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Assessing the role of filler atoms in skutterudites and synthesis and characterization of new filled skutterudites

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Title:
Assessing the role of filler atoms in skutterudites and synthesis and characterization of new filled skutterudites
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Book
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English
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Fowler, Grant E
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University of South Florida
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Skutterudites
Thermal conductivity
Physics
Phonons
Thermoelectrics
Dissertations, Academic -- Physics -- Masters -- USF
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theses   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: For the past decade interest in skutterudites has been significant as a potentially viable material for thermoelectrics. One way to improve the effectiveness of these materials is to lower their thermal conductivity. Lattice thermal conductivity of a series of La- and Yb-filled skutterudite antimonides (with varying filling fraction) has been modeled with different phonon scattering parameters using the debye approximation. It was found that filler atoms both increase point defect scattering and resonance scattering. Subsequently, the thermal conductivity of partially-filled skutterudites AxCo4Sb12, where A = La, Eu and Yb, is analyzed using the Debye model in order to correlate the data with the type of filler atom in evaluating the role of the filler atom in affecting the thermal conductivity. Partial void filling has resulted in relatively high thermoelectric figures of merit at moderately high temperatures. This idea is extended as new materials were synthesized with the intention of filling the voids in the CoGe1.5Se1.5 skutterudite, and analyzing the transport of these novel materials. Results of the analysis of this material are interesting and may indicate an amorphous phase of skutterudite present. Further work is needed to explore fully the implications of this new skutterudite and to fully understand its properties.
Thesis:
Thesis (M.A.)--University of South Florida, 2006.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
Statement of Responsibility:
by Grant E. Fowler.
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Title from PDF of title page.
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Document formatted into pages; contains 48 pages.

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ABSTRACT: For the past decade interest in skutterudites has been significant as a potentially viable material for thermoelectrics. One way to improve the effectiveness of these materials is to lower their thermal conductivity. Lattice thermal conductivity of a series of La- and Yb-filled skutterudite antimonides (with varying filling fraction) has been modeled with different phonon scattering parameters using the debye approximation. It was found that filler atoms both increase point defect scattering and resonance scattering. Subsequently, the thermal conductivity of partially-filled skutterudites AxCo4Sb12, where A = La, Eu and Yb, is analyzed using the Debye model in order to correlate the data with the type of filler atom in evaluating the role of the filler atom in affecting the thermal conductivity. Partial void filling has resulted in relatively high thermoelectric figures of merit at moderately high temperatures. This idea is extended as new materials were synthesized with the intention of filling the voids in the CoGe1.5Se1.5 skutterudite, and analyzing the transport of these novel materials. Results of the analysis of this material are interesting and may indicate an amorphous phase of skutterudite present. Further work is needed to explore fully the implications of this new skutterudite and to fully understand its properties.
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Assessing the Role of Filler Atoms in Skutterudites and Synthesis and Characterization of New Filled Skutterudites by Grant E. Fowler A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Physics College of Arts and Sciences University of South Florida Major Professor: George S. Nolas, Ph.D. Srikanth Hariharan, Ph.D. Lilia Woods, Ph.D. Date of Approval: July 11, 2006 Keywords: Skutterudites, Thermal Conduc tivity, Physics, Phonons, Thermoelectrics Copyright 2006, Grant E. Fowler

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To Mr. and Mrs. Neal, the teachers who showed me the power of physics.

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Acknowledgments I would like to thank the Petroleum Research Fund of The American Chemical Society for funding this research. I would like extend the highest appreciation to Dr. George Nolas for offering his ongoing encouragement, patience, extensive knowledge and ultimately for trusting in my abilities as a scientist. I wish to thank Dr. Jihui Yang for providing assistance with the modeling so ftware, and for the EPMA data he provided for this work. Thanks to Matthew Beekman fo r his patience, help a nd advice, to Joshua Martin for his expertise, aid, insight and also for the synt hesis of samples S025 and S029, and to Holly Rubin for her patience, assistance, and perspective. And I can never forget the sacrifices my family has made for me, my parents especially. Anything I do in this world is from their collectiv e support and wisdom, and I wouldn’t be this far without their help. Thank you all.

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i Table of Contents List of Tables ii List of Figures iii Abstract v 1 Introduction to Skutterudites 1 1.1 What is a Skutterudite and Why is it of Interest? 1 1.2 Transport in Skutterudites 3 2 Thermoelectrics: Concepts and Applications 6 2.1 Introduction and Figure of Merit 6 2.2 Applications of Thermoelectrics 8 2.3 Optimizing the Skutterudite Structure 10 3 Introduction to Thermal Conductivity Analysis and Related Tools 12 3.1 Development of a Comprehensive Theory of Thermal Conductivity 12 3.1.1 Grain Boundary Scattering 14 3.1.2 Point Defect Scattering 14 3.1.3 Phonon-Phonon Interactions 16 3.1.4 Resonance Scattering 16 3.1.5 Phonon-Electron Interactions 17 3.2 Method of Data Analysis and Fitting 18 3.2.1 Extracting Lattice Thermal Conductivity 18 3.2.2 Modeling Procedure and Description 18 4 The Results on Ln-Filled CoSb3 20 5 New Materials Synthesis to Explore Lanthanide-filled CoGe1.5Se1.5 34 5.1 Synthesis Process Details 34 5.2 Transport Measurement Results and Analysis 40 6 Conclusions and Future Directions 44 References 46

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ii List of Tables Table 4.1 Values of lattice thermal conductivity fit parameters as defined by Equations 4.1 and 4.2 for the different compositions of skutterudites. 22 Table 4.2 Fit parameter values for listed samples. 32 Table 5.1 Room temperature data. 36

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iii List of Figures Figure 1.1 Naturally occurring chunk of skutterudite from Morocco. 1 Figure 1.2 The skutterudite structure. 2 Figure 2.1 Illustration of thermoelectric refrigeration (l) and power generation (r). 7 Figure 2.2 ZT vs. temperature for the current leading skutterudite materials compared to materials currently used in devices. 7 Figure 2.3 Lattice thermal conductivity vs. temperature for four skutterudites. 10 Figure 4.1 Lattice thermal conductivity as a function of temperature for samples of the formula LayCo4SnxSb12-x. 21 Figure 4.2 Fit for CoSb3 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). 23 Figure 4.3 Fit for La0.05Co4Sb12 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). 24 Figure 4.4 Fit for La0.23Co4Sb12 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). 25 Figure 4.5 Fit for La0.31Co4Sn1.48Sb11.2 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines) 26 Figure 4.6 Fit for La0.75Co4Sn2.58Sb9.78 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines) 26 Figure 4.7 Fit for La0.90Co4Sn2.44Sb10.03 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines) 27 Figure 4.8 Graph of prefactor A versus filling fraction y(1-y), with linear regime indicated. 28 Figure 4.9 Graph of prefactor C versus filling fraction y. 30

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iv Figure 4.10 Graph of fits to YbyCo4Sb12 series, where diamonds represent y=0, circles are y=0.066 and squares are y=0.19. 31 Figure 4.11 Lattice thermal conductivity for different filled skutterudites. 33 Figure 5.1 Structural analysis of samples. 35 Figure 5.2 Oxygen content (top) and total BSE image (bottom) of S029 (EPMA). 37 Figure 5.3 Se (top) and Ge (bottom) content in S029 (EPMA). 38 Figure 5.4 Co (top) and Yb (bottom) content in S029 (EPMA). 39 Figure 5.5 Thermal conductivity of various samples. 41 Figure 5.6 Plot of resistivity of ‘filled’ samples. 42 Figure 5.7 Seebeck coefficient for myriad samples. 43

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v Assessing the Role of Filler Atoms in Skutterudites and Synthesis and Characterization of New Filled Skutterudites Grant E. Fowler ABSTRACT For the past decade interest in skutterudites has been significant as a potentially viable material for thermoelectrics. One way to improve the effectiveness of these materials is to lower their thermal conductivity. Lattice thermal conductivity of a series of Laand Yb-filled skutterudite antimonides (with varying filling fraction) has been modeled with different phonon scattering parameters using the Debye approximation. It was found that filler atoms both increase point defect scattering and resonance scattering. Subsequently, the thermal conductivity of partially-filled skutterudites AxCo4Sb12, where A = La, Eu and Yb, is analyzed using the Debye model in order to correlate the data with the type of filler atom in evaluating the role of the filler atom in affecting the thermal conductivity. Partial void filling has resulted in relatively high thermoelectric figures of merit at moderately high temperatures. This idea is extended as new materials were synthesized with the intention of filling the voids in the CoGe1.5Se1.5 skutterudite, and analyzing the transport of these novel materials. Results of the analysis of this material are interesting and may indicate an amorphous phase of skutterudite present. Further work is needed to explore fully the implications of this new skutterudite and to fully understand its properties.

