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Dr Jonathan Skelton and Dr Joseph Flitcroft Department of Chemistry, University of Manchester ([email protected]) Theory-led discovery of high-performance thermoelectric materials for waste-heat recovery

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The global energy challenge 31 % 23 % 20 % 19 % 3 % 1000 MW nuclear power plant: o 650 MW waste heat o 3 % β‰ˆ 20 MW β‰ˆ 50,000 homes 300-500 W from exhaust gases: o 2 % lower fuel consumption o 2.4 Mt reduction in CO2 Thermoelectric generators allow waste heat to be recovered as electricity TEGs with ~3 % energy recovery (𝑍𝑇 = 1) are considered industrially viable 1. Provisional UK greenhouse gas emissions national statistics (published March 2022) 2. EPSRC Thermoelectric Network Roadmap (2018) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 2

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Thermoelectric materials 𝑍𝑇 = 𝑆2𝜎 πœ…el + πœ…latt 𝑇 𝑆 - Seebeck coefficient 𝜎 - electrical conductivity πœ…ele - electronic thermal conductivity πœ…lat - lattice thermal conductivity Tan et al., Chem. Rev. 116 (19), 12123 (2016) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 3

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An ab initio modelling workflow Crystal structure Convergence testing Geometry optimisation Phonon calculation πœ…latt Electronic structure 𝑆, 𝜎, πœ…el 𝑍𝑇 = 𝑆2Οƒ πœ…el + πœ…latt 𝑇 Scattering rates: DP, πœ€βˆž , π‘βˆ—, 𝐢𝑖𝑗 Part 2 Part 1 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 4

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Modelling thermal conductivity Togo et al., Phys. Rev. B 91, 094306 (2015) The simplest model for πœ…latt is the single-mode relaxation time approximation (SM-RTA) - a closed solution to the phonon Boltzmann transport equations 𝜿latt (𝑇) = 1 𝑁𝑉 ෍ πœ† πΆπœ† (𝑇)π’—πœ† βŠ— π’—πœ† πœπœ† (𝑇) πΆπœ† - phonon heat capacities π’—πœ† - phonon group velocities πœπœ† - phonon lifetimes (inverse linewidths Ξ“πœ† ) 𝑁 - number of 𝒒 in summation 𝑉 - unit cell volume Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 5

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Modelling thermal conductivity Tang and Skelton, J. Phys.: Condens. Matter 33, 164002 (2021) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 6

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Modelling thermal conductivity Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 7

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The IV-VI chalcogenides Zhao et al., Nature 508, 373 (2014) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 8

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A comparative study GeSe GeTe SnSe SnTe π‘ƒπ‘›π‘šπ‘Ž οƒΌ οƒΌ οƒΌ οƒΌ πΆπ‘šπ‘π‘š οƒΌ 𝑅3π‘š οƒΌ οƒΌ οƒΌ πΉπ‘šΰ΄€ 3π‘š οƒΌ οƒΌ π‘ƒπ‘›π‘šπ‘Ž πΆπ‘šπ‘π‘š 𝑅3π‘š πΉπ‘šΰ΄€ 3π‘š Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 9

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A comparative study πœ…π₯𝐚𝐭𝐭 (𝑇 = 300 K) [W m-1 K-1] SnSe (πΆπ‘šπ‘π‘š) 0.96 SnTe (π‘ƒπ‘›π‘šπ‘Ž) 1.09 GeTe (π‘ƒπ‘›π‘šπ‘Ž) 1.32 SnSe (π‘ƒπ‘›π‘šπ‘Ž) 1.36 GeTe (πΉπ‘šΰ΄€ 3π‘š) 1.57 GeSe (πΉπ‘šΰ΄€ 3π‘š) 1.67 GeSe (π‘ƒπ‘›π‘šπ‘Ž) 2.36 SnTe (𝑅3π‘š) 4.18 GeTe (𝑅3π‘š) 4.36 SnTe (πΉπ‘šΰ΄€ 3π‘š) 5.01 Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 10

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Group velocities vs. lifetimes 𝜿latt β‰ˆ 𝜏CRTA Γ— 1 𝑁𝑉 ෍ πœ† πœΏπœ† πœπœ† = 1 𝑁𝑉 ෍ πœ† πΆπœ† π’—πœ† βŠ— π’—πœ† Γ— 𝜏CRTA Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 11

