Exploration and Optimization of Tellurium‐Based Thermoelectrics

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and 873 K. [25] Likewise, p‐type TAGS can achieve 10.45% with a temperature gradient between 373 and 798 K. [15] The TE figure of merit can be looked at as one single term similar to the examples above, but this is generally found only in experimental conclusions. For the purpose of research, each term in the ZT equation is looked at individually to ascertain comparisons between different samples and variations in terms therein. It is therefore an important facet to discuss what physical factors affect each term in the figure of merit equation. 1.2.1. The Seebeck Coefficient The Seebeck coefficient (S), also referred to as the “thermopower”, represents the material’s ability to migrate charge carriers ii away from regions of high concentration. Thermopower was described in 1.1 as ∆ , which is its most basic form. Breaking S into its components yields Equation ∆ 1.3 shown here: 8 ∗ 3 3 Equation 1.3 Seebeck coefficient for metals and degenerate semiconductors Temperature aside, there are two key variables in this equation: the effective mass for the material ( ∗ ) is directly proportional to S, while a small number of charge carriers, , leads to a large S. Therefore one can think of variations in the Seebeck coefficient due to changes in either, or both, of these variables. The other terms of the equation are constants , , : the Boltzmann number, the electron’s charge, and Planck’s constant respectively. 1.2.2. Electrical Conductivity The electrical conductivity (σ) is quite simply a material’s ability to move charge carriers (electrons or the lack thereof – holes) through its crystal lattice. Applying this idea, σ can be calculated with Equation 1.4 (a) shown below encompassing the number of charge carriers , the mobility of the carrier , and the charge of an electron . Together, these convey important information regarding different materials’ behaviour with current flow and their electrons traversing energy gaps. ii Charge carriers are further explained in 2.3 on p20. 6
a b ∗ Equation 1.4 (a) Electrical conductivity (b) Carrier mobility The charge of an electron is constant, which leaves two variables in this equation: and . While is simply a concentration – albeit one with numerous classifications and applications – relies on the additional conditions shown in Equation 1.4 (b): – the relaxation time or time between carrier‐carrier collisions, and ∗ – the carrier’s effective mass. [26] 1.2.3. Thermal Conductivity Thermal conductivity () is also rather self‐explanatory; it is a measure of how much heat (i.e. phonons) travels through a material. Of the three factors featured from Equation 1.1, is the only one that is typically divided into two (or more) sub‐variables as demonstrated by Equation 1.5 (a): a el ph b el c ph v ph ph Equation 1.5 (a) Thermal conductivity (b) Electronic contribution (c) Lattice contribution The process of thermal conductivity can further be divided into el: the heat contributed from the charge carriers (electrons and holes) in the structure, and ph: the heat contributed from vibrations in the crystal lattice as a result of heat waves (phonons). The first of the terms, el, can be approximated by the Wiedemann‐Franz law [27] (Equation 1.5 (b)) for metals and narrow band gap semiconductors. [28] is known as the Lorenz number, theoretically calculated by Sommerfeld in 1927 [29] for metals and heavily‐ doped semiconductors as 2.45∙10 ‐8 WK ‐2 . Empirically, it has also been measured realising slightly different values for specific elements and compounds; PbTe (1.70∙10 ‐8 WK ‐2 ) [30] for example. The Wiedemann‐Franz law affords a convenient approximation of the electronic contribution, el, via examination of σ’s behaviour. ph (Equation 1.5 (c)), based on the kinetic theory of gases, is dependent on the specific heat per volume ( v) of the material, the phonon mean free path ( ph), and the speed of sound ( ph) due to the acoustic nature of lattice phonons. Though heavily doped semiconducting materials are often dominated by the latter term, ph is a crucial component to the behaviour and subsequent optimization of thermoelectric materials. [28] While the overall thermal conductivity is useful, advances towards nanostructured materials direct more and more interest towards the individual components including possible ph reductions with nano‐boundaries, impurity scattering, and other routes further discussed in 2.5. 7
Page 1 and 2: Exploration and Optimization of Tel
Page 3 and 4: Abstract Thermoelectric materials a
Page 5 and 6: Acknowledgements To begin, I would
Page 7 and 8: Table of Contents List of Figures..
