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Optimization study of ba-filled si-ge alloy type i semiconducting clathrates for thermoelectric applications

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Optimization study of ba-filled si-ge alloy type i semiconducting clathrates for thermoelectric applications
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Thermoelectric
Clathrate
Si-ge alloy
Transport measurements
Seebeck coefficient
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ABSTRACT: Thermoelectric phenomena couple thermal and electric currents, allowing for solid-state conversion of heat into electricity. For decades Radioisotope Thermoelectric Generators have supplied power to NASA satellites and deep space probes. A more accessible application to consumers is the automotive industry̕s aspiration to incorporate thermoelectrics into active waste heat recovery systems. Higher power demands require these new thermoelectric devices to operate at higher temperatures and higher efficiencies, justifying new materials research. Recently, clathrates have gained interest for thermoelectric applications due to the unique properties they possess.These properties are directly related to their crystal structure. Therefore, clathrates are not only of interest from the standpoint of potential thermoelectric applications but are also of scientific interest as they presents an opportunity to investigate fundamental properties of group-IV elements in novel crystal structures.Clathrates are a class of novel open-structured materials in which molecules or atoms of one species are completely enclosed within a framework comprised of another species. This work presents a systematic investigation of the electrical properties of type I clathrate alloys, specifically Si-Ge alloys, for the first time. A series of Ba8Ga16-ySixGe30-x+y clathrates with varying Si content were synthesized and their structural and transport properties were studied. Two additional series of type I clathrates were also synthesized and characterized and their properties compared to those of the Si-Ge alloys in order to develop an understanding of their structure-property relationships. The increasing Si content correlates to a dramatic increase in Seebeck coefficient even as the resistivity decreases, suggesting the complex interaction between the Ba and the Si substitution within the Ga16Ge30 framework significantly modifies the band structure.
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Thesis (M.S.)--University of South Florida, 2005.
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Optimization Study of Ba Filled Si Ge A lloy Type I Semiconducting Clathrates for Thermoelectric Applications B y Joshua Martin A t hesis s ubmitted in p artial f ulfillment o f the r equirements for the d egree of Master of Science Department of Physics College of Arts and Sciences University of South Florida Major Professor: G eorge S. Nolas Ph.D Srikanth Hariharan Ph.D Sarath Witanachchi, Ph.D Date of Approval: February 28, 2005 Keywords: t hermoelectric, c lathrate, Si Ge alloy t r ansport m easurements Seebeck c oefficient Copyright 2005, Joshua Martin

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Acknowledgements I thank NASA / JPL for funding this research. I thank Dr. Nolas for his patience, guidance, and the immense scientific insight and experience he in corporates into our research. I am the scientist that I am, and the scientist I will become because of him. I also thank Matthew Beekman for his advice, Sarah Erickson for all the projects she has helped me with, and Holly Rubin and Grant Fowler for all of their time and help. A special thanks to Sam Velenti, a talented machinist who provided the necessary fabrications for various components in this research. I thank Dr. Yang at General Motors R&D for provid ing the EPMA data for this research. I than k my family and friends for all of their support. I did not appear on this planet as I am today and anything I accomplish I owe them gratitude. I also thank God for His sometimes unrecognized but ever present support and guidance.

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i Table of Con tents List of Figures ii List of Tables v Abstract vi 1 Introduction to Thermoelectrics 1 1.1 Thermoelectric Phenomena 1 1.2 Applications 4 1.3 Performance Optimization 6 2 Introduction to Clathrates 10 2.1 Historical Perspective 10 2.2 Structural Properties 11 2.3 Clathrates as Potential Thermoelectric Materials 1 6 2.3.1 Thermal Conductivity 1 6 2.3.2 Electronic Transport Properties 1 8 3 Measuring Electrical Transport Properties 2 4 3.1 Measuring Resistivity 2 5 3.2 Measuring Seebeck Coefficient 2 9 3.3 Measurement Apparatus and Techniques 32 3.3.1 Measurement and Control Apparatus 32 3.3.2 LabVIEW Measurement Program 42 3.3.3 Sample Considerations 4 6 4 Optimization Studies on Ba 8 Ga 16 x Ge 30 +x and Ba 8 Ga 16 y Si x Ge 30 x +y 4 9 4.1 Synthesis 4 9 4.2 Structural and Chemical Properties Characterizat ion 51 4.3 Electrical Transport Properties 67 5 Summary and Future Directions 7 8 References 81

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ii List of Figures Figure 1. Seebeck effect for an isolated metal in a uniform t hermal gradient. 3 Figure 2. Peltier e ffect for a t hermoelectric c ouple. 3 Figure 3. Energy conversion diagra ms for a thermoelectric couple. 5 Figure 4. Optimal electrical properties for thermoelectric applications. 8 Figure 5. Type I clathrate crystal structure. 12 Figure 6. Lattice t hermal conductivity for representative polycr ystalline type I clathrates. 1 4 Figure 7. Temperature dependent lattice thermal conductivity for Sr 8 Ga 16 Ge 30 1 7 Figure 8. Temperature dependent re sistivity for selected type I clathrates. 1 8 Figure 9. Temperature dependent Seebeck coefficient for selected type I clathrates. 1 9 Figure 1 0. Temperature dependent resistivity and Seebeck for nominal compositions of Sr 8 Ga 16+x Ge 30 x 20 Figure 1 1 Theoretical ZT for Sr 8 Ga 16 Ge 30 and Ba 8 Ga 16 Ge 30 21 Figure 1 2 Theoretical ZT for B a 8 Ga 16 Ge 30 and Ba 8 Ga 16 Si 30 23 Figure 1 3 Effects of Peltier heating between voltage probes as a function of current duration. 2 6 Figure 1 4 Uncertainty as calibrated by four te st thermocouples 30 Figure 1 5 Photogra phs of the measurement apparatus. 33 Figure 1 6 I llustration of sample holder, sample mount, contact pads, and

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iii contact pins 35 Figure 1 7 Illustration of sample holder detailing contact positions 35 Figure 1 8 Illustration detailing internal front panel connections 38 Figure 19 Illustration detailing external front panel electrical connections 3 9 Figure 2 0 2001 SCAN S cannercard connections 40 Figure 2 1 LabVIEW front panel image. 45 F igure 2 2 LabVIEW diagram image illustrating the graphical program. 45 Figure 2 3 NIST Stainless Steel s tandard resistivity calibration graph. 4 8 Figure 2 4 Photomicrograph for CLB and CLC. 54 Figure 2 5 Photomicrograph for CL1 and CL3 55 Figure 2 6 XRD patterns for representative Ba 8 Ga 16 x Ge 30+x clathrates. 57 Figure 2 7 XRD patterns for representative Ba 8 Ga 16 y Si x Ge 30 x+y clathrates. 5 8 Figure 2 8 BSE image and Barium BSE image for CLC 61 Figure 29 Gallium BSE image and Germanium BSE image for CLC. 62 Figure 3 0 Oxygen BSE image CLC. 63 Figure 3 1 BSE image and Barium BSE image for CL3. 64 Figure 3 2 Gallium BSE image and Germanium BSE image CL3 65 Figure 3 3 Silicon BSE image and Oxygen BSE image CL3 66 Figure 3 4 Temperature dependent resistivity for the four Ba 8 Ga 16 x Ge 30+x specimens. 6 8 Figure 3 5 Arrhenius plot for CLC. 6 9 Figure 3 6 Resistivity v. t emperature of CLD. 6 9 Figure 3 7 Temperature dependent Seebeck for the four Ba 8 Ga 16 x Ge 30+x specimens. 70 Figure 3 8 Temperature dependent resistivity for the four Ba 8 Ga 16 y Si x Ge 30 x+y specimens. 71

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iv Figure 39 Temperature dependent resistivity for CL1. 71 Figure 4 0 Temperature dependent Seebeck for the four Ba 8 Ga 16 y Si x Ge 30 x+y specimens. 73 Figure 4 1 Temperature dependent resistivity and Seebeck coefficient for three Sr filled Si Ge alloy type I clathrates. 77

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v List of Tables Table I. Comparison of interatomic distances and esti mated polyhedra size for representative clathrates. 1 3 Table II. Ionic radii for typical type I clathrate guest atoms. 1 3 Table III. Total serie s resistance used to calculate the current sourced through a sample. 2 8 Table IV. Pin label designations for all connections. 3 7 Table V. Ba 8 Ga 16 x Ge 30+x series room temperature data summary. 5 7 Table VI. Ba 8 Ga 16 y Si x Ge 30 x+y series room temperature data summary 5 8 Table VII. Room temperature mobility and effective mass for all n type samples. 75

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vi Optimization S tudy of Ba Filled Si Ge Alloy Type I Semiconducting Clathrates for Thermoelectric Applications Joshua Martin ABSTRACT Thermoelectric phenomena couple thermal and electric currents, allowing for solid state conversion of heat into electricity For dec ades Radioisotope Thermoelectric Generators have supplied power to NASA satellites and deep space probes. A more accessible application to consumers is the automotive industrys aspiration to incorporate thermoelectrics into active waste heat recovery sys tems. Higher power demands require these new thermoelectric devices to operate at higher temperatures and higher efficiencies, justifying new materials research. Recently, clathrates have gained interest for thermoelectric applications due to the unique properties they possess. These properties are directly related to their crystal structure. T herefore clathrates are not only of interest from the standpoint of potential thermoelectric applications but are also of scientific interest as they presents an opportunity to investigate fundamental properties of group IV elements in novel crystal structures. Clathrates are a class of novel open structured materials in which molecules or atoms of one species are completely enclosed within a framework comprise d of another species. T his work presents a systematic investigat ion of the electrical properties of type I clathrate alloys, specifically Si Ge alloys, for the first time. A series of Ba 8 Ga 16 y Si x Ge 30 x+y clathrates with varying Si content were synthesiz ed and their structural and transport properties were studied. Two additional series of type I clathrates were also synthesized and characterized and their

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vii properties compared to th ose of the Si Ge alloys in order to develop an understanding of their stru cture property relationships. The increasing Si content correlates to a dramatic increase in Seebeck coefficient even as the resistivity decreases, suggesting the complex interaction between the Ba and the Si substitution within the Ga 16 Ge 30 framework sig nificantly modifies the band structure. This unique relationship has not been observed in typical semiconducting materials and identifies a thermoelectric optimization route for these type I clathrates

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1 1 Introduction to Thermoelectrics 1.1 Thermoelectric Phenomena Thermoelectric phenomena couple e lectrical and thermal currents, allowing a solid state transfer of energy. The most fundamental of these, the Seebeck effect, relates a voltage gradient across a conductor to its imposing therma l gradient. The value of this ratio yields the Seebeck c oefficient For a uniform conductor in a thermal grad ient t hermally excited charge carriers in the hot end diffuse down the concentration gradient to occupy the lower energy states in the cold end generating a voltage difference (see F igure 1) In n type (p type) semiconductors, th is potential establishes in the direction (opposite direction) of the thermal gradient resulting in a negative (positive) Seebeck. A temperature gradient T D across the junction of two dissimilar conductors also generates an electric potential ab V D as in Thomas Seebecks 1 1821 observation where T V ab ab D D = a (1) represents the Seebeck c oefficient for the junct ion. Years later in 1834, Jean Peltier 2 observ ed that the passage of an electric current through the junction of two dissimilar conductors results in the liberation or absorption of heat at the junction. Since conductors forming an ohmic contact share Fe rmi levels, passing a current through a metal/n type semiconductor junction requires an electron to acquire energy as it enters the conduction band and to release energy as it passes through an n type semiconductor/metal junction (illustrated in Figure 2). The rate of thermal exchange at each junction is given by I IT Q ab ab P P = = a (2)

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2 where I is the current through the junction at temperature T and ab P is the Peltier coefficient of the junction. Although the Seebeck and Peltier effects define the thermoelectric properties observed in the junction of two dissimilar conductors, the Thomson effect 3 defines the bulk thermoelectric property of a single conductor. Current passing thr ough a homogeneous material in a thermal gradient results in the reversible flow of heat, defined by the Thomson coefficient 1 1 = dx dT dx dq I t (3) where dx dq is the rate of heating per unit length and dx dT is the temperature gradient. The equations dT d T ab b a a t t = (4) and T ab ab a = P (5) comprise the Kelvin relations and relate the fundamental thermoelectric phenomena.