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Group velocities vs. lifetimes 𝜿latt β‰ˆ 𝜏CRTA Γ— 1 𝑁𝑉 ෍ πœ† πœΏπœ† πœπœ† = 1 𝑁𝑉 ෍ πœ† πΆπœ† π’—πœ† βŠ— π’—πœ† Γ— 𝜏CRTA Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 12

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Group velocities vs. lifetimes πœ…π₯𝐚𝐭𝐭 [W m-1 K-1] Ξ€ πœ…π₯𝐚𝐭𝐭 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] SnTe (π‘ƒπ‘›π‘šπ‘Ž) 1.09 0.27 3.98 GeTe (π‘ƒπ‘›π‘šπ‘Ž) 1.32 0.34 3.91 SnSe (π‘ƒπ‘›π‘šπ‘Ž) 1.36 0.35 3.89 GeSe (π‘ƒπ‘›π‘šπ‘Ž) 2.36 0.39 6.03 SnTe (𝑅3π‘š) 4.18 0.69 6.07 GeTe (𝑅3π‘š) 4.36 0.87 5.01 SnTe (πΉπ‘šΰ΄€ 3π‘š) 5.01 1.07 4.67 SnSe (πΆπ‘šπ‘π‘š) 0.96 1.09 0.88 GeTe (πΉπ‘šΰ΄€ 3π‘š) 1.67 2.99 0.56 GeSe (πΉπ‘šΰ΄€ 3π‘š) 1.57 3.29 0.48 Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 13

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Group velocities vs. lifetimes Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 14

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Group velocities vs. lifetimes πœ…π₯𝐚𝐭𝐭 [W m-1 K-1] Ξ€ πœ…π₯𝐚𝐭𝐭 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] GeSe (πΉπ‘šΰ΄€ 3π‘š) 1.57 3.29 0.48 GeTe (πΉπ‘šΰ΄€ 3π‘š) 1.67 2.99 0.56 SnSe (πΆπ‘šπ‘π‘š) 0.96 1.09 0.88 SnSe (π‘ƒπ‘›π‘šπ‘Ž) 1.36 0.35 3.89 SnTe (π‘ƒπ‘›π‘šπ‘Ž) 1.32 0.34 3.91 SnTe (𝑅3π‘š) 1.09 0.27 3.98 SnTe (πΉπ‘šΰ΄€ 3π‘š) 5.01 1.07 4.67 GeTe (𝑅3π‘š) 4.36 0.87 5.01 GeSe (π‘ƒπ‘›π‘šπ‘Ž) 2.36 0.39 6.03 SnTe (𝑅3π‘š) 4.18 0.69 6.07 Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 15

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Anharmonicity vs. β€œselection rules” Ξ“πœ† = 36πœ‹ ℏ2 ෍ πœ†β€²πœ†β€²β€² Ξ¦βˆ’πœ†πœ†β€²πœ†β€²β€² 2 Γ— { π‘›πœ†β€² + π‘›πœ†β€²β€² + 1 𝛿 πœ” βˆ’ πœ”πœ†β€² βˆ’ πœ”πœ†β€²β€² + π‘›πœ†β€² βˆ’ π‘›πœ†β€²β€² 𝛿 πœ” + πœ”πœ†β€² βˆ’ πœ”πœ†β€²β€² βˆ’ 𝛿 πœ” βˆ’ πœ”πœ†β€² + πœ”πœ†β€²β€² } Decay Collision Three-phonon interaction strength (includes conservation of momentum) Conservation of energy Togo et al., Phys. Rev. B 91, 094306 (2015) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 16

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Anharmonicity vs. β€œselection rules” 𝜏λ = 1 2πœ‹Ξ“πœ† Ξ“πœ† β‰ˆ 36πœ‹ ℏ2 𝑁2 (π’’πœ† , πœ”πœ† ) Γ— π‘ƒπœ† and Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 17

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Anharmonicity vs. β€œselection rules” π‘ƒπ‘›π‘šπ‘Ž Other phases Other phases π‘ƒπ‘›π‘šπ‘Ž 𝜏λ = 1 2πœ‹Ξ“πœ† Ξ“πœ† β‰ˆ 36πœ‹ ℏ2 𝑁2 (π’’πœ† , πœ”πœ† ) Γ— π‘ƒπœ† and Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 18