PAGE 9

1 1 Introduction to Skutterudites 1.1 What is a Skutterudite and Why is it of Interest? The word “skutterudite” is a term, much like the similar term perovskite, that refers to a classification of compounds. It describes, inst ead of a particular compound, a type of material having identical crystal stru cture to that of a natural mineral, cobalt arsenide (CoAs3), first found around 1845 in the ti ny mining village of Skotterud, Norway, near the border with Sweden. Th ese body-centered-cubic materials consist of 32 atoms per cubic unit cell and all share the Im3 space group. One of the most prominent features of this cr ystal structure is that it can incorporate two atoms per cubic unit cell in “voids” within the structure. Skutterudites have show n to accommodate La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, and Yb1,2,3 as well as Tl4 and even Ge5. Figure 1.1: Naturally occurring chunk of skutterudite from Morocco. (Photo used with permission from Alan Guisewite’s collection in the Carnegie-Mellon Mineral Collection Images)

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2 Figure 1.2: The skutterudite structure. The yello w atoms are the pnicogen sites, blue atoms are the transition metal, and the voids are shown as (filling) the space inside the green polyhedron, and again below (absent) in the space between the blue poly hedra whose vertices represent pnicogen sites. Reproduced by permission of the MRS Bulletin ( www.mrs.org/bulletin ) from G.S. Nolas, J. Poon, and M. Kanatzidis, MRS Bulletin 31 3 (2006) p. 199, Fig. 1. The general formula for filled skutterudites is simply RM4X12 with R representing the filler atom, M is the transition me tal site, and X is the pnicogen site.2 Flexibility in the composition of such a structure tends to le ad itself to a questio n of bonding. Figure 1.1 shows the skutterudite structur e explicitly. As is seen in Figure 1.2, the pnicogen sites form polyhedra, and the volume between thes e polyhedra is a 12-fold cage of pnicogen atoms allowing for the inclusion of a filler at om, which is then very loosely bound to the rest of the crystal structure. The transiti on metal atom is enclosed within the pnicogen cages, or blue polyhedra below. As a resu lt, the X-X bonding is quite strong, due to its

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3 shorter length and covalent nature, while M is never the nearest neighbor to another M atom.3 The M-X bonding is also close and t hus strong as well. Simply put, the skutterudite crystal structure contains cages which encapsulate metal atoms, within a very stable cubic structure. It should also be noted that the pnicogen sites as well as the transition metal sites can be doped, and it has been shown necessary in order to charge compensate for the addition of some filler atoms at higher concentrations.1 In response to filler atom valency, doping (either on the meta l site or on the pnicogen site) is a common strategy to form novel compounds. An example is LaIr3Ge3Sb9, where the Ge should mitigate the La valency contribution.3 The route of charge compensation on the metal site is also common, as is seen by the construction of LaFe4-xCoxSb12.3 1.2 Transport in Skutterudites Skutterudites can be metals or semic onductors, and can, with careful forethought, be engineered to be semiconducting, with a low thermal conductivity and thus of high interest for thermoelectrics appl ications. The goal, in general, for the skutterudite system was first proposed by Slack,6 which is to synthesize a Phonon-Glass, Electron-Crystal material, or PGEC. The idea behind the PGEC concept is to obtain materials with good electrical properties together with very poor thermal conduction. This is really an optimization for the ZT or the figure of merit of a thermoelectric material, given simply as: T ZT2 1.1 where the Seebeck ( ), the electric al conductivity ( ), and the total thermal conductivity ( ) are related. Thus, it is reasonable that th e electrically crystalline but glass-like

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4 phonon behavior constitutes a clever approach to engineering a materi al to exhibit high ZT values. Binary skutterudites have s hown excellent electroni c properties, with mobilities similar to that of GaAs.1 The drawback to binary sk utterudites is that they possess large thermal conductivities. In an e ffort to reduce thermal conductivity, filled skutterudites are still being e xplored as a new way to fully realize the PGEC concept. The idea of filling skutterudites is of intere st for the purposes of tuning materials to exhibit particular properties, in a sense they can be thought of as designer materials, in this case enhancement of thermal resistan ce and electronic conducti on for thermoelectrics are of foremost importance, which will be disc ussed in greater detail in Chapter 2. The role of the filler atom is mainly to provi de an additional phonon scattering mechanism (via resonance scattering, or a “rattling” effect).6 This type of res onance scattering is corroborated with ADP data, and remains a us eful way to attempt to achieve the near minimum thermal conductivity, or glasslike thermal conductivity temperature dependence needed to use these materials feasibly6 as will be discussed in detail in Chapters 3 and 4. The introduction of filler atoms into th e skutterudite structure will necessarily alter the electronic properties of the materials, and in general, only atoms small enough to fit inside the voids will form. The valence of the filler atom is of particular importance, especially since the bonding has b een predicted to be mostly i onic in nature for the filler atom to pnicogen cage.3 A good example of this is CeFe4P12, where the Fe4P12 system is deficient by 4 electrons, leaving the tetravalent form of Ce as an obvious choice as a filler atom, and indeed this compound forms.3 In addition, size concerns start to take effect, meaning that the void size can vary depe nding on the precise element used on the

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5 pnicogen site, for instance antimonide skutterud ites allow for the larges t interstitial voids of the pnicogens known to form skutterudites. By the same token, a pnicogen that creates too large of an icosahedral voi d will have unusual bonding of the f iller atom to the rest of the pnicogen framework, and thus may not cont ract the pnicogen cage as in the previous example, and may alter the valency of the filler atom, altering th e electronic properties severely, as in the case of CeFe4Sb12, which exhibits a metallic conduction.3 Of course, if the void is too small (or filler atom too large) the filler atom won’t physically fit into the vacancy. So careful planning must be done in or der to assure that th ere is a fair chance that the intended composition can be achieve d. Also, maximum filler atom percentages have been observed for various compounds. Th is has been observed for several species of La atom, as in Th (max. 22%) in CoAs3, La (max. 23%) in CoSb3, and Ce (max. 10%) in CoSb3.3 Attempts to achieve a greater filli ng fraction generally result in secondary phases forming with the rare earth and the other constituent elements. Filler atoms drastically decrease the therma l conductivity in most cases, and this will be discussed in the next chapter in relation to the optimiza tion characteristics for high ZT materials.

