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Synthesis and characterization of type II silicon and germanium clathrates

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Synthesis and characterization of type II silicon and germanium clathrates
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Beekman, Matthew K
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Clathrate
Thermal conductivity
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Silicon
Dissertations, Academic -- Physics -- Masters -- USF
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ABSTRACT: Clathrate materials comprise compounds in which guest atoms or molecules can be encapsulated inside atomic cages formed by host framework polyhedra. The unique relationship that exists between the guest species and its host results in a wide range of physical phenomena, and offers the ability to study the physics of structure-property relationships in crystalline solids. Clathrates are actively being investigated in fields such as thermoelectrics, superconductivity, optoelectronics, and photovoltaics among others. The structural subset known as type II clathrates have been studied far less than other clathrates, and this forms the impetus for the present work. In particular, the known "composition space" of type II clathrates is small, thus the need for a better understanding of possible compositions is evident. A basic research investigation into the synthesis and characterization of silicon and germanium type II clathrates was performed using a range of synthetic, crysta llographic, chemical, calorimetric, and transport measurement techniques. A series of framework substituted type II germanium clathrates has been synthesized for the first time, and transport measurements indicate that these compounds show metallic behavior. In the course of the investigation into type II germanium clathrates, a new zeolite-like framework compound with its corresponding novel crystal structure has been discovered and characterized. This compound can be described by the composition Na1-xGe3 (0 < x < 1), and corresponds to a new binary phase in the Na-Ge system. One of the most interesting aspects of type II clathrates is the ability to create compounds in which the framework cages are partially occupied, as this offers the unique opportunity to study the material properties as a function of guest content. A series of type II sodium-silicon clathrates NaxSi136 (0 < x < 24) has been synthesized in higher purity than previously reported for as-synthesized products. The tra nsport properties of the NaxSi136 clathrates exhibit a clear dependence on the guest content x. In particular, we present for the first time thermal conductivity measurements on NaxSi136 clathrates, and observe evidence that the guest atoms in type II clathrates affect the thermal transport in these materials. Some of the crystalline NaxSi136 compounds studied exhibit very low thermal conductivities, comparable in magnitude to amorphous materials. In addition, for the first time clear evidence from transport measurements was found that resonance phonon scattering may be present in type II clathrates, as is also the case in the type I subset.
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Thesis (M.A.)--University of South Florida, 2006.
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Synthesis and Characterization of Type II Silicon and Germanium Clathrates by Matthew K. Beekman 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. Sarath Witanachchi, Ph.D. Lilia Woods, Ph.D. Date of Approval: March 7, 2006 Keywords: clathrate, thermal conductivity, tran sport properties, mate rials science, silicon 2006, Matthew K. Beekman

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In memory of Randy. My first lab mate, and a friend who will be missed.

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Acknowledgements I wish to express my sincere gratitude for continued funding provided to me through the University of South Florida Pr esidential Doctoral Fellowship, which has helped to make possible the research presente d in the pages that follow. I also wish to acknowledge funding for the sili con clathrate work provided by the U.S. Department of Energy Office of Basic Energy Sciences, and for the germanium clathrate work provided by the Office of Naval Research. I would like to extend my sincere thanks and deep appreciation to my advisor Prof. George Nolas. His patience as a teacher, enthusiasm as a scientist, and guidance as a ment or continue to be essential in my growth as a scientist. I would also like to thank Prof. Jan Gryko of Jacksonville State University for his assistance with Rietveld refinement and hot-pre ssing of the silicon clathrates, and for his insight into the preparation of silicon cl athrates. I gratefully acknowledge Dr. Winnie Wong-Ng from the National Institute of Standards and Technology and Dr. James Kaduk at Innovene for their assistance in solv ing the structure of the new compound Na1xGe3. Thank you to Dr. Chris Kendziora of the Navel Research Laboratory for collecting Raman scattering data. Thanks goes to my coworkers in our research group the Novel Materials Laboratory, who help make our lab a great environment to work in. Special thanks to Josh Martin for his insight and advice regardi ng our transport measurements system, to Josh and Grant Fowler for cont inuing stimulating conversations on science, and to Holly Rubin for her help wi th the synthesis in this work. Finally, I thank my parents for the love and support they have always given me and to Teresa for her continued patience and support.

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i Table of Contents List of Tables iii List of Figures iv Abstract vii 1 Introduction 1 2 An Overview of Type II Clathrates 6 2.1 Structural Features 6 2.2 Previous Work 9 2.2.1 Electrical Properties 11 2.2.2 Thermal and Vibrational Properties 15 2.3 Applications 20 3 Synthesis and Sample Preparation 26 3.1 Degassing of Silicides and Germanides 26 3.1.1 Preparation of NaxSi136 Clathrates 26 3.1.2 Preparation of NaxGe136 Clathrates and the New Phase Na1xGe3 31 3.1.3 Other Silicides and Germanides 32 3.2 Direct Synthesis of Cs8Na16MyGe136y Clathrates (M = Ag, Cu) 34 3.3 Partially Filled Type II Ge Clathrates 37 4 Structural and Chemical Characterization 39 4.1 Characterization of NaxSi136 Clathrates 39 4.2 Characterization of Cs8Na16MyGe136y Clathrates (M = Ag, Cu) 45 4.3 The New Compound Na1xGe3 49 5 Transport Properties 53 5.1 Experimental Details 53 5.2 Transport Properties of NaxSi136 Clathrates 54 5.3 Transport Properties of Cs8Na16CuyGe136y Clathrates 60 6 Summary and Future Directions 67

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ii References 70 Bibliography 74

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iii List of Tables Table 2.1 Comparison of ionic radii of the alkali metals with the approximate van der Waals radii of the em pty space in the small (20atom) and large (28-atom) cages in silicon and germanium type II clathrates, after Bobev and Sevov. 9 Table 2.2 Rattler frequencies in cm-1 as determined from Raman scattering, ADPs from single crystal XRD, and theoretical calculations. 18 Table 3.1 Structures of various silicides and germanides and the products obtained by their thermal decomposition. 33 Table 4.1 Structure and composition of Na1Si136 and Na8Si136. 42 Table 4.2 Preliminary structural data for the novel phase Na0.7Ge3, space group P6/m, a = 15.05399(5) , c = 3.96845(2) . 50

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iv List of Figures Figure 1.1 An example of the cage-like stru cture of clathrate materials. 3 Figure 2.1 Structure of the type II clathrate. 7 Figure 2.2 Temperature dependence of re sistivity (round symbols) and Seebeck coefficient (square symbols) for polycrystalline samples of Cs8Na16Si136 (filled symbols) and Cs8Na16Ge136 (open symbols). 13 Figure 2.3 Arrhenius plot of the resistance for Si136. 14 Figure 2.4 Temperature dependent ADPs for (a) Rb8Na16Si136, (b) Cs8Na16Si136, (c) Rb8Na16Ge136, and (d) Cs8Na16Ge136, determined from single crystal X-ray diffraction. 16 Figure 2.5 Raman scattering spectra of Si136 and Cs8Na16Si136. 17 Figure 2.6 Thermal conductivity of the cr ystalline silicon clathrate Si136 and Cs8Na16Si136. 19 Figure 2.7 Schematic of a thermoelectric couple for power generation. 22 Figure 2.8 Band diagram schematic of ca rrier generation in a p-n homojunction. 24 Figure 3.1 Crystal structure of the Zintl phase NaSi, emphasizing the Si4 4cluster units (blue) and Na+ ions (orange). 27 Figure 3.2 Schematic of the vacuum furnace apparatus designed for degassing of the silicides and germanides, and for further degassing of the clathrates. 28 Figure 3.3 Qualitative representation of phase percentages from products obtained from thermal decomposition of NaGe. 31

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v Figure 3.4 Temperature schedule for the synthesis of the framework substituted type II germanium clathrates. 35 Figure 3.5 Small as-grown crystallites of Cs8Na16CuyGe136y. 36 Figure 3.6 Lattice parameter of NaxRb8Ge136, as measured after vacuum degassing at the indicated temperature. 38 Figure 4.1 Simulated theoretical X-ray diffraction patterns for NaxSi136 clathrates as a function of the Na content x calculated using the PowderCell computer software. 40 Figure 4.2 Refinement of powder XRD data for Na1S136. Peaks associated with Na8Si46 and diamond-structure silicon are indicated by arrows. 41 Figure 4.3 GSAS fit of the pow der XRD data for Na8Si136. 42 Figure 4.4 Stokes Raman scattering spectra for Na1Si136 and Na8Si136. 43 Figure 4.5 Heat flow as a function of temperature for NaxSi136 samples with x = 0, 1, and 8, determined by DSC measurements. 44 Figure 4.6 Powder XRD patterns for Cs8Na16AgyGe136y clathrates. 46 Figure 4.7 Powder XRD patterns for Cs8Na16CuyGe136y clathrates. 47 Figure 4.8 Lattice parameter as a function of transition metal content for the Cs8Na16CuyGe136y (closed circles) and Cs8Na16AgyGe136y (open triangles) clathrates. 48 Figure 4.9 A schematic of the structure of NaGe3, viewed along the c -axis at a slight tilt. 50 Figure 4.10 Powder X-ray diffraction of Na1xGe3. 52 Figure 5.1 Temperature dependent electrical resistivity of Na1Si136 (closed circles) and Na8Si136 (open cicles), along with Cs8Na16Si136 (closed squares). 54 Figure 5.2 Temperature dependent thermal conductivity of Na1Si136 (closed circles) and Na8Si136 (open circles), along with that of single crystal diamond structur e silicon (dashed line). 55

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vi Figure 5.3 Low temperature lattice thermal conductivity for single crystalline Sr8Ga16Ge30 (circles) and Eu8Ga16Ge30 (squares). 58 Figure 5.4 Temperature dependence of the electrical resistivity of Cs8Na16CuyGe136y, with y = 0, 5, and 8, indicating the metallic behavior of these materials. 59 Figure 5.5 Temperature dependence of the Seebeck coefficient of Cs8Na16CuyGe136y, with y = 0, 5, and 8. 61 Figure 5.6 Temperature dependence of the thermal conductivity for Cs8Na16CuyGe136y with y = 0, 5, and 8. 62 Figure 5.7 Verification of losses due to radiation during the thermal conductivity measurement. 64

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vii Synthesis and Characterization of Type II Silicon and Germanium Clathrates Matthew K. Beekman ABSTRACT Clathrate materials comprise compounds in which guest atoms or molecules can be encapsulated inside atomic cages form ed by host framework polyhedra. The unique relationship that exists between the guest spec ies and its host results in a wide range of physical phenomena, and offers the ability to study the physics of structure-property relationships in crystalline solids. Clathrates are actively being investigated in fields such as thermoelectrics, superconductivity, optoe lectronics, and phot ovoltaics among others. The structural subset known as type II clathrates have been studied far less than other clathrates, and this forms the impetus for the present work. In particular, the known “composition space” of type II clathrates is small, thus the need for a better understanding of possible compositions is eviden t. A basic research investigation into the synthesis and characterization of silicon and germanium type II clathrates was performed using a range of synthetic, crystallographi c, chemical, calorimetric, and transport measurement techniques. A series of framew ork substituted type II germanium clathrates has been synthesized for the first time, and transport measurements indicate that these compounds show metallic behavior. In the co urse of the investigation into type II germanium clathrates, a new zeolite-like framework compound with its corresponding novel crystal structure has been discovered and characterized. This compound can be described by the composition Na1xGe3 (0 < x < 1), and corresponds to a new binary phase

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viii in the Na-Ge system. One of the most interestin g aspects of type II clathrates is the ability to create compounds in which the framework cag es are partially occupied, as this offers the unique opportunity to study the material pr operties as a function of guest content. A series of type II sodium-silicon clathrates NaxSi136 (0 < x < 24) has been synthesized in higher purity than previously reported for as-synthesi zed products. The transport properties of the NaxSi136 clathrates exhibit a clear dependence on the guest content x In particular, we present for the first tim e thermal conductivity measurements on NaxSi136 clathrates, and observe evidence that the guest atoms in type II clathrates affect the thermal transport in these materi als. Some of the crystalline NaxSi136 compounds studied exhibit very low thermal conductivities, comparable in magnitude to amorphous materials. In addition, for the first time clear evidence from transport measurements was found that resonance phonon scatteri ng may be present in type II clathrates, as is also the case in the type I subset.