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3 Figure 1. Seebeck e ffect for an i solated m etal in a uniform thermal gradient Electrons diffuse from the hot to the cold side generating a voltage Energy vs. Fermi Dirac distribution diagrams indicate the probability of filled energy states for both the hot and the col d side s Figure 2. Peltier e ffect for a t hermoelectric c ouple Passing a current through the thermoelectric couple results in the transfer of thermal energy via the charge carriers. Also shown are Fermi Dirac distribution diagrams illustrat ing the relative difference in occupied energy states for each metal/semiconductor junction. E f E f E f E f h e heat absorbed heat released e

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4 1.2 Applications A thermoelectric device consists of pairs of n and p type semiconducting segments (thermoelectric couples) connected e lectrically in series and thermally in parallel (Figure 3) This arrangement facilitates practical energy conversion by allowing sufficient heat transport via the charge carriers In o ne application, point cooling and temperature stabilization, thermoele ctrics offer several distinct advantages over traditional methods of refrigeration. These include minimal maintenance (no moving parts), the absence of environmentally hazardous coolants, precise temperature control, quiet and compact operation, and reve rsible heat pumping. Such characteristics permit the incorporation of a thermoelectric device into electronic component packages, ICs, and sensors, often operating in unusually harsh environments. Thermoelectric devices also offer the elegance of solid state power generation, the application of interest in this present study Considerable investments by NASA and other agencies have established the RTG, or radioisotope thermoelectric generator, as an integral component of space exploration. RTGs conve rt heat generated by the natural decay of plutonium into electricity, supplying power to satellites and deep space probes. Higher power demands require thermoelectric devices to operate at higher temperatures, justifying new materials research. Other a pplications include waste heat recovery and small scale remote power generation

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5 P N P N Active Cooling Heat Rejection Heat Source Heat Sink Refrigeration Power Generation I Load I Figure 3. Energy conversion diagrams for a thermoelectric couple. Passing an electric current through the couple results in the transfer of thermal energy via the cha rge carriers, providing refrigeration. Imposing a thermal gradient across the couple generates a thermoelectric voltage, sourcing a current through the load.

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6 1.3 Performance Optimization The coefficient of performance for thermoelectr ic refrigeration defined as the ratio of the rate of heat extraction from the source to the rate of expenditure of electrical energy, is given by: 4 ( ) ( ) [ ] f a a a a = = + Q W IT K T I R I T IR C p n C p n D D 1 2 2 (6) where C T ( H T ) is the tempe rature of the cold (hot) side, C H T T T = D K is the total parallel thermal conductance, and R is the total s eries resistance of the couple. In the absence of irreversible effects, T T C D = f the Carnot limit. Similarly, the efficiency of thermoelectric power generation is given by 4 ( ) [ ] ( ) h a a a a = = + W Q I T IR K T IT I R H p n p n H D D 1 2 2 (7) where W is the power delivered to an external load and H Q is positive for he at flow from the source to the sink. The value of I that maximizes h depends upon the ratio of the cross sectional area ( A ) to the length ( L ) of each thermoelectric seg ment. These relative dimensions also optimize the figure of merit for a couple, ( ) RK Z n p 2 a a = by minimiz ing the product of RK This occurs w hen 2 1 = p n n p n p p n A L A L k r k r (8) and, consequently, the figure of merit be comes

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7 ( ) ( ) ( ) Z p n p p n n = + a a r k r k 2 1 2 1 2 (9) Generally, a materials individual Z is expressed as th e dimensionless figure of merit ZT T = a s k 2 (10) where s is the electrical conductivity and L E k k k + = is the thermal conductivity, the summation of both electrical and phonon contributions, respectively. Thermoelectric materials boasting optimal electrical properties exhibit carrier concentrations intrinsic to semiconductors, which le d Ioffe 5 to suggest the search for thermoelectric materials focus upon mixed semiconductors comprised of heavy atoms. This concept reduces k while maximizing the power factor s a 2 (see Figure 4) Further criteria 6 include: 1 High crystal symmetry with the electronic bands near the Fermi level and many valleys. 2. Heavy element compounds with small electronegativity differences between constituent elements. 3. Energy gap of about 10 T k B where T is the temperature of operation and B k is Boltzmanns constant. A more novel and elegant approach to identify potential thermoelectric materials, proposed by G.A. Slack, 7 suggests a phonon g lass electro n single crystal (PG EC). An ideal PGEC material would possess thermal properties similar to an amorphous material (low thermal conductivity with anomalous temperature dependence) and electrical properties similar to a good single crystal semiconductor Crystal systems exhib iting this low, glass like thermal conductivity 8 share the following features:

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8 Fig ure 4. Optimal electrical properties for thermoelectric applications. While insulators demonstrate a high Seebeck coefficient, they also exhib it a low electrical conductivity. Metals demonstrate a high electrical conductivity but a low Seebeck coefficient. As shown by the power factor curve S 2 s semiconductors should exhibit an ideal carrier concentration for thermoelectric applications. 5 1. They possess loose atoms or molecules whose translational or rotational positions are not well defined and possess two or more metastable positions. 2. There is no long range correlation between the positions of the loos e atoms or molecules. 3. The mass of these loose atoms or molecules is at least 3% of the total mass of the crystal. 4. Disorder produced by point defect scattering cannot lead to glass like thermal conductivity An open structured framework governing the band structure would define the electronic transport properties while weakly bound atoms would effectively scatter heat carrying phonons by rattling about their lattice site Such a crystal system could satisfy the ideal

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9 PGEC concept One crystal system pr oposed by Slack to fulfill the PGEC requirements a nd prove a good thermoelectric is the c lathrate.

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10 2 Introduction to Clathrates 2.1 Historical Perspective Clathrates form by the inclusion of atoms or molecules of one type into voids of an encapsulating crystal structure of another The gas hydrate, or ice clathrate, entraps gas molecules within a tetrahedral hydrogen bonded framework of H 2 O molecules. Since the initial discovery of the chlorine water molecule by Davy 9 in 1811, several other inclusive molecules also appear ed to form these clathrate hydrates, such as noble gases, halogens, hydrocarbons, sulfur dioxide, methyl iodide and chloroform. Naturally occurring ice clathrates encapsulating methane 10 may also represent an e normous untapped energy reserve beneath the sea floor. Research conducted in 1965 by Kasper e t al 11 revealed a Si clathrate phase isomorphic to the gas hydrates. Further efforts also confirmed several distinct clathrate types for Si, Ge and Sn framewor ks encapsulating alkaline atoms. 12

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11 2.2 Structural Properties Although several clathrate structural variants exist, those of the type I shar e emphasis in most thermoelectric research. The type I clathrate structure is represented by the general formula X 8 E 46 where X correspond s to an alkali metal or alkali earth guest atom and E to a tetrahedrally (sp 3 ) bonded group IV element such as S i Ge, or Sn. Type I ternary compounds also exist of the form X 8 B 16 E 30 where B may represent Zn, Cd, Al, Ga, In, As, Sb, or Bi. For ternary compounds, b onding is analogous to Zintl phases 13 T he encapsulated guest atoms donate their valence electrons to the electronegative host atoms, resulting in a stable octet (closed valence shell) These valence e l ectrons form the covalently bonded host framework while the guest atoms form weak bonds with the cages Two distinct face sharing polyhedra conceptually comprise the type I cubic unit cell (space group n Pm 3 ): 2 pentagonal dodecahedra, E 20 and 6 tetrakaidecahedra, E 24 each creating a void with m 3 and 2 4 m symmetry, respectfully (see Figure 5). Analogous to their diamond structured compounds, the E E E bond angles average close to the characteri stic 109.5 ranging from 105 to 126. However, this clathrate structure deviates from the diamond structured counterparts in their larger average interatomic distances and larger (~15%) volume per group IV atom, demonstrating the relative openness of th e clathrate crystal structure. 12 Interatomic distances calculated from refined atom positions allow the estimation of polyhedra size as a function of the encapsulated guest atom, assumed to reside in the center of each cage. Table I illustrates this com parison for Sr 8 Ga 16 Ge 30 Ba 8 Ga 16 Ge 30 and K 8 Ga 16 Ge 30 with bond lengths calculated by Schujman et al ., 14 Eisenmann et al ., 15

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12 and Westerhaus and Schuster, 16 respectively. The ideal structure 1 4 assumes empty cages and identical nearest neighbor interatomic di stances, where actual values deviate by % or less. With the introduction of various filler atoms, both polyhedra expand slightly. However, the tetrakaidecahedra diameters remain uninfluenced by the size of the filler atom while the pentagonal dodecahed ra expand minimally. This corroborates the generally weak bonding between the guest atoms and the host framework (weaker for the tetrakaidecahedra). Figure 5 The type I structure is formed by two pe n tagonal dodecahedra and six lower symmetry tetrakaidecahedra in the cubic unit cell connected by shared faces. The open ci r c les re p resent group IV atoms that comprise the framework while the dark circles inside the polyh ed ra represent guest a t oms. 12

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13 Table I Comparison of i n teratomic d istances and e stimated p olyhedra s ize for r epresentative c lathrates Bond Ideal Ge 46 ( ) Sr 8 Ga 16 Ge 30 Ba 8 Ga 16 Ge 30 K 8 Ga 16 Ge 30 2.4496 2.495 2.5007 2.494 Me(1)-atom(2) 3.339 3.434 3.435 3.439 Me(2)-atom(3) 3.529 3.594 3.623 3.618 r 1 (dodecahedra) 2.114 2.187 2.185 2.192 r 2 (tetrakaidecahedra) 2.304 2.369 2.373 2.371 d The average interatomic distance d is given by 4 3 2 1 5 6 13 d d d d d + + + = The numbers 1, 2, and 3 represent the 6c, 16i, and 24k sites, respectively for the group IV atoms, and Me(1) and Me(2) represent the 2a (dodecahedra) and 6d (tetrakaidecahedra) sites, respectively of the guest atoms. r 1 =[2(Me(1) atom(2) d ]/2 and r 2 =[2(Me(2) atom(3) d ]/2 Table II Ionic radii for typical type I clathrate guest atoms. Ion Ionic radius () Na 1+ 1.00 K 1+ 1.38 Rb 1+ 1.50 Cs 1+ 1.70 Eu 2+ 1.17 Sr 2+ 1.18 Ba 2+ 1.38 Comparison of guest atom radii (see Table II) with polyhedra size suggests smaller ions may more effectively rattle about within their cages, scattering lattice phonons and suppressing the lattice thermal conduction. Figure 6 demonstrates this difference in temperature dependent thermal conductivity for several type I clathrates. Various measurement techniques, including theoretical calculati ons, 17 18 structural information, 19 20 21 ultrasonic attenuation measurements, 22 23 and optical spectroscopy 24 confirm the correlation between this dynamic disorder in the guest atoms and the observed effects on phonon modes. Temperature dependent structural refi nements

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14 Figure 6 Lattice t hermal conductivity for representative polycrystalline type I clathrates. 12 from single crystal and powder Sr 8 Ga 16 Ge 30 (and Eu 8 Ga 16 Ge 30 ) reveal comparatively larger anisotropic atomic displacement parameters (ADPs) for Sr(2) ( and Eu [ 2 ]) by nearly an order of magnitude relative to the framework atoms 25 (see also Einsenmann et al 1 5 ) Th e large zero temperature ADP implies a static disorder for the guest atom in the tetrakaidecahedra in addition to the dynamic disorder. Neutron diffraction data on Sr 8 Ga 16 Ge 30 also led Chakoumakos et al 26 to suggest a split site model for Sr (2) Due to a non uniform electrostatic potential within the polyhedra, the Sr ion may energetically favor certain points T hus, splitting the Sr (or Eu) position into four equivalent sites within

