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h [electronic resource] :
structural and transport properties characterization /
by Randolph Ertenberg.
[Tampa, Fla.] :
University of South Florida,
Thesis (M.S.)--University of South Florida, 2003.
Includes bibliographical references.
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ABSTRACT: Skutterudites have been of great interest for thermoelectric applications over the last ten years. Scientific interest has focused on the unique transport properties Skutterudites possess due to the unique crystal structure. Technical interest has grown since it was discovered that some compounds rival the current best thermoelectric materials. To further the understanding of this material system, and optimize its thermoelectric properties, the synthesis and characterization of polycrystalline n- and p-type CoGeSe was undertaken. Structural, morphological, chemical, electrical, thermal and magnetic properties were studied. These data are compared to those of the binary Skutterudite CoSb3. The results of this study show a very sensitive dependence of the physical properties on stoichiometry. While the thermoelectric figure of merit is low in these materials, it is apparent that optimization via doping and "void filling" will lead to improved thermoelectric properties.
Adviser: Nolas, George S.
t USF Electronic Theses and Dissertations.
x sv 11/07/03
CoGe 1.5 Se 1.5 : S tructural and T ransport Properties C haracterization by Randolph Ertenberg A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Physics College of Arts and Sciences University of South Florida Major Professor: G eorge S. Nolas, Ph.D. Robert Chang, Ph.D. Pritish Mukherjee, Ph.D. Date of Approval: October 21, 2003 Keywords: Thermoelectric, Semiconductor, Skutterudite Material, Physics Copyright by Randolph E rtenberg 2003 All rights reserved
Acknowledgements I would like to thank Dr. Jihui Yang for carrying out low temperature measurements.
i Table of Contents List of Tables i i List of Figures i i i Abstract iv Chapter O ne: Thermoelectrics 1.1 Overview 1 1.2 Introduction to Thermoelectric Materials 3 1.3 Introduction to Thermoelectric Devices 6 Chapter Two: Skutterudites 2.1 Introduction to Skutterudites 9 2.2 Skutterudite Crystal Structure 9 2.3 Skutterudite E lectrical and Thermal Properties 14 Chapter Three: CoGe 1.5 Se 1.5 3.1 Introduction to CoGe 1.5 Se 1.5 19 3.2 Specimen Preparation 2 1 3.3 Crystal Structure 2 5 3.4 Electrical Properties 2 7 3.5 Thermal Properties 3 1 3.6 Magnetic Properties 3 3 Chapter Four: Summary of Results 3 5 References 3 6
ii List of Tables Table 1 Comparison of Doping in CoSb3. 1 4 Table 2 Data on CoGe 1.5 Se 1.5 2 6
iii List of Figures Figure 1 1. Seebeck Effect Illustrated. 1 Figure 1 2. Pe ltier Effect Illustrated. 2 Figure 1 3 Dependence of S and s on Carrier Concentration. 6 Figure 1 4. Thermoelectric Effect Illustrated. 7 Figure 1 5. Images of Power Generation. 8 Figure 2 1. Cubic View of Skutterudite 10 Figure 2 2. Realistic View of Skutterudite Unit Cell. 1 2 Figure 2 3. Thermal Conductivity of Filled Skutterudites 1 7 Figure 3 1. The Electrical Resistivity of CoGe 1.5 Se 1.5 and CoSb 3 2 7 versu s Temperature. Figure 3 2. Seebeck Coefficient v ersus Temperature of CoGe 1.5 Se 1.5 29 Figure 3 3. Lattice Thermal Conductivity for CoGe 1.5 Se 1.5 Versus Temperature. 3 1 Figure 3 4. Magnetic Susceptibility of Polycrystalline CoGe 1.5 Se 1.5 3 3
iv CoGe 1.5 Se 1.5 : Structural and Transport Properties Characterization Randol ph Ertenberg ABSTRACT Skutterudites have been of great interest for thermoelectric applications over the last ten years. Scientific interest has focused on the unique transport properties Skutterudites posse s s due to the unique crystal structure. Tec hnical interest has grown since it was discovered that some compounds rival the current best thermoelectric materials. To further the understanding of this material system, and optimize its thermoelectric properties, the synthesis and characterization of polycrystalline n and p type CoGe 1.5 Se 1.5 was undertaken. Structural, morphological, chemical, electrical, thermal and magnetic properties were studied These data are compared to those of the binary Skutterudite CoSb 3 The results of this study show a v ery sensitive dependence of the physical properties on stoichiometry. While the thermoelectric figure of merit is low in these materials, it is apparent that optimization via doping and void filling will lead to improved thermoelectric properties.
1 C hapter One: Thermoelectrics 1.1 Overview The long struggle to achieve high efficiency refrigeration or power generation with thermoelectrics began in the early 1800s when Thomas Seebeck and Jean Peltier explored the relationships between temperature an d electricity in materials. In 1821, Seebeck [ 1 ] discovered that a junction between two dissimilar materials, A and B, exposed to a temperature gradient formed an electric potential. (Figure 1 1) Figure 1 1. Seebeck Effect Illustrated. Junction s between two dissimilar materials, A and B are exposed to a temperature difference between T 1 and T 2 and a voltage forms between c and d. Later, in 1834, Peltier [ 1 ] discovered that when a current was run through a junction of two dissimilar materials such as bismuth and antimony, heating or cooling occurred at the junction (Figure 1 2) This process was reversible for both heating and for cooling. These properties, called the Seebeck and Peltier effect respectively, allow the creation of a temp erature gradient from a voltage difference, or a voltage difference from
2 Figure 1 2. Peltier Effect Illustrated. The current flows through the junction between the two materials, A and B, causing heat to be absorbed, or cooling. If the current i s reversed, heat will be released. Both processes are reversible. a temperature gradient. Using fundamental thermodynamic arguments W. Thomson showed the close relationship between the Seebeck and Peltier effects in 1857 . With the exception of Alt enkirchs derivation of thermoelectric efficiency in 1911 [ 2 ], progress in the field was negligible after the basic thermodynamic effects had been thoroughly described and understood. In the early twentieth century, the microscopic understanding of elect ronic interactions within crystals was developed. This work led to the materials currently employed for solid state refrigeration and power generation namely Bi 2 Te 3 alloys and Si Ge alloys. Bi 2 Te 3 alloys have small band gaps and are typically used for re frigeration applications while Si Ge alloys are optimized for high temperature applications from approximately 600K to 1300K, and have band gaps of about 1 eV. During the last forty years, s mall composi tional changes have resulted in incremental improvem ents in the thermoelectric properties of these alloys. However, these materials have changed very little since their discovery more than 40 years ago