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1 1 Introduction The term clathrate refers to any group of material s that has the ability to contain atomic or molecular “guest” species within a “host” network or latti ce. The structure of these “inclusion compounds” is such that there exist voids that may be filled by the guest species. Strictly speaking, true clathrates are those compounds which crystallize even in the absence of the guest. Examples include th e skutterudites and va rious oxide zeolites, though many more examples exist in which the host lattice only forms in the presence of the guests. These are sometimes referred to as the crypto-clathrates.1 However, the structures discussed in this work are collectiv ely referred to simply as clathrates in the literature. For more than one hundred years, H2O has been known to form the compounds referred to today as the clathrate hydrat es, where the host lattice is formed by tetrahedrally coordinated, hydrogen bonded H2O molecules in much the same manner as common ice.2 Also known as gas or liquid hydrates, these compounds constitute structural phases of ice, and can encapsulat e molecules or atoms in voids formed by the crystal structure, such as meth ane or xenon with compositions (CH4)8(H2O)46 and Xe8(H2O)46, respectively. The methanecontaining ice clathrates are naturally occurring and can be found under the sea in Polar Regions, as well as the Gulf of Mexico and the

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2 Caspian Sea.3 There has been much interest in th e potential of these clathrates as a useable source of energy, and it has been suggested that if the huge amounts of methane trapped in this form could be harvested it could potentially replace the world’s entire fossil fuel reserves combined.3,4 Ironically, contributions to global warming have also been speculated due to release of methan e from the gas hydrates found in the oceans,3 and gas hydrates have been known to cause flow assurance and safety problems by forming in oil and gas pipelines.4 Recently, the potential for i ce clathrates as a hydrogen storage medium has also been discussed.5 To date, geometrically ther e are nine main possible st ructures that fall in the general class of clathrate materials, though experimental examples have not been produced for all of these structures.6 In addition to the nine basi c types, structural variants or derivatives have been repor ted including isomers or superstructure variants of the type I clathrates.7-9 The crystal structure of the type I cl athrate, the structure type that has received the most attention, is shown in Figure 1.1. A structural theme common to all clathrate materials are constituent polyhedra th at form the crystal structure. Typically these polyhedra share faces in an arrangeme nt allowing for the inclusion of the guest species inside, and include pentagonal dodecahedra, tetrakaidecahedra, and hexakaidecahedra. For the majority of clathrat e materials, the framework consists wholly or partially of the group IV el ements silicon, germanium, or tin, with the guest species being alkali or alkaline earth atoms, and the rare earth europium. It was not until the 1960’s that “inorgani c” clathrates were first synthesized and investigated. In a systematic study of the th ermal degradation of alkali silicides (e.g.,

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3 (a) (b) Figure 1.1 An example of the cage-like struct ure of clathrate materials. (a) Crystal structure of the type I clathrate, viewed along the [001] direction at a slight tilt. The simple cubic unit cell is outlined in the upper left. (b) The face-sharing polyhedra that constitute the type I clathrate crystal structure. NaSi, KSi, etc.), Kasper et al .10 reported that cubic phases isostructural with the gas hydrates were formed that were deficien t in the alkali metal. These compounds comprised the silicon and germanium analogue s to the type I and type II clathrate hydrates. A more thorough report of th is work was later given by Cros et al .11 Initially, these silicon and germanium cl athrates were intere sting due to their unique crystal structure, but the physical properties of these materials were not extensively studied. However, in the past ten years new appro aches to materials research have renewed interest in these and simila r materials, and clathrates have proved a extremely rich source of varied a nd often novel phenomena. For example, superconducting,12,13,14 thermoelectric,1,15 photovoltaic and optoelectronic,16,17,18

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4 magnetic19,20 and mechanical21,22 properties of clathrates ar e currently being investigated by several groups. Clathrates such as the type I Na2Ba6Si46, 12 Ba8Si46,13 and the type IX Ba24Ge100 14 comprise unique superconductors. Type I clathrates such as Sr8Ga16Ge30 and Eu8Ga16Ge30 exhibit very low thermal conductiv ities with glasslike temperature dependences.23 Paired with the good electr ical properties found in Sr8Ga16Ge30, clathrates are raising continued interest for thermoelectric applications.15 Carbon clathrates, as yet not produced experimentally, have been pred icted to be the second hardest materials known to humankind.21 Some applications of interest fo r type II clathrates are discussed in Chapter 2. In addition to potential app lications, clathrate materials c ontinue to be of interest for reasons of basic science as well. From a chemical and physical point of view, these materials allow for the study of the physics of compounds possessing isomorphic structures with greatly varying properties, rang ing from metals24,25 to semiconductors15,26 to superconductors,12-14 and magnetic materials19,20 as well. Also, many variants appear to adhere to the Zintl formulation of charge balance in extended solids. This chemical aspect has been investigated by several research groups.6,27 Perhaps the most conspicuous aspect of clathrate materials is the guest host intera ction. For example, th e localized vibrational modes of the guest atoms in several clathr ate compounds resonantly scatter the heatcarrying framework acoustic phonons, great ly reducing the thermal conductivity.1 Most reports on clathrates thus far have concentrated on the type I structure, though in recent years other structures such as the type VIII and type IX are receiving increased attention. In general, type II clathrates have been studied far less extensively.

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5 The impetus for the present work is the need for a better understanding of the physical properties of type II clathrates, and moreove r a deeper investigation into the possible “composition space” for these materials.

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6 2 An Overview of Type II Clathrates This chapter reviews the important structur al aspects of the type II clathrates, and some of the prior work that has been perf ormed. The emphasis here is on structural and transport properties, and those aspects of the materials which can affect the electronic and thermal transport. 2.1 Structural Features The type II clathrates crys tallize with the space group m Fd 3 and can be depicted by the general formula AxE136 (0 < x < 24), where A has to date empirically been observed to be Na, K, Rb, Cs, or Ba and E re presents Si, Ge, or Sn. The E atoms form an sp3 tetrahedrally bonded framework, in which the E atoms reside at the vertices of sixteen pentagonal dodecahedra and eight hexakaide cahedra constituting the conventional unit cell (see Figure 2.1). The 136 framework atoms pe r conventional unit cell reside at three distinct crystallographic sites: 8 a 32 e and 96 g in the Wyckoff notation. The A atoms reside inside the atomic cages formed by the polyhedra at the 8 b (larger hexacaidecahedra) and 16 c (smaller dodecahedra) sites. Th e conspicuous aspect that differentiates type II clathrates from the other structure types is the possibility of

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7 (a) (b) Figure 2.1 Structure of the type II clathrate. (a) The hexakaidecahedron (larger cage) and pentagonal dodecahedron (smaller cage) that make up the type II clathrate crystal structure. (b) A depiction of the conventional unit cell of the type II clathrate crystal structure, vi ewed along the [110] direction. fractionally filling the voids in type II clathrates, as seen in the formula AxE136. Thus type II clathrates may be synthesized such that essentially all of the voids are empty ( x = 0), stoichiometrically filled were each site is occupied ( x = 24), or a range of values in between. Previous work on these materials is reviewed below. As may be seen from careful examinati on of the crystal structure (Figure 2.1), type II clathrates can be view ed as a derivative of the di amond crystal structure. Both structures are composed of tetrahedral sp3 bonded atoms, and the cl athrate structure can be thought of as an “expanded” version of the diamond structure. Typically the E-E-E bond angles range from 105 to 126 in the clathrates, and average close to the 109.5 angle that is characteris tic of the diamond structure.1 However, the volume per framework atom in the clathrate is appr oximately 15% larger than the corresponding

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8 diamond structure, and this is an indica tion of the “openness” of the clathrates.1 The type II clathrate structure is related to the diamond structure in another in teresting way, and an alternative way to visualize the type II clathrates is to position the centers of the hexakaidecahedra at the sites of an enlarged diamond lattice. The pentagonal dodecahedra are then automatically form ed in the spaces between the larger hexakaidecahedra. Thus the polyhedra share faces, filling three dimensional space. Table 2.1 gives an idea of the relative sizes of alkali guest atoms and the cages in which they reside, taken from the work of Bobev and Sevov.28 From this table, a clear geometrical correlation is apparent between th e relative sizes of the guest and cage, and which compounds have been experimentally observed. For example, type II clathrates with K, Rb, or Cs occupying the smaller cage have not been observed in silicon or germanium clathrates, due to these guests being too large to “fit” in the smaller dodecahedra. From the information in Table 2.1, one may also estimate the available space the guest species has to move around inside their respective cages; note that the guests inside the larger hexacaidecahedra have more “room” to move. This point will be revisited below.

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9Table 2.1 Comparison of ionic radiia of the alkali metals with the approximate van der Waals radii of the empty spaceb in the small (20-atom) and large (28-atom) cages in silicon and germanium type II clathrates, after Bobev and Sevov.28 The differencesc between cage and guest sizes are given by 20 and 28 for the small and large cages, respectively; negative numbers in parenthesis indicate a guest ionic radius that is larger than the cage. All values are given in angstroms. Guest ion Ionic Radiusa Small cage radiusb Large cage radiusb 20 c 28 c Silicon framework Na 1.02 1.10 1.85 0.08 0.83 K 1.38 1.10 1.85 (-0.28)d 0.47d Rb 1.49 1.10 1.85 (-0.39)d 0.36 Cs 1.70 1.10 1.85 (-0.60)d 0.15 Germanium framework Na 1.02 1.25 2.00 0.23 0.98 K 1.38 1.25 2.00 (-0.13)d 0.62d Rb 1.49 1.25 2.00 (-0.24)d 0.51 Cs 1.70 1.25 2.00 (-0.45)d 0.30 a Ionic radii are those calculated for various oxides, taken from Ref. 29. b Calculated by taking the shortest A-E distance for the respective cage and subtracting the van der Waals radius of the E atom. Thus this is a measure of the smallest dimension of the cage. c = (Cage radius) – (Ionic radius) d A guest that has not been experimentally observed at this site. 2.2 Previous Work To date, only a very limited number of compositions have been reported for inorganic type II clathrates. In their entirety, they are: NaxSi136 and NaxGe136 (0 < x < 24), and Cs7Si136;11 Rb8Na16Si136, Cs8Na16Si136, Rb8Na16Ge136, and Cs8Na16Ge136;28 Ba8Na16Si136;30 Ba8Ga32Sn104;31 and Cs8Ge136.32 A completely guest free clathrate Si136 was also synthesized33 in which essentially all of th e framework cages are empty (less

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10 than 600 pmm sodium), constituting a new allotr ope of elemental silicon. From this short list, it is clear that much wo rk still remains to be done to increase the known composition space of type II clathrates, and this is a driving motivation for the present work. As mentioned above, the pioneering studies on inorganic type II clathrates were performed by Cros et al .11,34 Clathrates with general composition NaxSi136 were synthesized and characterized chemically and structurally. Compositions of Cs7Si136 and NaxGe136 were also reported, but until the pres ent work these have not been reproduced. The materials were initially of interest for th eir peculiar structures, but until recently little more work was carried out. In general, type II clathrates have not been extensively studied. However, significant work has been performed on the sodium-silicon materials, NaxSi136, and this system has by far been the most studied of the type II clathrates. In these materials the guest-host interaction is of prime interest, in this case the various interactions between the sodium guests and the silicon framework. Expe rimental investigati ons include powder Xray diffraction,35,36 inelastic neutron scattering,37 Raman scattering,38,39 X-ray photoemission spectroscopy (XPS),40 extended X-ray absorption fine structure (EXAFS),41,42 electron spin resonance (ESR),43 nuclear magnetic resonance (NMR),44-48 magnetic measurements,11 and initial electrical transport measurements.11 Theoretical calculations have investigated the possible guest displacement,49,50 electronic and band structure,16,18,51-53 energetics,16,18,51,53 and lattice vibr ational properties.54,55,56 It is important to note that although these material s were of the first inorganic clathrates discovered over forty years ago,10 until the present work their transport properties have