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Anharmonicity vs. β€œselection rules” 𝝉𝐂𝐑𝐓𝐀 [ps] ΰ·© 𝑷 Γ— πŸ‘π’π’‚ 𝟐 [eV2] Ξ€ ΰ·© π‘΅πŸ πŸ‘π’π’‚ 𝟐 [THz-1] SnTe (π‘ƒπ‘›π‘šπ‘Ž) 3.98 9.07 Γ— 10-9 1.70 Γ— 10-2 SnSe (π‘ƒπ‘›π‘šπ‘Ž) 3.89 1.20 Γ— 10-8 1.31 Γ— 10-2 GeTe (π‘ƒπ‘›π‘šπ‘Ž) 3.91 1.35 Γ— 10-8 1.15 Γ— 10-2 GeSe (π‘ƒπ‘›π‘šπ‘Ž) 6.03 1.36 Γ— 10-8 7.44 Γ— 10-3 SnTe (𝑅3π‘š) 6.07 5.20 Γ— 10-8 1.93 Γ— 10-3 GeTe (𝑅3π‘š) 5.01 8.97 Γ— 10-8 1.36 Γ— 10-3 SnTe (πΉπ‘šΰ΄€ 3π‘š) 4.67 1.09 Γ— 10-7 1.20 Γ— 10-3 SnSe (πΆπ‘šπ‘π‘š) 0.88 1.46 Γ— 10-7 4.74 Γ— 10-3 GeTe (πΉπ‘šΰ΄€ 3π‘š) 0.56 1.31 Γ— 10-6 8.35 Γ— 10-4 GeSe (πΉπ‘šΰ΄€ 3π‘š) 0.48 2.24 Γ— 10-6 5.69 Γ— 10-4 Calculate an averaged number of scattering pathways from 𝜏CRTA and ΰ·¨ 𝑃: ΰ·© 𝑁2 = ℏ2 72πœ‹2 ΰ·¨ π‘ƒπœCRTA Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 19

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Trends in structure type π‘ƒπ‘›π‘šπ‘Ž πΆπ‘šπ‘π‘š 𝑅3π‘š πΉπ‘šΰ΄€ 3π‘š Lower 𝒗λ : smaller Ξ€ πœ…latt 𝜏CRTA Stronger anharmonicity: larger ΰ·¨ 𝑃 β†’ shorter 𝜏CRTA More allowed scattering pathways: larger ΰ·© 𝑁2 β†’ shorter 𝜏CRTA Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 20

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Interpretation: group velocities Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Walsh et al., Chem. Soc. Rev. 40, 4455 (2011) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 21

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Trends in structure type πΆπ‘šπ‘π‘š SnSe: ? Low symmetry οƒΌ Large(-ish) cell (π‘›π‘Ž = 4) οƒΌ Sn constrained to a locally-symmetric environment πœ‹-cubic SnSe: ? High symmetry οƒΌ (Very) large cell (π‘›π‘Ž = 64)  Sn local geometry similar to π‘ƒπ‘›π‘šπ‘Ž phase Abutbul et al., CrystEngComm 18, 1918 (2016) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 22

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𝝅-cubic SnSe Zhang et al., in prep. Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 23

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An ab initio modelling workflow Crystal structure Convergence testing Geometry optimisation Phonon calculation πœ…latt Electronic structure 𝑆, 𝜎, πœ…el 𝑍𝑇 = 𝑆2Οƒ πœ…el + πœ…latt 𝑇 Scattering rates: DP, πœ€βˆž , π‘βˆ—, 𝐢𝑖𝑗 Part 1 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 24 Part 2

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Modelling electrical properties Ganose et al., Nature Comm. 12, 2222 (2021) We first define the spectral conductivity tensor: Σ𝛼𝛽 πœ–, 𝑇 = 1 8πœ‹3 ෍ 𝑗 ΰΆ± π‘£π’Œπ‘—,𝛼 π‘£π’Œπ‘—,𝛽 πœπ’Œπ‘— 𝑇 𝛿 πœ– βˆ’ πœ–π’Œπ‘— π‘‘π’Œ This is used to calculate the 𝑛th-order moments of the generalised transport coefficients: ℒ𝛼𝛽 𝑛 πœ–F , 𝑇 = ΰΆ± Σ𝛼𝛽 πœ–, 𝑇 πœ– βˆ’ πœ–F 𝑛 βˆ’ πœ•π‘“ πœ–, πœ–F , 𝑇 πœ•πœ– πœ•πœ– 𝑓 πœ–, πœ–F , 𝑇 = 1 exp Ξ€ πœ– βˆ’ πœ–F π‘˜B 𝑇 + 1 Where: o The π’—π’Œπ‘— are obtained from a high-quality band structure o The πœπ’Œπ‘— can be: treated as a constant 𝜏el ; approximated by model equations for different scattering processes; or calculated from the electron-phonon coupling o The πœ–F (= πœ‡) is set by the DoS and a specified extrinsic carrier concentration 𝑛 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 25