3 while they have not yet been surpassed. It is believed that materials with far better properties can be m ade, vastly improving the effi ciency of thermoelectric devices. One current candidate for this effort are compounds with the Skutterudite crystal structure. This class of materials drew interest for thermoelectric applications when it was realized that i t had many of the properties that are desirable for high figures of merit, such as large carrier mobilities and a large unit cell with heavy atomic masses [3 ]. A most interesting structural aspect of these materials is the presence of voids in the structu re that can be interstitially filled. As will be described later, this significantly lowers the thermal conductivity, an important factor for good thermoelectrics. This unique property makes Skutterudites a material of great interest. In this thesis I will report on a new variant of this structure, CoGe 1.5 Se 1.5 Properties important for understanding the physics of these novel materials as well as the potential development for thermoelectric applications, such as structural, morphological, chemical, e lectrical, thermal and magnetic characteristics have been investigated. This material shows strong dependence on stoichiometry in that slight variations completely alter the transport properties 1.2 Introduction to Thermoelectric Materials A fundame ntal physical property that is key to the evaluation of thermoelectrics is the Seebeck effect. Its magnitude is given by the Seebeck coefficient S defined as T V S D = (1)
4 where V is the open circ uit voltage and D T is the difference in temperature. This states that a voltage difference applied to a junction of two dissimilar materials creates a temperature gradient. Conversely, a temperature gradient across a thermoelectric material generates a v oltage difference. I n general, when the charge carriers are electrons, S is negative, and S is positive for holes. An overall measure of the thermoelectric potency of a given material is the dimensionless thermoelectric figure of merit, ZT [2 ], defined as T S ZT L e k k s + = 2 (2) where T is the temperature, S is the Seebeck coefficient, s is the electrical conductivity, k e is the electr onic component of the thermal conductivity and k L is the lattice contribution. Thus the best thermoelectric mater ials will possess good electrical properties together with a low thermal conductivity The current best thermoelect r ics have ZT ~1 in the temperature range of interest. This value has been a practical upper limit for more than 30 years, yet no theoretical reason exists fo r why it cannot be larger [2 ]. As shown from equation (2), the main characteristics for a good thermoelectric material are high electrical conductivity, high Seebeck coefficient, and low thermal conductivity. What are the fundamental mate rial properties that govern the se physical properties and how can the y be maximized? To begin to answer these questions, it is useful to think in terms of ideal materials. High Seebeck coefficients are typical of large band gap materials, insulators, wit h S values typically on the order of 1 V/K. Seebeck
5 coefficients typically decrease as the carrier concentration increases. Thus semiconductors tend to have S values on the order of 100 m V/K and metals typically have S values of 1 10 m V/K. Conductivity in semiconductors, however, tends to increase as carrier concentration increases. Therefore, in attempting to achieve a high ZT high S values in insulators are negated by extremely poor electrical conductivity, and the excellent electrical conductivity of metals is negated by the very low Seebeck coefficient. Thus the electrical conductivity and Seebeck coefficient typically exhibit opposite dependencies on the carrier concentration. Fig 1 3 demonstrates these dependencies and also shows how the power f actor, S 2 s varies with carrier concentration. The carrier concentration also has a direct effect on the electr onic component of the thermal conductivity k e I n the Wiedemann Franz approximation [2 ] s k T L e 0 = (3) where L 0 is th e Lorentz number equal to about 2.45 X 10 8 W W K 2 at room temperature. T and s relate the electronic part of the thermal conductivity to the electrical conductivity. Thus tailoring a material through doping to the desired carrier concentration has a la rge effect on the figure of merit. In addition to the direct effects of the carrier concentration, the bonding and crystal structure play an important role in creating effective thermoelectric materials. While these properties affect S s and k e by alte ring the band structure, they also strongly affect k L By varying the elemental composition to form a variety of different compounds, one may alter all these interrelated properties. While there are literally
6 Figure 1 3. Dependence of S and s on Ca rrier Concentration. Values of the Seebeck coefficient ( S ) electrical conductivity ( s ) and power factor ( S 2 s ) vs. carrier concentration. thousands of possible compounds to create, the predicted best combination of these properties direct the sea rch to the semiconductor region since maximal power factors in semiconductors can generally be found in the range where the carrier concentration is approximately 10 19 cm 3 (Fi gure 1 3) [4 ]. 1.3 Introduction to Thermoelectric Devices The two principle uses for thermoelectrics are refrigeration and power generation. These applications are illustrated in Figure 1 4 which shows a diagram of a simplified
7 Figure 1 4. Thermoelectric Effect Illustrated. The thermoelectric effect illu strated for (a) cooling and (b) power generation applications. The current direction, I is shown in both cases. thermoelectric module composed of an n type and a p type leg connected through metallic electrical contact pads (bl ack bars). In order for this effect to be useful, a large enough current must be allowed to pass through the junction at the required voltage. Ideally no heat would be transferred in this process. However, to generate a current, the electrons must be d riven from the hot to the cold, taking heat with them. A balance between this heat loss and power conversion must be made. A ny heat that travels through other means, such as through the rmal conduction, is wasted energy. A final effect that lowers efficien cy is the Ohmic resistance. T hus t he larger conductivities result in smaller resistive loss es Applications for thermoelectric refrigeration include cooling of infrared detectors, low noise amplifiers and computer chips where localized cooling and tempe rature stability is essential This stability is due to the fact that thermoelectrics are solid state devices On the other hand, power generation requires a heat source. The temperature difference between the heat source and the heat sink generates a v oltage across the
8 device. This voltage causes an electric current through the n and p type legs resulting in power generation across the load for thermoelectric power conversion. Better thermoelectric materials result in larger voltages and more curre nt consequently producing more efficient devices. Thermoelectric power generation is currently the main source of energy in deep space spacecraft. The heat source is plutonium, and the heat sink is provided by the cold vacuum of space. (Figure 1 5) Thi s source can last for a very long time as shown by the Voyager probes. A potentially beneficial future use for this type of power conversion is in the automobile industry. By utilizing waste exhaust heat from combustion engines, energy can be harnessed i n order to run a vehicles electrical systems. In general, the advantages of all these solid state thermoelectric devices are compactness, quietness (no moving parts) and long term reliability. Figure1 5. Images of Power Generation. The diagr am shows how a plutonium heat source is used to generate electricity. The RTGs are Radioactive Thermoelectric Generators are about four feet tall and used in spacecraft such as Cassini.