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11 not been well characterized. In particul ar, no prior reports exist on the thermal conductivity of sodium filled NaxSi136 type II clathrates. Recently, Reny et al .35 and Ramachandran et al .36 independently systematically synthesized and structura lly characterized the NaxSi136 clathrates for a wide range of values of x Rietveld refinement of the powder X-ra y diffraction data for each sample was performed in both studies. As also shown in the present work, the powder diffraction patterns of the type II clathrates depend se nsitively on both the gue st type and content x Thus refinement of the X-ray diffraction data allows a method for determining both content and relative oc cupancy of the cages. 2.2.1 Electrical Properties In terms of scientific merit, the type II clathrates offer material systems in which the physical properties may be studied as th e composition is varied in a controlled manner. As mentioned above, type II clathrates offer the ability to partially fill the crystal cages, and as is shown in the present work this has a remarkable effect on the transport properties in these materials. It was known in the initial work from Cros et al .11 that the sodium content x in NaxSi136 clathrates has a significant e ffect on the electri cal properties. The lower sodium content ( x < 11) materials were reported to behave as semiconductors or insulators with respectable Seebeck coeffi cients, while the higher alkali content results in metallic behavior.11,57

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12 Several other researchers further investigat ed the Na-Si clathrat es, with particular interest in the possible metal-to-insulator transition that appears to occur with composition.11,57 In analogy with alkali-doped C60 fullerenes, the NaxSi136 clathrates were investigated for superconductivit y, but with negative results.58 Several mechanisms for both the electronic conduction a nd the transition from insulating to metallic behavior in NaxSi136 clathrates have been suggested. Mott57 explained the transi tion in terms of a “Na-band,” which comes into existence as the average distance between Na guests becomes less as the content increases. Anothe r model describes the conduction in terms of shallow impurity levels from the sodi um atoms, from which electrons may be thermally excited into the fr amework conduction bands. Demkov et al .51 discussed the transition in terms of a Jahn-Teller distor tion with sodium filling, causing a modification of the band structure resulting in a split-off ha lf-filled band inside of the electronic gap. It is still an open question as for exactly which value of x the transition occurs, though there is agreement that it is between 8 and 12. The underlying physics of the metal-toinsulator transition and the m echanisms of conduction in NaxSi136 have not been determined unequivocally. More recently, Nolas et al.25 have reported on the electr ical and thermal properties of stoichiometric type II silicon and germaniu m clathrates, in which all of the cages are filled by alkali metal guests. As shown in Figure 2.2, type II clathrates such as Cs8Na16Si136 and Cs8Na16Ge136 possess metallic properties, such as low Seebeck coefficients and resistivities that increase with increasing temperature. These results were consistent with NMR measurements performed on Cs8Na16Si136,59 Rb8Na16Si136,60 and

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13 Figure 2.2 Temperature dependence of resistivity (roun d symbols) and Seebeck coefficient (square symbols) for polycrystalline samples of Cs8Na16Si136 (filled symbols) and Cs8Na16Ge136 (open symbols). Reprinted with permission from G.S. Nolas, D.G. Vanderneer, A.P. Wilkinson, and J.L. Cohn, J. Appl. Phys. 91 8970 (2002). Copyright 2002, American Institute of Physics. Cs8Na16Ge136 61 which also showed metallic behavior for these materials. Band structure calculations32 indicate that the Ferm i level lies clearly within the conduction band in Cs8Na16Ge136, consistent with the above experiments. In the initial work on the guest free clathrate Si136,17 Gryko et al. reported results from resistance (see Figure 2.3) as well as optical absorption measurements. These indicated Si136 has a wide band gap of approximately 2 eV, in good agreement with previous theoretical calculations.16 Thus on the expansion of silicon from diamond structure to the “open” type II clathrate stru cture, the band gap increases by a factor of almost 2.

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14 Figure 2.3 Arrhenius plot of the resistance for Si136.17 The fit to the high temperature data indicates the intrinsic band gap to be ~ 2 eV. Reprinted figure with permission from J. Gryko, P.F. McMillan, R.F. Marzke, G.K. Ramachandran, D. Patton, S.K. Deb, and O.F. Sankey, Phys. Rev. B 62 R7707 (2000). Copyright 2000 by the American Physical Society. Web: http://link.aps.org/abstract/PRB/v62/pR7707 Very recently, we have synthesized and characterized for the first time the clathrate Cs8Ge136.32 The material was synthesized by c ontrolled degassing of Na from Cs8Na16Ge136, until essentially all of the smalle r cages are empty. NMR and electrical resistivity measurements on Cs8Ge136 showed this material is also metallic, also consistent with band structure calcu lations performed on this material.32 A significant result of this work showed that Ge type II clathrates are indeed stable under partial occupation, thus offering a potenti al route toward tuning the el ectrical properties in these materials for thermoelectric applications.

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15 2.2.2 Thermal and Vibrational Properties As with type I clathrates, the guest-hos t interactions and their relation to the thermal properties is of particular interest in type II clathrates. As discussed in this section, previous work suggest s that the guests in type II clathrates undergo large, anharmonic vibrations inside their atomic cages. The effect s these local modes may have on the lattice thermal co nductivity are therefore of prime interest. The isotropic atomic displacement parameter (ADP or Ueq) is a measure of the mean square displacement (averaged over all directions) of an atom about its “equilibrium” site in a crystal.62 Using single crystal X-ray diffraction, Nolas et al .25 have measured the temperature dependence of the AD Ps for stoichiometric type II Si and Ge clathrates; the results are presented in Fi g. 2.4. For all four compounds, the alkali guests exhibit significantly larger ADPs than the framework atoms, and also show much stronger temperature dependencies. This is an indication that the al kali guests “rattle” in their atomic cages, corresponding to a relativ ely large amplitude dynamic disorder. Also note that the ADP data for the various guest s also shows good qualitative agreement with the difference in sizes of guest and cage, as given in Table 2.1. Sp ecifically, a trend is apparent that the larger the difference between cage and guest, the larger the ADP and the more pronounced the temperature dependence. The vibrational propert ies of some type II clathrates have also been studied using Raman spectroscopy. Nolas et al .63 reported the Raman spectra for stoichiometric type II clathrates and for Si136, as shown in Figure 2.5. The local vibrational mode of the Cs

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16 Figure 2.4 Temperature dependent ADPs for (a) Rb8Na16Si136, (b) Cs8Na16Si136, (c) Rb8Na16Ge136, and (d) Cs8Na16Ge136, determined from single crystal X-ray diffraction. Reprinted with permission from G.S. Nolas, D.G. Vanderneer, A.P. Wilkinson, and J.L. Cohn, J. Appl. Phys. 91, 8970 (2002). Copyright 2002, American Institute of Physics. atom in the lager E28 cage is in fact an optic mode and is Raman active. The site symmetry at the Na atom in the smaller E20 cage results in this mode not being Raman active, thus this “rattle” m ode is not present in the sp ectra. Clearly, the mode at approximately 50 cm-1 can be attributed to the rattling motion of the Cs atom in its cage, as this mode is completely absent in the unfilled clathrate Si136. (a) (d) (c) (b)

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17 Figure 2.5 Raman scattering spectra of Si136 and Cs8Na16Si136. Note that the optic mode of the Cs atom in the bottom spectrum is clearly absent in the spectra for Si136 in which no guest atoms are present. Reprinted with permission from G.S. Nolas, C.A. Kendziora, J. Gryko, J. Dong, C.W. Myles, A. Poddar, and O.F. Sankey, J. Appl. Phys. 92, 7225 (2002). Copyr ight 2002, American Institute of Physics. The frequencies of some guest atoms in type II clathrates ar e given in Table 2.2, as determined from ADP data,25 Raman scattering,63 and theoretical calculations.64 It has been shown62,65 that an estimate of the vibrational frequencies of weakly bonded atoms in a crystal can be extracted from ADP data by assuming a simple harmonic oscillator model to describe the guest atom’s motion. Th is method can also be used to estimate some of the physical properties of the mate rial, such as the latti ce thermal conductivity and Debye temperature, D.65 The frequencies in the table agree qualitatively, and all are

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18Table 2.2 Rattler frequencies in cm-1 as determined from Raman scattering,63 ADPs from single crystal XRD,25 and theoretical calculations.63,64 Compound Cs or Rb Na Cs or Rb Na Cs or Rb Na ADP Raman Theory Cs8Na16Si136 53.4 141 57 --64 120 Rb8Na16Si136 55.0 130 --------Cs8Na16Ge136 41.8 117 18 --21 89 Rb8Na16Ge136 42.9 127 --------quite low. Indeed, theoretical calculations64 of phonon dispersion show that the “rattler” modes cut the acoustic phonon branches, indica ting the possibility fo r strong interaction between the guest and framework vibrations. Recently, the thermal conductivities of some type II clathrates have been reported.25,66,67 The results for the unf illed silicon clathrate Si136 and completely filled Cs8Na16Si136 are compared in Figure 2.6. The empty clathrate Si136 has a remarkably low thermal conductivity, almost 30 times lower than elemental diamond-structured silicon at room temperature, and appro aches that of amorphous SiO2 (a-SiO2; glass). This result is consistent with a theoretical calculation of the thermal c onductivity of an unfilled type I clathrate Ge46, which showed an order of magnitude decrease as compared to diamond structured germanium. Because Si136 is essentially an electrical insulator,17 thermal conduction in this material is almost entirely due to the lattice c ontribution. The notable aspect of this result is that the thermal conductivity is low ev en in the absence of “rattler” atoms inside the cages, where the resonant phonon scattering mechan ism present in some type I clathrates is absent in Si136. The stoichiometric Cs8Na16Si136 has a relatively higher

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19 Fig. 2.6 Thermal conductivity of the crystalline silicon clathrate Si136 and Cs8Na16Si136. The solid line indicates what would be a T3 dependence. Reproduced with permission from M. Beekman, G.S. Nolas, J. Gryko, G.A. Lamberto n, Jr., T.M. Tritt, and C. A. Kendziora, Electrochem ical Society Proceedings 200327 217 (2004). Copyright 2003, the Electrochemical Society. thermal conductivity, which can be attributed to the large electronic contribution due to the metallic properties of this material. Howe ver, using the approach described by Sales et al .,65 Nolas et al .25 estimated from the ADP data that the room temperature lattice thermal conductivity of Cs8Na16Si136 to be on the order of 2 W/m-K.

