Exploration and Optimization of Tellurium‐Based Thermoelectrics

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Equation 4.2 Bragg's law: nλ 2dhkl·sinθ Having represent the distance between crystallographic planes , the angle between the plane and the X‐ray beam, an integer value and , again, the wavelength of the X‐ray beam. Therefore two X‐ray beams diffracting off the sample at the same times must travel a distance of if they are to be observed during experimental data acquisition. Since all diffraction experiments used take advantage of a monochromatic wavelength, is precisely known allowing one to observe different combinations of and . As values of versus progress, differentiations can be made between possible space symmetries (i.e. tetragonal, cubic, etc.) based on the reflections that are present in the X‐ray patterns. Higher symmetry patterns consist of reflections having fewer unique values than their respective lower symmetry equivalents because many reflections will be related to each other through symmetry operations. Consider both a cubic and orthorhombic system. In the cubic system, all dimensions are equivalent, leading to the same observed reflection for (100), (010), (001) planes whilst the orthorhombic system, containing three different directions, has separate reflections for each. This phenomenon can be used to follow the distortions along a, b, c of structures as a function of chemical substitution or temperature, etc. The observed reflections in reciprocal space and their corresponding position and intensity comprise the raw experimental information. The complete description of scattering within the crystal is described by the equation for the scattering factor , which is the sum of the atomic scattering, , of each unique atom, , in the crystal and its relation to Miller Indices and atomic position . This relationship is depicted below in Equation 4.3 (a). All information about the crystal structure and its atoms is contained within , whose square is proportional to the intensity, , as follows: ∝ | | . a ∑ b ∑ ∑ ∑ Equation 4.3 (a) Structure factor ‐ exponential form. (b) Electron density within crystal. 40
The closely related electron density (Equation 4.3 (b)) is associated with the structure factor via the Fourier transform function, which allows for a convenient scientific relationship: If a crystal’s structure factors are known, one can calculate the precise locations of electron density in the crystal and therefore, know the precise location of the atoms and their sizes within. Diffraction is the affected X‐rays, in this case, bending or modulating due to the presence of electrons. Electron density not only controls diffraction, but provides information on the size of the atoms involved due to each element’s unique electron density. Because the scattered X‐ray beam is reduced during diffraction as with the amplitude, a scaling factor, , and two corrections – Lorentz, , (geometrical) and (polarization) – are added to Equation 4.4 displayed below, the experimental intensity is equivalent to the square of the wave’s amplitude or structure factor . ∙ Equation 4.4 Diffracted intensity. This provides a comparison between the observed reflections in reciprocal space and their corresponding calculations determined from a structural model. 4.1. Powder X‐Ray Diffraction (p‐XRD) Experimentally, a polycrystalline solid‐state sample is undoubtedly easier to obtain than a single crystal of the same sample. That is, a sample that is comprised of small crystallites typically on the order of 0.1 – 100 μm and randomly oriented, or stacked along specific orientations. When a monochromatic beam of X‐rays hits a powdered sample, the diffraction no longer occurs in a set direction as discussed above, but continues in all directions (that obey Bragg’s Law) as a Debye‐Sherrer diffraction cone (Figure 4.1) – named for the Dutch and Swiss physicists who, in 1915, first attempted the technique with a strip of photographic film surrounding their sample as a collection method for the diffracted marks. Figure 4.1 Debye‐Scherrer powder diffraction cone. [125] 41
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 and 24: Hence it follows that a good thermo
Page 25 and 26: a b ∗ Equation 1.4 (a) Ele
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: Chapter 4. X‐Ray Diffraction Anal
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
Page 75 and 76: Figure 5.6 Home‐made electrical c
Page 77 and 78: The SEM is constructed from an elec
Page 79 and 80: The EDX measurement system utilized
Page 81 and 82: 2 4 ext Equation 6.2 Ma
Page 83 and 84: Section III - Layered Bi2Te3 Compou
Page 85 and 86: aforementioned studies address the
Page 87 and 88: Pb‐based compound (~‐60 V∙K
Page 89 and 90: also differ in 2 there, while the r
Page 91 and 92: Table 7.2 LeBail data for phase‐p
Page 93 and 94: The physical properties, as mention
Page 95 and 96: Upon examination of the power facto
Page 97 and 98: Sn2Bi2Te5 was eventually found pure
Page 99 and 100: From the understanding of this comp
Page 101 and 102: Table 8.1 Rietveld refinements on S
Page 103 and 104: Although there is evidence here of
Page 105 and 106: Figure 8.3 DOS calculation comparis
Page 107 and 108: In order to better determine if the
Page 109 and 110:
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
Page 155 and 156:
Chapter 13. Modifications of Tl9SbT
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Table 13.1 Rietveld refinements for
Page 159 and 160:
make an observable trend despite th
Page 161 and 162:
The electrical conductivity values
Page 163 and 164:
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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