Exploration and Optimization of Tellurium‐Based Thermoelectrics

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factor of Bi is comparable to Tl so even with its inclusion, the suggested quantity of Sn in the crystal was unreasonable. Thus, mixing on the 4c (M(1)) site was comprised of Tl, Sn and Bi based on anisotropic displacement parameter values as well as previous data from Tl9BiTe6 [244] or Tl9.05Sn0.95Te6 [245] or Tl10‐xLaxTe6 [236] were treated whilst the M(2) site was left fully occupied with Tl. Refinements converged smoothly without showing any abnormalities. Due to the difficulty of differentiating Tl from Bi scattering, EDX data taken on the crystal allowed us to fix Bi as ⅓ of the 4c site. The formula Tl8.67Sn0.63Bi0.70Te6 was refined to Tl8.66Sn0.67Bi0.67Te6, which leaves the atomic sites within 5 % of the nominal composition. In order to monitor the unit cell parameters of a wider range of samples, Rietveld refinements were performed on the samples with nominal x = 0.60, y = 0.40; x = 0.50, y = 0.50; and x = 1.00, y = 0.33. Data were collected on the aforementioned INEL diffractometer for approximately 12 hours in each case; all powders showed no additional phases in the resulting diffractograms. Crystallographic details of the data collections are summarized in Table 12.1, the atomic positions, isotropic displacement parameters, and occupancies of Tl10‐x‐ySnxBiyTe6 in Table A.3, and the bond ranges in Table A.4. 12.2.1.4. Electronic Structure Calculations Self‐consistent tight‐binding first principles LMTO calculations, as previously discussed were implemented here. Three different models were calculated in 4/ including the Sn‐Bi equivalent compound, Tl9Sn0.5Bi0.5Te6, the Sn‐heavy Tl8.5Sn1Bi0.5Te6 and the Bi‐rich Tl9Sn0.5Bi1Te6. All compounds are originally of space group 4/. The wavefunctions used in the calculations are as follows: for Tl 6s, 6p, 6d and 5f; for Sn 5s, 5p, and 5d and 4f; for Bi 6s, 6p, 6d and 5f; and for Te 5s, 5p, and 5d and 4f. The eigenvalue problems were solved on the basis of 1728 evenly‐dispersed k points within the irreproducible wedge of the first Brillouin zone, respectively, selected with an improved tetrahedron method. [203] 12.3. Results and Discussion 12.3.1. Crystal Structure A crystal of nominal composition Tl8.67Sn0.63Bi0.70Te6 was selected for single crystal diffraction in order to determine the lattice parameters and verify the atomic site positions and occupancies. This crystal structure was refined to Tl8.66Sn0.67Bi0.67Te6 and is analogous to Figure 10.1, with equal parts 130
Tl/Sn/Bi present in the 4c Wyckoff site (M(1)), whilst the second Tl site (M(2), 16l) contains only Tl. There are no Te–Te bonds in this system. The M(1) atoms are coordinated to four Te1 (3.25 Å) and two Te2 atoms (3.32 Å) via an octahedral coordination elongated along the c direction. The M(2) atoms are surrounded by five Te atoms with bond lengths between 3.16 Å and 3.59 Å. The structures contain weak Tl–Tl bonds between 3.50 Å and 3.67 Å forming two Tl8 clusters per unit cell, analogous to elemental S8 crowns. Tl–Tl bonds are formed only with M(2), not with M(1). Rietveld refinements on three additional samples were utilized to monitor changes in the unit cell parameters from stoichiometry to stoichiometry. While the unit cell parameters such as dimensions and volume could be refined, the same problem with respect to three atoms – Tl/Sn/Bi – on the same Wyckoff position (4a) meant that in each case, the atoms were fixed at their nominal compositions while U values for each site could be refined from the “conventional” 0.025 during the Rietveld procedure. Subsequent EDX measurements on each of these samples yielded acceptable matches. With a volume of 1019.87 Å 3 , the single crystal data on Tl8.66Sn0.67Bi0.67Te6 is the largest of the measured unit cells. According to the refined powder data, the next largest unit cell has a volume of 1015.9 Å 3 for “Tl9Sn0.50Bi0.50Te6” followed by “Tl9Sn0.60Bi0.40Te6” with 1012.5 Å 3 . The final measured cell was “Tl8.67Sn1.00Bi0.33Te6” yielding the smallest volume of 998.2 Å 3 . Table 12.1 Crystallographic information for Tl 10‐x‐ySn xBi yTe 6. Chemical formula Tl9Sn0.60Bi0.40Te6 Tl9Sn0.50Bi0.50Te6 Tl8.67Sn1.00Bi0.33Te6 Tl8.66Sn0.67Bi0.67Te6 M [g/mol] 2759.74 2768.76 2725.14 2754.37 T [K] 296(2) 296(2) 296(2) 296(2) λ [Å] 1.5406 1.5406 1.5406 0.71073 space group 4/ 4/ 4/ 4/ a [Å] = b 8.8709(5) 8.8698(4) 8.789(6) 8.8549(3) c [Å] 12.8661(8) 12.9132(7) 12.922(9) 13.0069(9) V [Å 3 ] 1012.47(16) 1015.93(15) 998.2(22) 1019.86(9) Z 2 2 2 2 RFoa \ RwFo 2b 0.041 \ 0.0927 RP c \ RB d 0.0639 \ 0.0742 0.0762 \ 0.0864 0.0828 \ 0.0905 a RFo ||Fo|‐|Fc||/|Fo| b RwFo 2 ΣwFo 2 ‐Fc 22/ΣwFo 22 1/2 c RP |yo ‐ yc| / |yo| d RB |Io ‐Ic| / |Io| Additional tables including Wyckoff positions and bond distances for the four samples are stored in the appendix of this document (Table A.3). 131
Page 1 and 2:
Exploration and Optimization of Tel
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Abstract Thermoelectric materials a
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Acknowledgements To begin, I would
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Table of Contents List of Figures..