Page 9 and 10: 9.3.1. Heating, XRD, and Structural
Page 11 and 12: List of Figures Figure 1.1 (a) Pelt
Page 13 and 14: Figure 9.2 Selected DOS calculation
Page 15 and 16: List of Equations Equation 1.1 Dime
Page 17 and 18: Table B.1 Atomic positions, isotrop
Page 19 and 20: Section I: Fundamentals Background
Page 21 and 22: Opposing the Peltier Effect is the
Page 23: Hence it follows that a good thermo
Page 27 and 28: Historically, thermoelectric materi
Page 29 and 30: 1.3.2. Advantages and Disadvantages
Page 31 and 32: common stoichiometry studied with c
Page 33 and 34: Figure 1.8 (a) Ge Quantum Dots [74]
Page 35 and 36: Chapter 2. Background of the Solid
Page 37 and 38: 2.2. Defects, Non‐Stoichiometry a
Page 39 and 40: electric field draws electrons towa
Page 41 and 42: ∑ known as a Bloch function, w
Page 43 and 44: orbital Hamilton population [96] i
Page 45 and 46: 2.5.1. Doping and Substitution: Tun
Page 47 and 48: The major problem with exclusively
Page 49 and 50: Chapter 3. Synthesis Techniques All
Page 51 and 52: Since reactions are driven by both
Page 53 and 54: Table 3.1 Commonly used fluxes. [12
Page 55 and 56: The procedure is carried‐out on a
Page 57 and 58: Chapter 4. X‐Ray Diffraction Anal
Page 59 and 60: The closely related electron densit
Page 61 and 62: The majority of samples emerge from
Page 63 and 64: int ∑ mean ∑ | | Equat
Page 65 and 66: 4.3.1. Rietveld Method In 1967, Hug
Page 67 and 68: Chapter 5. Physical Property Measur
Page 69 and 70: The electrical conductivity, σ, is
Page 71 and 72: a p b 0.1388 53 c Equati
Page 73 and 74: measurement implies that there was
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Figure 5.6 Home‐made electrical c
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The SEM is constructed from an elec
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The EDX measurement system utilized
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2 4 ext Equation 6.2 Ma
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Section III - Layered Bi2Te3 Compou
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aforementioned studies address the
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Pb‐based compound (~‐60 V∙K
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also differ in 2 there, while the r
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Table 7.2 LeBail data for phase‐p
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The physical properties, as mention
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Upon examination of the power facto
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Sn2Bi2Te5 was eventually found pure
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From the understanding of this comp
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Table 8.1 Rietveld refinements on S
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Although there is evidence here of
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Figure 8.3 DOS calculation comparis
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In order to better determine if the
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8.3.3. Physical Property Measuremen
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Figure 8.7 Thermal conductivity (le
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the thermal conductivity slope that
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8.4. Conclusions and Future Work A
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in Chapter 3 (except Arc Melting) w
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Table 9.2 LeBail refinements on var
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9.2.3.1. Doping Trials: [Tr]xSn1‐
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9.2.3.2. Substitution Trials: [Tr]x
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One can observe a variety of grain
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9.2.5. Conclusions Drawn from SnBi4
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SnBi4Te7, but suggest similar albei
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9.4. Project Summary and Future Wor
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Chapter 10. Introduction to Tl5Te3
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Figure 10.2 DOS calculations for Tl
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Thallium‐based chalcogenides clea
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: 36.3 (expected: 48.8 : 13.8 : 37.
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sintering of these pellets. A cold
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Figure 11.2 Thermoelectric properti
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at 319 K, increasing smoothly to 0.
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purity upon the first heating with
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Tl/Sn/Bi present in the 4c Wyckoff
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V∙K ‐1 at 592 K. As the bismuth
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Electrical conductivity values are
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Chapter 13. Modifications of Tl9SbT
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Table 13.1 Rietveld refinements for
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make an observable trend despite th
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The electrical conductivity values
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Section V - Ba Late‐Transition‐
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Obviously, compounds possessing the
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Table 14.1 Known Ba‐Cg‐Q compou
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All samples were analyzed by means
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crystal structure study of the Se
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As emphasized in Figure 15.2 (b), t
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The Cu-Cu COHP curve, cumulated ove
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Chapter 16. Ba3Cu17‐x(S,Te)11 and
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the selenide‐telluride before, th
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surrounded by three Q1 atoms. Besid
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Figure 16.3 The three‐dimensional
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Figure 16.5 Seebeck coefficient (le
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Chapter 17. Ba2Cu7‐xTe6 17.1. Int
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Table 17.1 Crystallographic Data fo
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Table 17.2 Atomic coordinates, Ueq
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17.3.2. Electronic Structure Calcul
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Figure 17.6 Crystal orbital Hamilto
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Section VI - Supplementary Informat
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[33] Rowe, D. M.; Kuznetsov, V. L.;
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[90] Albright, T. A.; Burdett, J. K
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[156] Cottenier, S., Density Functi
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[219] Toure, A. A.; Kra, G.; Eholie
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[294] Kanno, R.; Ohno, K.; Kawamoto
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Table A.3 Atomic positions and Ueq
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Table B.2 Selected interatomic dist
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Table B.5 Atomic coordinates and Ue
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Table B.7 Selected interatomic dist
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Exploration and Optimization of Tellurium‐Based Thermoelectrics

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