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15 the {100} plane may better describe the ADP data. This suggests a tunneling disorder where the guest atom jumps between different energetically preferred positions. Not surprisi ngly then, Eu 2+ guest atoms demonstrate a greater influence in suppressing the lattice thermal conductivity than Sr 2+ atoms d ue to their smaller radi i larger mass (almost twice as massive), and a larger ADP. The combination of the two ions, as in Sr 4 Eu 4 G a 16 Ge 30 introduces six discrete resonant scattering frequencies (three for each ion) and exhibits the lowest k comparatively. While Ba clathrates possess a low lattice thermal conductivity, the ir temperature dependence is more typi cal of crystalline materials and differs wi th respect to the Eu and Sr clathrates due to the larger Ba 2+ ion size, diminishing the low frequency heat carrying phonon scatt ering

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16 2.3 Clathrates as Potential Thermoelectric Materials 2.3.1 Thermal Conductivity Although several type I clathrates have been synthesized, few studies detail their potential as thermoelectric materials, with even less research pertaining to high temperature measurements. Pioneering m easurements by Nolas et al 27 on semic onducting Ge clathrates indicate the unique thermal conductivit y of these compounds Temperature dependent k for a phase pure polycrystalline Sr 8 Ga 16 Ge 30 sample, shown in F igure 7, indicates glasslike thermal conduction, with a magni tude and temperature dependence similar to an amorphous material. Although k values exceed those of a morphous Ge ( a Ge ) at room temperature, they remain less than a morp h ous quartz ( a SiO 2 ) above 100 K. The low temperature data exhib its a T 2 temperature dependence, also characteristic o f amorphous materials. Extrapolations of the electronic contribution to the total lattice thermal conductivity using the Wiedemann Franz relation reveal the total lattice thermal conductivity comprised almost entirely from lattice contributions. While high frequency optic phonons in the clathrate exhibit low or zero group velocity and contribute little to the total thermal conductivity, low frequency acoustic phonons contribute the most, having the hig her group velocity. These d ata on Sr 8 Ga 16 Ge 30 indicates low frequency scattering mechanisms replace traditional alloy phonon scattering. Considerable research into the thermal conductivity of type I clathrates 12 has established the existence of phonon g lass lattice conduction in few compounds This stresses the need to optimize the electrical properties of this materi al system for thermoelectric applications.

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17 Figure 7. Temperature dependent lattice thermal conductivity for Sr 8 Ga 16 Ge 30 12 Temperature (K) 0.01 0.1 1 10 100 1000 Thermal Conductivity (W/mK) 0.0001 0.001 0.01 0.1 1 10 100 1000 Ge crystal a-SiO 2 Sr 8 Ga 16 Ge 30 a-Ge

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18 2.3.2 Electronic Transport Properties Electrical transport property i nvestigations by Kuznetsov et al 28 of several IV 30 III 16 II 8 B B A compounds over the range 100 870 K indicate an estimated ZT = 0.7 for Ba 8 Ga 16 Ge 30 at 700 K and 0.87 for Ba 8 Ga 16 Si 30 at 870 K. A far more exte nsive analysis by Mudryk et al 29 characterizes a series of Ba and Eu substituted type I clathrates, including Cu stabilized variants, with various framework substitutions. These include Al, Ga, or In atoms occupying Si or Ge host sites (see F igures 8 and 9) Although th e s e compositions demonstrate the variety of transport properties available with in the clathrate system, t hey do not offer direct insight into structure property relationships or correlate these properties to carrier concentration. Figure 8. Temperature dependent resistivity for selected type I clathrates. 29

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19 Figure 9. Temperature dependent Seebeck coefficient for selected type I clathrates. 2 9 Nominal co mpositions of Sr 8 Ga 16+x Ge 30 x prepared and characterized by Nolas et al 30 represent the only doping study on type I clathrates to date. Since Ga substitution in the Ge framework produces charge compensation for the divalent Sr ions, a slight compositional change in the Ga to Ge ratio within a fixed Sr concentration results in varied carrier concentrations. Temperature dependent resistivity and Seebeck coefficient are shown in Figure 10 As the carrier concentration increases, the Seebeck decrease s, and decreases also with decreasing temperature, typical for heavily doped semiconductors. These data yielded a calculated ZT 0.25 at 300 K and an estimated ZT = 1 for T > 700 K. Theoretical band structure calculations by Blake et al 31 examine the effect of changing the metal ion within the clathrate as well as vary ing the carrier concentration for both p and n type doped Sr 8 Ga 16 Ge 30 Ba 8 Ga 16 Ge 30 Ba 8 Ga 16 Si 30 and Ba 8 In 16 S n 30

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20 Seebeck Coefficient (microV/K) -300 -240 -180 -120 -60 0 Temperature (K) 0 50 100 150 200 250 300 350 Resistivity (mohm-cm) 1 10 100 7X10 19 cm -3 10 19 cm -3 10 20 cm -3 (A) (B) Figure 10. Temperature dependent resistivity and Seebeck for n ominal compositions of Sr 8 Ga 16+x Ge 30 x 30

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21 Figure 1 1 (a) ZT as a function of p doping and temperature. (b) ZT as a function of n doping. 3 1 These calculations estimate the band gap for Sr 8 Ga 16 Ge 30 and Ba 8 Ga 16 Ge 30 at 0.3 eV and 0.6 eV, respective ly ( as estimated from F igure 5 in Blake et al 3 1 ) Optical absorption data on Sr 8 Ga 16 Ge 30 estimate the band gap at 0.05 eV. 1 4 The larger band gap in Ba 8 Ga 16 Ge 30 gives it a higher ZT max (where T max is the temperature at which maximum ZT is observed ) than S r 8 Ga 16 Ge 30 Coupled to a higher melting point 2 8 this feature potentially

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22 allows Ba 8 Ga 16 Ge 30 to operate at high temperatures. Maximal predicted ZTs (>1) for p doped samples of Sr 8 Ga 16 Ge 30 and Ba 8 Ga 16 Ge 30 (shown in F igure 1 1 [ a ] ) indicate an optimal carri er concentration of 15.4 x 10 19 holes/cm 3 and 15.1 x 10 19 holes/cm 3 respectively at 600 K Figure 1 1 ( b ) demonstrates pronounced differences in performance for the two n doped samples at 600 K and with different optimal carrier concentrations Although the Sr clathrate exhibits a calculated maximum ZT of 1.5, the theoretical ZT calculations for the Ba clathrate only approaches 0.8. Previous work by Blake et al 32 offers insight into why these electronic properties differ While bonding orbitals between the metal atoms and antibonding molecular orbitals (sp 3 ) of the framework form the lowest conduction bands, bonding between the Ga Ge and Ge Ge orbitals comprise the valence bands, almost completely localized on the framework. The smaller Sr ions migrate further away from the center of the tetrakaidecahedral cages than do the Ba ions, stabilizing the nearby Ga Ge orbitals and destabilizing the further away Ge Ge orbitals. This anisotropic interaction of Sr with the framework lowers the energy of the unit cell and perturbs the shape of t he valence bands, altering the electronic properties. Since in p doped materials the ZT heavily depends upon the valence band structure, substitution of Ga 16 Si 30 for Ga 16 Ge 30 results in a lower performance thermoelectric. In the Ge clathrate, holes possess a higher mobility than in the Si clathrate. Theoretical ZTs for Ba 8 Ga 16 Ge 30 and Ba 8 Ga 16 Si 30 are shown in F igure 1 2 3 1

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23 Figure 1 2 a) ZT as a function of p doping and temperature. (b) ZT as a function of n doping. 3 1

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24 3 Measuring Electrical Transport Properties Understanding and investigating structure property relationships necessitates accurate materials characterization. The measurement of key transport properties gives conte xt to new materials and relates these properties to changes in structure and in composition. Since low temperature electrical property measurements reveal the most significant insight into the fundamental physics, the Novel Materials Laboratorys transpor t propert ies measurement system was constructed to examine temperature dependent resistivity and Seebeck coefficient in the range 300 K 12 K through specific design emphasis upon the unique challenges inherent in measuring thermoelectric materials. With the future inclusion of temperature dependent thermal conductivity measurements, this system will simultaneously characterize all the terms necessary to calculate a materials ZT. This arrangement proves fiscally effective and time efficient while also b enefiting accuracy in the figure of merit through simultaneous measurements on an identical sample with identical contacts.

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25 3. 1 Measuring Resistivity R esistivity measurements require an indirect four probe method in which one pair of lead wires sources current through the bulk p arallelopiped and a separate pair measures the corresponding voltage drop. This eliminates discrete voltage contributions from lead wires and sample contacts. Concurrent dimensional measurements result in the resistivity given by r = V I A l o (11) where V is the measured voltage drop, I the current sourced through the sample, A the cross sectional area, and l o the effective length between the voltage leads. The simultaneous electrical property me asurement design of this system enables the copper wires of the two type T thermocouples to also serve as voltage probes. To ensure ohmic contact, two shallow divots bored within the specimen surface were electronically plated with a thin nickel film prio r to tinning and direct soldering of contact wires. Positioning these voltage contacts away from the current contacts according to w l l o 2 (where l is the sample length and w is the sample thickness) guarantees homogeneous current flow whe re the voltage is measured Current contacts were soldered directly to the nickel plated face on each sample end. Measuring resistivity in thermoelectric materials presents unique difficulties. Finite thermal gradients arising from joule heating or the Seebeck measurement superimpose a thermoelectric voltage D V = a D T onto the resistive voltage drop. Fortunately, alternating current polarity and averaging the subsequent voltage measurements eliminates these Seebeck voltage contributions

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26 V IR = V ( I + ) + a D T [ ] V ( I ) + a D T [ ] 2 (12) as well as directional inhomogeneous current flow. A more challenging problem arises from Peltier heat The passage of current through the junction of two dissimilar materials results in the liberation or the absorption of heat, in this case at each current contact. Depending upon the direction of the current flow, attempts to measure the resistivity contribute to standing temperature gradients across the specimen and consequently increase the Seebeck voltage. Unfortun ately, the reversal of current reverses the direction of both the temperature gradient and its corresponding Seebeck voltage, nullifying any benefit incurred by averaging the two readings. While the imposed Peltier thermal gradient requires a finite tim e to propagate, the resistive voltage can be Figure 1 3 Effects of the Peltier heating on the voltage between the probes as a function of current duration. No te the plateau region between 1.1 1.3 s wherein the Peltier heat generated Seebeck voltage does not contribute to the resistive voltage 3 3

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27 measured instantaneously. According to Nishida 33 (Figure 1 3 ), this plateau region has a maximal duration of 1.1 1.3 seconds. To negate the Peltier heat requires fast switching of current polarity. Curre nt sourced by a Keithley 2400 SourceMeter does not necessarily indicate the actual current sourced through the specimen. Instead, the measured voltage drop across a high precision resistor of known value in series with the specimen provides the required a ccuracy. The series resistance value, measured separately on a Keithley 2001 Multimeter, includes the total resistance of the resistor, connecting wires, and the rotary switch between the series resistance voltage contacts, detailed in Table III Dependi ng on specimen resistivity, the front panel rotary knob selects an appropriate series resistance value (0.1, 1, 10, 100, 1 k, or 10 k ohms ). For good thermoelectric semiconducting materials the series resistance is typically set to 10 ohms. The series re sistance voltage drop and the resistivity voltage drop were measured on a 2001 SCAN S cannercards channel 6 and channel 3, respectively, by the Keithley 2001 Multimeter, with an uncertainty of 1 V. Therefore, the contributing magnitude of this uncertainty to the total error in the resistivity depends on selecting an appropriate current value as to maximize the measured voltage difference. The geometric factor (A/ l o ) remains the most dramatic s ource of error in the resistivity measurement. Utilizing a calibrated micrometer, concurrent cross sectional geometry measurements at three longitudinally equidistant positions yield an average cross sectional area value ( A ) Measurement uncertainty of 0 .0005 in a 2 mm span (0.0787) results in a 0.64 % error. A Bauch and Laumb optical ster e oscope provides for the practical and consistent measurement of effective length ( l o ) For each new magnification setting, the optical reticle built into the left e yepiece must be calibrated using a USAF resolution test target (RES 2 ). Comparing the measured line length for a

