XRD spectrum, which has been a problem in synthesizing the type-II Na24Si136 clathrate.66 Annealing at 7000C leads to the decomposition of the type-II phase to elemental Si (the respective Si peaks in the XRD spectrum are indicated by in Figure 3.3).
44 2 Theta (Degrees) 2030405060 Intensity (Arbitrary Units) 0 5000 10000 15000 NaSi Na8Si46Na24Si136 + Na8Si46 ( ) Na24Si136Na24Si136 + Si ( )* * 500oC 585oC 600oC 665oC 700oCsample holder Figure 3.3 Formation of different phases at different temperatures starting from a same precursor Na4Si4. Another set of experiments was performed to analyze the formation of different phases for different times, resulting in differe nt yield of the produc t material, with the respective phases still being observed at th e appropriate temperatures according to Figure 3.3. We found that the highest yield was achieved at approximately 8 hours, with longer times giving smaller yield, and eventua lly after annealing the precursor for more than 24 hours the clathrates decompose to elemental Si. The Si host lattice for Na24 Si136 consists of sixteen pentagonal dodecahedra and eight hexacaidecahedra (Figure 3.4), in a face-centered cubic un it cell with lattice parameter a =14.62 with the space group Fd3 m Unlike the Na8Si46, Na24Si136 is a nonstoichiometric phase with all the cages not necessarily occupied. The maximum number of alkali metal atoms occupying the polyhedral cages is x =24, with sixteen atoms inside
45 the pentagonal dodecahedra, and eight atoms inside the hexakaidecahedra. The framework atoms reside at three di stinctive crystallographic sites 8 a 32 e and 96 g and the guest atoms reside at 8 b and 16 c sites. There are 24 Na atoms and 136 Si atoms per unit cell. The structure contains 5-membered and 6-membered rings and the high proportion of 5-membered rings makes the st ructure energetically competitive with diamond.26 Figure 3.4 Schematic diagram of the two building polyhedral cages in the Na24Si136 structure. A single crystal of Na24Si136 with approximate dimensions 0.13 0.22 0.27 mm3, was used for the X-ray crystallographic analysis. The X-ray intensity data were measured at 200(2) K, in the same way described in chapter 2.2. A total of 3030 frames were collected with a scan width of 0.30 in and an exposure time of 12 sec/frame using Apex2 (Bruker, 2005). The total data collection time was 15.00 hours. The frames were integrated with Apex2 software p ackage using a narrow-frame integration algorithm. The integration of the data using a Cubic uni t cell yielded a total of 12553 reflections to a maximum angle of 29.98, of which 262 were independent (completeness = 100.0%, Rint = 1.83%, Rsig = 0.40%) and 260 were greater than 2( I ). The final cell dimensions of a = 14.7121(1) , b = 14.7121(1) , c = 14.7121(1) , = 90, = 90, = 90, V = 3184.37(4) 3, are based upon the refinement of the XYZ centroids of 11765 reflections with 2.4 < < 32.4 using Apex2. Analysis of the data
46 showed 0 % decay during data collection. Data were corrected for absorption effects with the Semi-empirical from equivalents me thod using SADABS (Sheldrick, 1996). The minimum and maximum transmission coefficients were 0.746 and 0.832. The structure was solved and refined using the SHELXS-97 (Sheldrick, 1990) and SHELXL-97 (Sheldrick, 1997) software in the space group Fd3 m with Z = 8 for the formula unit Na3Si17. The final anisotropic full-matrix least-squares refinement on F2 with 18 variables converged at R1=1.15 % for the observed data and wR2=2.90 % for all data. The goodness-of-fit was 1.000. The larg est peak on the final difference map was 0.203 e /3 and the largest hole was -0.122 e /3. On the basis of the final model, the calculated density was 2.280 g/cm3 and F (000), 2168 e The details of the single crystal refinement are given in Table 3.1. Similarly to the case of Na8Si46 the isotropic atomic displacement parameters Ueq (Table 3.2) for both Na1 and Na2 atoms, positioned at 2 a and 6 d sites, respectively, are much larger than those of the atoms consti tuting the framework, showing the relative stiffness of the framework with respect to the more Â“rattlingÂ” behavior of the guest atoms. The anisotropic displacement parameters (ADPs) for the atoms in the structure of Na24Si136 are listed in Table 3.3, and the bond le ngths for the respective atoms are listed in Table 3.4. Comparison between the bond lengths for Na24Si136 of the present work with the bond lengths for NaxSi136 ( x =1, 20.5) from Cross et al.74 agrees with the general tendency of the Si-Si bond lengths to decr ease upon removal of Na atoms from the polyhedral cages. The Na-Si bond lengths on the other hand show both tendencies, to increase and decrease when additional Na atoms are introduced in the polyhedral cages.
