Predicting thermoelectric performance using first-principles modelling

Presented at the Graphene Engineering and Innovation Centre at the University of Manchester on 14th July 2025.

Transcript

1. Dr Jonathan Skelton Department of Chemistry, University of Manchester (jonathan.skelton@manchester.ac.uk) Predicting thermoelectric performance using first-principles modelling
2. Energy efficiency Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 2 https://flowcharts.llnl.gov/sites/flowcharts/files/2024-12/energy-2023-united-states.png
3. Thermoelectric power Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 3 (a) adapted from K. Brazier via Wikimedia Commons (CC BY-SA 4.0)
4. Challenge 1: balancing 𝒁𝑻 Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 4 𝑍𝑇 = 𝑆!𝜎 𝜅"#" + 𝜅#$% 𝑇 𝑆 - Seebeck coefficient 𝜎 - electrical conductivity 𝜅!"! - electronic thermal conductivity 𝜅"#$ - lattice thermal conductivity Based on data from Flitcroft et al., Solids 3 (1), 155 (2022)
5. Challenge 2: low-temperature 𝒁𝑻 Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 5 A major challenge to obtaining large 𝑍𝑇 for low-grade heat recovery is the 𝜅"#$$ : current industry-standard Bi2 Te3 is unsuitable for widespread adoption due to the scarcity of Te Turek et al., Energies 17, 2084 (2024) Freer et al., J. Phys: Energy 4, 022002 (2022) WHP / PWh 𝑇 < 100 °C 0.66 (51.1%) 𝑇 = 100-300 °C 0.25 (19%) 𝑇 > 300 °C 0.39 (29.9%) Total 1.29
6. An ab initio modelling workflow Crystal structure Convergence testing Geometry optimisation Phonon calculation 𝜅!"## Electronic structure 𝑆, 𝜎, 𝜅$! 𝑍𝑇 = 𝑆%σ 𝜅$! + 𝜅!"## 𝑇 Scattering rates: DP, 𝜔&' , 𝜀( , 𝑍∗, 𝐶, 𝑒(+) Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 6
7. Modelling thermal conductivity The simplest model for 𝜅"#$$ is the single-mode relaxation time approximation (SM-RTA) - a closed solution to the phonon Boltzmann transport equations 𝜿!"## (𝑇) = 1 𝑁𝑉 ) $ 𝐶$ (𝑇)𝒗$ ⊗ 𝒗$ 𝜏$ (𝑇) 𝐶% - phonon heat capacities 𝒗% - phonon group velocities 𝜏% - phonon lifetimes (inverse linewidths Γ% ) 𝑁 - number of 𝒒 in summation 𝑉 - unit cell volume Togo et al., Phys. Rev. B 91, 094306 (2015) Tang and Skelton, J. Phys: Condens. Matter 33 (16), 164002 (2020) Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 7
8. Modelling electrical properties Ganose et al., Nature Comm. 12, 2222 (2021) We first define the spectral conductivity tensor: Σ&' 𝜖, 𝑇 = 1 8𝜋( 4 ) 5 𝑣𝒌),& 𝑣𝒌),' 𝜏𝒌) 𝑇 𝛿 𝜖 − 𝜖𝒌) 𝑑𝒌 This is used to calculate the 𝑛th-order moments of the generalised transport coefficients: ℒ&' , 𝜖- , 𝑇 = 5 Σ&' 𝜖, 𝑇 𝜖 − 𝜖- , − 𝜕𝑓 𝜖, 𝜖- , 𝑇 𝜕𝜖 𝜕𝜖 𝑓 𝜖, 𝜖- , 𝑇 = 1 exp ⁄ 𝜖 − 𝜖- 𝑘. 𝑇 + 1 Where: o The 𝒗𝒌) are obtained from a high-quality band structure o The 𝜏𝒌) can be: treated as a constant 𝜏!" ; approximated by model equations for different scattering processes; or calculated from the electron-phonon coupling o The 𝜖- (= 𝜇) is set by the DoS and a specified extrinsic carrier concentration 𝑛 Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 8