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28 selected group and element number to the actual calculated line length generates a correction factor. Since voltage contacts retain the poten tial of their centers, the optical reticle measures divot radii and the distance between the inner edge of the two divots to calculate the effective length. Measurement uncertainty of 0.0005 for a 0.0150 diameter divot at 30 x magnification results in a 3 .3 % error. Table III Total series resistance used to calculate the current sourced through a sample. Resistor ( W ) Total Series Resistance ( W ) 0.1 0.3971 1 1.3036 10 10.3589 100 100.039 1,000 999.70 10,000 9,9726

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29 3. 2 Measuring Seebeck Coefficient The Seebeck coefficient measures the entropy per charge carrier by relating the thermoelectric voltage to its imposing temperature gradient a = D V D T = V H V C T H T C (13) where V H T H and V C T C are the voltage and temperature of the hot side and cold side, respect ive ly. A small 10 k W thick film chip resistor epoxied to one end of the sample generates the thermal gradient while the other end, soldered to the sample contact pad on the sample mount, serves as the heat sink. At each stabilized temperature of interest, current sourced through the resistor by a Kepco ABC 125 1DM Power Supply varies a small thermal gradient across the sample where D T = 2 % 5 % of the sample temperature. The voltage is then recorded as a function of the thermal gradient and the slope yields the Seebeck coefficient. Two type T thermocouples soldered into separate nickel plated divots along a single longitudinal face provide an accurate and stable temperature reading in the range 300 K to 12 K. The hot thermocouple ( T H ) voltage difference and the cold thermocouple ( T C ) voltage difference were measured on the 2001 SCAN S cannercards channel 1 and channel 2, respectively, by the Keithley 2001 Multimeter An iterative solution using these voltage differences calculates each thermocouple temperature. Sample wires soldered to cont act pins in thermal contact with the sample holder serve as the thermocouple reference junction, measured by a DT 670B CO silicon diode Uncertainty as calibrated by four test thermocouples in reference to this temperature diode contributes a maximum of 0.2 K in the higher temperature range shown in Figure

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30 Temperature At Diode B (K) 0 50 100 150 200 250 300 Diode B minus TC -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 CLB CLA CL4 CL2 Figure 1 4 Uncertainty as calibrated by four test thermocouples in reference to temperature diode B. 1 4 and even less at lower temperatures. The maximum unce rtainty is 1% throughout the temperature range. Small diameter contact wires (0.001) minimize thermal losses due to conduction. The Seebeck voltage drop was measured on the 2001 SCAN S cannercards channel 3 by the Keithley 2001 Multimeter, with an un certainty of 1 V. Therefore, the contributing magnitude of this uncertainty to the total error in the Seebeck depends on imposing an appropriate thermal gradient as to maximize the measured voltage difference. Since these voltage contacts also serve as the copper lead s for each thermocouple, measurement of both the voltage and the temperature difference occur at an identical location. The measured Seebeck value includes both the sample

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31 contribution as well as the copper contact wire contribution, which must be subtrac ted from the measured value to obtain the sample value Using a polynomial fit to the measured temperature dependent Seebeck coefficient for copper provides the necessary correction a Sample = a Copper a Measured

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32 3.3 Measurement Apparatus and Techniques 3. 3.1 Measurement and Control Apparatus A Janis closed cycle refrigerator (CCR) system enables the convenient achievement of cryogenic temperatures. Based on the Gifford McMahon thermodynamic cycle, the APD cryogenics Inc. HC 2D 1 Helium Compressor first compresses 99.995% purity helium refrigerant gas at an operating supply pressure of 330 350 psig, subsequently delivered to the Janis CCS 200 Expander model DE 202 where a reciprocating motor controlled displacer admits the compressed helium and upon expansion provides refrigeration. Typical refrigeration capacity is 8.8 W at 77 K for the first stage and 2.2 W at 20 K for the second stage. The sample holder assembles to this second stage cold head. A custom designed and constructed Bosch Aluminum S tructural Framing System using 45 x 45 mm extruded aluminum profiles and connecting gussets provides a rigid framework table for the expander. To further suppress expander vibrations, leveling feet and rubber isolation pads were assembled to the aluminum framework legs. Multi angle connectors bolted to the expanders custom 5/8 thick aluminum mount, also isolated via rubber pads, enable a near 90 rotation from vertical of the expander unit to facilitate more ergonomic sample mounting (shown in Figure 1 5 ) The custom sample holder (Figure 1 5 ) consists of three discrete components machined from a single 4 diameter oxygen free copper ingot according to the AutoCAD schematic drawings. A separate 0.3750 thick brass sample holder connector provides a mi nimal thermal barrier between the sample holder and the cryostat cold head to eliminate the transfer of acute temperature oscillations from the cold head. Apiezon N thermal grease facili ta tes maximal thermal contact between the

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33 Figure 1 5 Photographs of the measurement apparatus: the electronics cabinet housing the Keithley 2001 Multimeter, the Keithley 2400 SourceMeter, the Lakeshore Temperature Controller, and the Kepco Power Supply; the cryostat cold head and sample holder; the helium compressor, cr yostat and cryostat table; and the cryostat in its rotated down position for sample mounting.

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34 cold head, the sample holder connector, and the sample holder. Four 0.3125 copper cubes were also fabricated from oxygen free copper to serve as removable samp le mounts expediting the sample preparation/sample measurement cycle 0.1mm thick indium foil provides a consistent thermal contact between the sample mount and the top of the sample holder. T he included cryostat radiation shield mounts to the first sta ge of the cold head Specialized alumina contact pads provide a bridge between the sample contacts and the electrical interface to the external measurement apparatus. A thin copper film covering the rear surface of the alumina pads permits a direct solde r (50% Pb/50% Sn) to each side of the sample holder. Metal contact pins soldered to six discrete vertically spaced rectangular copper films on the aluminas front surface enable a convenient contact point for the samples contact leads (see Figures 1 6 and 1 7 ) Each sample mount also contains a single contact pad for sample mounting. By achieving favorable thermal contact with the sample holder, these solderable alumina contact pads eliminate thermal gradients between the sample contact points and the cry ostats electrical interface connections to the front panel, minimizing thermal conduction across the sample lead wires while simultaneously electrically isolating each contact. A 10 pin feedthrough on the cryostat instrumentation skirt mediates sample connections between the Lakeshore 331 Temperature Controller and the two cryostat diodes A and B. Temperature diode A, located on cryostat stage 1 just above heater 1, is a DT 670B CO silicon d iode. Temperature diode B, screwed to the top of the sample h older via a pressure mount, is also a DT 670B CO silicon diode. Wiring labels derived from the alphabetical pin assignments, shown in Table IV, are distributed in pairs to accommodate the signals. Within the cryostat, diode B voltage measuring pairs FH consist of 36 long finely twisted Belden 8085 0.008 square mm 38 AWG heavy armored p oly thermaleze magnet copper wires, soldered to the 10 pin feedthrough ( 50% Pb/ 50%

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35 Front View Side View B A F H D C J E G K Figure 1 6 Illustration of sample holder, sample mount, contact pads, and contact pins. Contact pin labels (A K) detail contact positions connected to the 19 pin feedthrough on the cryostat. Sample Holder B Constantan T H A Copper T H F Resistor VH Resistor IConstantan T C D Copper T C C Resistivity I+ J Resistor V+ E Resistor I+ G K Resistivity ISample Heater Sample Figure 1 7 Illustration of sample holder detailing contact positions from the contact pins to the sample.

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36 Sn). Current sourcing pairs EG consist of 36 long finely twisted Belden 8083 0.02 square mm 34 AWG heavy armored poly thermaleze magnet copper wires, soldered to the 10 pin feedthrough with 50% Pb/50% Sn solder. These wires are soldered to silicon diode B with Ostalloy 281 42% Sn/58% Bi solder. Diode A connections arrived preassembled by Janis A 19 pin feedthrough on the cryostat instrumentation skirt mediates sample connections between the external measurement apparatus and the contact pads within the cryostat. Wiring labels de rived from the alphabetical pin assignments, shown in Table IV are distributed in pairs to accommodate the signals. Within the cryostat, voltage measuring pairs (AB, CD, EF, RS) consist of 36 long finely twisted Belden 8085 0.008 square mm 38 AWG heavy armored poly thermaleze magnet copper wires, soldered to the 19 pin feedthrough and the contact pads with 50% Pb/50% Sn. Current sourcing pairs (GH, JK, LM, and reserve leads NP, TU, and V) consist of 36 long finely twisted Belden 8083 0.02 square mm 34 AWG heavy armored poly thermaleze magnet copper wires, soldered to the 19 pin feedthrough and the contact pads with 50% Pb/50% Sn. The small diameter wires minimize thermally conductive losses. Forming a ribbon spiral up the cold head, these wires were t wice wrapped around the copper blocks on each of the two cooling stages and secured in place via Teflon tape. This ensures good thermal contact, prohibiting stray thermal gradients along the connection wires. Seventeen feet of 3M 3750 Series 13 discrete twisted pair (color coded) shielded round cable connects the 19 pin cryostat feedthrough (soldered using 50% Pb/50% Sn) to the front panel. The front panel electronics box distributes all cryostat connections to their respective measurement apparatus, p rovides a troubleshooting hub, and centralizes all other miscellaneous measurement circuitry. Figure 1 8 details the internal front panel connections from the 19 pin cryostat feedthrough to the dual banana plug binding posts

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37 Table IV Pin label designati ons for all connections. Pin Label Designation Pin Label Designation A Copper T H A Diode A I+ B Constantan T H B Diode A V+ C Copper T C C Diode A ID Constantan T C D Diode A VE Resistor V+ E Diode B I+ F Resistor VF Diode B V+ G Resistor I+ G Diode B IH Resistor IH Diode B VJ Resistivity I+ J 50 Ohm Heater K Resistivity IK 50 Ohm Heater L Heater 2 I+ M Heater 2 IN Reserve P Reserve R Reserve S Reserve T Reserve U Reserve V Reserve 19-Pin Passthrough 10-Pin Passthrough secured on the panel. The AB, CD, EF, and GH binding posts directly connect to the AB, CD, EF, and GH cryostat leads. Binding post J (positive resistivity current) first conducts through a rotary knob and a known series resistance before the J cryostat current lead. Binding post K (negative resistivity current) directly connects to the K cryostat current lead. The series voltage drop V+ measures the voltage on J prior to the rotary knob and V measure s the voltage on J after the series resistors. H1 IN designates heater current sourced from the Lakeshore 331 Temperature Controller to heater 1 (located just under stage 2, near diode A), where the p ositive (+) conducts through a 3/4 A fuse and a 0 1 A a mmeter before connecting to H1 OUT (+). H1 IN ( ) directly connects to H1 OUT ( ). H2 designates the secondary heater (located on the sample holder itself), where binding post L first conducts through a 1/16 A fuse and a 0 100 mA milliammeter before conn ecting to the L cryostat current lead.

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38 A B C D E F G H J K + IN OUT + + H1 H2 V 0.1 1.0 10 1 K 10 K 100 1/16 A Ammeter Milliammeter 3/4 A To Cryostat 19 Pin Feedthrough L M Series Resistance Front Panel Figure 1 8 Illustration detailing internal front panel connections between the front panel, the ammeters, the fuses, the rotary knob controlling the series resistance (in Ohms) and connections to the 19 pin cryostat feedthrough

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39 To Cryostat 10 Pin Feedthrough Front Panel Rear Panel Keithley 2400 Sourcemeter Keithley 2001 Multimeter 2001 SCAN Scannercard Kepco ABC 125-1DM LakeShore 331 Temperature Controller A B C D E F G H J K + IN OUT + + H1 H2 A B C D E F + G H H2 V V L M L M Figure 19 Illustration detailing electrical connections between the front panel, rear panel, and the instrumentation.