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20 2.3 Applications In addition to the interesti ng physics that can be learne d from type II clathrates, these materials hold promise for a number of applications. One of the reasons for the recent surge in interest in clathrates is due to the discovery of superconductivity in some clathrate materials. The first repor t was for the type I clathrate Ba2Na6Si46,12 and further reports soon followed. These materials are un ique in that they are covalently bonded superconductors. Investigations into superconductiv ity in type II clathr ates have thus far produced negative results.58 However, if found superconducti ng type II clathrates could offer a useful system for studying the effect s of the guest conten t on the superconducting state, since the former may be varied in these materials. Type II clathrate materials are also of interest for se veral potential applications involving the solid state convers ion of energy. For example, these materials are raising continued interest in the field of thermoelectrics, 68 which is the conversion of electrical energy to thermal energy, and vice versa. For certain materials, imposing a temperature gradient across the material induces a co rresponding electrical voltage. Under open circuit and linear response conditions, this voltage V is simply proportional to the temperature difference, so that T S V (2.1) where S is a bulk material property know as the Seebeck coefficient or thermopower, and

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21 T is the imposing temperature difference across the material. This most basic thermoelectric effect is known as the S eebeck effect, and by c onvention the sign of S is negative (positive) if the majority carriers are electrons (holes). In metals, the simplest picture69 of the Seebeck effect can be described in terms of the differing thermal velocity distributions of charge carriers at the hot and cold ends, in th e steady state resulting in an accumulation of net charge at the cold end and an accompanying potential difference typically on the order of a fe w up to tens of V for a T of 1 K. The effect is significantly larger in semiconductors,69 due to the fact that in a ddition to the differing thermal velocity distributions, the Fermi-Dirac distribu tions at the hot and co ld ends may also be appreciably different, thus a dditionally causing varying carr ier excitation with position. Thus semiconductors typically have Seebeck coefficients of a few hundred to a few thousand V/K. The usefulness of a thermoelectric material is given by its dimensionless figure of merit ZT where T S ZT 2 (2.2) Here is the electr ical conductivity, is the total thermal conductivity ( = e + L, the sum of the electronic and lattice contributions, respectively), and T is the absolute temperature. The Seebeck effect can be used to generate power, converting the energy from a heat source into electrical current when a thermoelectric circu it is connected to a load. Figure 2.7 shows a schematic of a thermo electric couple, in which n-type and p-

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22 PN Heat Source Heat SinkLoadI Figure 2.7 Schematic of a thermoelectric couple designed for power generation. Reprinted with permission from Ref. 70. type materials are connected elect rically in series and thermally in parallel, and a load is connected to the circuit. The imposing temper ature difference causes a current to flow in the circuit, thus generating power. Currently, state of the art thermoelectri c materials for power generation have ZT on the order of or less than 1, resulting in efficienci es for thermoelectric power generation that are less than 30% of the Carnot limit.68 Thus power generation using thermoelectric technology has been limited to ni che applications, or in situations where reliability and longevity outweigh efficiency a nd performance. An example is the case of

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23 Radioisotope Thermoelectric Generators (R TGs) that provide the onboard power for NASA deep space probes such as Voyager or Cassini. Within the past two decades there ha s been much renewed interest in thermoelectric materials research. One reason for this is Slack’s concept of the ideal “Phonon Glass Electron Crystal” (PGEC) material.71 From Eq. (2.1), it is clear that a good thermoelectric material must simultaneous ly possess good electri cal properties (i.e. high electrical conductivity a nd Seebeck coefficient) and low thermal conductivity. Thus Slack proposed the design or discovery of materials that would conduct heat like a structural glass (“Phonon Glass”) yet conduct el ectricity as in a high quality single crystal semiconductor (“Electron Crystal”). In particular, Slack suggested72 that clathrate materials may fulfill the requirements of a PGEC, and investigations by Nolas et al .15 among others73,74,75 have shown this approach to be valid in the search for new thermoelectric materials. In addition to the good semiconducting properties that some clathrates possess, several variants have been shown to have very low thermal conductivities and in a few cases literally “glasslike.”23 The low thermal conductivity of these materials has been attr ibuted to the resonant scat tering of the heat carrying framework acoustic phonons by the localized vibration modes of the guest atoms.23 As discussed above, type II clathrates possess many similar properites as type I clathrates, in particular the guest atoms in t ype II clathrates also display large anharmonic motion inside of their cages. The lattice therma l conductivities of type II clathrates are in general expected to be quite lo w. In addition, the ability to pa rtially fill the cages in type II clathrates allows for an a dditional control for simultaneously tuning all of the transport

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24 V alence band Conduction band Photon Carrier generation n-type material p -t yp e material e h+Fermi level Built-in electric field properties in these materials. A deeper understanding of the tr ansport properties in type II clathrates is needed in order to assess the potential these materials hold for thermoelectric applications. Another potential application for type II clathrates is for photovoltaics, or the direct conversion of light to electricity. T echnologies such as photovoltaics are currently attracting much attention as candidates to fulfill the world’s increasing energy needs. However, currently the relatively low efficien cy and high fabrication costs of solar cells form a barrier preventing photovoltaics from significantly contribu ting to global energy production. Figure 2.8 shows a simplified band di agram schematic of a conventional p-n homojunction used for photovoltaic conversi on of light into el ectricity. Typically, production level solar cells have used a si licon p-n junction design, which has been shown to have a 31% maximum energy conversion efficiency.76 Figure 2.8 Band diagram schematic of carrier generation in a p-n homojunction. The built-in electric field caused by the p-n junction allows for separation of photo-generated electrons (e) and holes (h+).

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25 Commentary on the present status and future of photovoltaic technology has led to the classification of first, secon d, and third generation PV materials.77,78,79 First generation PV technology is based on singl e crystal and polycrys talline silicon wafer devices. Second generation PV cells use thin film technology and include CdS/CdTe and amorphous Si/SiGe or Si/H materials. Th e proposal for third ge neration PV materials78 includes finding (a) new approaches that drama tically increase the efficiency of devices, via material mechanisms that are not limited to the 31% target efficiency of a single junction device,76 and (b) development of technologies and materials possessing moderate efficiencies but at a drastically reduced cost. Success in either or bot h of these areas could enable photovoltaics to become a feasible large-scale energy conversion technology.78 Type II clathrates first a ttracted attention for phot ovoltaic and optoelectronic applications upon the theoretical prediction16 and experimental confirmation17 that the type II clathrate Si136 is a wide 2 eV band gap insula tor, corresponding to absorption in the visible part of the electromagnetic spectrum. As Si136 is a silicon-based material, type II silicon clathrates could be integrated in to currently used silicon technology. Moreover, theoretical calculations by Moriguchi et al .80 show that alloyed Si136xGex clathrates possess direct band gaps in the range 1.2 to 2.0 eV. NaxSi136 clathrates have also been investigated53 in hopes of finding potential intermediate band materials,81 an approach directed towards finding materials that are not constrained to the Shockley-Queisser 31% limit. The present work is part of an ongoing effort of experimenta lly investigating the merit of type II clathrates for th e above technological applications.

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26 3 Synthesis and Sample Preparation 3.1 Degassing of Silicides and Germanides One route to the synthesis of type II clat hrates is through the controlled vacuum decomposition known as “degassing” of alkali or alkaline earth sili cides and germanides. Several silicides and germanides were inves tigated in the present work, the synthesis results of which are pres ented in this section. 3.1.1 Preparation of NaxSi136 clathrates The NaxSi136 specimens produced in this work were synthesized using a multistep process, based on a modified procedur e compared to what has been previously reported in the literature.11 First, high purity sodium metal (Alfa Aesar, 99.95%) and silicon powder (High Purity Chemicals, 99.999 %) were combined in the ratio 1:(1 + ) silicon to sodium, where ~ 0.05 to 0.2. The additional Na metal ensures the complete reaction of the silicon and compensates for th e high vapor pressure of Na at elevated temperatures. The product is the Zintl com pound NaSi (see Figure 3.1), with an excess of sodium. NaSi is very reactive in air and mois ture, thus all handling of the materials was

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27 Figure 3.1 Crystal structure of the Zintl phase NaSi, emphasizing the Si4 4cluster units (blue) and Na+ ions (orange). The monoclinic unit cell is outlined. carried out in a nitrogen-filled glove box (VAC Atmospheres NEXUS System) with oxygen levels less than 5 ppm. All NaSi pr oducts were analyzed using powder X-ray diffraction (Rigaku MiniFlex and Bruker-Axs D8 Focus) and the diffraction patterns compared to those in the literature82 to ensure the NaSi structure had formed and to verify the absence of unreacted elemental silicon. The silicides were sealed under nitrogen on a glass plate sample holder by thin plastic sealed with vacuum grease, to avoid decomposition during X-ray diffraction measurements. In the next step, small portions (~ 250 mg) of NaSi were ground to very fine powders inside of the nitrogen-filled glove box. The powder was placed into fused quartz boats, and then into a inch diameter fused quartz tube that was sealed on one end and open at the other, the quartz boat with samp le being placed at the sealed end. All quartz tubes and boats were fabricated onsite in the Novel Materials Laboratory. A vacuum

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28 Figure 3.2 Schematic of the custom vacuum furnace appara tus designed for degassing of the silicides and germanides, and for further de gassing of the clathrates. coupling and valve was then attached to the ope n end of the tube and the valve closed to ensure that the sample volume remained unde r a nitrogen atmosphe re during the process of removal from the glove box and attaching to the vacuum system. Upon attaching to the vaccum system, the line was first evacuated and then the coupling valve opened to avoid the sample coming in contact with air. A schematic of the custom-designed vacuum furnace apparatus is shown in Figure 3.2. Upon reaching a vacuum of 10-5 to 10-6 torr, the tube and sample were inserted into a tube furnace, preheated to approximately 275oC. A thermocouple was placed alongside the tube to measure the furnace temperature at the position of the sample continuously throughout the synthesis process. Heating the NaSi at 275oC for approximately 12 hours evaporated excess Na metal from the sample, which in turn

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29 condensed on the inside of the quartz tube out side of the furnace. A small “test tube” was also placed in this region to minimize any sodium vapor entering the vacuum line. After being held at 275oC, the sample was then slowly heated to a temperature between 410 and 430oC at an average rate of 1-2oC/min. As seen in Fig. 3.1, the structure of NaSi consists of Na+ ions coordinated with tetrahedral Si4 4units. As the temperature is increased, the sodium ions are “evaporat ed” from the structure, likely as a neutral species, presumably causing the Si clusters to “close in” on the remaining Na ions forming the clathrate structures. The evaporat ed Na is allowed to condense on the inside of the tube, in the region outside of the furn ace. Using the above procedure, samples with nominal compositions Na1Si136, Na8Si136, Na12Si136, and Na16Si136 were synthesized. The synthetic products are very fine bluish powde rs, and the clathrates are stable in air, moisture, and strong acids (excluding hydrofluoric acid). As is well known to those skilled in the synthesis of Na-Si clathrates, the type II structure is not the only possi ble product resulting from the above procedure. In fact, the type I clathrate Na8Si46 is also commonly found as an impurity and it has been quite difficult to avoid forming this phase.35,36 Previous authors have reported the type I phase constituting as much as 50% by we ight of the synthesis products.36 Inasmuch as Na8Si46 and NaxSi136 have different densities, Ramachandran et al.36 were able to reduce the percent of the former in their samples to between 1 and 10%, usi ng a density separation technique. In the present work, we have ach ieved a much higher purity of the type II NaxSi136 “as synthesized” than previously repo rted, without the need for additional separation techniques. Although all of the specific synt hesis details were not given in the

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30 previous works, we can hypothesize some of the reasons that have led to better results in this study. Great care was taken to grind the Na Si to very fine powders before degassing, and this appears to increase the fraction of the NaxSi136 phase. Also, in general higher yield of NaxSi136 was obtained by slowly heating the si licide to the synthesis temperature, though this is in contrast to the results of Gryko83 who found that “fla sh-degassing” using rapid heating rates minimizes the Na8Si46 fraction. Theoretical calculations16,53 of the total energy predict that the NaxSi136 structure is slightly mo re thermodynamically stable (lower total energy) than the Na8Si46 structure, thus a slower rate of heating could allow the former to form in higher yield. Generall y better results were al so achieved in the present study by using smaller amounts of starting material. Initial microprobe analysis indicated a significant presence of oxygen (> 5 wt%) in our NaxSi136 specimens. Therefore, a procedure was employed for all samples in which the powders where first washed with a 5 M aqueous solution of hydrochloric acid, then washed with distilled water, and finally washed with ethanol and then dried under vacuum. The procedure was carried out inside a nitrogen-filled glove bag, and all liquids were bubbled with high purity nitrogen gas pr ior to washing in order to remove oxygen dissolved in the liquids. This procedure produced samples with greatly reduced oxygen content (< 1 wt%). After the acid washing procedure, the powder NaxSi136 specimens were further ground using an alumina mortar and pestle in an inert nitrogen atmosphere, and then densified by hot-pressing at 220oC and 5 kbar for 12 hours. This produced specimens with densities of approximately 70% of the th eoretical X-ray density. We note that this

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31 0 20 40 60 80 100 27029031033035037039041043 0 Degas Temperature (C)Relative XRD Intensity (Normalized %) Ge Na1-xGe3NaxGe136NaGedensity is rather low, resulting from the challenge posed in the densification of siliconbased clathrates. Methods of obtaining higher density, such as spark plasma sintering (SPS), are currently being investigated. 3.1.2 Preparation of NaxGe136 clathrates and the new phase Na1-xGe3 An extensive and systematic invest igation into the synthesis of NaxGe136 was also undertaken. The synthesis methods were es sentially those expl ained above for NaxSi136, but using the Zintl phase NaGe as starting material. The results of the investigation are qualitatively summarized in Figure 3.3, which shows the relative percentages of various products observed in the powder X-ray diffraction (XRD) patterns, determined from the Figure 3.3 Qualitative representation of phase percentages from products obtained from thermal decomposition of NaGe.

