Theory-Led Control of Heat Transport in Thermoelectric Materials

Presented at the Future Leaders Network for Nanoscale Energy Harvesting incubator event.

Transcript

1. J. M. Skelton Department of Chemistry, University of Manchester (jonathan.skelton@manchester.ac.uk) Theory-Led Control of Heat Transport in Thermoelectric Materials
2. The global energy challenge Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 2 Dr Jonathan M. Skelton 34 % 26 % 19 % 18 % 3 % 1000 MW nuclear power plant: o 650 MW waste heat o 3 % ≈ 20 MW ≈ 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 June 2020) 2. EPSRC Thermoelectric Network Roadmap (2018)
3. Thermoelectric materials Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 3 Dr Jonathan M. Skelton 𝑍𝑇 = 𝑆2𝜎 𝜅ele + 𝜅lat 𝑇 𝑆 - Seebeck coefficient 𝜎 - electrical conductivity 𝜅ele - electronic thermal conductivity 𝜅lat - lattice thermal conductivity G. Tan et al., Chem. Rev. 116 (19), 12123 (2016)
4. Acknowledgements CMD29, 23rd August 2022 | Slide 4 Dr Jonathan M. Skelton ... plus mentors and collaborators too numerous to mention
5. Modelling thermal conductivity Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 5 Dr Jonathan M. Skelton A. Togo et al., Phys. Rev. B 91, 094306 (2015) 𝜿latt (𝑇) = 1 𝑁𝑉0 ෍ 𝜆 𝜿𝜆 (𝑇) 1 𝑁𝑉0 ෍ 𝜆 𝐶𝜆 (𝑇)𝒗𝜆 ⊗ 𝒗𝜆 𝜏𝜆 (𝑇) The simplest model for 𝜅latt is the single-mode relaxation time approximation (SM-RTA) - a closed solution to the phonon Boltzmann transport equations Modal heat capacity Mode group velocity 𝜕𝜔λ 𝜕𝐪 Average over phonon modes λ Phonon MFP Mode lifetime 𝜏λ = 1 2Γλ 𝚲𝜆 𝑇 = 𝒗𝜆 𝜏𝜆 𝑇
6. Modelling thermal conductivity Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 6 Dr Jonathan M. Skelton A. Togo et al., Phys. Rev. B 91, 094306 (2015) J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) CoSb3
7. Modelling thermal conductivity Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 7 Dr Jonathan M. Skelton J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021)
8. Modelling thermal conductivity Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 8 Dr Jonathan M. Skelton A. Gold-Parker et al., PNAS 115 (47), 11905 (2018) GaAs MAPbI3
9. Modelling thermal conductivity Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 9 Dr Jonathan M. Skelton CoSb3 CoSb3 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021)
10. Modelling thermal conductivity Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 10 Dr Jonathan M. Skelton CoSb3 CoSb3 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021)
11. 𝒗𝜆 vs. 𝜏𝜆 : the CRTA model Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 11 Dr Jonathan M. Skelton Consider again the SM-RTA model: 𝜿latt = 1 𝑁𝑉0 ෍ 𝜆 𝜿𝜆 = 1 𝑁𝑉0 ෍ 𝜆 𝐶𝜆 𝒗𝜆 ⊗ 𝒗𝜆 𝜏𝜆 Replace the 𝜏𝜆 with a constant lifetime (relaxation time) 𝜏CRTA defined as follows: 𝜿latt 𝜏CRTA = 1 𝑁𝑉0 ෍ 𝜆 𝜿𝜆 𝜏𝜆 = 1 𝑁𝑉0 ෍ 𝜆 𝐶𝜆 𝒗𝜆 ⊗ 𝒗𝜆 𝜿latt ≈ 1 𝑁𝑉0 ෍ 𝜆 𝐶𝜆 𝒗𝜆 ⊗ 𝒗𝜆 × 𝜏CRTA HA AH HA AH J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021)
12. 𝒗𝜆 vs. 𝜏𝜆 : Si clathrates Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 12 Dr Jonathan M. Skelton B. Wei et al., in preparation