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40 A B C D A C B D E F + Ribbon Cable Input to Keithley 2001 Multimeter Figure 2 0 2001 SCAN S cannercard connections. Figure 19 details the electrical connections betwee n the front panel, the rear panel, and the measurement apparatus. 36 Multi stacking dual banana plug cables comprise all connections to the front panel. AB, CD, EF, GH, V(+) V( ), and H2 LM cables connect to separate binding posts on the rear panel loc ated behind all measurement apparatus in the electronics cabinet. Rear binding posts AB, CD, EF, and V(+) V( ) connect to the 2001 SCAN Scannercard in the Keithley 2001 Multimeter via 40 long 28 AWG 5 twisted pair ribbon cable. Each channel measures vol tage differences and requires a Hi (+) and Lo ( ) input. Rear panel binding post connections to the S cannercard are shown in Figure 2 0 where AB, CD, AC, BD, EF, and V+V voltage contacts correspond to Hi and Lo measurement channels 1, 2, 3, 4, 5, and 6, respectively. I n 2 pole mode, all 10 distinct S cannercard channels are actively read through output A, connected via banana plug cable to the rear binding post on the Keithely 2001 Multimeter. Rear panel binding post GH connects to the Kepco ABC 125 1DM via 16 AWG twisted pair wire. Rear panel binding post LM connects to the analog outputs on the LakeShore 331 Temperature Controller via 16 AWG twisted pair wire. H1 OUT front panel binding post connects to the multi stacking banana plug on the 10 pin cry ostat feedthrough cable and the H1 IN binding post connects to the heater output banana terminals on the LakeShore 331 Temperature Controller. Binding post JK directly connects

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41 via banana plug cable to the rear terminals of the Keithley 2400 sourcemeter.

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42 3.3.2 LabVIEW Measurement Program The Keithley 2001 Multimeter, Keithley 2400 SourceMeter, Lakeshore 331 Temperature Controller, and the Kepco ABC 125 1DM Power Supply interface the computer through IEEE 488.2 GPIB communications bus. The Nati onal Instruments LabVIEW graphical programming language provides adaptable sequencing, automated data acquisition, simplified command interactions between the computer and the measurement apparatus, efficient data manipulation and storage, and real time mo nitoring. A programmed user friendly graphical front panel (Figure 2 1 ) enables the necessary program interface, facilitating input parameters such as cross sectional area, effective length, heater current, resistivity current, and temperature cycling. Th is custom program (Figure 2 2 ) allows for three distinct temperature zones, each with separate intervals, as well as measurement during the cooling cycle or both cooling and heating cycles, to identify potential inconsistencies in the data. Temperature dep endent resistivity and Seebeck graphs update acquired data in real time. The measurement sequence proceeds as follows, measuring on the cooling cycle: 1. The program is initialized to user selected input parameters. A tab delimited spreadsheet file is creat ed containing input parameters as well as column labels for data acquisition. 2. Based on the input temperature zones and intervals, an array is initialized to include all setpoint values. 3. The Lakeshore 331 Temperature Controller is initialized, set for pre programmed zone tuning PID, and Lakeshore calibration curves are set for diode A and B.

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43 4. The setpoint array is indexed at the beginning of each new while loop iteration to select the next setpoint value. This value is transferred to the Temperature Contro ller. 5. Once Temperature diode A has stabilized at the setpoint within 50 m K for 2 minutes, loop control shifts to diode B. Once temperature diode B has stabilized at the setpoint within 50 mK for 1 minute the program executes the next sequence. 6. The Keith ley 2400 Sourcemeter is initialized and the ou t put turned on according the user selected input value. 7. After waiting 0.5 s, the Keithley 2001 Multimeter measures S cannercard channels 3 and 6, the resistivity voltage difference and the series resistance vo ltage difference, respectively. 8. The polarity of the sourced resistivity current is instantaneously switched. After 0.5 s, the Kei thley 2001 Multimeter measures S cannercard channels 3 and 6, the resistivity voltage difference and the series resistance volt age difference, respectively. The current is turned off. 9. All necessary calculations are performed to yield the resistivity value. The temperature at diode B is also recorded and passed to an array. 10. If the measured resistivity voltage drop is less than 10 0 mV, an algori th m increases the amount of current sourced for the next iteration and setpoint to maintain the desired accuracy. If the measured resistivity voltage drop is more than 500 mV, an algori th m decreases the amount of current sourced during the next loop iteration until a minimum value of 1 mA is reached. 11. Temperature diode B is read and recorded for the initial Seebeck temperature. 12. The user defined heater current is transferred to the Kepco Power Supply and turned on in constant current mode.

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44 13. After waiting 2 4 s (user selectable) for thermal propagation, the Keithley 2001 Multimeter measures the voltage on channels 1, 2, and 3, for the thermocouples and the Seebeck voltage drop, respectively. These values are measured in 1 second intervals for a total of 5 iterations. Temperature diode B is measured and serves as the reference junction. Heater current is turned off. 14. A complex algorithm inputs the thermocouple voltage and using an iterative solution determines the temperature. 15. The slope of the calculated linear fit of the voltage difference array and the temperature difference array yields the measured Seebeck coefficient. 16. Temperature diode B is read again. The mean sample temperature T is recorded and is used to determine the value of the copper wire correction factor. T he measured Seebeck coefficient is subtracted from the Seebeck of copper, calculated by a polynomial fit to measured temperature dependent Seebeck data for copper. 34 17. All acquired data and calculated values are indexed into an array and appended to the data file created earlier. 18. Resistivity and Seebeck values are updated on the front panel graph. 19. The next loop iteration begins at the next setpoint and steps 4 18 repeat until the measurement cycle is complete.

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45 Figure 2 1 LabVIEW front panel image. Figure 2 2 LabVIEW diagram image illustrating the graphical representation of program functions.

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46 3. 3.3 Sample Considerations Hot pressed polycrystalline specimens cut to the ideal specific dimensions 2 x 2 x 5 mm 3 were prepared for electrical transport property measurements. Using a 5 speed Dremel and Press, no. 80 drill bits ( 0.3429 mm) inserted according to ideal measurement geometry along a single longitudinal face bored two divots into each specimen 0.4 mm in diame ter. A methanol wash eliminated specimen particulates. To prepare the specimen surface for nickel plating, a Hunter Products ElectroPlating System and degreaser pen (12V operating potential) first removed trace residues. Following a thorough DI water ri nse, an anodized aqueous solution nickel pen (7.5V operating potential) deposited a thin nickel metal layer over the negatively biased specimen, covering each thermocouple divot and resistivity current contacts J and K (sample ends). Nickel was chosen as a plating film due to its excellent wetting properties as well as the absence of diffusion at the nickel/clathrate material interface. A final DI rinse clears the remaining aqueous solution. All longitudinal faces were briefly sanded with 600 SiC paper p ending visible removal of nickel plating extraneous to contact points. Utilizing a calibrated micrometer, concurrent cross sectional geometry measurements at three longitudinally equidistant positions yielded an average cross sectional area value (althoug h the specimens were cut with a precision wire saw) Nickel plated sample ends were tinned using a Weller WES51 soldering iron, a custom 1/64 conical tip, acid free flux, and Ostalloy 281 solder, used for all sample contacts. Having a low solidus temper ature of 138 C, this 42% Sn/ 58% Bi alloy provides for quick and convenient soldering/desoldering of contact wires while preventing the accidental removal of cryostat connections to the sample holder contact pads. Next, the specimens negative

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47 current co ntact surface K was soldered directly to the tinned Cu film on the sample mounts contact pad using a Barnstead/Thermolyne hotplate to heat the mount beyond the solders solidus temperature. A tinned Omega Engineering, Inc. 0.001 bare copper wire was the n soldered to the specimens positive current contact point J and another to the specimens negative current contact point K by direct solder to the sample mounts contact pad, each in a geometry respecting the sample holders contact pin locations. To p repare the sample heater, a 10 k O thick film metal glaze on ceramic resistor measuring 1.0 x 0.5 x 0.35 mm 3 was first sanded with 600 SiC paper, removing the film contacts on the bottom face. Four Omega Engineering, Inc. 0.001 bare copper wires were sold ered to the tinned contacts on longitudinally opposing sides of the sample heater to provide the G and H heater current contacts and the E and F voltage contacts. This sample heater was then mounted to the free end of the specimen using thermally conducti ve and electrical ly insulating Stycast Epoxy. The two T type thermocouples were fashioned by arc melting an Omega Engineering, Inc. 0.001 bare copper wire and an Omega Engineering, Inc. 0.001 bare constantan wire in acetone to prevent oxidation. These thermocouples were then soldered into the two tinned divots in a geometry respecting the sample holders pin contact locations. The effective length was measured, the sample mount was screwed into the sample holder isolated via indium foil, and the sample lead wires were soldered to their respectful pins using Ostalloy 281 solder. This measurement system was calibrated with standards of known values to determine accuracy. Although resistivity standards are abundant, there are none for the S eebeck coefficient. Instead, measurements from established systems corroborate the accuracy of this system s Seebeck measurement. The Novel Materials Laboratory resistivity measurement on the NIST stainless steel standard agreed within experimental uncer tainty (Figure 2 3 ) Resistivity and Seebeck coefficient measurements on a

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48 skutterudite and on p type B i 2 Te 3 also agreed with measurements performed at Clemson University. Figure 2 3 NIST S tainless Steel Standard resistivity as measured by the Novel Mate rials Laboratory (circles) and NIST (squares). Error bars represent the minimum 3.3% uncertainty in the effective length measurement l o 550 600 650 700 750 800 850 900 0.00 50.00 100.00 150.00 200.00 250.00 300.00 Te mperature (K) Resistivity (nOhm-m)

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49 4 Optimization Studies on Ba 8 Ga 16 x Ge 30 +x and Ba 8 Ga 16 y Si x Ge 30 x +y 4.1 Synthesis S amples of Ba 8 Ga 16 x Ge 3 0+x were prepared by reacting stoichiometric quantities of high purity elements within pyrolitic boron nitride crucibles. Subsequent to direct mixing of 99% Ba (Aldrich) finely powdered 99.999% Ge (HPC, Japan) hand milled to 325 mesh ( 45m ) and 99.9999% Ga (Chameleon Reagent) inside an oxygen and moisture free nitrogen glovebox (Vacuum Atmospheres) these samples were sealed within a quartz ampoule unde r a low pressure (<1 atm) nitrogen atmosphere, heated slowly at 1 K/min to 1000 C f or 24 hours, then cooled to room temperature at 2 K/min using a Mellen Series TC12 3x36M 3Z Vertical Solid Tubular Furnace Note t he solidification temperature of a 65 at. % Ge / 35 at. % Ga melt on the G a G e binary phase diagram is about 875C, while re ports on the melting temperature of Ba 8 Ga 16 Ge 30 are 9 74 C 2 8 and 9 57 C 1 5 compared to 7 74 C 2 8 and 7 64 C 1 5 for Sr 8 Ga 16 Ge 30 and 11 97 C 2 8 and 1 111 C 1 5 for Ba 8 Ga 16 Si 30 S amples of Ba 8 Ga 16 y Si x Ge 30 x +y were prepared by reacting stoichiometric quantities of h igh purity elements within pyrolitic boron nitride crucibles. Subsequent to direct mixing of 99% Ba (Aldrich) finely powdered 99.999% Ge and 99.999% Si (HPC, Japan) hand milled to 325 mesh 45 m, and 99.9999% Ga (Chameleon Reagent) inside an oxygen and m oisture free nitrogen glovebox (Vacuum Atmospheres) these samples were sealed within a quartz ampoule under a low pressure (<1 atm) nitrogen atmosphere, heated slowly at 1 K/min to 900 C for 72 hours, then cooled at 2 K/min using a Lindberg Model #54233 Tubular Furnace To facilitate homogeneity, the samples were hand powdered to 325 mesh under nitrogen atmosphere cold compacted at

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50 8,000 lbs. (Carver Laboratory Press, model C using custom designed 0.5 diameter stainless steel punches and die ) and si ntere d according to the previous thermal treatment. This procedure was repeated twice.