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6 2 Thermoelectrics: Concepts and Applications 2.1 Introduction and Figure of Merit Thermoelectricity, as the name implies, is a direct, solid-state mechanism whereby a thermal gradient is used to manife st a voltage gradient, with the converse also true. The thermoelectric effect, as the ba se phenomenon is known, is a combination of two slightly more simple eff ects: the Seebeck effect and th e Peltier effect. Both were discovered in the first half of the 19th century, by Thomas Seebeck and Jean Peltier, respectively. Seebeck’s observation was that for a junction of two different materials, a temperature gradient can produce a voltage gradient across the materials.7 Peltier found that passing a current through two different materials in series, heat is absorbed or rejected from the junction.8 This is the principle behi nd the common thermocouple, found in myriad laboratories across the world toda y. Shortly after these discoveries, in 1851 Lord Kelvin (then known only as William Thompson) uncovered a way to think of the thermoelectric properties of a single materi al, and thus characterize the Peltier and Seebeck effects for isolated bulk materials.9 Figure 2.1 illustrates the basic configuration for a thermoelectric device, which incorporat es both pand n-type semiconductor legs connected in series for the electrical circuit but in parallel for the thermal circuit. The left side of the figure is an exam ple of active cooling, where a voltage applied to the device results in refrigeration and the right side fi gure is an example of power generation, where

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7 Figure 2.1: Illustration of thermoelectric refrigeration (l) and power generation (r). Figure 2.2: ZT vs. temperature for the current lead ing skutterudite materials compared to materials currently used in devices. Reprinted from Journa l of Materials Research, copyright 2005, Materials Research Society.10

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8 the thermal gradient induces a voltage difference (and thus a current ‘I’) across a load (or a resistor ‘R’). 2.2 Applications of Thermoelectrics Skutterudite materials are most suited for power generation applications, due to the favorable ZT values occurring at high temper atures, as is seen in Figure 2.2. State of the art thermoelectric materials appear to be “capped” at a ZT of ~1 for the past thirty years, yet no ceiling is predicted by theory.11 Skutterudites have a ZT>1, as in Figure 2.2, outperforming the modern best material used for power genera tion, Si-Ge alloys. Current uses for these power generation applic ations involve radioisotope thermoelectric generators, or RTG’s, which couple Pu-238 as a heat source ove r a thermoelectric element (Si-Ge alloy) to the rather cold ambient temperature of space. NASA has used RTG’s to power most space missions includi ng and outside of Mars orbits (due to decreased solar intensity and therefore reduced solar panel power). Some examples include the Voyager, Pioneer, Viking, Pathfi nder (including smaller individual units for the Mars rover) Cassini-Huygens, and in Janua ry of 2006, the New Horizons probe set to arrive at Pluto approximatel y in 2015. Other power genera tion applications are further from practical use, again due to materials limitations that limit overall efficiency. One prime example is the use of th ermoelectric elements to extrac t additional efficiency out of engines (specifically gasoline and diesel vehicl es) by utilizing the radi ator, the exhaust or other waste heat as a heat s ource and coupling to the atmos pheric temperature as a cold sink, providing a meaningful temperature gradient Of course, this implies a voltage can be drawn from the existing conditions provide d by a hot engine, and can be used to supplement (if not entirely replace) standard alternators as a means for powering the

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9 hefty electrical load of mode rn autos. Countless other uses can be imagined, and even personal watches have been manufactured and sold, powered by a thermoelectric array. Following the idea of the characterization of a particular materi al’s thermoelectric capability, it is quite comm on to introduce the thermoelectric figure of merit of a material, given as: T ZT2 2.1 where the higher the ZT, the better the materi al is at thermoelectri c conversion. Equation 2.1 relates then, the Seebeck ( ), the electrical conductivity ( ), and the total thermal conductivity ( ), the last of which is assumed to be electronic lattice total 2.2 where the total thermal conductiv ity of the material is e qual to the addition of both phonon (lattice) and electr on contributions. The Seebeck co efficient, although previously phenomenologically described, is now defined11 more precisely as: T V 2.3 Upon inspection of the figure of merit, it is easily concluded that the Seebeck coefficient and electrical conductivity must be maximi zed, whilst simultaneously decreasing thermal conductivity. This lead s naturally to the question: “Wha t sort of materials should be investigated for thermoelectric research?” Th e answer is one that continually changes, based on the scientific Zeitgeist and the stat e-of-the-art. The most current view of thermoelectric materials is born of Slack in the early 1990’s, w hose PGEC model was introduced earlier in this manuscript in Chapte r 1. This PGEC model typifies a clever

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10 approach to thermoelectric materials resear ch, with reduction of thermal conductivity the focus of the work herein. Slack also pointed out that this appro ach indicates to the skutterudite class of material s as a prime candidate for study.6 2.3 Optimizing the Skutterudite Structure As is seen from the figure of merit for thermoelectricity, a reduction in thermal conductivity is one avenue of improving the ZT and thus the overall effectiveness of a material’s thermoelectric properties. Equati on 2.2 reveals that thermal conductivity must be lowered by decreasing the electronic portion, the lattice contribution, or both. One of the main reasons why the skutterudite system is of high interest is related to the structural voids in the crystal structure, which allow for a reduction in latt ice thermal conductivity if they are filled with “rattler” atoms. Thes e rattler atoms can be any number of elements, as described earlier in Chapter 1. But in general, the pattern for finding the most effective rattlers is given by Figure 2.3. Figure 2.3: Lattice thermal conductivity vs. temperature for four skutterudites. Reprinted from G.S. Nolas and G. Slack, et al. J. Appl. Phys 79 Copyright 1996, American Institute of Physics.

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11 Figure 2.3 shows that the heavier the filler at om, the more effectiv e the rattle mechanism is at scattering phonons. There is an excep tion though, where Nd is less heavy than Sm and yet remains lower in thermal conductivity. This is due to lo w-lying ionic energy levels in the Nd that offer an additional scattering, and thus an even lower thermal conductivity. It is also a patte rn that the smaller the atom the more effective it is at scattering soft phonons. The size is relevant as this gives the atom more room to move about inside the void, and thus can scatter phonons better. Therefore, it is in general true that filled skutterudites have lower ther mal conductivity than unfilled, and that filling with the smallest and heaviest atoms provides the maximum effect of thermal conductivity reduction. This provides an op timization approach where the thermal conductivity can be customized and minimized per skutterudite structure, allowing for these thermoelectric materials to manifest their full potential both scientifically and technologically.

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12 3 Introduction to Thermal Conducti vity Analysis and Related Tools 3.1 Development of a Comprehensive Theory of Thermal Conductivity A coherent and thorough understanding of thermal conductivity was developed (historically) by continual impr ovement of different models and approaches. The first method of treating this concept comes from statistical mechanics, where the Law of Dulong and Petit specifies the high temperature limit to the heat capacity (which is linearly related to the thermal conductivity).12 The greatest drawback to this model is its inability to describe temperature dependent thermal behavior. The next significant contribution to the ar ea came from Einstein. In this approach the atoms of the lattice are treated as independent harmoni c oscillators. Einstein’s technique is reminiscent of Planck ’s blackbody radiation: a lattice of M atoms is treated as a group of 3M non-interacting single-dimension ha rmonic oscillators operating with only one frequency.12 The energy is then quantized based on frequency. The largest drawback to this model is the poor agreemen t with low temperature thermal conductivity. Experimental evidence shows that the low temperature dependence of materials is T3; this temperature dependence is not predicted by the Einstein model. The final major step towards theoretica lly describing the thermal conductivity was made by Debye, who developed a method to mathematically describe the low temperature limit.12 In the Einstein model, the soli d is modeled as a series of noninteracting atoms, whereas the Debye model correlates these into an interacting continuous medium. The Debye model does make some significant assumptions, as

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13 discussed below, but they are quite reas onable when considering the proper low temperature dependence. The model assumes an “elastically isotr opic” and continuous solid. This assumes that the atomic bonding is the same in all directions of the crystal, which in the analogy of a harmonic oscillator, corresponds to the “spring constant” of the system. The Debye model further assumes that the cut off for elastic waves is limited at 3M consistent with the degrees of freedom and is reasonable, since the longer wavelengths matter at low temperatures. The velocity of sound is assumed the same up to the high end limiting temperature, comm only know as the Debye temperature, or D where the law of Dulong and Petit domina tes afterward at all higher temperatures.12 In the Debye model the lattice thermal conductivity is given12 by the integral: T x C x B B LDd x e e x T k k 0 2 1 4 3 2) 1 ( ) ( 2 Eq. 3.1 where the dimensionless quantity T k xB/ kB is the Boltzmann constant, the phonon frequency, the reduced Planck constant, D the Debye temperature, the sound velocity through the structure, and C the phonon scattering relaxation time. Taking into consideration four phonon scattering mechanisms, which is what will be used in modeling the skutterudites, c -1 is written13 as: 2 2 2 2 2 4 1) ( ) 3 exp( o D CC T T B A L Eq. 3.2 where L is the grain size, 0 is the resonance frequency and the coefficients A, B and C are the fitting parameters. The terms in E quation 3.2 represent grain boundary scattering, point-defect scattering, Umklapp scatteri ng and resonance scattering, respectively.13 The