47 Table 3.1 Crystal data and structure refinement for Na24Si136, single crystal XRD. ______________________________________________________________________________________ Formula weight 546.50 Temperature 200(2) K Wavelength 0.71073 Crystal size 0.27 0.22 0.13 mm3 Crystal habit blue prism Crystal system Cubic Space group Fd3 m Unit cell dimensions a = 14.7121(1) = 90 b = 14.7121(1) = 90 c = 14.7121(1) = 90 Volume 3184.37(4) 3 Z 8 (empirical formula Na3Si17) Density, calc 2.280 g/cm3 Absorption coefficient, 1.411 mm-1 F (000) 2168e Diffractometer Bruker Smar t Apex II CCD area detector Radiation source fine-focus sealed tube, MoK Detector distance 5.000 cm Detector resolution 8.333 pixels/mm Total frames 3030 Frame size 512 pixels Frame width -0.30 Exposure per frame 12 sec Total measurement time 15.00 hours Data collection method and scans range for data collection 2.40 to 29.98 Index ranges -20 h 20, -20 k 20, -20 l 20 Reflections collected 12553 Independent reflections 262 Observed reflection, I >2( I ) 260 Coverage of independent reflections 100.0 % Variation in check reflections 0 % Absorption correction Semi-empirical from equivalents SADABS (Sheldrick, 1996) Max. and min. transmission 0.832 and 0.746 Structure solution technique direct Structure solution program SHELXS-97 (Sheldrick, 1990) Refinement technique Full-matrix least-squares on F2 Refinement program SHELXL-97 (Sheldrick, 1997) Function minimized w ( Fo 2 Fc 2)2 Data / restraints / parameters 262 / 0 / 18 Goodness-of-fit on F2 1.000 /max 0.001 Final R indices: R1, I > 2( I ) 0.0115 wR2, all data 0.0290 Rint 0.0183 Rsig 0.0040 Weighting scheme w = 1/[2( Fo 2)+(0.01 P )2+12 P ], P = [max( Fo 2 ,0)+2 Fo 2]/3 Extinction coefficient 0.00031(4) Largest diff. peak and hole 0.203 and -0.122e /3 ______________________________________________________________________________________ R1 = || Fo ||Fc||/ |Fo|, wR 2 = [ w ( Fo 2 Fc 2)2/ w ( Fo 2)2]1/2
48 Table 3.2 Atomic coordinates and equivalent* isotropic atomic displacement parameters (2) for Na24Si136. ______________________________________________________________________________________ Atom Site x/a y/b z/c Ueq ______________________________________________________________________________________ Na1** 8 b 0.1250 0.1250 0.1466(7) 0.049(3) Na2 16 c 0.5000 0.0000 0.0000 0.0152(2) Si1 2 a 0.6250 0.1250 0.1250 0.00613(18) Si2 32 c 0.871284(19) 0.067382(13) 0.067382(13) 0.00649(8) Si3 96 g 0.717951(19) 0.032049(19) 0.032049(19) 0.00636(10) ______________________________________________________________________________________ Ueq is defined as one third of the trace of the orthogonalized Uij tensor. ** Na1 occupation facto r = 1/6. Table 3.3 Anisotropic atomic displacement parameters* (2) for Na24Si136. ______________________________________________________________________________________ Atom U11 U22 U33 U23 U13 U12 ______________________________________________________________________________________ Na1 0.056(4) 0.056(4) 0.034(4) 0.000 0.000 0.000(2) Na2 0.0152(2) 0.0152(2) 0.0152(2) -0.0011(3) -0.0011(3) -0.0011(3) Si1 0.00613(18) 0.00613(18) 0.00613(18) 0.000 0.000 0.000 Si2 0.00683(13) 0.00632(9) 0.00632(9) 0.00040(9) 0.00002(6) 0.00002(6) Si3 0.00636(10) 0.00636(10) 0.00636(10) -0.00001(9) 0.00001(9) 0.00001(9) ______________________________________________________________________________________ The anisotropic atomic displacement factor exponent takes the form: 22 [ h2a*2U11 + ... + 2hka*b*U12 ] Table 3.4 Bond lengths () for Na24Si136. __________________________________ Na1-Si2 3.619(10) 2 Na1-Si2 3.785((7) 4 Na1-Si2 3.8642(15) 4 Na1-Si2 4.001(3) 4 Na1-Si2 4.0114(7) 2 Na1-Si2 4.0201(10) 2 Na1-Si2 4.225(10) 2 Na1-Si2 4.234(8) 4 Na1-Si3 3.827(5) 2 Na1-Si3 4.194(7) 2 Na2-Si1 3.1853(1) 2 Na2-Si2 3.3742(2) 12 Na2-Si3 3.2751(3) 6 Si1-Si3 2.3685(5) 4 Si2-Si2 2.3578(3) 2 Si2-Si2 2.3976(6) Si2-Si3 2.3726(3) Si3-Si1 2.3686(5) Si3-Si2 2.3726(3) 3 _________________________________
49 3.2 Transport properties of Na24Si136 single crystals The only data reported to date on trans port properties of si ngle crystals of Na24Si136 is from Beekman et al.120 on single crystal obtained by SPS. Here we report on S and measurements on single crystals obtained by the Novel method. The mounting configuration for measuring th e transport properties on singl e crystals shown in Figure 2.5 was also employed in the case of Na24Si136 single crystals. A crystal with size ~0.5 mm was mounted as shown in Figure 3.5. Figure 3.5 A photograph of a mounted single crystal Na24Si136 for transport properties measurements. The temperature dependences and magnitudes of (empty circles) and S (filled circles) are shown in Figure 3.6. They cl early indicate metallic behavior. The observed value of (45 -cm at room temperature) is, to th e best of our knowledge, lower than any other intermetallic clathrate reported to date, with the ex ception of SPS grown87 Na24Si136 (Table 3.5). This is an indication of both the metallic conduction of this composition and the high quality of the single crystals. Another indicator of the quality and the crystallinity of Na24Si136 is the RRR value of approximately 17, which is higher than any other polycrystalline intermetallic clathrate and comparable to the RRR for