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51 4.2 Structural and Chemical Properties Characterization The samples chosen for transport measurements demonstrat ed the best homogeneity and phase purity. Other samples synthesized with e xtended deviations in Ga to Ge ratios resulted in samples heavily comprised of impurity phases. S amples exhibiting a deviation of less than 4.6% from the stoichiometric Ga content were thus chosen for characterization. To facilitate structural, chemical, and electrical properties characterization, s amples were powdered to 325 mesh and inserted within a 0.5 inner diameter cylindrical graphite die, situated between molybdenum punches and isolated via graphite foil This i solation prevents reaction between the sample and the metal punches while simplifying release of the pellet following densification. The specimens were then cold compacted at 1500 lbs. (securing the hot press die) and hot pressed (Thermal Technology Inc. Hot Press, Model # HP20 4560 20) under nitrogen flow to achieve maximal densification For the Ba 8 Ga 16 x Ge 30+x specimens, an applied uniaxial pressure of 45 MPa at 650 C for 2 hours yi elded densities shown in Table V as percent of the calculated theoret ical density ( 5.84 g/cm 3 for Ba 8 Ga 16 Ge 30 ) CLD demonstrates a higher than 100 percent theoretical density due to the presence of impurity phases. For the Ba 8 Ga 16 y Si x Ge 30 x +y specimens, an applied uniaxial pressure of 47 MPa at 675 C for 2 hours yielde d densities shown in Table V I Calculated theoretical densities for each sample according to increasing Si content were 5.64 g/cm 3 5.65 g/cm 3 5.58 g/cm 3 and 5.58 g/cm 3 respectively. Although uniform from s ample to samp le, the measured densities remai n lower than the ir theoretical densities. After removing the graphite foil, sample pellets were cut into parallel o pipeds according to dimension specifications described in chapter 3 using a South Bay

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5 2 Technology, Inc. Model 850 wire saw and slurry solutio n consisting of 23 micron boron carbide abrasive powder and glycerine. A small segment from each sample mounted in epoxy resin facilitated the extensive polishing procedure for optical metallographic analysis, including grain size measurements. This proc edure utilized the South Bay Technology Inc. Model 900 Grinder/Polisher with various SiC polishing papers (600, 800, 1200, and 4000) to remove the initial layers of epoxy and sample. The final stages remove remaining scratches introduced by previous polis hing measures These include a 3.0 micron alumina suspension over a nylon polishing pad and a 1.0 micron and 0.3 micron deaglomerated suspension over M ultitex pads. Aqua Regia etched the polished surface to clarify the grain boundaries. A Unimet Unitr on 8731 stereoscopic microscope together with a Panasonic Model GPKR222 CCD camera controlled through Videum Capture software allowed the imaging and phot ographing of grain micrographs. Employing the linea r intercept, or Heyn Procedure, three representati ve field photomicrographs of the specimen yielded average grain size by counting the number of grain boundary intersections by a straight line with a length sufficient to yield at least 5 0 such intersections in the selected magnification. The mean interce pt length 35 PM L L T = 3 (14) provides a quantitative parameter for any space filling grain o f arbi trary shape, size or position, where L T is the test line length provided by a calibrated transparency, M is the magnif ication, and P is the number of grain boundary intersections. The equivalent grain size number G was calculated for each photomicrograph by the equation 3 log 64 6 00 10 L G = (15) These values w ere averaged and curve fitted using ASTM Standard 36 data to yield the nominal average grain diameter Measured grain sizes for Ba 8 Ga 16 x Ge 30+x and

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53 Ba 8 Ga 16 y Si x Ge 30 x +y samples are reported in tables V and V I respectively. Representative photomicrographs for CLB and CLC, and for CL1 and CL3 are shown in F igures 2 4 and 2 5 respectively

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54 Figure 2 4 Photomicrograph for CLB (top) at 1000 x magnification with an estimated grains size at 6.0 microns. Photomicrograph for CLC (bottom) at 1000 x magnification with an estimated grain size at 6.2 microns.

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55 Figure 2 5 Photomicrograph for CL1 at 1000 x magnification (top) with an estimated grain size at 5.9 microns. Photomicrograph for CL 3 (bottom) at 1000 x magnification with an estimated grain size at 6.0 microns.

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56 Powder X ray diffraction (XRD) analy sis confirmed the presence of type I clathrate phase for each polycrystalline specimen, using a Rigaku Miniflex tabletop diffractometer with monochromatic Cu K a radiation ( 1540592 0 = l nm ), sampling at 0.05 increments in th e interval 20 = 2 q = 60 at a rate of 1/min. JADE v3.1 software facilitated analysis by identifying peak locations, implementing a hybrid algorithm of trend oriented searches in the intensity and in the Savitzky Golay 2 nd derivative space. Correlating the a ddition of NIST Standard Si 640c Reference Material in to the powdered specimens to standard line position s enabled the generation of a correction factor, calibrating the diffraction data. Calculation of lattice parameters incorporated diffraction from the (320), (3 21), (530), (531), (600), and the (611) planes and are reported for Ba 8 Ga 16 x Ge 30+x and Ba 8 Ga 16 y Si x Ge 30 x +y in tables V and V I respectively XRD patterns for Ba 8 Ga 16 x Ge 30+x and Ba 8 Ga 16 y Si x Ge 30 x +y samples are shown in Figures 2 6 and 2 7 respectively with Si standard peaks labeled accordingly. Peak intensities were normalized with respect to diffraction from the (321) plane. While CLC demonstrates an ideal, phase pure type I c lathrate diffraction pattern t he first peak in CLA and CLB reveals trace Ge impurit ies in addition to the clathrate phase XRD patterns for CLD reveal an additional impurity phase The presence of denser impurity grains in the low density open structured clathrate compound r easonably explain s the observed higher than theoreti cal density. Due to similar bond lengths for Ga and Ge, the lattice parameters for this series of samples remain nearly identical. For the Ba 8 Ga 16 y Si x Ge 30 x +y series, XRD scans were conducted both with and without Si standard to identify any Si impurit y phases. While CL1 demonstrates a trace Ge impurity, CL2, CL3, and CL4 exhibit the type I clathrate phase only. Due to a smaller bond length for Si as compared to Ga and Ge, the lattice parameters decrease as the Si content increases.

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57 2 q (degree) 20 30 40 50 60 Intensity (arbitrary unit) Ba 8.03 Ga 16.23 Ge 29.74 Ba 7.95 Ga 15.80 Ge 30.25 Ba 7.98 Ga 15.43 Ge 30.59 Ba 7.92 Ga 15.26 Ge 30.82 Si Si Si Si Si Si Si Si Si Si Si Si CLA CLB CLC CLD * (222) (320) (321) (400) (410) (411) (421) (520) (530) (531) (600) (611) (620) (541) Figure 2 6 XRD spectra for four Ba 8 Ga 16 x Ge 30+x clathrates. Si standard peaks are labeled accordingly. Arrows indicate impurity phases in CLD. (*) indicate Ge peaks. Table V Four Ge Clathrates indicating stoichiometries obta ined via atomic percentages using EPMA analysis, the lattice parameter a o in angstroms, the measured percent theoretical density, D, the average grain size in microns, th e Seebeck coefficient a in V/K, the resistivity r in mO cm, the measured carrier concentration n o in cm 3 the mobility m in cm 2 /V s, at room temperature. As the p type sample (CLD) demonstrates possible dual conduction, 4 probe DC Hall measurements are not useful. Label Stoichiometry a o D Grain Size a r n o m CLA Ba 7.92 Ga 15.26 Ge 30.82 10.781.006 90.8 12 -70.8 21.4 1.08x10 20 3.31 CLB Ba 7.98 Ga 15.43 Ge 30.59 10.788.001 91.8 6.0 -82.2 12.3 1.36x10 20 3.64 CLC Ba 7.95 Ga 15.80 Ge 30.25 10.786.002 90.4 6.2 -159 51.6 9.13x10 19 1.30 CLD Ba 8.03 Ga 16.23 Ge 29.74 10.786.004 100.5 10 35.2 7.30

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58 2 q (degree) 20 30 40 50 60 Intensity (arbitrary unit) Ba 8.10 Ga 15.82 Si 5.11 Ge 24.98 Ba 8.09 Ga 15.76 Si 4.96 Ge 25.19 Ba 8.08 Ga 15.83 Si 3.54 Ge 26.54 Ba 8.05 Ga 15.55 Si 3.49 Ge 26.91 Si Si Si Si Si Si Si Si Si Si Si Si CL1 CL2 CL3 CL4 (222) (320) (321) (400) (410) (411) (421) (520) (530) (531) (600) (611) (620) (541) Figure 2 7 XRD spectra for four Ba 8 Ga 16 y Si x Ge 30 x+y clathrates. Si standard peaks are labeled accordingly. Table V I Four Ge Clathrates indicating stoichiometries obtained via atomic percenta ges using EPMA analysis, the lattice parameter, a o in angstroms, the measured percent theoretical density, D, the average grain size in microns, the Seebeck coefficient, a in V/K, the resistivity, r in mO cm, the measured carrier concentration, n o in cm 3 the mobility, m in cm 2 /V s, at room temperature. As the p type sample (CL1) demonstrates possible dual conduction, 4 probe DC Hall measurements are not useful. Label Stoichiometry a o D Grain Size a r n o m CL1 Ba 8.05 Ga 15.55 Si 3.49 Ge 26.91 10.762.005 85.1 5.9 14.2 16.7 CL2 Ba 8.08 Ga 15.83 Si 3.54 Ge 26.54 10.757.005 80.7 6.4 -64.9 559 5.18x10 17 22.2 CL3 Ba 8.09 Ga 15.76 Si 4.96 Ge 25.19 10.748.004 83.2 6.0 -77.6 378 7.77x10 17 25.1 CL4 Ba 8.10 Ga 15.82 Si 5.11 Ge 24.98 10.743.005 83.3 5.9 -84.7 187 5.63x10 18 5.39

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59 Electron Probe Micro a nalysis (EPMA) conducted at General Motors R&D provid ed chemical compositions and elemental spatial relationships for each specimen. Stoichiometries were calculated from average atomic percentages obtained via hi gh energy electron bombardment and recording of Wavelength Dispersive spectra characteristic to the emitted species. Compositions for the Ba 8 Ga 16 x Ge 30+x series demonstrate d a deviation in Ga to Ge ratios, as reported in Table V and indicate d an increasi ng concentration of Ga as the Ge content decrease d EPMA confirmed phase purity for CLC and the trace Ge impurity in CLA and CLB in addition to the type I clathrate phase Analysis of CLD indicated two distinct trace impurity phases, one with nominal com position 19.5% Ba, 65.4% Ga, 15.0% Ge and the other 31.9% Ba, 30.3% Ga, 37.9% Ge, in atomic percentages. While the latter phase remains unidentifie d the stoichiometry of the former was Ba 6.05 Ga 20.27 Ge 4.6 8 a Ga doped type IV clathrate (Ba 6 Ge 25 ) It has been reported that t ype I V clathrates form during the synthesis of type I clathrates Type IV clathrates are comprised of pentagonal dodecahedra helically condensed by the sharing of only three pentagonal faces. 37 Compositions for the Ba 8 Ga 16 y Si x Ge 30 x + y series demonstrate d a deviation in Ga to Ge ratios, as reported in Table V I Although it was attempted to maintain an identical Si content for each specimen with the stoichiometry Ba 8 Ga 16 y Si 8 Ge 30 +y the Si to Ge ratio s also varie d Attempted deviation s in Ga content from the more energetically favorable stoichiometric value resulted in the variable Si content. While unidentified by XRD, EPMA indicated a trace amount of Si impurity for CL1, CL2, CL3, and CL4 and confirmed the trace Ge impurity for CL1 in addition to the type I clathrate phase B ackscattered electron (BSE) images confirmed specimen homogeneity, indicat ing c omposition dependent spatial distributions for targeted elements Ba, Ga, Ge, and O for the Ba 8 Ga 16 x Ge 30+x series and Ba, Ga, Ge, Si, and O for the Ba 8 Ga 16 y Si x Ge 30 x +y

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60 series. The inclusion of oxygen identifies trace oxide grains as well as trace surface oxides. Although synthesis occurred under a low pressure nitrogen atmosphere, the Ba 8 Ga 16 y Si x Ge 30 x +y samples were briefly expo sed to oxygen following ejection from the cold press die between annealing. This explains the greater amount of oxide grains as compared to the Ba 8 Ga 16 x Ge 30+x series. R epresentative false color images for CLC and CL3 shown respectively in Figures 2 8 3 0 and 3 1 3 3 corroborate the measured average grain diameters. Qualitative analysis demonstrates a homogeneous concentration distribution from grain to grain for each element Since the t race impurity phases congregate into isolated grains they becom e insu lating centers and do not affect the clathrate bulk transport properties.