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14 grain boundary scattering limits the phonon wa velengths by scatteri ng at each grain boundary. Point defect scattering is caused by defects or impuriti es (including alloying on a particular crystallographic site) resulti ng in a decrease in cr ystal harmonicity and thus scatters phonons. Umklapp scatteri ng is the standard phonon-phonon interaction mechanism. Resonance scattering is essentia l to modeling the loosel y-bound filler atoms. It has been found that this choice of phonon re laxation mechanisms is reasonable, as this is sufficient to describe all of the ways in which phonons are (si gnificantly) scattered within skutterudites.14, 15 Next, the specifics of each mechanism will be discussed. 3.1.1 Grain Boundary Scattering In the fitted data described in the fo llowing chapter, the grain boundary scattering term uses the value from CoSb3 and leaves L to be a fitting para meter for the grain size. This is sometimes referred to as a ‘c haracteristic length’ which inhibits the low temperature/longest wavelength phonons and is responsible for the T3 dependence of thermal conductivity down to zer o Kelvin. This is sensible, as a single crystal sample would have the dimensions of the crystal as the limiting size on the phonon wavelength. The skutterudite samples analyzed in the next chapter are polyc rystalline. This constitutes a grain boundary sca ttering effect independent of the dimensions of the sample. The fitting term L then represents an order of magnitude average of the grain sizes in the sample. 3.1.2 Point Defect Scattering The point defect term is a standard al loy scattering or Raleigh scattering term used to describe the effect of imperfections or defects in the crystal lattice, including lattice vacancies. The strength of the coefficient14 represents the combined effect of two

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15 basic mechanisms, one is a mass fluctuation scat tering term and the othe r is a strain field effect term, the first and second term respectively, in Eq. 3.3: } ] / ) [( ) / {(2 2 i i i iM M x Eq. 3.3 where M represents the mass of the host lattice atom and Mi is the mass of the impurity atom, and represents the host matrix atom’s radius and i is the radius of the impurity atom in its own lattice, and is an adjustable parameter.14 This is linearly relatable to the A term through Equation 3.4: 3 34 v Ai Eq. 3.4 which shows an additional dependence of the A parameter on the alloy volume, 3 and the cube of the Debye velocity v .14 A convenient way to think of these constituent scattering mechanisms is to assume a simple one-dimen sional chain of coupled harmonic oscillators with masses representing atoms and springs/s pring constants emblematic of the atomic bonding, or the strain field. Obviously such a system of masses and springs is affected greatly by changes in masses of atoms from one atom to another as well as changes in the spring constant. Thus, it is easy to see how these types of differen ces affect the phonons in the crystal. It has a T4 dependence, and thus is very important to limit the thermal conductivity at higher te mperature, although it affects thermal conductivity at nearly all temperatures. It has been used in many studies on thermal conductivity, as has grain boundary scattering.13,14,16 3.1.3 Phonon-Phonon Interactions The Umklapp term is a standard high temperature, phonon-phonon interaction scattering term, with the value for D for CoSb3 assumed. Normal processes are those in

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16 which the collisions of two phonons give rise to a third, which then serves as a phonon flux from hot end to cold end, conserving mo mentum in the lattice. Umklapp, German for “flipping over,” refers to those collisions where two phonons collide and give rise to a third and a reciprocal lattice vector.12 This is not a normal proce ss, and thus, this sort of scattering is not momentum conserving and as a result, gives rise to a thermal resistance.12 When normal and Umklapp processes are considered, the desired transfer of energy is achieved without the net transport of phonons.12 Umklapp processes generally are quite significant at high temperatur es where phonon-phonon inte ractions are common and all phonon modes are excited, and thus serve as the main limit on thermal conductivity at higher te mperatures in much the same wa y that low temperature thermal conductivity is limited by a grai n boundary scattering mechanism.17 3.1.4 Resonance Scattering Finally, a resonance scatteri ng term is used as an esse ntial scattering mechanism, describing the looseness of the filler at om’s bonding, and modeled with a simple Lorentzian term. This type of scattering is generally limited to lattices with loosely bound atoms within the framework, or ‘sof t’ phonon modes. These softer phonon modes are modeled most appropriately with an Einstein model of thermal transport. This is precisely because of the looser bonding of the filler atom to the Sb-site cage. Thus, two models must be used simultaneously, both the Debye model and the Einstein model. This can be achieved by introducing a resonant-style scattering mechanism, in this case a very basic term. This type of phonon resonant sc attering was first desc ribed by Pohl for KNO2 in 1962.18 A more complicated type of approach was described in Walker and Pohl the following year for KCl crystals with various ionic impurities.16 Here, the simpler form is

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17 adequate, as the results are both corroborated by other meas urements and fit the data extraordinarily well, as is evidenced in the results described in Chapter 4. One example of confirming evidence for this model of the filler atoms in skutterudites creating additional phonon scattering comes from atomic displacement parameter (ADP) data. ADP data are obtained from temperature depende nt structural data (e .g. X ray diffraction) and can be used to obtain a measure of the m ean square displacement of an atom from its designated crystallographic site thereby providing a measur e of temperature-dependent movement.19 ADP data suggests that f illed skutterudites (e.g. LaFe4Sb12 and YbFe4Sb12) reveal a clear temperature dependent ADP of the filler atoms indicating they are more loosely bound (than th e framework atoms).19 Thus they may be better understood using an Einstein model where th ey represent oscillators th at can scatter phonons. 3.1.5 Phonon-electron Interactions Very strong carrier-phonon in teractions are expected for materials that possess carriers with large effectiv e masses usually associated with impurity band conduction.20 The carrier-phonon scattering is thus not considered here for s kutterudites due to the lack of evidence of impurity band conduction or other mechanisms that could lead to significantly increased carrier effective masses. 3.2 Method of Data Analysis and Fitting 3.2.1 Extracting Lattice Thermal Conductivity Data First, it is important to note that the total thermal c onductivity is comprised of the electronic and lattice contri butions, as per Eq. 3.5. L e total Eq. 3.5

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18 In this manner, if the electronic contributi on can be determined, it can be subtracted to yield the lattice thermal conduc tivity, which is the essential data needed to model the lattice phonon scattering mechanisms. The electronic component of the therma l conductivity can be estimated using the Wiedeman-Franz relationship, which relates electrical and thermal conductivity in the following manner: 2 23 e k TB e Eq. 3.6 where kB is Boltzmann’s constant, is electrica l conductivity, T is temperature, e is thermal conductivity, and e is the charge of an electron.12 The right hand side of Eq. 3.6 is the ideal Lorentz number. The Lorentz numb er varies slightly fo r different materials,12 however we will use the ideal Lorentz number defined by Eq. 3.6. 3.2.2 Modeling Procedure and Description Data (from references 22 and 23) for the low temperature lattice thermal conductivity was fitted using our program written in Mathcad 7. It is important to note that any mathematical software capable of so lving the Debye integral is indeed able to perform the same analysis and produce the sa me results. The program is basically a minimization of least squares fi tting from theoretical values and the experimental data. The initial or “guess” values given in the initi al iteration of the program are later refined into the proper values that gi ve the least error in the fit. The computations then produce the next best approximation (numerically). Th ese more accurate fitting values were then re-entered as the original inputs. The pr ocedure was repeated iteratively, ultimately producing a set of values which did not cha nge upon input, thus i ndicating that these

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19 were the best values possible for the least squares minimization met hod. Each of these fitting parameters has been uniquely defined using a minimization of least squares fit function (the difference between the value of the fit with that of the data), yielding only those results with a high levels of agr eement with the experimental data.