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32 relative intensities of the diffraction peaks in the individual sp ectra. The figure was compiled from the XRD spectra of more than two dozen separate samples. As shown in the figure, the type II clathrate NaxGe136 was found to form in the range of 350 to 370oC, but the yield was very low. Thus produc tion of large enough pure samples for further characterization was not possi ble. However, over a broade r range of temperature an initially unidentifiable Na-Ge phase was found to be the dominant synthesis product. As discussed in Section 4.5, as a pa rt of this work the crystal structure of the unknown phase has been solved and its composition was determined to be Na1xGe3 (0 < x < 1). This constitutes the discovery of a new bi nary compound in the Na-Ge system. 3.1.3 Other Silicides and Germanides In the course of this work, severa l other silicides and germanides were investigated, however none produced type II cl athrates in the high yield as found with NaSi. As discussed in Section 2.1, there appe ars to be relative si ze constraints between guest and framework polyhedra that limit the fo rmation of the clathr ates (see Table 2.1). Upon further analysis of our re sults, combined with those in the literature, there appears also to be correlation between the starting stru ctures of the silicides and germanides and the products that are formed upon th eir thermal decomposition. One common characteristic of all silicides (germanides) that decompose to produce clathrates is the presence of Si4 4(Ge4 4-) clusters, which are coordinated wi th alkali or al kaline earth ions. Presumably, upon degassing of the alkali or alka line earth atoms these clusters reorganize

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33 and connect to form the frameworks of th e clathrate compounds. Thus, empirically the presence of these four-atom clusters seems to be necessary for formation of the fourbonded clathrate frameworks using the contro lled vacuum decomposition technique. Table 3.1 presents the structures of a vari ety of silicides and germanides and the products that are obtained upon their th ermal decomposition under vacuum, compiled from the present work and from the litera ture. Most of the st arting materials are Table 3.1 Structures of various silicides and germanides and the products obtained by their thermal decomposition. The original references are given in a ddition to the present work. Results from the present work are shown in red. Type II products are shown in bold. Compound Space Group Lattice Structural Isotype Decomposition Products NaSi C 2/ c 84 monoclinic NaSi NaxSi136,11 Na8Si46 11 KSi n P 3 485 cubic KSi K8Si46 11 RbSi n P 3 485 cubic KSi Rb8xSi46 11 CsSi n P 3 485 cubic KSi CsxSi136 11 NaGe P 21/ c 84 monoclinic NaGe NaxGe136,11 Na1xGe3 KGe n P 3 485 cubic KSi K8Ge4611 RbGe n P 3 485 cubic KSi Rb8Ge4611 NaKGe2 n P 3 485 cubic KSi NaxKyGe136, NaxKyGe46NaRbGe2 n P 3 485 cubic KSi NaxRbyGe46NaRbSi2 unknown unknown unknown Rb8Na16Si13660 NaCsSi2 unknown unknown unknown Cs8Na16Si13659 BaNa2Si4 unknown monoclinic unknown NaxBa6Si46,12 Ba8Na16Si13630 BaNa2Ge4 unknown unknown unknown Ba24Ge100 86

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34 cubic, and result in type I clathrate as th e majority phase. Overall, the only starting material found to produce type II clathrate in high yield is NaSi. Note that none of the other silicides or germanides listed in this table shares the NaSi crystal structure, though NaGe is monoclinic but with different sp ace group symmetry. This tabulation suggests that the design or discovery of starting materials with the de sired structures may be an appropriate approach for the synthesis of t ype II silicon and germanium clathrates using the Zintl phase decomposition method. We al so note that several of the clathrate compositions, including NaxKyGe46, NaxRbyGe46, and NaxKyGe136, were previously unreported. 3.2 Direct Synthesis of Cs8Na16MyGe136y Clathrates (M = Ag, Cu) It was recently shown28 that type II clathrates can also be synthesized by direct reaction of the elements. For the first time, we have synthesized in the present work type II germanium clathrates in which the framework germanium atoms are substituted by other species, specifically transition metal elem ents. This shows that type II clathrates are stable under framework substitution, opening ne w doors to synthesis of novel type II clathrates. In particular, this proves the ability to “dope” thes e compounds with other atomic species, which holds promise for contro l of the electronic properties of type II clathrates. A series of silver and copper substitu ted samples was synthesized by the direct reaction of high purity Na ( 99.95%, Alfa Aesar), Cs (99.98%, Alfa Aesar), Ge (99.999%,

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35 High Purity Elements), and Ag (99.9%, Al fa Aesar) or Cu (99.9%, Alfa Aesar). Stoichiometric amounts of the elements were combined in tungsten crucibles and sealed in steel canisters (see Figure 3.4) under nitroge n atmosphere. The steel canisters were in turn sealed inside quartz ampoules The mixtures were held at 800oC for 2 days, slowly cooled to 650oC, and then held at this temperature for 7 days. The samples were then allowed to cool to room temperature; the synthesis schedule is show in Figure 3.4. We note that the use of tungsten crucibles as opposed to niobium28 avoids reaction of the crucible with germanium, allowing for a higher synthesis temperature and thus approximately one-third the synthesis time (nine days as opposed to three to four weeks) as previously reported in the synthesis of st oichiometric type II germanium clathrates.25,28 Figure 3.4 Temperature schedule for the synthesis of the framework substituted type II germanium clathrates.

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36 Using this procedure, series of Cs8Na16CuyGe136y ( y = 2.667, 3.14, 5, 8, 10, 16) and Cs8Na16AgyGe136y ( y = 2.667, 5, 8) clathrates were s ynthesized. Here Cs atoms occupy the larger hexacaidecahedra and Na atom s occupy the smaller dodecahedra, and the transition metals substitute for the Ge at oms on the framework. The products generally consist of coarsely grained crystalline pow ders along with some larger crystals (see Figure 3.5), and are stable in air and mo isture. Cu substituted samples with y = 5 and 8 were ground to 325 mesh and hot pressed at 400oC into pellets of approximately 80% of the theoretical X-ray density. From X-ray diffraction, no structural transformation of these samples was detected after hot-pressing. Figure 3.5 Small clusters of as-grown crystallites of Cs8Na16CuyGe136y clathrates. 1 mm

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37 3.3 Partially Filled Type II Germanium Clathrates As mentioned in Section 2.2, recently we have reported for the first time on the synthesis of partially filled type II clathrate Cs8Ge136.32 Although the type I germanium clathrates are found to be much less st able with respect to partial filling,87 type II clathrates can be synthesized with th e framework polyhedra partially occupied. Other type II germanium clathrates can also be synthe sized with partial occupation. In the present work, a partially occupied NaxRb8Ge136 clathrate was produced. First, a “fully loaded” Rb8Na16Ge136 clathrate was synthesized. Stoichiometric amounts of high purity Na, Rb, and Ge were combined in a tungsten crucible, and the reaction of the constituents carried out in a similar manner as in the metal substituted clathrates above. The resulting Rb8Na16Ge136 clathrate was then ground to very fine powder, and degassed under high vacuum at a temperature of 310oC for 24 hours, using the apparatus shown in Figure 3.2. The sa mple was then reground under nitrogen, degassed again at increa sed temperature of 320oC. This process was repeated, each time increasing the temperature by 10 to 15oC, resulting in the dega ssing of Na from the structure. As shown in Figure 3.6, as the degassing procedure pr ogressed the lattice parameter showed a decrease, corresponding to a slight shrinking of the structure on removal of the Na guests. Also, from the inset of Figure 3.6 it is clear that the structure is stable with respect to partia l occupation of the voids, as was also found in the case of Cs8Gs136.32 These results reveal yet another avenue that can be explored in synthesizing novel type II clathrates, and also may offer a way to control the physical properties of these materials.

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38 Degas Temperature ( o C) 0100200300400500 Lattice Parameter () 15.30 15.35 15.40 15.45 15.50 2theta (degrees) 2030405060 Intensity (arbitrary units) * *Pre-degassing Post-degassing Figure 3.6 Lattice parameter of NaxRb8Ge136, as measured after vacuum degassing at the indicated temperature. Open and closed circles indicate results fr om the present work on two different samples, while the open triangle is from the work of Gryko (unp ublished). The inset shows that the integrity of the clathrate framework is maintained after the procedure; an “*” indicates an internal NIST silicon standard, used to calibrate the peak positions.

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39 4 Structural and Chemical Characterization 4.1 Characterization of NaxSi136 Clathrates In has been shown previously35,36 that the X-ray diffrac tion (XRD) spectra of NaxSi136 clathrates are highly de pendent on the Na content x This is illustrated in Figure 4.1, which shows simulated theoretical powder XRD spectra for NaxSi136 clathrates, as a function of the sodium content x These theoretical spectra we re calculated by inputting NaxSi136 structural details into the cr ystallography software PowderCell.88 Note that the relative intensities of the Bragg peaks disp lay a clear dependence on the Na content, especially for the (311), ( 222), (511), and (531) reflections This allows for the guest content of samples to be determined quantit atively via refinement of experimental XRD data. Furthermore, the relative intensities ar e also dependent upon the relative occupancy of the two distinct polyhedron sites. We have employed the Generali zed Structure Analysis Software89 (GSAS) suite as well as the PowderCell88 computer program to perf orm Rietveld analysis and refinement on the NaxSi136 specimens in this study. Th e principle behind Rietveld analysis90 is to perform a non-linear least squares fit to expe rimental diffraction data using a structural model. Structural (i.e. lattice parameters, atomic positions, etc.) and instrumental (i.e. peak shape, pr ofile coefficients, zero shift, etc. ) parameters may all be

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40 Degrees 2 2030405060 Intensity (arb. units) (331) (400) (422) (311) (440) (531) (711) (620) (553) (733) (555) (822) (840) (753) (442) (220) (222) (511) (533) x = 0 x = 4 x = 8 x = 12 x = 16 x = 20 x = 24 Figure 4.1 Simulated theoretical X-ray diffraction patterns for NaxSi136 clathrates as a function of the Na content x calculated using the PowderCell computer software. The lattice parameters were kept constant for all compositions, and the 8 b (larger cage) site was filled first as x was increased.

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41 Degrees 2 10203040506070 Intensity (arb. units) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + silicon Na8Si46Na 0.6 Si 136 : 98.9% Na 8 Si 46 : 0.4% Silicon: 0.7%refined, in order to determine the structural details of the sample under investigation. Since the diffraction patterns of NaxSi136 clathrates depend sensitively on the guest atom content, refinement of the X -ray diffraction data allows for the determination of the guest concentration. As noted in Section 3.1.1, high purity NaxSi136 samples were synthesized with nominal Na contents of x = 1, 8, 12, and 16. Type II sodium-silicon clathrates with x = 1 and 8 were characterized in more detail. Figures 4.2 and 4.3 show typical refined powder diffraction patterns for Na1Si136 and Na8Si136, respectively. The compositions determined from refinement of the X-ray diffraction da ta were in turn corroborated from Energy Dispersive X-ray Spectroscopy (EDS) performe d by Dr. Jan Gryko at Jacksonville State Figure 4.2 Refinement of powder XRD data for Na1S136. Peaks associated with Na8Si46 and diamondstructure silicon are indicated by arrows.