50 Na24Si136 grown by SPS. We note that at the lowe st temperature of our measurement (12 K), d/dT >0 which indicates that the residual resi stivity has still not yet been reached. Temperature (K) 050100150200250300 Resistivity (m -cm) 0.0 0.1 0.2 0.3 0.4 0.5 Seebeck Coefficient ( V/K) -10 -8 -6 -4 -2 0 2 Figure 3.6 (empty circles) and S (filled circles) for a single crystal of Na24Si136. S remains low in the entire temperature range and approaches zero value at low temperatures as expected for a meta llic material. The negative sign of S is consistent with the fact that electrons ar e the majority carriers. The thermal conductivity of Na24Si136 is shown in Figure 3.7. It is compared with of several polycrystallin e semiconductors (Figure 3.7) and found to be high, consistent with the metallic behavior obser ved in the electrical properties. The Sn clathrate exhibits temperature depend ence typical of crystalline insulators16, with decreasing with increasing T approximately as 1/ T a signature of Umklapp-processes. The two Ge clathrates have more than an order of magnitude lower at low temperatures with magnitudes similar to th at of amorphous material.
51 Table 3.5 Comparison of the room temperature re sistivities and residual resistance ratios RRR= R (300 K)/ R ( T0) for the Na24Si136 specimen of the present work and several intermetallic clathrate specimens of type II showing metallic or Â“metallic-likeÂ” resistivities (i.e. d/ dt is positive definite over the entire temperature interval of measurement). T0 is the lowest temperature at which the corresponding resistivity was reported. ____________________________________________________________________________________________________________ Composition Form Synthesis Method Carrier Type (300 K) T0 (K) RRR Ref. (m -cm) ____________________________________________________________________________________________________________ Na24Si136 single crystal novel method n 0.045 12 17 Present Work Na24Si136 single crystal SPS n 0.029 12 14 Beekman Cs8Na16Si136 polycrystalline direct reacti on of n 0.68 9 2.4 Nolas stoichiometric mixture Cs8Ge136 polycrystalline dega ssing of n 9.2 6 1.8 Gryko Cs8Na16Ge136 ____________________________________________________________________________________________________________
52 Temperature (K) 050100150200250300 Thermal Conductivity (Wm-1K-1) 0.1 1.0 10.0 Ba 8 Ga 16 Si 30 Cs 8 Sn 44 Sr 8 Ga 16 Ge 30 Sr 4 Eu 4 Ga 16 Ge 30 Na 24 Si 136Figure 3.7 Thermal conductivity of Na24Si136 single crystals in comparison with polycrystalline clathrate materials Na24Si136 has unequivocally much higher compared to these clathrates due to its electronic contribution, which is small in semiconductor materials. The resonant scattering of acoustic phonons because of the Â‘rat tlingÂ’ of the guest atoms is present in all materials shown in Figure 3.7 and this is cl early not the reason of the high thermal conductivity for Na24Si136.
53 It is important to notice that the rela tive uncertainty in the measurements of and is quite high (we estimate it to be on th e order of 30%), due to the difficulty in determination of the cross-sec tional area of the irregularly shaped crystals. However, the obtained results can be interpreted as more accurate representation of the intrinsic properties in this material relative to the same measurements on a polycrystalline specimens, for which grain bounda ry effects can dominate. 17, 67,86
54 4. Resistivity, Seebeck Coefficien t and Thermal Conductivity of Sn24P19.3Br8 and Sn17Zn7P22Br8 Much less is known about th e thermoelectric properties of tin clathrates with cationic framework encapsulating anionic guests. In this chapter the transport properties of two Sn-clathrates with type I hydrate crystal structure with Br guests, Sn24P19.3Br8 and Sn17Zn7P22Br8, were investigated. The results are di scussed in terms of the potential for thermoelectric applications. The two specimens Sn24P19.3Br8 and Sn17Zn7P22Br8 were prepared by Dr. A.V. Shevelkov.125,126 Tin, zinc, red phosphorus, and tin bromide were used as starting materials. Their stoichiometric mixtures were reacted in sealed under vacuum silica tubes at 450C for 5 days. The resulting material was ground to fine powder and annealed for 14 days at a 550C and 300C for Sn24P19.3Br8 and Sn17Zn7P22Br8, respectively. Powder x-ray diffracti on data was indexed to the type I clathrate structure ( n Pm 3). The type I clathrate crystal structure can be described as a three-dimensional framework composed of tetrahedrally-bonded phosphorus and metal atoms. The framework can be thought of as being formed by six tetrakaidecahedra and two dodecahedra, formed by the pnicogen atoms, with bromine atoms residing inside polyhedra, as shown in Figure 4.1.