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20 4 The Results on Ln-Filled CoSb3 The first compound to be discussed is the unfilled CoSb3 skutterudite. CoSb3 has no “filler” atom, and thus, the phonon relaxation time has been simplified. It does not contain a resonance term to reduce thermal conductivity, as the additional scattering mechanism is unphysical, i.e. there are no fille r atoms present to “r attle.” The fit is shown in Fig. 4.1 and is used as a refere nce guide to understandi ng the reduced thermal conductivity of the partially filled skutterudites. The fitting parameters obtained for CoSb3 listed in Table 4.1 are consistent with an earlier study from Yang on the same skutterudite system.15 Again, the Debye integral and the expression used to define the phonon relaxation time are given as equations 3.1 and 3.2 respectively. The terms in the equation represent grain boundary, po int defect, phonon-phonon Umklapp, and phonon resonant scatterings, respectively. The expressions for phonon-phonon scattering and resonant scattering are e ssentially empirical. D and values for CoSb3 were used in all our fitting analyses, and are 287 K and 2700 m/s, respectively.23 Very strong carrierphonon interaction in sku tterudites is expected for carri ers with very large effective masses usually associated with impurity band conduction.20 The carrier-phonon scattering is thus not considered due to the lack of evidence of impurity band conduction or other mechanisms that could lead to very large ca rrier effective mass for samples studied. The solid lines fit the data well for all La sp ecimens over the two orders of magnitude temperature range, however, much more informa tion can be obtained by inspecting

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21 Temperature (K) 10100 L (W m-1 K-1) 1 10 100 Figure 4.1: Lattice thermal conductivity as a function of temperature for samples of the formula LayCo4SnxSb12-x. Top-most hexagons represent CoSb3, or y=0, diamonds show y=0.05, down-pointing triangles are y=0.23, and lower hexagons are y=0.90, circles are y=0.75, and the lower triangles represent y=0.31. Note the unfilled (y=0) thermal conductivity is at least an order of magnitude higher than the filled skutterudites. Accepted for publi cation in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24

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22Table 4.1: Values of lattice thermal conductivity fit pa rameters as defined by Equations 4.1 and 4.2 for the different compositions of skutterudites. Accepted for publication in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24 piecewise graphs of each scattering parameter and then by analyzing the values of the individual fit parameters for each compos ition. Table 4.1 allows for an expanded discussion on the specific trending seen in th is series, and figures 4.2 through 4.7 show the scattering mechanisms isolated with the same fit values used to see the individual effects of each parameter. Composition L (m) A ( 10-43 s3) B (10-18 s K-1) C (1033 s-3) 0 (THz) CoSb3 5.772 2.591 5.375 0 --La0.05Co4Sb12 24.51 6.321 0.193 5.099 10.325 La0.23Co4Sb12 32.16 16.297 0.366 24.134 10.998 La0.31Co4Sn1.48Sb11.2 23.31 49.321 0.177 22.368 10.386 La0.75Co4Sn2.58Sb9.78 22.32 46.121 0.103 24.956 10.571 La0.90Co4Sn2.44Sb10.03 47.27 46.291 0.158 27.253 9.493 Yb0.066Co4Sb12 0.597477.266 1.384 0.504 3.012 Yb0.19Co4Sb12 4.471 186.799 2.254 3.072 3.409

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23 Figure 4.2: Fit for CoSb3 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). Open circles mark the raw data. Accepted for publication in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24 First, the fit of CoSb3 is shown in Fig. 4.2, with each fit parameter graphed separately with the same value as the to tal fit demands. The breakdown of the earlier graph into this “parts-and-whole” view allows the significance of each scattering mechanism to be fully understood. For instance, the mechanism most dominant at lower temp eratures is clearly grain boundary, as is expected. On the ot her end, high temperature phonon scattering is due to Umklapp processes and is again consiste nt with what one would expect with this model. Point defect scattering and grain bounda ry scattering are adde d to show the peak is well defined by these terms in this unfilled skutterudite. Temperature (K) 1101001000 L (Wm-1K-1) 1 10 100 Boundary Boundary & Pt. Defect Umklapp

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24 Figure 4.3: Fit for La0.05Co4Sb12 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). Open circles mark the raw data. Accepted for publication in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24 For the La0.05Co4Sb12 sample shown in Fig. 4.3, the same reasoning as that which explained the CoSb3 (Fig. 4.2) explains the grain boundary temperature dependence as well as the Umklapp term’s temperature depe ndence. The most significant difference is the fact that for this composition resonant scattering is required in order to properly fit the data, and define the peak of the fit accura tely. It should also be noted that the CoSb3 data was fitted using a resonance term, but the results were that the term was negligible (orders of magnitude small) a nd thus, the model is consiste nt with the physics of the system. Temperature (K) 1101001000 L (Wm-1K-1) 1 10 Boundary Umklapp Boundary & Pt. Defect Boundary, Pt. Defect & Resonance

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25 Figure 4.4: Fit for La0.23Co4Sb12 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). Open circles mark the raw data. Accepted for publication in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24 Figures 4.4 through 4.7 show fits for the ot her partially filled skutterudites in the series, separating out piecewise the elements that, when summed, equal the thicker total fit line, which is the same as that in the original graph. Again, Figure 4.4 shows the influence of the high and low temperature limitin g fit terms, as well as illustrates clearly the need to include the res onance term to define the thermal conductivity well. Temperature (K) 101001000 L (Wm-1K-1) 1 10 Boundary Umklapp Boundary & Pt. Defect Boundary, Pt. Defect & Resonance

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26 Figure 4.5: Fit for La0.31Co4Sn1.48Sb11.2 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). Open circles mark the raw data. Accepted for publication in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24 Figure 4.6: Fit for La0.75Co4Sn2.58Sb9.78 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). Open circles mark the raw data. Accepted for publication in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24 Temperature (K) 1101001000 L (Wm-1K-1) 1 10 Boundary Umklapp Boundary & Pt. Defect Boundary, Pt. Defect & Resonance Temperature (K) 1101001000 L (Wm-1K-1) 1 10 Boundary Umklapp Boundary & Pt. Defect Boundary, Pt. Defect & Resonance

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27 Figure 4.7: Fit for La0.90Co4Sn2.44Sb10.03 illustrating the final fit (thick dark line) and the constituent fit parameters graphed in isolation (dashed lines). Open circles mark the raw data. Accepted for publication in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24 As shown in Table 4.1, the acceptable values for the grain size, L were obtained. These values are well within the range of sizes allowed by the synthesis method. Secondly, Umklapp scattering, the coefficient B in the model, is self-consistent, showing higher values for higher levels of attenuation at higher thermal conduc tivity values. The addition of the filler atom lowers the overall thermal conductivity and thus, the attenuation needed from this scattering m echanism is reduced. The frequency of the resonance term C is consistent with multiple data, both experimental and theoretical. Keppens et al.25 inelastic neutron scatte ring data indicates an Einstein resonance of 10.474 THz, while X-ray Absorption Fine St ructure (EXAFS) studies by Cao et al.26 Temperature (K) 1101001000 L (Wm-1K-1) 1 10 Boundary Umklapp Boundary & Pt. Defect Boundary, Pt. Defect & Resonance

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28 y(1-y) where LayCo4Sb12-xSnx 0.000.050.100.150.200.2 5 A (10-43 s3) 0 10 20 30 40 50 60 x = 0 x = 2.44 x = 2.58 x = 1.48 Figure 4.8: Graph of prefactor A versus filling fraction y(1-y), with linear regime indicated. Accepted for publication in the Journal of Applied Physics. Copyright 2006, American Institute of Physics.24 finds a value of 10.343 THz. These are all in good agreement with the Theoretical lattice dynamics calculations s how a frequency of 9.688 THz.27 values listed in Table 4.1. Trending in the A and C parameters is aided immensely by Figs. 4.8 and 4.9. Figure 4.8 shows the fitting parameter A versus filling fraction y(1-y) is linear for x=0, which is both reasonable and expected, si nce this mechanism directly relates to the disorder of the crystal. Poin t defect scattering should be mo st prominent when there is a maximum disorder to the point defects and the lattice atoms. Thus, any concentration above (or below) 50% of defect atoms beco mes a more ordered lattice of the higher concentration atoms, increasing crystallin ity again. Note, however, the significant increase in the importance of point def ect scattering in the Sn-doped samples.