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42 Figure 4.3 GSAS fit of the powder XRD data for Na8Si136. The peak at approximately 33 degrees is due to the presence of a small amount (~ 5 wt%) of Na8Si46 in the sample. Data collected and fit by Dr. Jan Gryko, Jacksonville State University. Table 4.1 Structure and composition of Na1Si136 and Na8Si136. Compositions are given as determined from EDS and XRD refinement. Grain size was determined from optical micrographs taken on polished densified samples, according to ASTM Standard E112-88 Sample Nominal Composition Composition From EDS Composition From XRD Average Grain Size ( m) Approximate wt% of Na8Si46 Na1Si136 Na1.7Si136 Na0.6Si136 4.5 0.5 Na8Si136 Na8.4Si136 Na8.8Si136 3.1 5.0

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43 University. Some structural a nd compositional de tails for the Na1Si136 and Na8Si136 samples are given in Table 4.1. One very useful method for characterizat ion of the vibrati onal properties of materials is Raman scattering spectroscopy. Th e Raman effect is due to the inelastic scattering of light from a material corresponding to the gain or loss of energy in the material such as in the creation or an nihilation of phonons. As shown in Figure 4.4, Raman spectra were collected for Na1Si136 and Na8Si136 by Dr. Chris Kendziora at the Naval Research Laboratory in Washingt on, D.C. The figure shows Stokes Raman scattering spectra for the two samples in both parallel (VV) and perpendicular (HV) Figure 4.4 Stokes Raman scattering spectra for Na1Si136 and Na8Si136. VV indicates parallel polarization, HV indicates perpendicular polariza tion. The arrows indicate the Si136 framework modes. Na8Si136 – HV Na8Si136 – VV Na8Si136 – HV 514nm Na1Si136 – VV Na1Si136 – HV

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44 Temperature ( o C) 100200300400500600700 Heat Flow (arb. units, exo = up) Na1Si136Na8Si136Si136polarizations using a 647 nm laser line. Also shown are data for Na8Si136 using 514 nm laser light. The arrows in the figure indicat e the Raman active silicon framework modes, as determined in a prior work,63 and these spectra are a test ament to the high quality of the Na1Si136 and Na8Si136 samples. To investigate the stability of type II silicon clathr ates, differential scanning calorimetry (DSC) measurements were pe rformed using a TA Instruments Q600, under flowing nitrogen gas at a pressure of 1 atm., in the range 100 to 800oC. Figure 4.5 shows heat flow as a functi on of temperature for NaxSi136 samples with x = 0,17 1, and 8. The NaxSi136 clathrates are stable until slightly above 600oC, at which point exothermic decomposition to diamond structure silicon o ccurs, as verified by post-DSC XRD. The Figure 4.5 Heat flow as a function of temperature for NaxSi136 samples with x = 0, 1, and 8.

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45 fact that decomposition is exothermic agrees qualitatively with theoretical calculations that predict the type II silicon framework to be slightly higher in energy than the ground state of diamond structure silicon.16 It is interesting to note th at at synthesis temperatures (under vacuum of ~ 10-6 torr) in excess of 450oC, diamond-structure silicon becomes an increasingly larger and eventually total percen tage of the synthesis products. Thus clearly the stability of these materials is de pendent on pressure. The relatively high decomposition temperature of the type II silic on clathrates indicates these materials may hold promise for applications at elevated temperatures. 4.2 Characterization of Cs8Na16MyGe136y Clathrates (M = Ag, Cu) The type II germanium clathrates synt hesized in this study constitute the first framework substituted type II clathrates synthesi zed to date, with the single exception of the report of Ba16Ga32Sn104 which was rather described as a Zintl compound.30 The results from the initial powder X -ray diffraction measurements (Rigaku MiniFlex diffractometer) for the type II germanium clathr ates are shown in Figure 4.6 (Ag-substituted) and Figure 4.7 (Cu-substi tuted). From the diffraction patterns, the samples all appear essentially single-phase, with the excepti on of an occasional very weak peak at approximately 27 degrees 2 attributed to a trace amount of unreacted elemental germanium. The NIST 640c internal silicon standard (p eaks indicated by a “*” in the bottom spectra of both figures) was a dded to the samples for XRD in order to correct the peak positions for possible sample displacement and instrumental factors in

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46 2theta (degrees) 2030405060 Intensity (arbitray units) y = 0 a = 15.4780.007 y = 2.667 a = 15.4990.008 y = 5.000 a = 15.5000.016 y = 8.000 a = 15.5020.018 (311) (222) (331) (400) (422) (333) (440) (531) (642) (620) (731) (733) (660) (751) (911) (642) (442)* * calculation of lattice parameters. As seen in Figure 4.8, the lattice pa rameters of the Agsubstituted type II germanium clathrates increased with s ubstitution, while those for the Cu-substituted samples decreased. The latter re sults are consistent with previous reports on Cu-substituted type I germanium clathrates, which also showed a decrease in lattice parameter.91 For both Ag and Cu samples, the leveli ng out of the lattice parameter with Figure 4.6 Powder XRD patterns for Cs8Na16AgyGe136y clathrates. An “*” indicates a peak due to the NIST internal silicon standard used to calibrate the spectra, which is present in all patterns for 2theta corrections used in the calculation of lattice parameters.

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47 Degrees 2 2030405060 Intensity (arbitraty units) y = 0 a = 15.4780.007 y = 3.140 a = 15.4400.016 y = 2.667 a = 15.4350.023 y = 5.000 a = 15.4080.014 y = 8.000 a = 15.3990.013 y = 10.000 a = 15.3900.017 y = 16.000 a = 15.3960.012(331) (400) (422) (333) (440) (531) (642) (620) (731) (733) (660) (751) (911) (642) (442) * Figure 4.7 Powder XRD patterns for Cs8Na16CuyGe136y clathrates. The “*” indicates a NIST internal silicon standard used to calibrate the spectra, which is present in all patterns for 2theta corrections used in the calculation of lattice parameters.

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48 Transition metal content (y) 024681012141618 Lattice paramete r (angstroms) 15.36 15.38 15.40 15.42 15.44 15.46 15.48 15.50 15.52 15.54 Figure 4.8 Lattice parameter as a function of transition metal content for the Cs8Na16CuyGe136y (closed circles) and Cs8Na16AgyGe136y (open triangles) clathrates. The Ag -substituted clathrates showed and increase in lattice parameter, while the Cu-substituted samples showed a decrease. The leveling out of the lattice parameters may indicate a solubility limit has been reached. doping concentration indicates that a solubility limit may have been reached for transition metal substitution, occurring at y ~ 3 for Ag and y ~ 8 for Cu. Transport properties were measured on Cu substituted samples with y = 5 and 8. Energy dispersive X-ray spectroscopy indicated average compositions of Cs10.2Na16.2Cu4.7Ge131.3 and Cs9.1Na14.4Cu7.7Ge128.3 for these two samples, respectively. Hereafter, these samples will be referred to as Cs8Na16Cu5Ge131 and Cs8Na16Cu8Ge128.

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49 4.3 The New Compound Na1xGe3 As discussed in Section 3.2, an extensive investigation into the synthesis of NaGe type II clathrates resulted predominantly in an unidentifia ble Na-Ge phase. In order to identify this dominant phase, we initially turned to the literature. However, we found conflicting reports. Several binary compounds ha ve been reported fo r the Na-Ge system, including NaGe,84,85 Na12Ge17,92 Na3Ge,93 and NaGe4.94 Some of these reports, in particular for “NaGe4,”94 were disputed by other authors,95 who suggested instead that the compound was in fact Ge or even a clathrate phase.95,96 Upon comparing our powder Xray diffraction data to the available literatu re and diffraction databa ses, the question of the composition and structure of our unknown pha se remained. Thus, in order to help clarify the confusion in the li terature and perhaps better unde rstand the route to synthesis of Na-Ge type II clathrates, we have further characterized this phase. Using synchrotron X-ray diffraction experiments pe rformed on approximately 600 mg of material, Dr. Jame s Kaduk of Innovene and Dr Winnie Wong-Ng of NIST used a Monte Carlo simulation technique97 in order to solve the structure of the unknown phase. The structure was then refined by the Rietveld method90 using the GSAS software suite.89 From these results, we present a preliminary structural model for this new material. The structure was indexed to a hexagonal unit cell with space group P 6/ m and cell constants a = 15.05399(5) and c = 3.96845(2) . Some of the important structural details for the new compound are given in Tabl e 4.2, and the preliminary crystal structure is shown in Figure 4.9.

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50Table 4.2 Preliminary structural data for the novel phase Na0.7Ge3, space group P6/m, a = 15.05399(5) , c = 3.96845(2) . Atom X y Z Uiso ( 2) Site Occ. Ge1 .37332(8) .26958(8) 0 .0115(4) 1 Ge2 .04088(9) .59174(8) 0 .0106(4) 1 Ge3 .52012(9) .15164(9) .0052(3) 1 Ge4 .48411(10) .30138(7) .0071(3) 1 Na5 2/3 1/3 0 .02 1 Na6 .2539(6) .0639(7) .088(4) .617(9) Figure 4.9 A schematic of the structure of NaGe3, viewed along the c -axis at a slight tilt. Na atoms are shown in orange, the Ge atoms in dark pink. The hexagonal unit cell is enlarged in the upper right, with the crystallographic site designations labeled. Ge1 Ge3 Ge4 Na5 Ge2 Na6

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51 The material crystallizes in a comple x zeolite-like structure, in which the framework of the structure is built from Ge while Na at oms are found to be situated inside the broad channel (Na6) as well as in the smaller hexagonal channels (Na5). In the broad channel, the six Na6 sites are related to each other by 6-fold symmetry. Note from Table 4.2 that while the Ge sites that define the framework of the structure are fully occupied, the Na sites in the broad channel (Na6) are only pa rtially filled in the sample studied. If all sites are fully occupied, the chemical formula is NaGe3. As a result of this partial occupancy, the chemical formula of this new phase is tentatively estimated to be Na0.7Ge3, and the general chemical formula can be written as Na1xGe3. Also from Table 4.2, the Na atoms at the Na6 sites possess a relatively large is otropic displacement parameter, implying either a large static or dynamic disorder at thes e sites in the broad channel. In the center of the broad channel, residual electron dens ity was observed at (0,0,), the exact nature of whic h has yet to be determined. Although the structural mode l proposed is preliminary, the model reproduces the experimental X-ray diffraction patterns very well. Figure 4.10 shows a simulated diffraction pattern calculated using the software PowderCell88 for NaGe3, i.e. with x = 0, as compared to an experimental X-ray diffraction pattern for Na1xGe3 collected at USF. As seen in the figure, the two patterns show excellent agreement in features, indicating the high quality of the preliminary model. The discovery of this new compound shows that there is still new science and complexity to be found in simple binary systems and its unique structure motivates further study which is currently underway by the author and coworkers.

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52 Degrees 2 2030405060 Intensity (arb. units) (300) (001) (130) (111) (201) (211) (230) (301) (410) (221) (131) (330) (231) (150) (501) (340) (250) (331) (151) (002) (102) (601) (341) (521) (620) (611) (312) (710) (531) (540) (142) (270) (332) (621) (101) (502) (411)Experimental XRD Na 1x Ge 3 Simulated XRD NaGe 3(500) (400) Figure 4.10 Powder X-ray diffraction of Na1xGe3. The lower spectrum is a simulated XRD pattern for NaGe3 ( x = 0) calculated using the PowderCell program, with the Bragg reflections indexed. The upper spectrum is an experimental XRD pattern from a Na1xGe3 sample. The two patterns show very good agreement in peak positions and relative intensities.