9 Chapter Two: Skutterudites 2.1 Introduction to Skutterudites Skutterudite refers to a class of compounds with a specific crystal structure. CoAs 3 is a mineral that was the first discovered in Skutterud, Norway, giving Skutterudites their name. Materials with this basic structure can be synthesized from many differe nt combinations of elements. These variations result in a large number of possible stoichiometries and thus a wide range of physical properties. These compounds can also be synthesiz ed to possess semiconducting properties. Another primary feature of the Skutterudite crystal structure is the presence of interstitial sites or voids, which can be filled with a variety of atoms. It is also relatively straightforward to synthesize many of the compounds using standard synthesis techniques. Materials with the Skutterudite crystal structure have shown good potential for thermoelectric applications. Over the last 10 years, research has resulted in steady progress, recently achieving a ZT>1 in Yb [ 5 ] and Eu [ 6 ] filled Skutterudites. It is hoped that further r esearch will result in greater improvements for thermoelectric power generation applications. 2.2 Skutterudite Crystal Structure The Skutterudite crystal structure is body centered cubic and has 32 atoms per cubic unit cell. It can be thought of as 8 octants with metal atoms, cobalt for instance, on
10 Figure 2 1. Cubic View of Skutterudite. The white atoms represent the metal sites such as Co and the black atoms represent the pnicogen sites such as Sb. The large gray atoms in the front top right and back bottom left represent the filler atoms such as Ce. the corner of each sub cube, the c crystallographic site of its space group, Im 3. Inside six of these octants are the centers of rings of four pnicogen atoms, such as Arsenic, on the g crystallographic site. Th e other two octants are empty. (Figure 2 1) The atoms are covalently bonded which produces a semiconducting behavior as well as contributes to its good thermal and electrical properties. The most basic formula for the unit cell is X 2 M 8 Y 24 where X represents the voids in the structure, two per cubic unit cell. These voids can be left vacant, partially filled or completely filled with a variety of elements including group 1 and 2 elements, such as Na or Sr, or one of the Lanthanid es, Ce or Eu for example. M represents metal ions, most commonly transition metals such as Cobalt, Rhenium, or Iridium. Y represents pnicogens from group V elements where Phosphorus, Arsenic, or Antimony are the most
11 common. The bonding (detailed later) in this structure leads to its semiconducting behavior. I n a binary S kutterudite, such as CoSb 3 there must be 192 valence electrons per cubic unit cell. The addition of dopants leads to a change in this number and the creation of either free electrons or holes. Typically, doping is accomplished on the M sites by using other transition metals such as Fe and Ni. On the Y sites, doping usually employs elements from group IV and VI such as Ge, Se or Sn. The bonding of this structure provides many of its i nteresting features. Each Y atom has four nearest neighbors, two metal atoms and two nonmetal atoms situated at the corners of a distorted tetrahedron. Both the M Y bond distances and the Y Y bond distances are short and nearly equal to the sum of the co valent radii, indicating strong covalent bonding. The Y Y bonding is essential to the stability of the Skutterudite structure and has a large influence on the physical properties. The M M distances, on the other hand, are quite large, indicating that lit tle bonding occurs between these atoms. The Y M bonds form a six fold coordinated irregular octahedron centered on the M atom. The interstitial ion, X, is twelve fold coordinated by the Y atom planar groups and is thereby enclosed in an irregular icosahe dral cage of Y atoms [ 7 ]. Figure 2 2 illustrates a complete unit cell for a filled S kutterudite centered at the position of one of the interstitial X or guest ions. Large X ray thermal parameters have been reported for these ions indicating that the y may rattle or participate in soft phonon modes in the voids of this crystal structure. Indeed, the thermal parameters of these ions increase with decreasing ionic size. As first pointed out by Slack [3 8 ] these ions are caged in the
12 Figure 2 2 Realistic View of Skutterudite Unit Cell. The Skutterudite unit cell centered at the void filler atom (da shed lines), which is enclosed in an irregular ico sahedral (12 fold coordinated) cage of pnicogen atoms (black circles) The white circles represent metal atoms. The bonding, however, is inaccurate. voids of this structure and, if smaller than the void in which they are caged, may rattle. This localized dynamic disorder interacts in a random manner with the lattice phonons resulting in s ubstantial phonon scattering, particularly the lower wavelength heat carrying modes. In terms of the electronic bonding, the Y and M atoms are covalently bonded as stated earlier. Each of the Y atoms contributes five electrons to the bonding. Two of the se electrons form the two s bonds to the nearest Y atoms. The other three electrons form the two bonds with the M atoms. The M atoms contribute 9 electrons to the bonding. Three of these form the d 2 sp 3 hybrid orbitals in the M Y bonds and the other six go to the low spin d 6 state generating diamagnetic behavior. In the case of filled Skutterudites, nearly all the filler elements have positive valences (typically +2 or +3 for the lanthanides) thus contributing extra electrons to the
13 192 electrons alread y present in the unit cell, leading to metallic behavior. For high levels of filling these ions and extra electrons also distort the band structure. To limit the metallic behavior and the band structure distortion, the filler elements must usually be charg e compensated through the doping of the M and Y sites. In fact, in order to obtain near ly 100 % filling, dopants are required. An additional form of doping comes from lattice vacancies. For example, CoSb 3 is always generated p type due to the presence of cobalt vacancies. Vacancies can be formed on the M or Y sites depending on the particular compositions. Much of the research focus on these materials has been on the binary Skutterudite s such as CoSb 3 As can be seen in Table 1, substantial doping stud ies on CoSb 3 have been performed. All these compounds have been studied to help understand the physics of this interesting material The general trends show that with increased doping levels, the resistivity decreases the carrier concentration increases the Seebeck magnitude d ecreases and there is a decrease in the thermal conductivity. The impact of these trends is better described in the next section. Much work has also been performed on filled Skutterudite s, with the current best, Yb .19 Co 4 Sb 12 sh owing the largest ZT for n type compou nds . However, work on both filled and unfilled binary Skutterudite s may have reached the limits of variations that can be synthesized. P erhaps an understanding of ternary S kutterudites such as CoGe 1.5 Se 1.5 would provide new avenues of research.