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29 Qualitatively, this is quite sensible, as an increase in dopants increases the number of sites that can scatter phonons Upon further inspection how ever, the mechanism behind this point defect scattering is not entirely clear. Point defect scattering can be broken down into two constituent mechanisms, one is mass fluctuation scattering, the other is strain field effect scattering, as described in Chapter 2. Considering the mass difference between Sn and Sb is only 3.06 amu, it is unlikely that the sole mechanism is mass fluctuation scattering. Instead, this increased point defect scattering could indeed be a strain field effect. There is little information that allows for greater understanding of how the Sb cage structure changes to incorporate Sn substitution, and thus, the exact details are not yet well understood. Also, note that the Sn concentration is quite high, especially when compared to earlier work by Yang,15 where that work showed no significant increase in point defect mechanisms, presumab ly due to the very small concentrations of Sn doping. Another possibility to explain this marked increa se in the importance of the point defect scattering mechanism is the poten tial for vacancies on the metal sites. This could lead to additional defect sites to scatter phonons via mass fluctuation. Figure 4.9 shows the resona nce fitting parameter C pl otted against the filling fraction y. The dotted line is a guide to the eye only. Clearly, a linear trend in the increase of C vs. y is reasonable, but there s eems to be a decreased effect as the fraction y increases beyond about 20 percent or so. Linear trending is sensible because the number of atoms that must be modeled with an Ei nstein-type term increases linearly, so the coefficient behaves similarly. There is a sa turation above 20% filling. Presumably, this relates to the fact that at any particular frequency there is a finite number of phonons to scatter, thus once phonons of this particular frequenc y have been effectively scattered,

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30 y 0.00.20.40.60.81.0 C (1033 s-3) 0 5 10 15 20 25 30 Figure 4.9: Graph of prefactor C ve rsus filling fraction y. The dashed line is a guide to the eye only. Accepted for publication in the Journal of Applied Physics. Co pyright 2006, American Institute of Physics.24 there will be no appreciable difference in the thermal conductivity by increasing the concentration of filler atom. Figure 4.10 shows temperature dependent lattice thermal conductivity data for a series of Yb-filled skutterudites, with fits to the data taken from elsewhere.22 The results are again excellent fits to the experimental data. A table does make analysis more clear, and referring to Table 4.1, the data is reas onable. Grain size is within the acceptable obtained sizes, A and C both show increases with increase d filler atom concentration, and resonance frequency is close to that previously reported15 by Yang, 384 20 THz. These values are however not similar to studies on YbFe4Sb12, where the Einstein frequency was gleaned from ADP measurements.28

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31 Temperature (K) 10100 L (W m1 K1 ) 1 10 100 Figure 4.10: Graph of fits to the YbyCo4Sb12 series, where diamonds represent y=0, circles are y=0.066 and squares are y=0.19. Reprinted from Journal of Materials Research, copyright 2005, Materials Research Society.10 From our analysis an Einstein temperature can be obtained, indicat ing the resonance of these vibrating atoms, and for this case, the temperature is 84K. With the addition of a Eu-filled skutteru dite (experimental data from reference 29), an analysis of lattice thermal co nduction mechanisms can be performed for somewhat similar filling fraction as a function of rare earth atom. Figure 4.11 shows the excellent fits to the data, and the fit parameters are listed in Table 4.2. Grain size is again reasonable amid the spread of values that ar e consistent with mean grain size, and in addition considering the samples were not uniformly prepared. This may also account for the wide range of values for the A prefactor, although these values do increase with increasing lanthanide mass, and decreasing size. The B prefactor dependence on lanthanide is largely unknown due to the fact that no data exists on the exact the Debye

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32 temperature, the Grneisen constant, or th e speed of sound in these samples. The resonance prefactor C is different for each specimen, de noting a possible difference in the bonding of the lanthanide to the antimony ‘ cage’ atoms. Here Eu is divalent,29 La is trivalent21 and Yb possesses mixed valence.22,30 The resonance frequency also shows Yb to possess the smallest resonance frequency, as it is the smallest and heaviest filler atom. Eu is intermediate between Yb and La while La possesses the largest resonance frequency. Consistent with the large body of research pub lished in the scientific literature on these materials1,3 the thermal conductivity of heavier, smaller filling atoms causes a greater reduction in L as compared to lighter, bigger atoms. Table 4.2: Fit parameter values for listed samples. Reprinted from Journal of Materials Research, copyright 2005, Materials Research Society.10 Sample L (m) A ( 10-43 s3) B (10-18 s K-1) C (1033 s-3) 0 (THz) CoSb3 5.8 2.59 5.38 0 --La0.23Co4Sb12 32 16.3 0.37 24.1 11.0 Eu0.20Co4Sb12 0.9 76.2 0.72 111.6 6.63 Yb0.19Co4Sb12 29 150 2.59 3.10 2.38

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33 T (K) 1101001000 L (W/m K) 0.1 1 10 100 Figure 4.11: Lattice thermal conductivity for differe nt filled skutterudites. Circles represent CoSb3, triangles La0.23Co4Sb12, diamonds Eu0.20Co4Sb12 and squares Yb0.19Co4Sb12. Reprinted from Journal of Materials Research, copyright 2005, Materials Research Society.

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34 5 New Materials Synthesis to Expl ore Possible Lanthanide-filled CoGe1.5Se1.5 5.1 Synthesis Process Details Previous work in the University of South Florida Novel Ma terials Laboratory investigated the synthesis and electrical and thermal properties of the ternary skutterudite Co4Ge6Se6.31 A natural continuation of this work was the synthesis of filled skutterudites of this type in order to investigate their transport properties. Early attempts included sample S025, nominally Ce0.4Co4Ge6Se6, sample S029, nominally Yb0.3Co4Ge6Se6, and S034, nominally Eu0.3Co4Ge6Se6. All samples were synthesized using high purity elements in boron nitride cr ucibles in a quartz ampoule th at was sealed after being evacuated and subsequently fill ed with nitrogen (a process re peated thrice) to thwart the effects of oxidation. Samples were heated to 700C for at least 4 days, removed, ground to 300 mesh, and then placed in the furnace with the same settings. This sintering was repeated twice per sample. Due to the high vapor pressure of selenium, a small amount of extra selenium (~8%) was added to these sa mples to prevent selenium deficient sample formation. Structural properties were eval uated from X-ray diffrac tion pattern analysis (employing a Rigaku Miniflex), with the positive criterion between filled and unfilled skutterudite assumed to be an increase in lattice parameter as the void encapsulates the filler atom, as is the case for all other skutterudites to date.1,2,3 This vital change was not present in the XRD patterns, and without furt her verification that the desired structure was synthesized, no more samples were synthe sized. The samples did appear crystalline however, and seemed to also be phase pure, with no secondary phases identified in the