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53 5 Transport Properties Possibly the most interes ting aspect of clathrate compounds is the transport phenomena these materials exhibit. The transp ort properties of several of the samples synthesized in this work have been st udied. New transport phenomena in type II clathrates are presented, with a central resu lt of this work being that the transport properties of type II clathrates depend st rongly on the guest content and on framework substitution. 5.1 Experimental Details All transport measurements were performed using a custom built apparatus,70 consisting of a closed-cycle helium cr yostat (Janis), Keith ley Instruments 2100 multimeter and 2400 current sourcemeters, a nd a Lakeshore temperature controller. Samples were mounted on a custom designe d sample holder, allowing electrical resistivity, Seebeck coefficient, and therma l conductivity measurements to be performed on the same sample simultaneously during th e same measurement cycle. Resistivity measurements were performed using a st andard four-probe arrangement. Seebeck coefficient measurements were performed at each temperature by controlled sweeping

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54 through temperature gradient and measuremen t of the corresponding voltage difference, the slope of the straight line fit yiel ding the Seebeck coefficient. For thermal conductivity, multiple temperature differences ar e stabilized at each temperature, and the slope of applied power versus temperature difference yields thermal conductance, from which thermal conductivity is extracted. Fo r all three measurements, geometrical considerations determine the largest portion of uncertainty in the measurement. For resistivity and thermal conductiv ity, the largest sour ce of uncertainty results from the measurement of the cross-sectional area and contact separations, the ratio of which is known as the geometrical factor. For Seebeck measurements, placement of the voltage and thermocouple contacts such th at they lie in the same cro ss-sectional plane is crucial. The room temperature uncertainty in the tran sport measurements is estimated to be 3.5% for resistivity, 5% for Seebeck coefficient, and 10% for thermal conductivity. Details of the transport measurement system and sample mounting process can be found in Ref. 70. 5.2 Transport Properties of NaxSi136 Clathrates As noted previously, the transport properties of NaxSi136 clathrates have not been well characterized, though these materials were some of the first inor ganic clathrates to be synthesized almost forty years ago.10 In the present work electrical resistivity and thermal conductivity measurements were performed on samples with compositions Na1Si136 and Na8Si136. To the best of our knowledge, th ere exist no previous reports on the thermal conductivity of NaxSi136 clathrates.

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55 Temperature (K) 050100150200250300 Resistivity (mohm-cm) 10-1100104105106107108109 Figure 5.1 Temperature dependent el ectrical resistivity of Na1Si136 (closed circles) and Na8Si136 (open cicles), along with Cs8Na16Si136 25 (closed squares). Temperature dependent electrical resistivity measurements for Na1Si136, Na8Si136 and Cs8Na16Si136 are shown in Figure 3. The data for Cs8Na16Si136 are taken from Ref. 25. The lack of low temperature measurements for the Na1Si136 specimen below 150 K is due to the exceedingly high resistiv ity. The effect of the alkali is evident, with the room temperature values for the resistivity sp anning seven orders of magnitude between Cs8Na16Si136 and Na1Si136, and the resistivity decreasing with increased alkali content. The “completely filled” stoichiometric clathrate Cs8Na16Si136, which has Cs atoms inside all of the hexakaidecahedra and Na atoms inside the smaller dodecahedra, exhibits metallic conduction,25 while Na1Si136 and Na8Si136 show activated temperature

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56 dependences. We note that since the density of these two specimens is relatively low (~ 70% of the theoretical X-ray density), there may be a large contribution to the resistivity due to poor contact between the pol ycrystalline grains. Thus the magnitude of the intrinsic resistiv ity of the materials may be lower than that shown in Figure 5.1. Nevertheless the data indicates the Na concentration direct ly influences the electrical properties. The room temperature resistivities for Na1Si136 and Na8Si136 differ by approximately two orders of magnitude, in ag reement with the trend in room temperature electrical conductivity reported by Cros et al .11 Obtaining high density is a challenge in silicon-based clathrates and we are currently investigating di fferent avenues in order to address this issue. The lattice thermal conductivity, g, as a function of temperature for Na1Si136 and Na8Si136 is shown in Fig. 5.2 along with that of single crystal diam ond-structure silicon.98 The data for the type II silicon clathrates have been adjusted for porosity.99,100 Since the resistivities of Na1Si136 and Na8Si136 are large, thermal conduction by electrons can be neglected, assuming a Wiedemann-Franz relati on, thus the thermal conductivity for these type II silicon clathrates can be regard ed as entirely due to the lattice. Na1Si136 shows a very low g, much lower than that of diamond-st ructure silicon. A similar result was found previously for the guest-free clathrate Si136.66 First principles calculations101 of the thermal conductivity for a "guest-fre e" clathrate (hypothetical type-I Ge46) indicated a ten-fold decrease in lattice thermal conductiv ity compared with that of the diamondstructure semiconductor (Ge) due to scat tering of heat-carrying acoustic phonons by zone-boundary modes "folded back" due to the increase in unit cell size.100 It is

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57 Temperature (K) 10100 g (W/mK) 1 100 1000 Figure 5.2 Temperature dependent thermal conductivity of Na1Si136 (closed circles) and Na8Si136 (open circles), along with that of single cr ystal diamond structure silicon (dashed line). interesting to note that the values we reported for Si136 66 are lower than that of Na1Si136, for temperatures less than 300 K ( g at ~ 300 K are similar within experimental error). Although the reason for this is not entirely understood, the inte nsive processing needed to produce a completely empty clathrate,17 which involves repeated washing with concentrated acids and heat treatment under vacuum, could cause la ttice defects, thus resulting in further lowering of th e thermal conductivity relative to NaxSi136 clathrates that have not undergone such pro cessing. Nevertheless, evidently low g values are achieved in clathrate compounds with few or no atoms inside the polyhedra, due to the intrinsic vibrational properties of th e framework and the enlarged unit cell.

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58 Though similar to that of Na1Si136 for T < 20 K, g above 20 K for Na8Si136 shows a lower g with a very different temperature dependence compared with that of Na1Si136. The magnitude is very low, similar to th at of polycrystalline type I clathrates.23 In the range 50 to 70 K there is a clear “dip” in g. This feature in the temperature dependence of thermal conductivity has in the past been attributed to the resonance scattering of phonons by localized atomic or molecular vibrations.102,103,104 Such a feature can be understood qualitatively in te rms of the thermal occupati on of phonons. The interaction of localized vibrations with the heat carrying phonons in a solid will be strongest when the phonon frequency closely matches the freque ncy of the localized vibration, allowing for a resonant transfer of energy and scatte ring of the former. When the temperature is such that a significant population of phonons with frequencies near the resonant frequency carries the heat, a marked reduction in the thermal conductivity will result, hence causing a dip-like feature. Indee d, in type I clathrates such as Sr8Ga16Ge30 and Eu8Ga16Ge30,23,106 dips in the thermal conductivity were attributed to resonance scattering of the heat-carrying acoustic phonons by the lo calized vibrations of the guest atoms inside their cages, as shown in Figure 5.3. The significant suppr ession and dip-like feature of the thermal conduc tivity indicate a similar eff ect may be occurring in Na8Si136 where one-third of the polyhedra are occupi ed by Na. From previous measurements on Cs8Na16Si136 and other stoichiometric type II clathrates using single crystal XRD,25 the atomic displacement parameters (ADP) suggest that the “guest” atoms in the type II clathrates undergo large amp litude, localized vibrations. Th ese results were corroborated by Raman scattering experiments.63 Furthermore, inelas tic neutron scattering

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59 Figure 5.3 Low temperature lattice thermal conductivity for single crystalline Sr8Ga16Ge30 (circles) and Eu8Ga16Ge30 (squares).105 The dashed line is data for amorphous SiO2, and the solid lines at fits to the experimental data, which account for resonant phonon scattering. Reprinted figure with permission from G.S. Nolas, T.J.R. Weakly, J.L. Cohn, and R. Sharma, Phys. Rev. B 61 3845 (2000). Web: http://link.aps.org/ab stract/PRB/v61/p3845 measurements of the phonon density of states106 as well as theoretical calculations64 indicate a strong interaction exists between th e localized vibrations of the guests and the host phonon modes in type II clathrates. Optical and ultrasound measurements on Na1Si136 and Na8Si136 specimens, along with an investigation into NaxSi136 specimens with varying Na concentra tions, are currently underway. The thermal conductivity data presented here for Na1Si136 and Na8Si136 indicate that these materials are low thermal conduc tivity crystalline solids. In addition, g data on Na8Si136 may indicate localized disorder produ ced by the Na within the Si polyhedra

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60 resulting in a further reduction in g, as compared with low Na content type II silicon clathrates. To the best of our knowledge this constitutes the first evidence from transport measurements that the guest atoms have a dramatic effect on the thermal transport in type II clathrates. 5.3 Transport Properties of Cs8Na16CuyGe136y Clathrates The electrical resistivity, Seebeck co efficient, and thermal conductivity of Cs8Na16CuyGe136y clathrates with y = 5 and 8 are reported, and compared to Cs8Na16Ge136 ( y = 0). All data shown for Cs8Na16Ge136 ( y = 0) were taken from Ref. 25. It is shown that Cu substitution for Ge on the framework has a significant effect on all of the transport properties in these materials. Figure 5.4 shows the temperature dependence of the resistivity for Cu substituted samples. The effect of substituting Cu is an increase in the magnitude of the resistivity with increasing Cu concentration. All three materials exhibit metallic behavior, with resistivities that in crease approximately lin early with temperature. To our knowledge, no theoretical calculations exist for the electr onic structure of framework-substituted type II clathrates, though calculations32 for Cs8Na16Ge136 indicate this material to be a metal with a Fermi level clearly within the conducti on band, consistent with both transport25 and NMR61 measurements. In a simplified interp retation, the electropositive guests in clathrates can donate their valence electrons to the framework. The Cu in the framework would act as a “trivalent acceptor,” since three electrons are needed to become

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61 Figure 5.4 Temperature dependence of the electrical resistivity of Cs8Na16CuyGe136y, with y = 0,25 5, and 8, indicating the metallic behavior of these materials. isoelectronic with Ge and participate in th e tetrahedral bonding. T hus we can write the expression (Cs1+)8(Na1+)16(Cu3-)yGe136y. Within this picture, increasing the copper content would correspond to decreasing the num ber of majority carri ers per formula unit. This simplified picture is consistent with our resistivity measurements. In addition, the increased impurity scattering of the charge ca rriers by the Cu ions on the framework is a likely contributor to the increase in magnit ude of the resistivity with increasing Cu content. Measurements of the Seebeck coefficient ( S ) for these materials yielded interesting results, as shown in Figure 5.5. As expected for materials possessing metallic properties, the magnitudes of the Seebeck co efficients for the three samples are all Temperature (K) 050100150200250300350 Resistivity (mOhm-cm) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Cs 8 Na 16 Cu 5 Ge 131 Cs 8 Na 16 Ge 136 Cs 8 Na 16 Cu 8 Ge 128