14 Compound Nominal x Actual x r n S k Ref. 1000 1000 mO cm 10 19 cm 3 V/K W/mK Ni x Co (1 x) Sb 3 1 36.00 0 .35 580 0. 87 9,10 300K 5 18.00 1.20 390 0. 74 9,10 10 10.00 3.30 320 0. 83 9,10 Fe x Co (1 x) Sb 3 5 0.50 2.20 60 1 3 11 300K 20 0.40 5.80 48 0.9 1 11 100 1.35 9.20 45 0. 30 11 Cr x Co (1 x) Sb 3 10 0 .8 10.00 .17 12 300K 20 3.0 8.00 .22 12 50 8.1 5.00 .09 12 Fe x Co (1 x) Sb 3 10 1.40 120 0. 45 13 400K 120 0.80 65 0. 37 13 400 0.95 70 0. 25 13 Pt x Co (1 x) Sb 3 30 10 1.27 9.00 160 0. 70 13 300K 50 10 0.83 7.00 175 0. 60 13 100 40 0.56 15.0 0 145 0. 50 13 Pd x Co (1 x) Sb 3 10 10 2.86 3.00 240 0.8 5 13 300K 50 25 1.81 9.00 220 0. 45 13 200 50 1.25 20.00 165 0. 30 1 3 (Pt+Pd) x Co (1 x) Sb 3 60 40 0.67 15.00 150 0. 40 14 100 65 0.50 40.00 125 0. 26 14 CoSb (3 x) Te x 3 12.5 400 0. 9 15 30 1.2 5 275 0. 8 15 300 0.66 125 0. 5 15 Table 1 Comparison of Doping in CoSb3. Here, r is the resistivity, n is the carrier concentration, S is the Seebeck coefficient and k is the thermal conductivity. 2.3 Skutterudite Electr ical and Thermal Properties The electronic transport properties of binary Skutterudite s were first studied in the late 1950s and early 1960s, and centered on the properties of CoSb 3 [ 2, 16 ]. From temperature dependent electrical conductivity measuremen ts an energy gap of 0.5 eV was determined. This result is similar to the indirect gap estimated some forty years later by band structure calculations  These theoretical predictions also indicate that the undoped specimens should have low carrier conc entrations on the order of insulators.
15 However f or binary compounds, the lowest carrier concentration obtained is about 10 17 cm 3 [16 ] In addition, these binary compounds are almost always p type. Doping of these materials can bring them all the wa y into the metal lic regime with carrier concentrations >10 21 cm 3 It is therefore straightforward to obtain the optimum carrier concentration for thermoelectric applications. Table 1 demonstrates differences in carrier concentration of greater than 2 ord ers in magnitud e, with values ranging from 10 1 8 cm 3 to 4 10 20 cm 3 Thus these materials can be tailored to the desired carrier concentrations once a good base compound has been determined. T able 1 only shows compounds based on CoSb 3 but many other binar y compounds have been studied as well. W hen it was shown that these compounds could support high hole mobilities, it sparked the close scrutiny of the electronic properties of binary S kutterudites as potential thermoelectric materials. For example, Cailla t et al [1 8 ] reported single crystals of RhSb 3 with hole mobility as high as 10 4 cm 2 V 1 s 1 and CoSb 3 with mobilities approaching 2 3 cm 2 V 1 s 1 Both compounds were shown to possess large Seebeck coefficients consistent with their semiconducting beha vior. For the p type semiconductors these mobilities are comparable to that of GaAs and demonstrate the early inte rest in these semiconductors. ( Table 1) Related to the Hall mobilities, n type Skutterudites have relatively large Seebeck coefficients and ef fective masses whereas p type compounds have small Seebeck values and effective masses. As seen in the T able 1 S values from tens to hundreds of m V/K are often obtained. Als o, small changes in composition or dopant can result in positive or negative val ues for S For instance, doping with less than 0.01 percent nickel results
16 in the conversion from p type to n type behavior Adding 0.05 percent Fe makes for strongly p type behavior with an S value of 60 m V/K. This sensitivity to dopant is clear from Ta ble 1 with doping changes resulting in Seebeck coefficients from 125 m V/K to 45 m V/K. In most of the compounds in Table 1, as the carrier concentration increases, the resistivity decreases. Thus the p and n type doping tend to add carriers to the struc ture and lower the resistivity. However, this results in lower mobilities due to impurity scattering. In spite of this lower mobility, the increased carrier concentration results in lower S values. One exception to this trend is Fe. Increased levels of F e show an increase in resistivity with carrier concent ration. This demonstrates lower mobility leading to higher resistivity. The thermal properties of Skutterudite s are integral to their potential as thermoelectric materials. Perhaps the two most impor tant mechanisms for conducting heat are conductivity through the lattice and Wiedemann Franz conductivity due to charge carriers In semiconductors, it is the first of these properties that conducts most of the thermal energy. Various factors can contribu te to this process. For example, grain boundary scattering and lattice defects play an important role. However the most significant change in k L in S kutterudites comes from the addition of the filler elements. This can alter the lattice thermal conductiv ity by more than an order of magnitude as shown in Figure 2 3. The sizes of the voids and filler atoms create different ranges and amounts of scattering. Thus the larger elements such as Iridium and Antimony create a
17 Temperature ( K ) 1 10 100 1000 k L (W m -1 K -1 ) 0.0001 0.001 0.01 0.1 1 10 100 Ir 4 NdGe 3 Sb 9 Ir 4 Sm G e 3 Sb 9 IrSb 3 Ir 4 LaGe 3 Sb 9 k min Figure 2 3. Thermal Conductivity of Filled Skutterudites. The decrease in thermal conductivity is clearly shown as the smaller heavier atoms are placed in the voids. Ge is used for charge compensation. k min is the conductivity of an idealized Skut terudite with maximal phonon scattering . larger crystal structure and thus larger voids. The smallest unit cell is 7.7, found in CoP 3 and the largest is 9.25 in IrSb 3 [19 ]. Thus compounds with the Skutterudite crystal structure are of scientific interest due to their unique physical properties. They continue to be of technological interest as well, in particular as potential thermoelectric materials [ 2 ]. One important feature of these materials is the large number of different isostructural comp ositions that can be synthesized. The physical properties of these materials depend sensitively on their
18 compositions. In particular, the band structure, and thus transport, is dependent on the bonding of the pnicogen site [ 17 ] Thus changes on the pnic ogen site can result in a completely new transport in these materials The diversity of potential compositional variants remains one of the largest reasons why this material system continues to be of scientific and technological interest, and continues to be investigated by many research groups.