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61 Figure 2 8 BSE image (top) and Barium BSE image (bottom) for CLC

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62 Figure 29 Gallium BSE image ( top) and Germanium BSE image (bottom) for CLC

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63 Figure 3 0 Oxygen BS E image for CLC

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64 Figure 3 1 BSE image (top) and Barium BSE image (bottom) for CL3

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65 Figure 3 2 Gallium BSE image (top) and Germanium BSE image (bottom) for CL3

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66 Figure 3 3 Silicon BSE image (top) and Oxygen BSE image (bottom) for CL3

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67 4 3 E lectrical Transport Properties Stoichiometry deviations in G a content from charge compensated Ba 8 Ga 16 Ge 30 and Ba 8 Ga 16 Si x G e 30+x resulted in a v ar iation of carrier concentrations. A slight reduction in Ga content resulted i n a larger number of free carriers t he Ga acting as electron acceptors and Ba as electron donors. DC f our probe V an der P auw Hall measurements revealed room temperature carrier concentration s and mobilities for three n type and one p type sample s for each s pecimen series reported in tables V and V I for the Ba 8 Ga 16 x Ge 30+x series and the Ba 8 Ga 16 y Si x Ge 30 x +y series, respectively. Four probe resistivity and steady state Seebeck coefficient were measured as a function of descending temperature from 300 K to 12 K at approximately 10 K interval s shown in Figures 3 4 3 7 for the Ba 8 Ga 16 x Ge 30+x series and in Figures 3 8 4 0 for the Ba 8 Ga 16 y Si x Ge 30 x +y series, respectively. For the Ba 8 Ga 16 x Ge 30+x series, the n type sample with the lowest carrier concentration ( CLC, 9.13 x 10 19 cm 3 ) exhibited the greatest resistivity and the most pronounced semiconducting dependence, while the n type sample with the highest carrier concentration (CLB, 1.36 x 10 20 cm 3 ) exhibited a lower resistivity. Convergence in the Arrhenius plot for CLC (Figure 3 5 ) demonstrated a strong semiconducting dependence. Fitting this data to the relation [ ] T k E B a / exp 0 r r = yielded an activation energy E a of 61.8 meV. This could imply a band gap of 0.124 eV. The reported activation energy o f Sr 8 Ga 16 Ge 30 is 15 meV. 1 4 The p type sample demonstrated the lowest resistivity observed in the series, a nd a nonmonotonic temperature dependence (Figure 3 6 ). For T < 200 K CLD demonstrates a metallic like temperature dependence with d ? /dT > 0 while d ? /dT < 0 for T > 200 K. A s imilar nonmonotonic temperature dependence was observed in Ba 8 Ga 16 Sn 30 by Nol as et al 38

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68 Temperature (K) 0 50 100 150 200 250 300 Resistivity (mOhm-cm) 0 20 40 60 80 100 120 140 Temperature (K) 0 50 100 150 200 250 300 Resistivity (mOhm-cm) 0 5000 10000 15000 20000 25000 CLC CLA CLB CLD Figure 3 4 Temperature dependent resistivity for the four Ba 8 Ga 16 x Ge 30+x sample s and was considered to arise from impurity band conduction. This transition corresponds to a n increase in Seebeck with increasing temperature near 200 K and suggests conduction in impurity states or a possible dual conduction wherein the hole major ity carrier thermally depopulates more rapidly than the secondary electron conduction. Although the n type sample with the lowest carrier concentration exhibited the largest magnitude Seebeck (CLC, 159 at 300K), the other n type samples deviated from the expected trend: CLB, with a larger carrier concentration exhibited a larger magnitude Seebeck than CLA, with the lowest carrier concentration (Figure 3 7 ) Correlating these data to the EPMA stoichiometries alleviated this apparent discrepancy. As the Ga content increased, the number of acceptor states increased, explaining the

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69 1/T (K -1 ) 0.00 0.02 0.04 0.06 0.08 0.10 Ln( r ) 3 4 5 6 7 8 9 10 11 Figure 3 5 Arrhenius plot for CLC. Temperature (K) 0 50 100 150 200 250 300 Resistivity (mOhm-cm) 6.5 7.0 7.5 8.0 8.5 9.0 Figure 3 6 Resistivity v. Temperature of CLD

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70 Temperature (K) 0 50 100 150 200 250 300 Seebeck (microV/K) -150 -100 -50 0 50 CLD CLA CLB CLC Figure 3 7 Temperature dependent Seebeck coefficient for the four Ba 8 Ga 16 x Ge 30+x s ample s corresponding magnitude increase in Seebeck. The sample with the lowest Seebeck (CLA) demonstrated a slightly lower carrier concentration tha n expected due to Ba deficiency (see Table V ). For the Ba 8 Ga 16 y Si x Ge 30 x +y series, the n type sample with the lowest carrier concentration (CL2, 5.18 x 10 17 cm 3 ) also exhibited the greatest resistivity and the most pronounced semiconducting depende nce, while the n type sample with the highest carrier concentration (CL4, 5.63 x 10 18 cm 3 ) exhibited a lower resistivity (Figure 3 8 ) The p type sample demonstrated the lowest resistivity observed in the series, and a nonmonotonic temperature dependence, although less pronounced than in the Ba 8 Ga 16 x Ge 30+x series. For T < 2 3 0 K CL 1 demonstrates a metallic temperature

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71 Temperature (K) 0 50 100 150 200 250 300 Resistivity (mOhm-cm) 0 2000 4000 6000 8000 10000 12000 14000 CL2 CL3 CL4 CL1 Figure 3 8 Temperature dependent resistivity for the four Ba 8 Ga 16 y Si x Ge 30 x+y s ample s. Temperature (K) 210 220 230 240 250 260 Resistivity (mOhm-cm) 16.0 16.2 16.4 16.6 16.8 17.0 17.2 17.4 17.6 CL1 Figur e 39 Temperature dependent resistivity for CL1 in the interval 210 K 260 K indicating the unique t emperature dependenc e between 230 K and 2 4 0 K.

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72 dependence with d ?/dT > 0 and a semiconducting temperature dependence with d?/dT < 0 for T > 250 K. A more detailed measurement ( Figure 39 ) indicates a unique transition in temperature depend encies between 230 K and 24 0 K. The metallic temperature dependence may indicate conduction in impurity states or dual conduction Furt her study on this sample is needed to completely understand this phenomen on The large resistivities in this series are reasonably explained by observing the summation of the framework atoms is 45.91 for the 3 n type and 45.95 for the p type, less than the required 46. These vacancies may introduce defect states within the band gap. Since these defect states are presumably lower in energy than the conduction band states, electrons from the guest atoms would tend to prefer the se defect states, lowering the carrier concentration. With the introduction of smaller bond lengths from the Si atoms and the subsequent suppressi on of the lattice parameter, the large radius of the Ba ion may encourage vacancy formation. Although the Si content varied in amount for the 3 n type samples, the number of defects remained constant with in experimental uncertainty suggesting Si framework substitution may encourage this defect formation on preferred sites. Refinement studies on Ba 8 Si 46 x Ge x observed preferential occupancy for Ge on the 24 k sites first then the 16 i sites. 39 Si occupancy and vacancies were observed only for the 6 c sites. Comparison of the Seebeck coefficients (Figure 4 0 ) for the n type Ba 8 Ga 16 y Si x Ge 30 x +y series to their respective carrier concentrations illuminated an unexpected direct relationship: as the number of charge carriers increased the Seebeck magnitude also increased. Although the Ga to Ge ratios and the Ga to Si ratios varied, the Ga to group IV element ratios demonstrated no differentiation between the n type samples within experimental error (Ga/ IV for CL 2 = 0.526, CL 3 = 0.523, and CL 4 = 0.526). Thus, the changes in carrier concentration do not correlate to a variation in acceptor

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73 Temperature (K) 0 50 100 150 200 250 300 Seebeck (microV/K) -100 -80 -60 -40 -20 0 20 40 CL4 CL1 CL2 CL3 Figure 4 0 Temperatu re dependent Seebeck coefficient for the four Ba 8 Ga 16 y Si x Ge 30 x+y s amples levels. Suppression of the lattice parameter as the Si content increases, coupled to the increase in Seebeck coefficient suggests a deformation in the polyhedra due to the smalle r Si atoms that may increase the anisotropic overlap of the wavefunctions between the metallic bonding orbitals and the antibonding orbitals of the host atoms. This may alter the band structure and permit the simultaneous increase in carrier concentration and the Seebeck coefficient. Assuming a single carrier type in a parabolic band, the absence of mu l t i band effects, and ignoring the possibility of phonon drag, the carrier effective mass was estimated by expressing the Seebeck coefficient directly in ter ms of Fermi Dirac integrals 6

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74 + + = + + ) ( 2 3 ) ( 2 5 2 1 2 3 h h h a r r B F r F r e k (16) where B k corresponds to boltzmanns constant, e to the carrier charge, r to the exponent of the energy dependence of the carrier mean free path, x F to the Fermi integral of order x and T k E B F = h to the reduced Fermi energy. The + and sign correspond to valence band carriers and conduction band carriers, respectively. Possible dual conduction in the p type sample s limited this calculation to the n type samples. Fitting the measured Seebeck data to tabulated Fermi integral tables 40 41 yielded the reduced Fermi energy. For pure phonon scattering of the carriers (typical in crystals), r = 1/2; for scattering by ionize d impurities, r =3/2. A mixed scattering ( r =1/2) was assumed since the large radius Ba ions more effectively donate their valence electrons to the framework atoms, resulting in a wide charge redistribution where the Ba become ionized charge scatter s The known carrier concentration is given by ) ( ) )( ( 2 1 2 3 h F m m T N n o o = (17) where o m is the free electron mass, m is the effective mass, and 3 2 3 ) 2 ( 4 ) ( h kT m T N o o p = (18) or o N (300 K ) = 2.8321 x 10 19 cm 3 The e stimate d effective mass for the n type samples is shown in Table V II The estimated effective masses for the Ba 8 Ga 16 x Ge 30+x series and the Ba 8 Ga 16 y Si x Ge 30 x +y series are between those values previously reported by Sales e t al 20 for Eu 8 Ga 16 Ge 30 Sr 8 Ga 16 Ge 30 and Ba 8 Ga 16 Ge 30 ( 3m o ), and those reported by Nolas et al 30 for a Sr 8 Ga 16 Ge 30 series (<1m o ). In general, the samples with a larger m*