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Modelling electrical properties The 𝓛𝑛(πœ–F , 𝑇) are determined from a band structure, a model for the πœπ‘—π’Œ , and a specified 𝑛/𝑇: ℒ𝛼𝛽 𝑛 πœ–F , 𝑇 = ΰΆ± Σ𝛼𝛽 πœ–, 𝑇 πœ– βˆ’ πœ–F 𝑛 βˆ’ πœ•π‘“ πœ–, πœ–F , 𝑇 πœ•πœ– πœ•πœ– The electrical transport coefficients can be determined from the 𝓛𝑛(πœ–F , 𝑇) as: πœŽπ›Όπ›½ (πœ–F , 𝑇) = ℒ𝛼𝛽 0 (πœ–F , 𝑇) 𝑆𝛼𝛽 (πœ–F , 𝑇) = 1 𝑒𝑇 ℒ𝛼𝛽 1 (πœ–F , 𝑇) β„’ 𝛼𝛽 0 (πœ–F , 𝑇) πœ…el,𝛼𝛽 (πœ–F , 𝑇) = 1 𝑒2𝑇 ℒ𝛼𝛽 1 (πœ–F , 𝑇) 2 β„’ 𝛼𝛽 0 (πœ–F , 𝑇) βˆ’ ℒ𝛼𝛽 2 (πœ–F , 𝑇) Note that when using the CRTA (i.e. πœπ’Œπ‘— β†’ 𝜏el ): o The 𝑺 are the ratio of two 𝓛𝑛 and the 𝜏el cancel o The 𝝈 and 𝜿el are obtained with respect to 𝜏el (𝜏el ~ 10-14 s) Ganose et al., Nature Comm. 12, 2222 (2021) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 26

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Modelling electrical properties Flitcroft et al., Solids 3 (1), 155 (2022) Fixed 𝑇 = 800 K Fixed π‘›β„Ž = 1019 cm-3 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 27

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Oxychalcogenides: Bi2 ChO2 𝒂 [Γ…] 𝒃 [Γ…] 𝒄 [Γ…] 𝑽 [Γ…3] Bi2 SO2 3.81 3.81 11.90 173 Expt 3.87 3.84 11.92 177 Bi2 SeO2 3.87 3.87 12.12 182 Expt 3.88 3.88 12.21 184 Bi2 TeO2 3.96 3.96 12.68 199 Expt 3.98 3.98 12.70 201 Koyama et al., Acta Cryst. B 40, 105 (1984) Zhan et al., J. Am. Ceram. Soc. 98, 2465 (2015) Luu and Vaqueiro, J. Solid State Chem. 226, 219 (2015) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 28

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Lattice thermal conductivity 𝑇 [K] πœ…(Calc.) [Wm-1K-1] πœ…(Expt.) [Wm-1K-1] Bi2 SO2 300 2.62 2.9 Bi2 SeO2 800 0.97 0.71 Bi2 TeO2 300 0.95 0.91 Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Zhang et al., J. Mater. Chem. C 7, 14986 (2019) Pan et al., Nano Energy 69, 104394 (2020) Luu and Vaqueiro, J. Solid State Chen. 226, 219 (2015) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 29

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Electronic structure Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Pacquette et al., J. Photochem. Photobiol. A 277, 27 (2014) Tan et al., J. Am. Ceram. Soc. 101, 326 (2018) Luu and Vaqueiro, J. Solid State Chem. 226, 219 (2015) Bi2 SO2 : 𝐸g (Calc.) = 1.46 eV 𝐸g (Expt) = 1.5 eV Bi2 SeO2 : 𝐸g (Calc.) = 1.1 eV 𝐸g (Expt) = 1.77 eV Bi2 TeO2 : 𝐸g (Calc.) = 0.33 eV 𝐸g (Expt) = 0.23 eV Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 30