19 Chapter Three: CoGe 1.5 Se 1.5 3.1 Introduction to CoGe 1.5 Se 1.5 As outlined in the previous cha pter, a great deal of research h as focused on binary Skutterudites, and CoSb 3 in particular. Doping has primarily been performed on the metal site. The primary purpose of that research was to understand how the electronic band structure is changed due to doping. Having reached a basic understanding of how doping affects Skutterudites, it was decided that perhaps a full change in the foundation materials would generate different tran sport properties. At the least these experiments would provide more information on the Skutterudites band structure, leading to a further understanding of the physics of these material s and perhaps also lead to an enhancement of their thermoelectric properties. To this end, Ge and Se can replace Sb completely to generate a different Skutterudite material CoGe 1.5 Se 1.5 Much as GaAs has vastly different properties than pure Si, this n ew material demonstrates different transport properties as compared to CoSb 3 In addition to the wide range of binary compounds, ternary Skutterudite compounds with simultaneous substitution of group IV and group VI atoms on the pnicogen sites have been p reviously reported [20, 21]. These compounds should be semiconductors, as they are isoelectronic with CoSb 3 Ternary Skutterudites have been synthesized previously through various methods and some basic information about them was
20 gathered. The earliest wo rk was done by Korenstein et al  on CoGe 1.5 S 1.5 and CoGe 1.5 Se 1.5 synthesized with the chemical vapor transport method using iodine as the transport agent. Structural and magnetic measurements were then performed on the samples. The X ray data indicat ed that the structure was nearly identical to that of CoAs 3 with a probable short range ordering in CoGe 1.5 S 1.5 with rhombohedral symmetry. CoGe 1.5 S 1.5 had a lattice parameter of 8.017 a density of 5.54 g/cm 3 was diamagnetic, and found to decompose at 1000 C. CoGe 1.5 Se 1.5 had a lattice parameter of 8.299 a density of 6.62g/cm 3 was diamagnetic and decomposed at 800 C. This precipitated attempts by Lyons et al [ 21 ] to synthesize Ir and Rh containing compounds of similar compositions. Many sa mples were attempted using direct combination of the elements such as IrSn 1.5 Se 1.5 IrSi 1.5 S 1.5 IrSi 1.5 Se 1.5 RhSn 1.5 S 1.5 RhGe 1.5 Se 1.5 and RhSn 1.5 Se 1.5 In addition, the vapor deposition technique was attempted for both RhSn 1.5 S 1.5 and RhSn 1.5 Se 1.5 Al l of these specimens failed to produce pur e samples; h owever four single phase samples were synthesized: IrGe 1.5 S 1.5 with a lattice parameter of 8.2970, IrGe 1.5 Se 1.5 at 8.5591 IrSn 1.5 S 1.5 at 8.7059, and RhGe 1.5 S 1.5 with a lattice parameter of 8.2746. In addition, the X ray spectra showed some of the same ordering as seen by Korenstein et al . All of these samples demonstrated diamagnetic behavior. Sintered bars were made for IrGe 1.5 S 1.5 and IrGe 1.5 Se 1.5 for resistivity measurements Room temp erature values were 20 W cm for the Sulfide and 4 W cm for the Selenide. The data was taken over a range of a few hundred degrees and indicated activation energies of 0.11 and 0.076 eV respectively.
21 The success of synthesizing ternary Skutterudites, an d the lack of information on the transport properties led to our further studies on these mixed anion materials. Two specimens of CoGe 1.5 Se 1.5 were made, one p type and one n type. As will be discussed below, t he basic measurements of crystal structure an d density along with transport measurements were performed. 3.2 Specimen Preparation Typical specimen preparation began with the mixing of elements from 99.99% pure 22 mesh cobalt powder from Alfa Aesar, intrinsic germanium ground to 325 mesh in a Ni trogen atmosphere glove box, 99.999% pure selenium shot from Asar c o. The elements were weighed to within 0.2 mg of the stoichiometric target weights. First, the stoichiometry was used to roughly calculate the masses of each element needed to produce appro ximately 4 grams of each compound. Then selenium shot was measured and weighed to be within a few tenths of milligrams of the desired amount calculated above. The precise amount of selenium was then used to calculate the exact amounts needed to get the d esired stoichiometry. The initial specimen of Co 4 Ge 6 Se 6 (S002) use d the desired stoichiometry as the starting stoichiometry. It was found that selenium condensed outside of the specimen during heating, thus all later specimens (including S008) started wit h 9% extra selenium, for example Co 4 Ge 6 Se 6.5 to result in a Co 4 Ge 6 Se 6 composition. This value was calculated by determining the total loss during the synthesis process.
22 Having determined the stoichiometry, cobalt and germanium were weighed and mixed fo r 2 minutes. The resulting powders were placed with the selenium shot in a P yrolite boron nitride (BN) crucible and mixed again. The BN crucible was then placed at the bottom of a quartz ampoule with a disk of Grafoil placed over the crucible. A small piece of quartz tube was fitted inside the ampoule in preparation to make an air tight seal. Once the setup was completed, a custom vacuum purging system was used to purge oxygen out of the tube and replace it with nitrogen. The purging system used a We lch Duoseal 1405 vacuum pump. This was attached to a system of valves along with a line to the ultra high purity (99.999%) nitrogen tank and a pressure gauge. To connect the valve system to the quartz, reinforced rubber hose was connected to large diamet er vacuum hose. A seal was made between this large vacuum hose and the quartz through rugged hose clamps allowing for < 10 2 Torr of pressure in the tube Once a good seal was made, the tube was pumped for approximately 5 minutes and back filled with nit rogen. This procedure was repeated twice more, and left at slightly below one atmospheric pressure to aid in sealing. A hydrogen oxygen torch was used to fuse the small inner piece of quartz to the tube. Th is procedure ensured that the specimen inside the BN crucible was in an inert environment. The sealed quartz ampoule was then placed inside a Mellen TC12 tube furnace oriented vertically. The furnaces were set to achieve a zone of 700 degrees Celsius where the temperature did not vary more than 2 de grees over the length of the ampoules The specimens were left inside the furnace for four days after which time they were air
23 quenched. They were then visually inspected to check for Se condensation on the quartz. Once they were cooled to room temperatur e, the specimens were removed. The extra selenium was gathered and weighed separately to estimate the Se loss in each Specimen. The material was then evaluated for appearance and weighed. After the specimens were weighed, they were ground to a fine powder inside a nitrogen atmosphere glove box. The finely ground powder was then placed in a high strength steel die and cold pressed to 64,000 PSI using a Carver Laboratory Press to produce a pellet. The pellet was weighed and placed into a BN crucible, seale d in quartz with a similar procedure as described above, and put into the furnace at 700 degrees. It was heated for four days and then air quenched. This process of grinding and heating was performed for a total of three times, to produce a single phase s pecimen. For X ray diffraction measurements (XRD) a small amount of powder for each specimen was mixed with a small amount of a silicon standard (NIST 640c) and placed on a glass slide. A Rigaku Min i flex X ray Diffractometer was used. Typically the dif fraction spectra were taken between 20 and 80 degrees 2 Q An identification program (Jade ) in conjunction with Excel spreadsheet software was used to determine their lattice parameters and if any impurities were present. T he powdered specimen was then hot pressed (Thermal Technologies HP20 4560 20) in a graphite die with a 0.5 inch diameter. After being preloaded to 1,500 PSI, it was heated to 650 C while under 25,000 PSI of pressure in a nitrogen atmosphere for 2 hours. Grafoil was used to separat e the specimen from the molybdenum punches that applied the pressure.