55 Figure 4.1 Crystal structure of type I clathrate. The open circles represent the guest Br atoms occupying th e polyhedra formed by Sn, P, and Zn. The filled circles are the 6 c and 16 i crystallographic positions and the gray circles represent the 24 k crystallographic position. Reprinted with permission from Ref. 33 Copyri ght , American Institute of Physics. Although in general similar, th e lattice structures of Sn24P19.3Br8 and Sn17Zn7P22Br8 have important differences. The idealized type I clathrate framework is defined by three independent crystallographic positions, 6 c 16 i and 24 k In Sn24P19.3Br8 the Sn(3) (24 k ) position is split into two sites Sn(31) (6 c ) and Sn(32) (16 i ) while the 6 c and 16 i positions remain tetrahedrally bonded. Sn(32) forms two short covalent bonds with P(2) (16 i ), and one covalent bond with tin atom, Sn(31), and completes its coordination by three relatively distant (3.16 to 3.31 ) Sn(32) atoms (Figure 4.2).
56 Figure 4.2 Coordination of the metal atoms in Sn24P19.3Br8. The Sn(32)Â–Sn(32) bonding is shown in gray. Reprinted with permission from Ref. 33 Copyri ght , American Institute of Physics. In Sn17Zn7P22Br8 the the Sn(3) site is split into three closely lying positions, two of which are occupied by tin, Sn(31) and Sn(32), a nd the third occupied by zinc, Zn(33). Figure 4.3 Coordination of the atoms in Sn17Zn7P22Br8 Reprinted with permission from Ref. 33 Copyri ght , American Institute of Physics. Sn(31) 2.91 P(2) P(2) P(1) Sn(32) Sn ( 31 ) Sn ( 31 ) P ( 1 ) P ( 1 ) P ( 2 ) P ( 2 ) P ( 2 ) P ( 2 ) P ( 1 ) P ( 1 ) Zn ( 33 ) Sn ( 32 ) 2.88 2.57
57 Each metal atom is bound to two P(2) atoms and one P(1) atom and forms one covalent bond, Sn(31)Â–Sn(31) or Sn(32)Â–Zn(33) (Fi gure 4.3). The phosphorus atoms have very similar coordination in both structures. Th e P(2) atom forms one homonuclear PÂ–P bond and is surrounded by three (Sn,P) atoms formin g a distorted tetrahedron. The P(1) (16 c ) atom is surrounded by four (Sn,P) atoms formin g an almost regular tetrahedron. In both structures, the separation between the P(2) atoms is 2.18 typical for PÂ–P bonding. The P-Sn separations range from 2.46 to 2.69 in both compounds, while the PÂ–Zn separations in Sn17Zn7P22Br8 are shorter, ranging from 2.34 to 2.47 . The framework of Sn24P19.3Br8 contains fewer than 46 atoms, t hus there are vacancies (on the 6 c crystallographic sites). This is not the case for Sn17Zn7P22Br8. A detailed analysis of the structural characteristics of Sn24P19.3Br8 and Sn17Zn7P22Br8 is reported in Refs.125 and 126. Densification for transport measurem ents was achieved by hot-pressing the powdered specimens at 450C and 189 MPa for 2 h. A small amount of Sn4P3, estimated to be ~4 vol.%, was observed with XRD anal ysis after hot-pressing. The polycrystalline pellets were cut into parallelepipeds of dimensions 2 mm 2 mm 5 mm using a wire saw to reduce surface damage. Measurements of S and were performed using a radiation-shielded vacuum probe in a cu stom-designed closed-cycle refrigerator.127 The temperature dependence of ln for Sn24P19.3Br8 and Sn17Zn7P22Br8 is shown in Figure 4.4.