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35 Degrees 2 20304050607080 Intensity (arbitrary units) 0 1000 2000 3000 4000 (211) (310) (321) (330)Si Si(420)Si(431) (433)Si(361) (600) (422) (200) Figure 5.1: Structural analysis of samples. XRD patterns (including NIST silicon standard) for CoGe1.5Se1.5 (top) S025 (high middle) S029 (low middle) and GF007 (bottom). Spectra were shifted for clarity. Note that the spectra appear nearly identical and the lattice parameters do not change with filling concentration and type. XRD scans. Powders of these samples were sent to the University of Oregon (also synthesizing these materials us ing a much different technique)1 for X-ray Rietveld refinement. The results indicated that the samples were filled with the Lanthanide elements, but to a much lesser degree than the nominal composition would suggest. Instead of Ce at 40% filling, it was found to be only 13%; for Yb (nominally 30%), it was found to be only 14% filled, and the Eu ( nominally 25%) was found to be 11%. These results may indicate that some of the lantha nides had reacted into a secondary impurity phase; however, no such secondary phases were identifiable in the XRD data (see Figure 5.1). Upon refinement, no difference in la ttice parameter occu rred either, and the intensities of the first three Miller indices decreased in contrast to the unfilled structure, a 8.30 0.02 8.31 0.02 8.29 0.03 8.313 0.003

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36 change associated with successful filling of the voids. This led to an interesting quandary: where did the lanthanide s atoms go if only part of it is inside of the voids of the skutterudite? It was then postulated that it coul d be in an amorphous phase of skutterudite, virtually undetected in the extensive XRD analysis but wholly accounting for the whereabouts of the Ln atoms in the sa mples. Clearly, more investigation was needed in order to elucidate the physical nature of these sa mples. Electron Micro Probe Analysis (EPMA) was performed at General Motors. The results indicated different filling fractions than the Rietveld analysis perf ormed at the University of Oregon. In all of the instances, EPMA indicated lower f illing fractions than from XRD Rietveld refinement. Table 5.1 shows some physical pr operties for the three filled skutterudites described in this chapter. We show EPMA images of S029 are shown in Figures 5.2, 5.3 and 5.4 as examples of this technique. Similar images were obtained for the other samples. Figure 5.2 is an electron back sc attering image (BSE), and on top the imaging of the oxygen (false color enha nced) shows a low level of oxy gen on the sample. Figures 5.3 and 5.4 illustrate the relatively even di stribution of the constituent elements in the grains. They also reveal small regions with large concentrations of Yb and Se (Co and Ge deficient) that may be an indi cation of secondary amorphous phase(s). Table 5.1: Room temperature data. Stoichiometry, dens ity (as a percent of theore tical), Seebeck coefficient resistivity, and thermal conductivity for the skutterudites described in this chapter. Label Stoichiometry (EPMA) Density Seebeck (V/K) Resistivity ( mohm-cm) Thermal Conductivity (W/mK) S025 Ce0.007Co4Ge5.38Se5.16 93% 13.94 1596 5.67 S029 Yb0.02Co4Ge5.85Se5.41 99% 143.4 1073 6.36 GF007 Ce0.006Co4Ge5.77Se5.65 93% 154.5 1890 7.02

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37 Figure 5.2: Oxygen content (top) and total BSE image (bottom) of S029 (EPMA).

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38 Figure 5.3: Se (top) and Ge (bottom) content in S029 (EPMA).

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39 Figure 5.4: Co (top) and Yb (bottom) content in S029 (EPMA).

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405.2 Transport Measurement Results and Analysis Samples were hot pressed at 650C under N2 flow at 2300kg of uniaxial force for two hours. The resulting pellet was cut into 2x2x5mm3 parallelepipeds, polished with 4000 grit SiC paper on all sides to minimize surface area, and prepared for lowtemperature transport measurement on the Novel Materials Labor atory’s custom lowtemperature transport measurement apparatus,32 consisting of a closed-cycle helium cryostat, Keithley electronic measuremen t and power supply instrumentation, and Lakeshore temperature controlle r, with master control defaulted to a custom LabView controller program on a PC. Th e samples were indented and nickel-plated at specific points to facilitate better el ectrical contacts, a nd Stycast thermal epoxy used to mount the heater resistor and the thermocouples. Samp les were carefully pr epared and mounted on small copper blocks and then on to the custom -machined sample head in the cryostat with all contacts soldered to the pins in th e head. This system allowed simultaneous temperature dependent measurement of the S eebeck, electrical resistivity and thermal conductivity. Seebeck coefficient was obtained through the slope of the line of best fit for several voltage differences taken during a scan through thermal grad ients. Electrical resistivity measurements employed the sta ndard four-probe technique, while thermal conductivity was measured by st abilizing different temperatur es and then comparing the power going into the sample to the sample temperature, giving thermal conductivity of the material via thermal conductance. The ma in source of error in the entire system is essentially human in nature, as the geometry of the sample affects the measurement much more significantly than any other source of error. The cross-sectional area and the contact separation measurements introduce th e significant “geometrical factor” in the

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41 error of thermal conductivity and resistivity and accurate Seebeck measurements are highly contingent upon the consistency of the placement of the cont acts in the same cross-sectional plane, both siz eable tasks considering the dime nsions of the samples. At room temperature, the estim ated uncertainty for resist ivity is ~3%, for Seebeck coefficient is <5%, and for thermal conduc tivity is <10%. Reference 32 contains extensive details on this pro cedure and the associated erro rs and uncertainties. The results of the low-temperature transport meas urement are shown in Figures 5.5-5.7. Figure 5.5 shows the thermal conductivity of the four samples. As expected, the unfilled sample has the highest thermal conductivity. However, lattice thermal conductivity for the filled skutterudites is onl y ~10% smaller, typical of small filling fractions, as indicated by EM PA results (see Table 5.1). Temperature (K) 10100 Thermal Conductivity (W/mK) 1 10 100 Figure 5.5: Thermal conductivity of various samples. Circles represent CoGe1.5Se1.5, squares S025, triangles S029, and diamonds GF007.

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42 Further modeling was not performed due to a l ack of knowledge about the crystallinity of the filled samples. An amorphous phase presence would require modified phonon scattering parameters. Figure 5.6 shows the resistivity of the filled samples. The resistivity is too large for these skutterudites to be considered as viable thermoelectrics, yet these samples are interesting because this resistivity data is consistent with the potential for a composite skutterudite. Resistivity of these sample s is higher than that of the unfilled CoGe1.5Se1.5. The Seebeck coefficient (Figure 5.7) fo r these samples shows a somewhat similar temperature dependence as that for the unfilled sample, a decrease with decreasing temperatures, although the Seeb eck at room temperature is significantly higher for the unfilled sample by at least a factor of two. All samples decrease to near zero by ~150K. Temperature (K) 050100150200250300 Resistivity (Ohm-m) 10-210-1100101102 Figure 5.6: Plot of resis tivity of ‘filled’ samples. Squares are S025, triangles S029, and diamonds GF007.

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43 Temperature (K) 50100150200250300 Seebeck ( V/K) -100 0 100 200 300 400 Figure 5.7: Seebeck coefficient for my riad samples. Circles represent CoGe1.5Se1.5, squares S025, triangles S029, and diamonds GF007. Overall, transport measurements indicat e that these filled-skutterudites are of interest for further investigation. The potential for the exis tence of an amorphous skutterudite phase would prove very interesting, and impl y a composite material that requires further study to fully understand and subsequently optimize the material.