24 After hot pressing, the Grafoil was removed from the specimen, and a wire saw used to cut the specimen to minimize surface damage. Boron carbide suspended in a mixture of water and gl ycerin was used as the cutting fluid. A small piece was also cut and mounted in a one inch epoxy puck for metallographic analysis. The specimen in the puck was then polished in steps down to a final polishing round of 0.3 micron alumina. A solution of aq ua regia was used to etch the specimen and allow the grain structure to become clearly visible. A Unimet light microscope was used in conjunction with a Panasonic CCD camera to photograph the grains surface for analysis and grain size measurements The line boundary method (ASM Standard ) was used to determine the grain sizes. In addition to visual analysis, four probe resistivity and Seebeck measurements were performed at room temperature on specimens cut to 2 mm 3 To determine the Seebeck coeffic ient a custom made setup was used consisting of two copper disks 1 inch in diameter. One disk was attached to a large aluminum heat sink through a non electrically conducting, good thermally conducting glue. The other was mounted on a spring loaded pres s. A heater coil was located inside the upper disk and attached to a voltage source to raise the temperature. Two small holes were drilled into the sides of the disks for thermocouples. A multimeter was used to determine the voltage generated as the tem perature was varied. These room temperature measurements were in agreement with those described in section 3.4 below.
25 3.3 Crystal Structure Two particular CoGe 1.5 Se 1.5 specimens, labeled S002 and S008, will be described herein Each demonstrates the Sk utterudite crystal structure with the Ge and Se on the pnicogen sites and Co on the metal site. No clear ordering on the pnicogen site of Ge and Se has been determined from our XRD analysis ; however previous studies of this composition indicated short ran ge rhombohedral ordering. X ray diffraction patterns and electron probe microanalysis (EPMA) were used to determine the structure and composition of these compounds. Optical microscopy was used to evaluate the grain size of each specimen. The specimen S002 was made with a starting stoichiometry of CoGe 1.5 Se 1.5 exactly that for the Skutterudite structure with the same amounts of Ge and Se. The resultant stoichiometry was determined to be CoGe 1.452 Se 1.379 from ele ctron beam microprobe analysis ( E MP A ) wi th the Ge and Se concentrations assigned relative to full occupation of Co on the metal crystallographic site. This compound is an n type semi conductor. The evaporation and re condensation of Se from the specimen due to a possible 1 degree temperature gra dient in the range of the sample space of the furnace combined with the high vapor pressure of Se may have resulted in the low levels of Se The second specimen (S008) was synthesized with 9% extra Se to counter this loss or by starting with CoGe 1.5 Se 1.6 25, and resulted in a final stoichiometry of CoGe 1.431 Se 1.385 This specimen is a p type semiconductor. These specimens, along with others synthesized demonstrated a tendency towards a general stoichiometry of CoGe 1.45 Se 1.38
26 From the XRD data both S 002 and S008 have the same lattice parameters to within experimental uncertainty The two specimens were single phase in both the XRD and the E MP A a nalyses. Optical micrographs demonstrated pure phases and were also used to estimate the sizes of these p olycrystalline specimens. The room temperature physical parameters of the specimens are summarized in Table 2. The theoretical density for CoGe 1.5 Se 1.5 is 6.65g/cm 3 The expected densities calculated from the EPMA analysis show that S002 should be 6.35g/ cm 3 and S008 should be 6.32 g/cm 3 The measured densities show that the specimens were hot pressed to 88 and 92 percent respectively of their theoretical densities. As seen in T able 2, the specimens lattice parameters and grain sizes are similar, whil e their electrical properties are very different. Room temperature values for these properties were obtained as described in the section on specimen preparation. The specimens were sent to Dr. Jihui Yang of General Motors R&D for temperature dependent elec trical, thermal and magnetic measurements. The room temperature measurements agree with those of General Motors Transport properties were then modeled to understand the physics of the se compounds. Specimen a Grain Size d S r S002 8.306 0.008 4.6 5.61 550 1.2 S008 8.296 .0004 3.9 5.82 350 2.5 Table 2 Data on CoGe 1.5 Se 1.5 Here, a is the lattice parameter in d is the densit y in g/ cm 3 S is the Seebeck Coefficeint in m V / K, and r is the resistivity in W cm. All data are at room temperature.
27 3.4 Electrical Properties Figure 3 1 shows the resistivity vs. temperature data for S002 (CoGe 1.452 Se 1.379 ) and S008 (CoGe 1.431 Se 1.385 ). For comparison CoSb 3 is also shown in the figure. From F igure 1 r decreases with increasing te mper ature, showing typical semi conducting behavior for both specimens. Over the entire temperature range the CoGe 1.5 Se 1.5 specimens have higher r values than CoSb 3 with S002 showing the larger resistivity. 1000/T (K -1 ) 0 10 20 30 40 r (m W -cm) 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 CoSb 3 CoGe 1.452 Se 1.379 CoGe 1.431 Se 1.385 Figure 3 1. The Electrical Resistivit y of CoGe 1.5 Se 1.5 and CoSb 3 versus Temperature. CoGe 1.452 Se 1.379 is S002 and CoGe1 .431 Se 1.385 is S008. The solid line is a fit of the form r = r 0 exp[ E a / k B T ] to the higher temperature data, indicating E a = 0.168 eV.
28 The str aight line is a fit to the hi gh temperature data ( T > 300 K) using r = r 0 exp[ E a /k B T ], where E a is the activa tion energy. The fit results give E a = 0.168 eV and could imply an intrinsic semiconducting band gap of ~ 0.336 eV. A fit for S008 yields the same activation energy. This e stimated intrinsic band gap, higher than a gap of 0.102 eV for CoSb 3 [ 9]. Similar estimates on IrGe 1.5 S 1.5 and IrGe 1.5 Se 1.5 indicated an activation energy of ~ 0.1 eV; however, the authors in Ref. 20 suggested that the intrinsic gap may be even higher. We know of no band structure calculations for this material. At room temperature, r = 3.37 10 3 and 4.703 10 2 m W cm for S002 and S008 respectively. The difference increases with decreasing temperature. We speculate that the difference in r between specimens S 002 and S008 is due to the different amounts of vacancies on the g crystallographic site. As shown in Figure 3 2, the negative and positive S values indicate that electrons and holes are the majority carriers for S002 and S008 respectively. At room tempera ture a large value of 550 m VK 1 for S is observ ed for S002 decreasing to + 350 m VK 1 for S008. The upward trend for the higher temperature data for S002 is likely due to the increase in p type conduction for higher temperatures. Consistent with the S data our Hall measurements also show that the carriers are electrons for S002. The inset shows the electron concentrations obtained from the Hall measurements. At room temperature n ~ 3.5 10 18 cm 3 We believe prolonged hot pressing could cause lattice vaca ncies on the Ge or Se sites in CoGe 1.5 Se 1.5 resulting in n type electrical conduction for S002 [ 22, 23 ]. The sintered or quickly hot pressed undoped CoSb 3 specimens are usually p type semiconductors due to excess Sb, or deficient Co, in the crystal la ttice [ 24, 25 ].