58 0.000.020.040.060.08 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 3 4 5 6 7 8 9 T-1 (K-1)ln (Sm-1) ln (Sm-1) a) b) Figure 4.4 Electrical conductivity for (a) Sn24P19.3Br8 and (b) Sn17Zn7P22Br8. Reprinted with permission from Ref. 33 Copyri ght , American Institute of Physics. For Sn24P19.3Br8 decreases rapidly with decreasing temperature from room temperature to approximately 55 K, and is not strongly te mperature dependent from 55 K to 12 K. For Sn17Zn7P22Br8 decreases with decreasing temperatur e in the interval 300 K to 200 K, then continues to increase below 200 K. The band gap, Eg, for Sn17Zn7P22Br8 was estimated to be 0.11 eV from a linear fit to the data (Fig. 4.4b). This va lue is close to that reported previously.126 Figure 4.5 shows the temperature dependence of S from room temperature to 12 K for the two clathrates. For Sn17Zn7P22Br8 S increases slowly in the entire temperature range,
59 reaching a room-temperature value of 40 V/K. For Sn24P19.3Br8, S is relatively temperature independent from room temperat ure to 125 K, then decreases sharply to approximately zero. Temperature (K) 050100150200250300 Seebeck Coefficient ( V/K) 0 20 40 60 80 100 120 140 Figure 4.5 S for Sn24P19.3Br8 (black circles) and Sn17Zn7P22Br8 (open squares). Reprinted with permission from Ref. 33 Copyri ght , American Institute of Physics. The sharp decrease in S with decreasing temperature occu rs at approximately the same temperature as an abrupt change in This may be an indication of the onset of minoritycarrier conduction at this lo wer temperature range. Hall measurements on both specimens yielded positive but st rongly field-dependent Hall coeffi cients, suggesting contributions from multiple bands. The difference in the electrical transport for Sn24P19.3Br8 and Sn17Zn7P22Br8 may be attributed to the fine ye t important difference in the crystal structure of these two clathrates. In the latt er, all tin atoms have tetrahedral coordination made of one metal, Sn or Zn, and three phosphor us atoms. In the former, a part of the tin framework is surrounded by three covalently bonded atoms forming a trigonal pyramid and is further linked to three rather distant (3.2 to 3.4 ) tin atoms. In such a way a 3 + 3 distorted octahedral coor dination is formed for the Sn(2) atoms. On average, 10.8 out of 24 tin atoms in the unit cell have this type of coordination. The remaining 13.2 tin
60 atoms, Sn(1), possess Â‘normalÂ’ tetrahedral c oordination made of three P and one Sn atom. This structural difference adds complexity that may result in added carrier scattering. Shaturk et al.128 showed that the states just below th e Fermi level are mainly composed of the orbitals of the 3 + 3 bonded Sn atoms. In addition, cationic Sn-c lathrates with 3 + 3 bonded Sn atoms are narrow-gap semiconductors and display relatively high values of and S ,125 whereas those with only four-bonded tin atoms have much lower electrical conductivities.129 This results in a relative ly high power factor ( S2= 130 W/m K2 at room temperature) for Sn24P19.3Br8, higher than any other Snclathrate,9,130,131 and near the values of other type I clathrates. The relatively high power factor resulted in a room-temperature ZT of 0.03. Although very low, this ZT value is higher than any other Sn-cla thrate reported thus far.45 From the measured values of and the WiedemannÂ–Franz relation was employed to estimate and subtra ct the electronic component e = L0T/ (with Lorenz number L0 = 2.44 10-8 V2/K2), thus estimating th e lattice contribution L =-e. Figure 4.6 shows L for the polycrystalline Sn24P19.3Br8 and Sn17Zn7P22Br8 specimens. Sn24P19.3Br8 exhibits a nearly 1/ T temperature dependence between 50 K and 100 K, which is typical of crystalline dielectric materials dominated by phononÂ–phonon scattering.132 The low L values are due to the complex crystal structure, i.e., 56 atoms per unit cell, in these materials. The a dditional bonding induced between the Br and framework atoms neighboring the vacancies appa rently constrains the Br atoms, thus resulting in higher L values at lower temperatures. This has also been observed in Cs8Sn44.4 In the case of Sn17Zn7P22Br8 L slowly increases with decreasing temperature. It may be that the Â‘Â‘rattleÂ’Â’ vibrational modes, although more prominent than for Sn24P19.3Br8, are not within the range of the acoustic phonons. This has also been observed46,127 for Cs8Zn4Sn42 and Cs8Ga8Sn38. The Zn and P atoms in Sn17Zn7P22Br8 may also produce additional alloy scat tering which further suppresses L. The structural difference between these two compositions, ther efore, appears to be the source of their differing thermal conductivities.