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44 6 Conclusions and Future Directions The thermal conductivity of various filled skutterudites was successfully modeled and explicitly shows the importance of resonance scattering in filled skutterudites. Trending shows saturation of the resonance effect at approximately 20% filling, but also indicates that point defect scattering is highly signif icant as a phonon scattering mechanism. This mechanism can be enhanced with the addition of filler atoms, and by doping on the framework, with the use of both significant in th ese materials. This work attests to the importance of understanding the phonon scattering mech anisms fully when attempting to develop materials with dimini shed thermal conductivity. The analysis and fitting procedures can be used to model any solid’s thermal conductivity given the correct scattering terms in the phonon relaxation term in the Debye integral. The concept of filling the voids of skutterudites was extended in this work, where a ternary skutterudite was ‘filled’ with Ln -series atoms (e.g. Ce and Yb) in order to investigate the thermal and elec trical properties. The result s prove more than ordinary, and may indicate the presence of an amorphous skutterudite phase. The refined XRD data indicate some filling, and EPMA data confirms this. However, the location and properties of the remaining Lanthanide atom s is still indeterminate. The Seebeck coefficient is lower in these f illed samples compared to CoGe1.5Se1.5. The resistivity is too large for these materials to be considered as viable thermoelectric materials. The interesting findings however in dicate that filling ternary sk utterudites may be a difficult

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45 yet fascinating avenue for exploring thermoel ectric materials, with optimization possible if filling fractions can be improved and crystallinity better understood. Future directions for the investigation of thermal conductivity may include analyzing other filled skutterudites to determine if satu ration exists in the effect of resonance scattering and to wh at degree framework substituti on can enhance point defect scattering. Determination of whether strain field effects or mass fl uctuation effects are responsible for point defect scattering in other thermoelectric ma terials can guide the optimization of stoichiometry for thermal prope rties. Faster modeling software and more filled skutterudite synthesis is necessary fo r this avenue to be better explored. Future work for the synthesis of filled ternary skutterudites centers on improving the filling fraction of these materials, as well as determining how the filling is achieved. This may include novel synthesis technique s, for instance, forming intermediate compounds before synthesizing the filled stru cture to avoid rare earth secondary phases or selenium vapor loss. E xpanding on measurements should bring to light the location and role of the filler atom in the crystal structure. Other substitutions on the metal site may show different results, and are anothe r possible route of exploration into the properties and characteristics of filled ternary skutterudites (i.e. filled IrGe1.5Se1.5). Overall, this work has added to the growing knowledge of the thermal conductivity analysis of filled skutterudites, better determining the mechanisms behind the effects of a filler or rattler atom. It has also pointed to some interesting findings regarding filled ternary skutterudites, potentially leading to a skutterudite composite that may be of interest for thermoelectric mate rials as well as for the pursuit of pure fundamental scientific ma terials understanding.

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46 References 1. G. S. Nolas, D. T. Morelli, and T. M. Tritt, Annu. Rev. Mater. Sci 29 89 (1999), and references therein. 2. B.C. Sales: Filled Skutterudites in Handbook of the Physics and Chemistry of Rare Earths 33, 1 (Elsevier Science, Amsterdam, 2002). 3. C. Uher: Skutterudites: Pr ospective novel thermoelectrics in Semiconductors and Semimetals 69, 139 Terry M. Tritt (Ed.), Academ ic Press, (New York, 2000) and references therein. 4. B. C. Chakoumakos, and B. C. Sales, Skutterudites: Their st ructural response to filling, J. Alloys and Compounds 407, 87-93 (2006). 5. G. S. Nolas, C. A. Kendziora, and H. Takizawa, Polarized Ra man-scattering study of Ge and Sn filled CoSb3, J. Appl. Phys 95, 1 (2004). 6. G. A. Slack, “New Materials and Perf ormance Limits for Thermoelectric Cooling” in CRC Handbook of Thermoelectrics D.M. Rowe (Ed.) CRC Press, Boca Raton (1995). 7. T. J. Seebeck, Magnetische pol arisation der metalle und erze durck temperaturdifferenz, Abhandlungen de Deut Schen Akade mie de Wissenshafften zu Berlin 265-373 (1823). 8. J.C. Peltier, Nouvelles experiences sur la caloricite des courans electrique, Annales de Chimie. 56, 371-387 (1834). 9. W. Thomson, On a mechanical theory of thermoelectric currents, Proceedings of the Royal Society of Edingburgh 91 (1851). 10. G. S. Nolas and G. Fowler, Partial filling of skutterudi tes: Optimization for thermoelectric applications, J. Mater. Res. 20, 3234-3237 (2005). 11. G. S. Nolas, J.W. Sharp and H.J. Goldsmid, Thermoelectrics: Basic Principles and New Materials Developments (Springer-Verlag, Heidelberg, 2001). 12. C. Kittel, Intro. to Solid State Physics 5th ed. John Wiley & Sons, Inc. New York, (1976).

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47 13. J. Callaway, Model for Lattice Thermal Conductivity at Low Temperatures Phys. Rev 113, 1046 (1959) 14. B. Abeles, Lattice Thermal Conductivity of Disordered Semiconductor Alloys at High Temperatures, Phys. Rev 131, 1906-1911 (1963). 15. J. Yang, D.T. Morelli, G.P. Meisner, W. Chen, J.S. Dyck and C. Uher, Phys. Rev. B, 67, 165207 (2003). 16. C. T. Walker and R. O. P ohl, Phonon Scattering by Point Defects, Phys. Rev. 131, 1433 (1963). 17. R. Berman, Thermal Conduction in Solids Oxford University Press, Oxford, (1976). 18. R. O. Pohl, Phys. Rev. Letters 8, 481 (1962). 19. B. C. Sales, B .C. Chakouma kos, D. Mandrus, and J. W. Sharp, Journ. Solid State Chem. 146, 528-532 (1999). 20. J. Yang, D. T. Morelli, G. P. Meis ner, W. Chen, J. S. Dyck and C. Uher, Phys. Rev. B 65, 094115 (2002). 21. G. S. Nolas, J. L. Cohn, and G. A. Slack, Phys. Rev. B 58, 164 (1998). 22. G. S. Nolas, M. Kaeser, R. T. Littleton IV, and T. M. Tritt, Appl. Phy. Lett. 77, 1855 (2000). 23. D. T. Morelli, T. Caillat, J.-P. Fleurial A. Borshchevsky, and J. Vandersande, B. Chen, and C. Uher, Phy. Rev. B. 51, 9622 (1995). 24. G. S. Nolas, G. Fowler, and J. Yang, J. Appl. Phys. (in press) 25. V. Keppens, D. Mandrus, B. C. Sales, B. C. Chakoumakos, P. Dai, R. Coldea, M. B. Maple, D. A. Gajewski, E. J. Freeman and S. Bennignton: Localized vibrational modes in metallic solids. Nature 329, 876 (1998). 26. D. Cao, F. Bridges, P. Chesler, S. Bushart, E.D. Bauer and M.D. Maple, Phys. Rev B 70, 094109 (2004). 27. J.L. Feldman, D.J. Singh, I.I. Mazin, D. Mandrus and B.C. Sales Phys. Rev. B 61, R9209 (2000).

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48 28. Sales, B. C., Chakoumakos, Mandrus, D., Sharp, J. W., Dilley, N. R., Maple, M. B. “Atomic Displacement Parameters: A Useful To ol in the Search for New Thermoelectric Materials?”, in Thermoelectri c Materials 1998The Next Ge neration Materials for SmallScale Refrigeration and Powe r Generation Applications, 545, Eds. T. M. Tritt, M. G. Kanatzidis, G. D. Mahan a nd Hylon B. Lyon Jr. (1998). 29. G. A. Lamberton, S. Bhattacharya, R. T. Littleton, M. A. Kaeser, R. H. Tedstrom, T. M. Tritt, J. Yang, and G. S. Nolas, “High figure of merit in Eu-filled CoSb3 skutterudites” Appl. Phys. Lett 80 598 (2001). 30. N. R. Dilley, E. J. Freeman, E. D. Baue r and M. B. Maple, “Intermediate valence in the filled skutte rudite compound YbFe4Sb12”, Phys. Rev. B 58, 6287 (1998). 31. G. S. Nolas, J. Yang, and R. W. Ertenberg Phys. Rev. B 68, 193206 (2003). 32. For details, please see J. Martin: “Optimization Study of Ba-Filled Si-Ge Alloy Type I Semiconducting Clathrates for Thermoelect ric Applications” Un iversity of South Florida Master’s Thesis (2005).