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75 Table V II Room temperature mobility m in cm 2 /V s, and estimated effective m ass for six n type samples. Label Stoichiometry m m*/m o CLA Ba 7.92 Ga 15.26 Ge 30.82 3.31 0.395 CLB Ba 7.98 Ga 15.43 Ge 30.59 3.64 0.607 CLC Ba 7.95 Ga 15.80 Ge 30.25 1.30 0.976 CL2 Ba 8.08 Ga 15.83 Si 3.54 Ge 26.54 22.2 0.0112 CL3 Ba 8.09 Ga 15.76 Si 4.96 Ge 25.19 25.1 0.0167 CL4 Ba 8.10 Ga 15.82 Si 5.11 Ge 24.98 5.39 0.0727 demonstrate a smaller carrier mobility. For the Ba 8 Ga 16 x Ge 30+x series the m* increases as the Ga content increases. For the Ba 8 Ga 16 y Si x Ge 30 x +y series, the m* increases as the Si content increases and also as the carrier concentration increases. The Ba 8 Ga 16 y Si x Ge 30 x +y series exhibits larger mobilities with effective masses one order of magnitude lower than in the Ba 8 Ga 16 x Ge 30+x series, suggesting a profound alteration of the band curvature. Th is supports the previous indications that Si substitution in the Ba 8 Ga 16 Ge 30 framework significantly modifies the band structure. In order to determine if the atypical transport (as compared to bulk thermoelectrics) observed in the Ba 8 Ga 16 y Si x Ge 30 x +y s eries were a function of Si substitution within the Ga 16 Ge 30 framework or a complex interaction between the Ba and the Si Ge alloy framework a series of Sr filled Si Ge alloy type I clathrates were synthesized and characterized This new series was prepa red by reacting stoichiometric quantities of high purity elements within pyrolitic boron nitride crucibles. Subsequent to direct mixing of 99.95 % distilled dendritic Sr ( Alfa Aesar ), finely powdered 99.999% Ge and 99.999% Si (HPC, Japan) hand milled to 32 5 mesh 45 m, and 99.9999% Ga (Chameleon Reagent) inside an oxygen and moisture free nitrogen glovebox (Vacuum Atmospheres), these samples were sealed within a quartz ampoule under a low pressure (<1 atm) nitrogen atmosphere, heated slowly at 1 K/min to 10 00 C for 72 hours, then cooled at 2 K/min, using a Lindberg Model #54233 Tubular Furnace. To facilitate homogeneity, the

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76 samples were hand powdered to 325 mesh under nitrogen atmosphere, cold compacted at 8,000 lbs. of pressure and sintered in a sealed quartz ampoule under a low pressure (<1 atm) nitrogen atmosphere, heated slowly at 1 K/min to 695 C for 144 hours, then cooled at 2 K/min. Resistivity and Seebeck coefficient were measured from room temperature to 12 K in approximately 10 K intervals an d are shown in Figure 4 1 Note the relative similarity in transport values. Correlating these data to chemical compositions obtained from EPMA indicate a slight increase in Seebeck coefficient as the Si content increases within a fixed Ga group IV elemen t ratio but an increase in resistivity with an increase in Si content. Although typical for semiconducting clathrates, these relationships differ with respect to the Ba filled Si Ge alloy series. This suggests the dramatic increase in Seebeck coefficient even as the resistivity decreases in the Ba filled Si Ge alloys is an interaction between the Ba and the Si Ge alloy framework and not simply a function of Si substitution within the Ga 16 Ge 30 framework.

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77 Figure 4 1 Temperat ure dependent resistivity and Seebeck coefficient for three Sr filled Si Ge alloy type I clathrates. Resistivity (mOhm-cm) 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 Temperature (K) 0 50 100 150 200 250 300 Seebeck (microV/K) -120 -100 -80 -60 -40 -20 Sr 7.44 Ga 15.54 Si 1.57 Ge 29.45 Sr 7.57 Ga 15.65 Si 3.72 Ge 27.06 Sr 7.46 Ga 15.74 Si 5.00 Ge 25.79 Sr 7.44 Ga 15.54 Si 1.57 Ge 29.45 Sr 7.57 Ga 15.65 Si 3.72 Ge 27.06 Sr 7.46 Ga 15.74 Si 5.00 Ge 25.79

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78 5 Summary and Future Work Stoichiometry deviations in Ga content from charge compensated Ba 8 Ga 16 Ge 30 resulted in a narrow variation of carrier conc entrations for the Ba 8 Ga 16 x Ge 30+x series. A slight reduction in Ga content (increase of Ge content) resulted in an increase in carrier concentration Following extensive structural and chemical characterization, the electrical properties were measured o n the three n type samples and the one p type sample. CLC exhibited the largest room temperature Seebeck coefficient ( 159 V/K) for this series, the largest resistivity (51.6 mO cm), and the most pronounced semiconducting temperature dependence. Convergence in the Arrhenius plot for CLC yielded an activation energy of 61.8 meV. The p type sample (C LD) exhibited the lowest resistivity for the series (7.30 mO cm) and a nonmonotonic temperature dependence. This transition corresponded to a dramatic increase in Seebeck with increasing temperature, suggesting a possible dual conduction or conduction in impurity bands. Expanding on this foundation, a series of Ba filled Si Ge a lloy clathrates were prepared and characterized Electrical transport property measurements for this Ba 8 Ga 16 y Si x Ge 30 x +y series indicated resistivities one order of magnitude la rger than their non alloyed counterparts for the three n type samples. The carrier concentrations for these samples were also nearly two orders in magnitude lower than the Ba 8 Ga 16 x Ge 30+x series. Framework vacancies implied by the EPMA data suggest elect rons from the guest atoms prefer to occupy these defect states within the band gap, lowering the carrier concentration. A nalysis of EPMA data for the three n type samples also revealed identical Ga to group IV element ratios but a variation in Si to Ge ra tios. T h e increasing Si

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79 content correlates to a dramatic increase in Seebeck coefficient even as the resistivity decreases. This unique relationship has not been observed in typical semiconducting materials and identifies a thermoelectric optimization ro ute for these type I clathrates Although the inclusion of Ba as the guest atom results in higher melting temperatures as compared to Sr, differences between these ions also result in the relative diminished electrical conductivity of Ba clathrates. B a, due to its lower electronegativity and larger radius than Sr, more effectively donates its valence electrons to fill the sp 3 bonding orbitals from the electron deficient Ga in the host framework, encouraging a pronounced charge redistribution. This low ers the valence band energies, widening the band gap. Larger formation energy for the Ba clathrate supports the enhanced stability of the framework bands. Theoretical band structure calculations by Madsen et al 42 confirm this interpretation. Furthermore the highly ionized Ba ion easily becomes a charge scattering center. These factors reasonably suppress the conductivity of the Ba 8 Ga 16 x Ge 30+x and the Ba 8 Ga 16 y Si x Ge 30 x +y clathrates. Fully understanding the complex interaction between the Ba and the Si Ge alloy framework in the type I clathrate requires further analysis. The synthesis methods and equipment employed in this research (direct mixing and sintering in quartz tubes) fix the maximum furnace temperature to 1000 C and thus limit the amount of Si substitution to relatively small quantities. Polycrystalline Ba 8 Ga x Ge 46 x clathrates with different Ga compositions (x = 12 20) have been grown by arc melting followed by spark plasma sintering technique s. 43 Ba 8 Si 46 x Ge x (0 = x = 23) type I clathrates have also been prepared under high pressure and high temperature conditions. 3 9 These methods may enable the further variation in Si to Ge ratios in Ba filled Si Ge alloy clathrates and even reduce framework defect formation X Ray photoemission spectroscopy could investigate electronic states as a function of Si content while RIXS could investigate the defect states. Temperature dependent Hall measurements would provide insight into the

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80 electronic properties of these alloy s to further understand the mechanisms and structure property relationships facilitating the increase in Seebeck coefficient with increasing Si framework substitution in these Ba filled Si Ge alloy clathrates. The maximum calculated room temperature ZT for the Ba 8 Ga 16 x Ge 30+x series was 0.015 (CLC) assuming ? = 1 W/m K Although the variation in Ga to Ge ratios resulted in a varied carrier concentration, none of these compositions demonstrated good thermoelectric properties, therefore no thermoelectric optimization route could be identified. The maximum calculated room temperature ZT for the Ba 8 Ga 16 y Si x Ge 30 x +y series was 0.0012 (CL4) assuming ? = 1 W/m K However, the unique thermoelectric optimization route identified by these materials demonstrat es why they remain of scientific and technological interest. In addition to increasing the Si content, further understanding these type I clathrate alloys should include investigating structure property relationships using large radius guest atoms other t han Ba and other framework substitutions with smaller radii atoms as compared to Ga and Ge.

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81 References 1 T.J Seebeck, Magnetische polarisation der metalle und erze durck temperatur differenz, Abhandlungen de Deut Sch en Akademie de Wissenshafften zu Berlin, 265 373 ( 1823) 2 J.C. Peltier, Nouvelles experiences sur la caloricite des courans electrique, Annales de Chimie. LVI, 371 387 (1834). 3 W. Thomson, On a mechanical theory of thermoelectric currents, Proceedings of the Royal Society of Edingburgh v 9 1 (1851). 4 H.J. Goldsmid, Electronic Refrigeration Pion Limited, London (1986). 5 A.F. Ioffe, Semiconductor Thermoelements and Thermoelectric Cooling Infosearch, London (1957). 6 G.S. Nolas, J. Sharp, and H.J. Goldsmid, Thermoelectrics: Basic Principles and New Materials Developments Springer (2001). 7 G.A. Slack, In CRC Handbook of Thermoelectrics Ed. By D.M. Rowe, CRC Press, Boca Raton, p. 407 (1995) 8 D .G. Cahill, S.K. Watson, and R.O. Pohl, Lower limit to the thermal conductivity of disordered crystals Phys. Rev. B 46 6131 (1992). 9 H. Davy, The elementary nature of chlorine, Ann. Chim 79 326 (1811). 10 E. Suess, G. Bohrmann, J. Greiner t, and E. Lausch, Flammable Ice, Scientific American Nov. 1999, p. 76. 11 J.S. Kasper, P. Hagenmuller, M. Pouchard and C. Cros, Clathrate structure of Silicon Na 8 Si 46 and Na x Si1 36 (x<11), Science 150 1713 (1965). 12 G.S. Nolas, G.A. Slack, S.B. Schujman, Semiconductor Clat h rates: A Phonon Glass Electron Crystal Material with Potential for Thermoelectric Applications, in Semiconductors and Semimetals Volume 69 ed. By T.M. Tritt, Academic Press, San Diego, 255 (2000). 13 R. Nesper, Structure and Chemical Bonding in Zintl Phases Containing Lithium, Prog. Solid St. Chem. 20 1 (1990). 14 S.B. Schujman G.S. Nolas, R.A. Young, C. Lind, A.P. Wilkinson, G.A. Slack, R. Patschke, M.G. Kanatzidis, M. Ulutagay, and S.J. Hwu Stru ctural analysis of the Sr 8 Ga 16 Ge 30 clathrate compound, J. Appl. Phys 8 7 1529 (2000).

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Optimization study of ba-filled si-ge alloy type i semiconducting clathrates for thermoelectric applications
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Thesis (M.S.)--University of South Florida, 2005.
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ABSTRACT: Thermoelectric phenomena couple thermal and electric currents, allowing for solid-state conversion of heat into electricity. For decades Radioisotope Thermoelectric Generators have supplied power to NASA satellites and deep space probes. A more accessible application to consumers is the automotive industrys aspiration to incorporate thermoelectrics into active waste heat recovery systems. Higher power demands require these new thermoelectric devices to operate at higher temperatures and higher efficiencies, justifying new materials research. Recently, clathrates have gained interest for thermoelectric applications due to the unique properties they possess.These properties are directly related to their crystal structure. Therefore, clathrates are not only of interest from the standpoint of potential thermoelectric applications but are also of scientific interest as they presents an opportunity to investigate fundamental properties of group-IV elements in novel crystal structures.Clathrates are a class of novel open-structured materials in which molecules or atoms of one species are completely enclosed within a framework comprised of another species. This work presents a systematic investigation of the electrical properties of type I clathrate alloys, specifically Si-Ge alloys, for the first time. A series of Ba8Ga16-ySixGe30-x+y clathrates with varying Si content were synthesized and their structural and transport properties were studied. Two additional series of type I clathrates were also synthesized and characterized and their properties compared to those of the Si-Ge alloys in order to develop an understanding of their structure-property relationships. The increasing Si content correlates to a dramatic increase in Seebeck coefficient even as the resistivity decreases, suggesting the complex interaction between the Ba and the Si substitution within the Ga16Ge30 framework significantly modifies the band structure.
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Seebeck coefficient.
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