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9.3.1. Heating, XRD, and Structural
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List of Figures Figure 1.1 (a) Pelt
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Figure 9.2 Selected DOS calculation
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List of Equations Equation 1.1 Dime
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Table B.1 Atomic positions, isotrop
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Section I: Fundamentals Background
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Opposing the Peltier Effect is the
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Hence it follows that a good thermo
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a b ∗ Equation 1.4 (a) Ele
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Historically, thermoelectric materi
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1.3.2. Advantages and Disadvantages
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common stoichiometry studied with c
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Figure 1.8 (a) Ge Quantum Dots [74]
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Chapter 2. Background of the Solid
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2.2. Defects, Non‐Stoichiometry a
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electric field draws electrons towa
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∑ known as a Bloch function, w
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orbital Hamilton population [96] i
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2.5.1. Doping and Substitution: Tun
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The major problem with exclusively
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Chapter 3. Synthesis Techniques All
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Since reactions are driven by both
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Table 3.1 Commonly used fluxes. [12
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The procedure is carried‐out on a
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Chapter 4. X‐Ray Diffraction Anal
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The closely related electron densit
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The majority of samples emerge from
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int ∑ mean ∑ | | Equat
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4.3.1. Rietveld Method In 1967, Hug
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Chapter 5. Physical Property Measur
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The electrical conductivity, σ, is
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a p b 0.1388 53 c Equati
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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
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
Page 111 and 112: Figure 8.7 Thermal conductivity (le
Page 113 and 114: the thermal conductivity slope that
Page 115 and 116: 8.4. Conclusions and Future Work A
Page 117 and 118: in Chapter 3 (except Arc Melting) w
Page 119 and 120: Table 9.2 LeBail refinements on var
Page 121 and 122: 9.2.3.1. Doping Trials: [Tr]xSn1‐
Page 123 and 124: 9.2.3.2. Substitution Trials: [Tr]x
Page 125 and 126: One can observe a variety of grain
Page 127 and 128: 9.2.5. Conclusions Drawn from SnBi4
Page 129 and 130: SnBi4Te7, but suggest similar albei
Page 131 and 132: 9.4. Project Summary and Future Wor
Page 133 and 134: Chapter 10. Introduction to Tl5Te3
Page 135 and 136: Figure 10.2 DOS calculations for Tl
Page 137 and 138: Thallium‐based chalcogenides clea
Page 139 and 140: : 36.3 (expected: 48.8 : 13.8 : 37.
Page 141 and 142: sintering of these pellets. A cold
Page 143 and 144: Figure 11.2 Thermoelectric properti
Page 145 and 146: at 319 K, increasing smoothly to 0.
Page 147: purity upon the first heating with
Page 151 and 152: V∙K ‐1 at 592 K. As the bismuth
Page 153 and 154: Electrical conductivity values are
Page 155 and 156: Chapter 13. Modifications of Tl9SbT
Page 157 and 158: 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‐
Page 165 and 166: Obviously, compounds possessing the
Page 167 and 168: Table 14.1 Known Ba‐Cg‐Q compou
Page 169 and 170: All samples were analyzed by means
Page 171 and 172: crystal structure study of the Se
Page 173 and 174: As emphasized in Figure 15.2 (b), t
Page 175 and 176: The Cu-Cu COHP curve, cumulated ove
Page 177 and 178: Chapter 16. Ba3Cu17‐x(S,Te)11 and
Page 179 and 180: the selenide‐telluride before, th
Page 181 and 182: surrounded by three Q1 atoms. Besid
Page 183 and 184: Figure 16.3 The three‐dimensional
Page 185 and 186: Figure 16.5 Seebeck coefficient (le
Page 187 and 188: Chapter 17. Ba2Cu7‐xTe6 17.1. Int
Page 189 and 190: Table 17.1 Crystallographic Data fo
Page 191 and 192: Table 17.2 Atomic coordinates, Ueq
Page 193 and 194: 17.3.2. Electronic Structure Calcul
Page 195 and 196: Figure 17.6 Crystal orbital Hamilto
Page 197 and 198: 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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