61 Temperature (K) 050100150 L (W/m-K) 1 2 3 4 5 Figure 4.6 L for Sn24P19.3Br8 (filled circles)and Sn17Zn7P22Br8 (open squares). The straight lines are fits to thedata employing Eqs. (4.1) and (4. 2). Reprinted with permission from Ref. 33 Copyri ght , American Institute of Physics. The solid lines in Figure 4.6 are theoretical fits to the experimental data using the Debye approximation.126,132,133 T x C x B B LDdx e e x T k k/ 0 2 1 4 3) 1 ( 2 (4.1) where the dimensionless quantity x= /kBT is the phonon frequency, kB is the Boltzmann constant, is the reduced Planck constant, D is the Debye temperature, is the speed of sound, and C is the phonon-scattering relaxation time. The phononscattering relaxation rate can be written as 2 2 2 0 2 2 4 1) ( 3 exp C T T B A LD C (4.2) where L is the grain size, 0 is the resonance frequency, and A B and C are fitting parameters, listed in Table 4.1. The four scatte ring mechanisms on the right-hand side of
62 Eq. 4.2 represent grain boundary, poi nt defect, phononÂ–phonon umklapp, and phonon resonant scatte ring, respectively. D and values used in the fitting are 238 K and 2,505 m/s, respectively.134 Table 4.1 Fit Parameters for the Two Polycrystalline Sn-Clathrates ________________________________________________________________________ Composition L ( m) A(104 s3) B(105 s K-1) C(s-3) 0 (THz) ________________________________________________________________________ Sn24P19.3Br8 9.58 1.406 2.067 0.1 13.364 Sn17Zn7P22Br8 3.58 2.221 0.824 6.72 109 4.768 ________________________________________________________________________ The values for L are similar to average grain size estimates using metallographic analysis. The A prefactor is larger for Sn17Zn7P22Br8 than for Sn24P19.3Br8, possibly due to the three-element alloying on the framework site for the former composition. The larger B prefactor for Sn24P19.3Br8 potentially indicates st ronger phononÂ–phonon sca ttering than that for Sn17Zn7P22Br8, although it is not clear why this would be the case since we do not know the exact Debye temperature and Grneisen constant for these compositions, two of the parameters that influence B As shown in Table 4.1, the values of C indicate very weak, if any, Â‘Â‘rattlingÂ’Â’ in Sn24P19.3Br8. This is presumably due to the shrinking of the tetrakaidecahedral cages within the framew ork due to the framework vacancies, whereas in Sn17Zn7P22Br8 this phonon-scatteri ng mechanism is much more pronounced. In addition, the limited space for the dynamic disord er of Br yields a th reefold difference in 0 for Sn24P19.3Br8 in comparison with Sn17Zn7P22Br8. In these fits we have assumed that the Br inside the dodecahedra do not produce the dynamic disorder observed for the guest atoms inside the tetrakaidecahedra, as has been demonstrated for other type I clathrates.46,130
63 5. Type VIII Eu8Ga16Ge30 clathrates for magnetic applications Magnetic refrigeration based on the magne tocaloric effect (MCE) is a topic of great interest.135 While the concept itself is very ol d and magnetic cooling for producing ultralow temperatures dates back to the 1920s the discovery of all oys exhibiting the so called giant MCE has renewed interest for solid-state cooling applications in the intermediate to room temperature (77Â–300 K) range.135-137 Therefore, magnetic refrigeration technology is a promising a lternative to convent ional gas compression techniques.135 Long-range ferromagnetism and lowfield giant MCE were observed in type VIII clathrate Eu8Ga16Ge30. The results indicate that this material undergoes a second-order, ferromagnetic-paramagnetic transition at ~13 K, with long-range ferromagnetic ordering. The low-field giant MCE, together with the absence of thermal hysteresis and field hysteresis, makes it a ve ry promising candidate material for active magnetic refrigeration in the low temperature regime below 20 K. 5.1 Magnetocalloric effect (MCE) The magnetocaloric effect (MCE) is a magneto-thermodynamic phenomenon in which an externally applied changing magnetic field can strongly affect the spin degrees of freedom in a solid that results in a re versible change in temperature in a given specimen.135 Magnetic materials can be thought of as having two different heat reservoirs: the phonon excitations related to the lattice degr ees of freedom, and magnetic excitations connected to the spin degrees of freedom. In the magnetic refrigeration cycle136 depicted in Figure 5.1, a magnetocaloric substance undergoes an adiabatic magnetiza tion, that is, initially randomly oriented magnetic moments are aligned by an external magnetic field, t hus leading to a decrease in the entropy of the system. The insulated environment prevents the heat form Â“escapingÂ” the material. Therefore, since the entropy change S in a system at a given temperature T absorbing an infinitesimal amount of heat Q is given as S = Q/T the net result is heating up of the specimen.