9. Modelling electrical properties The 𝓛,(𝜖- , 𝑇) are determined from a band structure, a model for the 𝜏)𝒌 , and a specified 𝑛/𝑇: ℒ&' , 𝜖- , 𝑇 = 5 Σ&' 𝜖, 𝑇 𝜖 − 𝜖- , − 𝜕𝑓 𝜖, 𝜖- , 𝑇 𝜕𝜖 𝜕𝜖 The electrical transport coefficients can be determined from the 𝓛,(𝜖- , 𝑇) as: 𝜎&' (𝜖- , 𝑇) = ℒ&' / (𝜖- , 𝑇) 𝑆&' (𝜖- , 𝑇) = 1 𝑒𝑇 ℒ&' 0 (𝜖- , 𝑇) ℒ&' / (𝜖- , 𝑇) 𝜅!",&' (𝜖- , 𝑇) = 1 𝑒1𝑇 ℒ&' 0 (𝜖- , 𝑇) 1 ℒ&' / (𝜖- , 𝑇) − ℒ&' 1 (𝜖- , 𝑇) Note that when using the CRTA (i.e. 𝜏𝒌) → 𝜏!" ): o The 𝑺 are the ratio of two 𝓛, and the 𝜏!" cancel o The 𝝈 and 𝜿!" are obtained with respect to 𝜏!" (𝜏!" ~ 10-14 s) Ganose et al., Nature Comm. 12, 2222 (2021) Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 9
10. 𝑷𝒏𝒎𝒂 SnCh: Electrical properties Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 10 Flitcroft et al., Solids 3 (1), 155 (2022) Fixed 𝑇 = 800 K Fixed 𝑛2 = 1019 cm-3
11. Bi2 ChO2 : Electrical properties Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) 𝑇 = 300 K 𝑇 = 800 K Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 11
12. Bi2 ChO2 : Figure of merit 𝒁𝑻 Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton MCC Conference, 5th July 2024 | Slide 12
13. 𝜿𝐥𝐚𝐭𝐭 and crystal structure Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 13 𝑃𝑛𝑚𝑎 𝐶𝑚𝑐𝑚 𝑅3𝑚 𝐹𝑚5 3𝑚 Lower 𝒗3 : smaller ⁄ 𝜅"#$$ 𝜏4567 Stronger anharmonicity: larger O 𝑃 → shorter 𝜏4567 Larger scattering phase space: larger Q 𝑁1 → shorter 𝜏4567 Guillemot et al., J. Mater. Chem. A 12, 2932 (2024)
14. “𝝅”-cubic SnCh Zhang et al., J. Mater. Chem. A 13, 5415 (2025) Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 14
15. “𝝅”-cubic SnCh Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 15 Zhang et al., J. Mater. Chem. A 13, 5415 (2025)
16. Summary Reducing energy waste is a key part of a coordinated response to climate change - given the right materials, thermoelectric power is ideally positioned to address this challenge There are two major challenges to materials discovery and optimisation: o Balancing the charge-carrier concentration to optimise the electrical properties o Minimising the 𝜅"#$$ , particularly at low temperature First-principles modelling can predict the electrical/thermal transport properties and the figure of merit 𝑍𝑇 with sufficient accuracy to: o Estimate the ”ballpark” n required to obtain the best performance o Define an operating 𝑇 and scope potential application areas This capability should improve in the near future with explicit electron-phonon coupling and more routine defect modelling One of our main interests is how to extract chemical insight – e.g. structure/property relationships – from the calculations to guide future materials discovery Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 16
17. Acknowledgements ... plus other students, mentors and collaborators too numerous to mention Dr J. M. Skelton GEIC Seminar, 14th July 2025 | Slide 17
18. These slides are available on Speaker Deck: https://bit.ly/4nLjvLN