29 T (K) 0 50 100 150 200 250 300 350 S ( m V/K) -800 -600 -400 -200 0 200 400 CoGe 1.452 Se 1.379 CoGe 1.431 Se 1.385 T (K) 100 150 200 250 300 c. c. (10 16 cm -3 ) -400 -300 -200 -100 0 100 Figure 3 2. Seebeck Coefficient Versus Temperature of CoGe 1.5 Se 1.5 Both n type S002 and p type S008 are shown. The inset shows carrier concentration from Hall measurements for the two specimens S008 is believed to have resulted i n p type electrical conduction due to the slight change in stoichiometries. This demonstrates the flexibility to control the properties of these materials through very precise balancing of the stoichiometry illustrated best by the dramatic change in S va lues from negative to positive for the small change in the Ge to Se ratio. The electron mobility varies roughly as T 0.66 near room temperature with values of 0.53 to 0.26 cm 2 V 1 s 1 from room temperature to 125 K. This indicates mixed ionized impurity an d acoustic lattice scattering of electrons.
30 For a single parabolic band S and n are given by [ 26 ] ) ( ) ( ) 1 ( ) ( ) 2 ( 1 h h h + + = + r r B F r F r e k S (11) ) ( 4 2 / 1 2 / 3 2 ] [ h p F h T k m n B = (12) where r is the exponent of the energy dependence o f the electron mean free path, m is the electron effective mass, e is the electron charge, h = E F / k B T is the reduced Fermi energy, E F is the Fermi energy, and F x is the Fermi integral of order x The + and signs in Eq. (11) are appropriate for holes and electrons, respectively. For electrons scattered by ionized impurities and acoustic phonons, r = 2 and 0, respectively. We use the intermediate value r = 1 for mixed scatterin g [ 27 ]. The room temperature S and n data yield m e = 2.55 m o where m o is the electron mass. This value of m e is slightly smaller than that of CoSb 3 [ 9 ]. The room temperature value of hole mobility for CoGe 1.431 Se 1.385 is ~ 35 cm 2 V 1 s 1 and varies approximately as T 6 between 160 K and 300 K. With the limited data points, it is difficult to ascertain the hole scattering mechanism however assuming r=1 m h = 0.1 m o Based on the much higher hole mobility, a small effective mass for holes is reasonable Similar results were found in CoSb 3 [ 10 ].
31 3.5 Thermal Properties T (K) 10 100 k L (W/m-K) 1 10 100 CoSe 1.5 Ge 1.5 Fit 300 30 Figure 3 3. Lattice Thermal Conductivity for CoGe 1.5 Se 1.5 (S002) Versus Temperature. The open squares are the experimental data and the line is a fit based on Eqs. (13) and (14). Figure 3 3 show the lattice thermal conductivity, k L of S002. T ypical temperature dependence for crystalline materials is observed with a room temperature value of 6 Wm 1 K 1 The total thermal conductivity can be written as k = k L + k e The electronic thermal conductivity k e was calculat ed using the Wiedemann Franz relation ( k e = L 0 T / r with L 0 = 2.45 10 8 V 2 K 2 ) from the measured r In this approximation
32 almost all of the thermal conduction is due to the lattice phonons because at all temperatures k e is less than 1% of k The k L values are lower than those of CoSb 3 w hich have k L ~ 8 Wm 1 K 1 at room temperature [ 10, 11, 28 ].T he solid line in Fig. 3 3 is a theoretical fit of the data using the Debye approximation: [ 10, 11, 2 9 ] = T x C x B B L D dx e e x T k k q t u p k 0 2 1 4 3 2 ) 1 ( 2 h (13) where T k x B w h = is dimensionless, w is the phonon frequency, B k is the Boltzmann constant, h is the reduced Planck constant, D q is the Debye temperature, u is the velocity of sound, and C t is the phonon scattering relaxation time. The phonon scattering relaxation rate 1 C t can be written as: ) 3 exp( 2 4 1 T T B A L D C q w w u t + + = (14) where L is the grain size and the coefficie nts A and B are the fitting parameters. The terms in Eq. ( 14 ) represent grain boundary scattering, point defect scattering, and phonon phonon Umklapp scattering, respectively. In the solid line theoretical fit of Fig. 3 3 L = 1.3 m m, A = 4.70 10 43 s 3 and B = 6.66 10 18 sK 1 The fitting parameters are very close to those of CoSb 3 [ 10, 11 ] e xcept that A (the pre factor for point defect
33 scattering) is approximately 2 times larger. This is reasonable in light of the large number of vacancies on the g crystallographic site indicated by E MP A. We expect that alloy scattering between Ge and Se plays a smaller role in the enhanced point defect phonon scattering in this specimen because of the small mass difference (~ 8%) between Ge and Se. The solid line in Fig. 3 4 models the overall temperature dependence of k L quite well over the entire temperature span. 3.6 Magnetic Properties In addition to the standard electronic and thermal property measurements, the magnetic moment M was found to v ary linearly with the magnetic field H for H < 5 T between 2 K and 300 K. The magnetic susceptibility ( H M = c measured at H = 0.5 T) as a function of temperature for both S002 and S008 is shown in Figure 3 4. Data for polycrystalline Co Sb 3 from Ref. 9 are also shown for comparison. For T > 100 K, both samples exhibit diamagnetic behavior almost identical to that of CoSb 3 This indicates that Co atoms assume the low spin d 6 electronic configuration, the same as in CoSb 3 The much larg er Curie Weiss type component for S002 at T < 100 K is believed to be due to the magnetic impurities (Fe and Ni) i n the starting material Co [25, 30 ].
34 T (K) 0 50 100 150 200 250 300 c (10 -28 emu/f.u.) 0 5 10 15 20 CoGe 1.452 Se 1.379 CoGe 1.431 Se 1.385 CoSb 3 Figure 3 4. Magnetic Susceptibility of Polycrystalline CoGe 1.5 Se 1.5 Data for polycrystalline CoS b 3 are also shown for comparison.