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Electrical transport Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 31

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Comparison to experiments Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 32

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Comparison to experiments Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 33

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Comparison to experiments Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) 𝑇 = 300 K 𝑇 = 800 K Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 34

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Predicted 𝒁𝑻 Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 35

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Predicted 𝒁𝑻 𝒁𝑻 𝒏 [cm-3] 𝑻 [K] 𝝈 [S cm-1] 𝑺 [Β΅V K-1] π‘ΊπŸπˆ [mW m-1 K-2] 𝜿𝐞π₯ [W m-1 K-1] 𝜿π₯𝐚𝐭𝐭 [W m-1 K-1] 𝜿𝐭𝐨𝐭 [W m-1 K-1] Bi2 SO2 (n) 0.33 2.5Γ—1019 900 120 -186 0.41 0.23 0.9 1.13 Bi2 SO2 (p) 0.72 4Γ—1019 900 24.7 545 0.73 2.63Γ—10-2 0.92 2.53 8Γ—1020 900 495 287 4.08 0.55 1.45 Bi2 SeO2 (n) 0.45 2.5Γ—1019 900 193 -180 0.62 0.39 0.87 1.25 Bi2 SeO2 (p) 1.12 5Γ—1019 900 44.4 512 1.16 6.56 Γ—10-2 0.93 2.62 5Γ—1020 900 436 318 4.41 0.65 1.51 Bi2 TeO2 (n) 1.05 5Γ—1019 900 554 -184 1.87 1.28 0.33 1.61 Bi2 TeO2 (p) 1.36 5Γ—1019 540 340 250 2.13 0.31 0.54 0.85 1.51 1020 640 538 213 2.45 0.58 0.46 1.04 𝑍𝑇max = 0.38 reported for n-type (Bi1.9 Ta0.1 )SeO2 @ 𝑛 = 2.1Γ—1019 + 𝑇 = 773 K 𝑍𝑇max = 0.13 reported for n-type Bi2 TeO2 @ 𝑛 = 1.1Γ—1019 cm-3 + 𝑇 = 573 K Tan et al., Adv. Energy Mater. 9, 1900354 (2019) Luu and Vaqueiro, J. Solid State Chem. 226, 219 (2015) Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 36

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Electrical properties of 𝝅-SnSe Zhang et al., in prep. Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 37

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𝒁𝑻 of 𝝅-SnSe Zhang et al., in prep. 𝒁𝑻 𝒏 [cm-3] 𝑻 [K] 𝝈 [S cm-1] 𝑺 [Β΅V K-1] π‘ΊπŸπˆ [mW m-1 K-2] 𝜿𝐞π₯ [W m-1 K-1] 𝜿π₯𝐚𝐭𝐭 [W m-1 K-1] 𝜿𝐭𝐨𝐭 [W m-1 K-1] Pnma (p) 2.07 3.16 Γ—1019 740 399 272 2.96 0.42 0.64 1.06 πœ‹-cubic (n) 2.83 1020 740 183 -355 2.31 0.25 0.36 0.61 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 38

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Summary High-performance thermoelectrics require a balance of a 𝑆 and 𝜎 and low πœ… = πœ…latt + πœ…el The πœ…latt can be modelled using the single-mode relaxation-time approximation: o Provides microscopic insight at the level of individual phonon modes o Analysis procedure to determine how differences in π‘£πœ† , πœπœ† , ΰ·¨ 𝑃 and ΰ·© 𝑁2 underpin differences in πœ…latt between materials o πœ…latt of flagship IV-VI chalcogenide TEs is a balance of inhomogeneous chemical bonding and anharmonicity introduced by tetrel lone pair activity The 𝑆, 𝜎 and πœ…el calculated from electronic-structure calculations and approximate models for the 𝜏el : o Reproduce experiments reasonably well, taking into account sample variation o Can be used to explore p- and n-type doping over a wide range of carrier concentrations and β€œuntangle” the interdependence of the 𝑆, 𝜎, πœ…el and 𝑛 Microscopic insight from the models, and useful predictive accuracy, allow this approach to be used to identify and characterise novel TEs Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 39

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Acknowledgements ... plus other students, mentors and collaborators too numerous to mention Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 40

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These slides are available on Speaker Deck: https://bit.ly/3xvfaaj