64 Figure 5.1 Schematic representation of a magnetic refrigeration cycle The second stage of the MCE is isomagnetic enthalpic transfer, where heat is removed from the system by fluid or gas, say liquid helium for example, while the magnetic field is unchanged. The third stage, known as adia batic demagnetization allows randomization of the magnetic moments by removing the ma gnetic field, which leads to cooling the material below the ambient temperature. At the final stage, the magnetocaloric material is placed in a thermal contact with the environmen t being cooled and heat migrates into the working material. Magnetic refrigeration based on the MCE has recently received increased attention as an alternative to the co mpression-evaporation techniques. Magnetic refrigeration is also an environmentally fr iendly cooling technology, in this way similar to thermoelectric refrigeration, that does not use ozone depleting chemicals, hazardous chemicals, or green house gasses.135 Another important difference between the magnetic refrigeration and the conventional gas-compressi on techniques is the higher efficiency in
65 the former one. Magnetic refr igerators working with Gd show 60% of the Carnot efficiency compared with only about 40% in the best gas-comp ression refrigerators.138 5.2 Crystal structure of type VIII Eu8Ga16Ge30 clathrate The structural investigations139 of Eu8Ga16Ge30 show that it has two structural modifications, affiliated with the type I and VIII clathrates, respectively (Figure 5.2). Figure 5.2 Crystal structure of type VIII Eu8Ga16Ge30 Both structures are characterized by covalent E46 networks ( E =Ga, Ge) of fourfold bonded E atoms with polyhedral cages occupi ed by Eu. The type I phase has two different polyhedral cages: E20 pentagonal dodecahedra centered by Eu1 and E24 tetrakaidecahedra centered by Eu2 (E u1:Eu2=1:3). There are two Eu1 (2 a sites) and six Eu2 (6 d sites) atoms per unit cell. The type VIII phase has only one type of cage, a distorted pentagonal dod ecahedron centered by Eu (8 c site) atom. The shortest Eu-Eu distance for type VIII Eu8Ga16Ge30 is 5.562 , whereas in the type I Eu8Ga16Ge30 it is 5.23 . The average distance between Eu and E atoms that form the surrounding E20 cage is 3.633 for the type VIII Eu8Ga16Ge30. For the type I Eu8Ga16Ge30 the average Eu1-E
66 and Eu-E distances are 3.482 and 3.846 , re spectively. There are 92 covalent bonds per unit cell, giving a total of 184 valence electrons that fill the valence band completely thus leading to semiconducting properties in these compounds. Measurements of the anisotropic displacement parameters47 show the stiffness of th e framework relative to the larger anisotropic displacements of the encapsulated Eu atoms. 5.3 Synthesis of type VIII Eu8Ga16Ge30 For both Eu8Ga16Ge30 structure types a stoichiome tric mixtures of high purity starting elements were placed in BN crucibles, sealed under nitrogen in a quartz tube and induction melted at 1100 0C. The cooling process de termines the product compound. Rapid water quenching leads to type I Eu8Ga16Ge30. Type VIII Eu8Ga16Ge30 is obtained from the type I phase. The type I specimen was heated at a rate of 20C/min to a final temperature of 6750C, and annealed at this temper ature for two weeks. XRD data obtained on compositions of both phases are given in Figure 5.3. Differential Scanning Calorimetry (DSC) investigations show an endothermal effect at TI=700C, that is attributed to the formation of the type I phase. The next thermal effect at TVIII=697C, originates from type VIII I transformation in the clathrates phase. According to Leoni et al.142 this transformation is a reconstructive one. This would explain its endothermal character. It has been shown that the reaction is dependent on the starting state of the speci men, e.g., on the grain size of the type I phase used as a precursor to form the type VIII phase.
67 Figure 5.3 XRD patterns for type I (a) and type VIII (b) phases 2 2030405060 Intensity (arb. units) 0 1000 2000 3000 2 2030405060 Intensity (arb. units) 0 2000 4000 6000 8000 a) b)
68 5.4 Type VIII Eu8Ga16Ge30 clathrate for magnetocaloric applications Magnetic measurements were done in Dr. HariharanÂ’s Laboratory, using a commercial physical property measuremen t system from Quantum Design in the temperature range of 5Â–300 K at applied fields up to 7 T. The magnetic isotherms were measured with a field step of 0.05 mT in the range of 0Â–3 T and with a temperature interval of 3 K (1 K in the proxi mity of the Curie temperature, TC) over a temperature range of 5Â–62 K. Figure 5.4 shows the temperature dependenc e of magnetization taken at a low applied field of 0.01 mT. Figure 5.4 Magnetization curves taken at 0.01 mT with increasing (heating) and decreasing (cooling) temp erature. The corresponding dM / dT curve for the heating branch is also overlaid to mark the transition temperature. The inset shows the magnetization curves taken at applied fields of 1, 2, and 3 T. Figure 5.4 shows data at higher fields of 1, 2, and 3 T. The Curie temperature ( TC ) of 12.6 K is defined by the minimum in dM / dT (also shown overlaid on the M T curve in Figure 5.4). To check for the presence of any thermal hysteresis in the transition region, we measured the magnetization both while he ating and cooling the specimen. As shown
69 in Figure 5.4, no thermal hysteresis is detect ed. This is beneficial for active magnetic refrigeration.137 An expected broadening of the transi tion takes place at larger applied fields but remains reasonably sharp even at a field of up to 3 T (ins et in Figure 5.4). In a study reported by Hu et al .140 the compound MnAs0.9Sb0.1 displayed a smooth temperature variation of the magnetization und er high fields, whereas the shape of the M T curve for MnAs was almost unchanged. As a result, MnAs exhibited a larger MCE compared to MnAs0.9Sb0.1.141 Our experimental observation reported here leads to a similar expectation that type VIII Eu8Ga16Ge30 clathrate compound would show a large magnetic entropy change in the vicinity of its TC. In Figure 5.5a we show a series of M H isotherms taken at temp erature intervals of T =3 K from 5 to 53 K spanning the ferromagnetic transition region. Figure 5.5 a) Magnetization isotherms measured at different temperatures between 5 and 53 K with 3 K interval. b) The H / M vs M 2 plots for representative temperatures around the TC.