35 Chapter Four: Summary of Results Many materials and synthesis techniques are currently being employed in the investigation of new and novel classes of materials for potential applications in tec hnologically important fields. Solid state thermoelectric power conversion is one field of interest. The investigation of a class of materials known as Skutterudites continues to be of interest for thermoelectric applications. The fact that many different compositions can be synthesized in this crystal structure, together with the ability to tune the transport properties as a function of stoichiometry, encourages researchers to pursue avenues of optimization within this class of materials. The basic und erstanding of the transport properties of the different compositions is key however and will be the basis for an in depth understanding and evaluation of the thermoelectric properties of these materials towards further optimization and development. In this report t he Skutterudites CoGe 1.452 Se 1.379 (S002) and CoGe 1.431 Se 1.385 (S008) were synthesized in order to further our basic knowledge and understanding of these interesting materials as well as begin an investigation into their potential for thermoelectri cs applications. It was observed that the electrical transport properties are quite different than that of CoSb 3 In particular a small compositional difference between the two specimens S002 and S008 had a dramatic effect on the carrier type, carrier co ncentration and S values. This is very interesting in terms of potential for optimization.
36 as it allows for the tuning of the electronic properties. The relatively high room temperature Seebeck coefficients are also promising for thermoelectric applica tions, although their high resistivity is an obstacle. R esearch on void filling and doping of these interesting materials is therefore warranted in continuing the research into these Skutterudites. In summary, the specimens prepared for this report were s ynthesized by mixing and reacting high purity Co, Ge and Se. These compounds are diamagnetic semiconductors with a relatively large band gap as compared to CoSb 3 The electrical and thermal conduction are influenced by the vacancies in the crystal lattic e because of the non stoichiometry of the specimens. The low mobility of CoGe 1.452 Se 1.379 and CoGe 1.431 Se 1.385 precludes them from being useful thermoelectric materials; however, the large Seebeck coefficients make them interesting for further investigati on. The carrier types in these compounds depend sensitively on vacancies as well as the ratio between Ge and Se, offering a method for tuning the electrical transport properties of these compounds. The room temperature thermoelectric figure of merit is ~ 0.0005. Although this value is low this research opened the door to further research into these and similar compositions of Skutterudites and began an in depth understanding of their transport properties. The work reported herein has been accepted for publication in Physical Review B and is scheduled for publication in November 2004.
37 References 1. W. Thomson, Proc. Roy. Soc. Edinburgh, Trans. 21 Part I, 123 (1857) 2. G.S. Nolas, J. Sharp, H. J. Goldsmid: Thermoelectrics: Basic Principles and New M aterials Developments (Springer, New York, 2001) 3. G.A. Slack and V. Tsoukala, J. Appl. Phys. 76 1665 (1994). 4. I. B. Cadoff, E. Miller: Thermoelectric Materials and Devices (Chapman & Hall, London, 1960) 5. G.S. Nolas, M. Kaeser, R. Littleton, IV and T.M. Tr itt, 'High figure of merit partially Ytterbium filled skutterudite materials', Appl. Phys. Lett. 77 1822 (2000). 6. G.A. Lamberton, Jr., S. Bhattacharya, R.T. Littleton IV, T.M. Tritt and G.S. Nolas, 'High figure of merit in Eu filled CoSb3 skutterudites', Appl. Phys. Lett. 80 598 (2002). 7. C. Uher, 21 st International Conference on Thermoelectrics, A2 1 #570 2002 8. G.A. Slack, Symp. Proc. Mater. Res. Soc. 478 47 (1997) 9. Jeffery S. Dyck, Wei Chen, Jihui Yang, Gregory P. Meisner, Ctirad Uher, Pysical Review B, 65 115204 (2002) 10. J. Yang, D.T. Morelli, G.P. Meisner, W. Chen, J.S. Dyck, C. Uher, Physical Review B, 65 094115 (2002) 11. J. Yang, G. P. Meisner, D.T. Morelli, C. Uher, Physical Review B, 63 014410 (2000) 12. J. Yang, M.G. Endres, G. P. Meisner, Physical Rev iew B, 66 014436 (2002) 13. S. Katsuyama, Y. Sihichijio, M. Ito, K Majima, H. Nagai, Journal of Applied Physics, 84 No. 12, 6708 ( 1998) 14. H. Tashiro, Y. Notohara, T. Sakakibara, H. Anno, K. Matsubara, 16 th International Conference on Thermoelectrics, 326, IE EE, 1997 15. Krzystof T. Wojciechowski, Materials Research Bulletin, 37 2023 2033, (2002) 16. J.P.Fleurial, T. Caillat, A. Borshchevsky 16 th International Conference on Thermoelectrics, 1, IEEE, 1997 17. I. Lefebvre Devos, M. Lassalle, X. Wallart, J. Olivier Fourca de, L. Monconduit, J.C. Jumas, Phys. Rev. B, 63 125110, (2001) 18. T. Caillat, J. P. Fleurial, and A.J. Borshchevsky, Cryst.Growth 166 722 (1996) 19. G.S. Nolas, G.A. Slack, D. T. Morelli, T. M. Tritt, A.C. Ehrlich, J. Appl. Phys, 79 4002 (1996) 20. R. Korenstein S. Soled, A. Wold, G. Collin, Inorganic Chemistry, 16, No. 9, 2344 (1977) 21. A. Lyons, R. P. Gruska, C. Case, S. N. Subbarao, A. Wold, Materials Research Buliten, 13, 125, (1978) 22. L. D. Dudkin and N. Kh. Abrikosov, Sov. Phys. Solid State 1 126 (1959) 23. J. W. Sharp, E. C. Jones, R. K. Williams, P. M. Martin, and B. C. Sales, J. Appl. Phys. 78 1013 (1995) 24. G.S. Nolas, D.T. Morelli, and T.M. Tritt, Annu. Rev. Mater. Sci. 29 89 (1999), and references therein 25. C. Uher, in Semiconductors and Semimetals Vol. 69 edited by Terry M. Tritt (Academic Press, New York, NY, 2000), pp. 139 254, and references therein 26. V. A. Johnson, Progress in Semiconductors edited by A. F. Gibson (Heywood, London, 1956), Vol. 1 pp. 65 97 27. G. A. Slack and M A. Hussain, J. Appl. Phys. 70 2694 (1991). 28. J. Callaway, Phys. Rev. 113 1046 (195 9) 29. G. S. Nolas, J. L. Cohn, and G. A. Slack, Phys. Rev. B 58 164 (1998) 30. H. Anno, K. Hatada, H. Shimizu, K. Matsubara, Y. Notohara, T. Sakakibara, H. Tashiro and K. Motoya, J. Appl. Phys. 83 5270 (199 8)