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62 relatively low. Upon Cu substitution from y = 0 to y = 5, the magnitude of the Seebeck coefficient increased by approximately a factor of 2 at 300 K. This is consistent with the increase in resistivity found for this Cu c ontent, and the simple picture outlined above. However, perhaps the most interesting aspect of the data is for the Cu content of y = 8. This material shows a very small value of S of –1.6 V/K at 300 K, which quickly decreases to zero at approximately 230 K, and then changes sign below this temperature. As the sign of the Seebeck coefficient is indicati ve of the type of majority charge carrier, the transition from negative to positive S indicates a transition fr om electron (n-type) to hole (p-type) conduction. This re sult constitutes the first obs ervation of p-type conduction in type II clathrates, and shows that framew ork-substitution in type II clathrates has a Figure 5.5 Temperature dependence of th e Seebeck coefficient for Cs8Na16CuyGe136y, with y = 0,25 5, and 8. The sample with y = 8 shows p-type conduction below 220 K. Temperature (K) 050100150200250300 Seebeck Coefficient ( V/K) -15 -10 -5 0 5 Cs 8 Na 16 Cu 5 Ge 131 Cs 8 Na 16 Ge 136 Cs 8 Na 16 Cu 8 Ge 128

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63 significant effect on the electrical properties in these materials. Within the simplified picture given above, the composition y = 8 corresponds to exact compensation of the 24 electrons per formula unit “donated” by the al kali guests to the framework, and the low magnitude and change of sign of the Seebeck coefficient may indica te dual conduction in this material. Again, theoretical calculations of the electronic structure in these materials may help to elucidate the underlying physics. The thermal conductivity was also found to be affected by the Cu substitution. Figure 5.6 shows the total measured and estimated lattice thermal conductivity. The thermal conductivity ( ) of a solid is typically expressed as the sum of electronic ( e) and lattice ( g) contributions, so that = e + g. Since the Cs8Na16CuyGe136y specimens behave as metallic conductors, there is expect ed to be a significant contribution from the Temperature (K) 10100 Lattice Thermal Conductivity (W/mK) 1 10 Cs8Na16Ge136 Cs8Na16Cu5Ge131 Cs8Na16Cu8Ge128 Temperature (K) 10100 Thermal Conductivity (W/mK) 1 10 Figure 5.6 Thermal conductivity of Cs8Na16CuyGe136y with y = 0,25 5, and 8. (a) Total measured thermal conductivity. (b) Estimated lattice thermal conductivity. (a) (b)

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64 charge carriers. To estimate the lattice thermal conductivity ( g = e) the electronic portion was estimated assuming the Weidemann-Franz relation e = L0T / where L0 = 2.4510-8 V2/K2 is the Lorenz number, T is the absolute temperature, and is the measured electrical resistivity. This was then subtracted from measured thermal conductivity. In addition, as th ese samples were approximately 80% of the theoretical Xray density, the data were also corrected for porosity.99,100 The results are shown in Figure 5.6(b), and indicated a slight decrease in the magnitude of the thermal conductivity with increasing Cu content. The reduction could c onceivably be due to point-defect scattering of phonons resulting from the difference in mass between Cu and Ge. No conclusive evidence was found here for resonance contribu tions to phonon scattering from the Cs or Na guests, though in the range 60 to 100 K, the same range in which the dip was observed for Na8Si136, the thermal co nductivity appears temperature independent for our y = 8 specimen. The data all show a significant upswing in the thermal conductivity at the higher temperatures. A common source of error in thermal conductivity measurements is from radiation absorbed or emitted from the sample if it is not at the sa me temperature as its surroundings, since this is a source of power not accounted for in the measurement. This can be explained using the Stefan-Boltzmann law, ) ( ) (4 4 0 4 4 0 S ST T C T T A P (5.1) where P is the total power radiated or absorbed, is the emissivity of the sample, is the

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65 Stefan-Boltzmann constant, A is the surface area of the sample, T0 is the temperature of the sample, TS is the temperature of the surroundings, and C = A is a constant. During measurement of the thermal conductivity, the samp le is not at uniform temperature, since a temperature difference of order T ~ 0.5 K is applied to the sample. If we assume the surroundings are at TS = T and the sample is at T0 = T + T we have ]} ) [( { } ) {(3 2 3 4 4 T C T T O T T C T T T C P (5.2) We have ignored terms of order ( T )2 and higher, since at all temper atures of interest T >> T It is clear then that this radiation effect should follow a T3 temperature dependence, and should be more important at higher temperatures. Figure 5.7 shows a method by which the presence of effects fr om radiation can by verified, using the Cs8Na16Ge136 sample25 as an example. The thermal conduc tivity is extrapolated from the mid-range temperature dependence, as indicat ed by the dashed line. This extrapolated portion is then subtracted from the m easured portion, giving the difference If there are significant radiation losses present, this difference is expected to follow a T3 dependence, as described above. As shown in the inset, this was found to be the case indicating that the upswing is in fact likel y due to radiation losses from the sample. Similar analysis was performed for the two Cu substituted samples, which also showed similar results. We note that the effect was much smaller in the Cu samples (see Figure 5.6), as compared to the Cs8Na16Ge136 sample which was measured on a system

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66 Figure 5.7 Verification of losses due to radiation duri ng the thermal conductiv ity measurement. The dashed line represents the thermal conductivity extrapolated from the mid-range temperatures. The inset shows the T3 dependence of indicating the upswing at the higher temperatures is likely due to radiation losses from the sample. elsewhere,25 indicating that the losses due to ra diation are small for our measurement system in the Novel Materials Laboratory, re inforcing the high quali ty of our transport measurements system. Temperature (K) 10100 Thermal Conductivity (W/m-K) 1 10 T 3 (10 6 K 3 ) 6810121416182022242628 (W/m-K) 0.6 0.8 1.0 1.2 1.4 1.6 Total measured thermal conductivity Extrapolated thermal conductivity

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67 6 Summary and Future Directions The impetus for the present work th roughout has been the need for deeper experimental investigation into the synthesis and physical properties of type II clathrates. This follows from the unique and interesting properties these materials possess, their potential for technological appl ications, and the significantly less attention that type II clathrates have received thus far as compared to the type I structural subset. In particular, a better understanding of the possible compos ition space for type II clathrates is needed in order to better quantify the prospects these materials hold for applications. In this section, some of the key results of this work are reviewed, and directions for future work are discussed. The present work has utilized a range of synthesis and charac terization techniques to explore new type II clathrate compositions as well as to study the structural and transport properties of these materials. For the first time, it has been shown that type II clathrates are stable under substitution of the framework species. The substitution of Cu for Ge in Cs8Na16CuyGe136y type II clathrates is found to si gnificantly affect the transport properties, in particular the electr onic transport. For Cu content of y = 8, a transition from n-type to p-type majority c onduction is observed below room te mperature, the first such

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68 observation of hole conduction in type II clathrates to date. These initial results suggest the possibility that the electrical properties of type II clathrates could be controlled via appropriate framework substitution, and give new direction for expanding the possible compositions in type II clathrates. An extensive investigation has been unde rtaken into the synthesis of type II clathrates by route of degassing of alkali a nd alkaline earth sili cides and germanides. NaxSi136 clathrates, materials whose wide optic al band gap is raising interest for photovoltaic applications, have been successf ully synthesized covering a range of Na content, with signifi cantly less type I Na8Si46 clathrate present as impurity as compared to the research found in the literature. NaxSi136 samples with x = 1, 8 have been studied in greater detail. These materials are stable up to 600oC, an encouraging result for higher temperature applications. The elec trical transport in these materials show resistivities that decrease with Na content, and activated temperature dependences for Na1Si136 and Na8Si136. This compared with the metallic behavior of the “fully loaded” Cs8Na16Si136 shows that the properties of type II silicon clathrates de pend strongly on the guest atom content and/or type. Indeed, the thermal conductivity measurements on theses materials also revealed striking results. Na1Si136 and Na8Si136 clathrates are shown to be lowthermal conductivity crystalline materials, in agreement with previous work on the completely unfilled clathrate Si136. Although these compounds appear to be “intrinsically” poor conductors of heat, the introduction of gu est Na atoms into the cages in Na8Si136 have a further dramatic effect. Th e thermal conductivity is reduced even lower, and the data show an unmistakable dip in the temperature dependence. As this

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69 phenomena has in the past b een associated with resona nt phonon scattering phenomena, this may constitute the first evid ence that localized vibrations of the guests in type II clathrates may scatter the h eat carrying phonons in type II cl athrates, as has also been found in type I clathrates. This warrants furt her investigation into the dynamics of the guests, which is currently underway. One challenge in the silicon-based type II clathrates is achieving high density in the compacted polycrystalline samples. Cu rrently used hot-pressing techniques have produced samples with densities of the orde r of 70% of the theo retical X-ray density. Although the clathrate framework was found to be stable to relatively high temperatures, hot-pressing at elevated temperature is exclude d as a possibility due to the sensitivity of the composition x with temperature. This combined with the rigidity of the silicon framework, and the inherent oxide layer that is ubiquitous in silicon materials, presents obstacles to obtaini ng high density in NaxSi136 clathrates. One possible route being investigated is Spark Plasma Sintering (SPS). In this met hod, high current densities are passed through a sample, resul ting in internal Joule heati ng, as opposed to external heating of the press die with a heater coil as in conventional hot-pre ssing techniques. This may hold promise in ensuring good contact be tween the grains through breaking of the oxide layer, with the added advantage of densification at lower temperatures. A number of other silicides and germanid es were also investigated. Analysis of the synthesis results, as well as the published literature revealed relationships between the crystal structures of the intermediate compounds and synthesis products observed. A systematic investigation into the synthesis of NaxGe136 did produce the clathrate, however

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70 the yield was too small and of poor quali ty to produce samples for transport measurements. Rather the dominant phase over a range of several tens of degrees Celsius consisted of a newly discovered com pound of general chemical formula Na1xGe3. The structural solution of the material revealed a novel crystal structure, and this new material warrants further study which is currently underway. In summary, this work has expanded the currently small body of knowledge that exists concerning type II clathrate mate rials, as well as opening new doors in the synthesis of clathrates. These materials cont inue to attract intere st due to the unique properties they possess, and the prospects they hold for usef ul applications. This work has shown clearly that type II clathrates offe r a class of materials in which new physics, materials science, and solid state chemistry can be discovered.

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Synthesis and characterization of type II silicon and germanium clathrates
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ABSTRACT: Clathrate materials comprise compounds in which guest atoms or molecules can be encapsulated inside atomic cages formed by host framework polyhedra. The unique relationship that exists between the guest species and its host results in a wide range of physical phenomena, and offers the ability to study the physics of structure-property relationships in crystalline solids. Clathrates are actively being investigated in fields such as thermoelectrics, superconductivity, optoelectronics, and photovoltaics among others. The structural subset known as type II clathrates have been studied far less than other clathrates, and this forms the impetus for the present work. In particular, the known "composition space" of type II clathrates is small, thus the need for a better understanding of possible compositions is evident. A basic research investigation into the synthesis and characterization of silicon and germanium type II clathrates was performed using a range of synthetic, crysta llographic, chemical, calorimetric, and transport measurement techniques. A series of framework substituted type II germanium clathrates has been synthesized for the first time, and transport measurements indicate that these compounds show metallic behavior. In the course of the investigation into type II germanium clathrates, a new zeolite-like framework compound with its corresponding novel crystal structure has been discovered and characterized. This compound can be described by the composition Na1-xGe3 (0 < x < 1), and corresponds to a new binary phase in the Na-Ge system. One of the most interesting aspects of type II clathrates is the ability to create compounds in which the framework cages are partially occupied, as this offers the unique opportunity to study the material properties as a function of guest content. A series of type II sodium-silicon clathrates NaxSi136 (0 < x < 24) has been synthesized in higher purity than previously reported for as-synthesized products. The tra nsport properties of the NaxSi136 clathrates exhibit a clear dependence on the guest content x. In particular, we present for the first time thermal conductivity measurements on NaxSi136 clathrates, and observe evidence that the guest atoms in type II clathrates affect the thermal transport in these materials. Some of the crystalline NaxSi136 compounds studied exhibit very low thermal conductivities, comparable in magnitude to amorphous materials. In addition, for the first time clear evidence from transport measurements was found that resonance phonon scattering may be present in type II clathrates, as is also the case in the type I subset.
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Clathrate.
Thermal conductivity.
Transport properties.
Materials science.
Silicon.
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