70 A sharp change in magnetization is clearly observed in Figure 5.5a as the temperature nears and eventually crosses over TC from ferromagnetic to paramagnetic states. A noticeable feature in Figure 5.5a is that a large proportion of the change in magnetization occurs below 2 T. This is beneficial for pract ical application of MC E materials at modest fields.135-137 Since the magnitude of MCE and its dependence on temperature and magnetic field are strongly dependent on th e nature of the corresponding magnetic phase transition,138 it is essential to analyze the magnetic transition further in this material. To do this, the measured data of the M H isotherms were converted into H / M versus M2 plots (the so called Arrott plots). These are shown in Figure 5.5b for representative temperatures near TC. According to the Banerjee criterion,141 the magnetic transition is of second order if all the H / M versus M 2 curves have a positive slope. On the other hand, if some of the H / M versus M 2 curves show a negative slope at some point, the transition is of first order.141,143 For the case of Eu8Ga16Ge30, the presence of the positive slope of the H / M versus M 2 curves indicates that the magnetic transition is of second order. This result is consistent with the absence of th ermal hysteresis (see Figur e 5.1) and the specific heat data,139 all of which points toward a second-or der magnetic transition. To elucidate the influences of the magne tic transition and long-range ferromagnetism on the MCE in Eu8Ga16Ge30, the magnetic entropy change SM( T ) is calculated from a family of isothermal M H curves (Fig. 5.4) using the Maxwell relation, 1 max0 0 H H MdH T M S (5.1) where M is the magnetization, H is the magnetic field, and T is the temperature. Figure 5.6 shows the magnetic entropy change SM( T ) as a function of temperature for different magnetic field changes up to 3 T. From Figure 5.6 SM reaches a very high value of 11.4 J /kg K at ~13 K for 0H =3 T, indicating that this clathrate belongs to a class of giant MCE materials. This value is about twice as large as that reported for DySb144 (~6.5 J /kg K at 11 K = 0H =3 T) and is almost equal to that reported for ErRu2Si2 145 (~12 J /kg K at 5.5 K for 0H =3 T) within a similar temperature range. It is also much larger than that of Gd137 (~10.2 J /kg K for 0H =5 T) and comparable with those of Gd5Si2Ge2 135 ( ~18 J /kg K for 0H =5 T) and
71 MnFeP0.45As0.55 138 (~18 J /kg K for 0H =5 T) near the transition re gion, although the transition temperatures vary in these latter materials. The relative cooling capacity, estimated using standard methods,137 is significantly larger for type VIII clathrate Eu8Ga16Ge30 (~87 J /kg) than for DySb 144 (~34 J /kg) and ErRu2Si2 145 (~55 J /kg) for the same field change of 2 T. Co mpared to other magnetocaloric materials,135,140,146 Eu8Ga16Ge30 has additional distinct technological advantages, such as no thermal hysteresis (Figure 5.1) and fi eld hysteresis (inset of Fi gure 5.6), which are desirable for active magnetic refrigeration cycles.135-137 These results indicate that this composition is a promising candidate for magnetic refrigeration in the low temperature region useful for helium and hydrogen liquefaction. The origin of the giant magnetic entropy change in Eu8Ga16Ge30 lies in the abrupt reduction in magnetization at the transition temperature. Moreover, the magnetic moment of 7.97 B for this material, as determined from the magnetization curve at 5 K (see inset of Figue 5.6), is nearly equal to the free-ion moment of 7.94 B. This, together with the existence of the long-range ferromagnetic order, clearly indicates a pa rallel alignment of all the Eu2+ magnetic moments and a strong coupling between these moments via the conduction-electron spins.139
72 Figure 5.6 Magnetic entropy change SM as a function of temperature ( T) extracted from M H T curves via the Maxwell relation. The inset sh ows the hysteresis loop measured at 5 K. Reprinted with permission from Ref. 33 Copyri ght , American Institute of Physics. This coupling remains strong at the transition temperature ( TC), as evidenced by the fact that the M T curves remain sharp under high applie d fields (see inset of Figure 5.4). Therefore the additional entropy change is attributed to the fact that the magnetic transition greatly enhances the effect of the applied magnetic field as the system enters a long-range three-dimensional ferromagnetic order completely from the paramagnetic phase within a narrow te mperature range around the TC. A recent study has shown that the existence of a short-range ferromagnetic or der (i.e., the presence of magnetic clusters) is a major obstacle for obtaining a large MC E response in magnetic materials due to the high energy required to realign the indivi dual spins by the applied magnetic field.147
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