13. 𝒗𝜆 vs. 𝜏𝜆 : Si clathrates Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 13 Dr Jonathan M. Skelton B. Wei et al., in preparation 𝜿latt ≈ 1 𝑁𝑉0 ෍ 𝜆 𝐶𝜆 𝒗𝜆 ⊗ 𝒗𝜆 × 𝜏CRTA
14. 𝒗𝜆 vs. 𝜏𝜆 : Si clathrates Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 14 Dr Jonathan M. Skelton 𝜿 (W m-1 K-1) Τ 𝜿 𝝉𝐂𝐑𝐓𝐀 (W m-1 K-1 ps-1) 𝝉𝐂𝐑𝐓𝐀 (ps) d-Si 136.24 5.002 27.24 oC24 40.92 2.295 17.83 K-II / C-I 43.54 0.829 52.52 K-V / C-VI 36.29 0.815 44.53 K-VII / C-V 31.16 0.770 40.45 C-II 6.33 0.458 13.81 Spacegroup 𝒏𝐚 𝐹𝑑ത 3𝑚 2 𝐶𝑚𝑐𝑚 12 𝑃𝑚ത 3𝑚 46 𝐶𝑚𝑚𝑚 40 𝑃63 /𝑚𝑚𝑐 68 𝐹𝑑ത 3𝑚 34 With the exception of the Clathrate-II structure, the harmonic Τ 𝜿 𝜏CRTA term correlates with: (1) the size of the primitive cell (𝑛a ); and (2) the spacegroup (crystal symmetry) Implies low group velocities are favoured by complex structures with large primitive cells and/or low symmetry B. Wei et al., in preparation
15. Analysing 𝜏𝜆 : phonon linewidths Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 15 Dr Jonathan M. Skelton Γ𝜆 (𝑇) = ෍ 𝜆′𝜆′′ Φ−𝜆𝜆′𝜆′′ 2 × { 𝑛𝜆′ (𝑇) − 𝑛𝜆′′ (𝑇) 𝛿 𝜔 + 𝜔𝜆′ − 𝜔𝜆′′ − 𝛿 𝜔 − 𝜔𝜆′ + 𝜔𝜆′′ + 𝑛𝜆′ (𝑇) + 𝑛𝜆′′ (𝑇) + 1 𝛿 𝜔 − 𝜔𝜆′ − 𝜔𝜆′′ } Collision Decay Three-phonon interaction strength - includes conservation of momentum(“anharmonicity”) Conservation of energy (“selection rules”) A. Togo et al., Phys. Rev. B 91, 094306 (2015)
16. Analysing 𝜏𝜆 : phonon linewidths Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 16 Dr Jonathan M. Skelton A. Togo et al., Phys. Rev. B 91, 094306 (2015) Approximate expression for Γ𝜆 : With: Γ𝜆 (𝑇) ≈ 18𝜋 ℏ2 ෨ 𝑃𝑁2 (𝒒𝜆 , 𝜔𝜆 , 𝑇) 𝑁2 𝒒𝜆 , 𝜔𝜆 , 𝑇 = 𝑁 2 (1) 𝒒𝜆 , 𝜔𝜆 , 𝑇 + 𝑁 2 (2) 𝒒𝜆 , 𝜔𝜆 , 𝑇 𝑁 2 (1) 𝒒𝜆 , 𝜔𝜆 , 𝑇 = 1 𝑁 ෍ 𝜆′𝜆′′ ∆(−𝒒𝜆 + 𝒒𝜆′ + 𝒒𝜆′′ ) 𝑛𝜆′ (𝑇) − 𝑛𝜆′′ (𝑇) × 𝛿 𝜔 + 𝜔𝜆′ − 𝜔𝜆′′ − 𝛿 𝜔 − 𝜔𝜆′ + 𝜔𝜆′′ 𝑁 2 (2) 𝒒𝜆 , 𝜔𝜆 , 𝑇 = 1 𝑁 ෍ 𝜆′𝜆′′ ∆(−𝒒𝜆 + 𝒒𝜆′ + 𝒒𝜆′′ ) 𝑛𝜆′ (𝑇) + 𝑛𝜆′′ (𝑇) + 1 𝛿 𝜔 − 𝜔𝜆′ − 𝜔𝜆′′
17. Analysing 𝜏𝜆 Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 17 Dr Jonathan M. Skelton B. Wei et al., in preparation Γ𝜆 (𝑇) ≈ 18𝜋 ℏ2 ෨ 𝑃𝑁2 (𝒒𝜆 , 𝜔𝜆 , 𝑇)
18. Workflow Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 18 Dr Jonathan M. Skelton 𝜿latt (𝑇) Τ 𝜿 𝜏CRTA 𝜏CRTA ഥ 𝑁2 ෨ 𝑃 Phonopy + Phono3py A. Togo and I. Tanka, Scr. Mater. 108, 1 (2015) A. Togo et al., Phys. Rev. B 91, 094306 (2015)
19. 𝒗𝜆 vs. 𝜏𝜆 : other TEs Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 19 Dr Jonathan M. Skelton 𝜅 [W m-1 K-1] Τ 𝜅 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] Si 136.24 5.002 27.2 SnS 2.15 0.718 3.00 SnSe 1.58 0.372 4.23 CoSb3 9.98 0.273 36.6 Bi2 S3 (Pnma) 0.90 0.423 2.14 Bi2 Se3 (R-3m) 1.82 0.293 6.20 Bi2 Te3 (R-3m) 0.87 0.199 4.41 J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021) J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) J. Cen, I. Pallikara and J. M. Skelton, Chem. Mater. 33 (21), 8404 (2021) B. Wei et al., in preparation
20. Reducing 𝒗𝜆 I: alloying Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 20 Dr Jonathan M. Skelton C.-C. Lin et al., Chem. Mater. 29 (12), 5344 (2017) SnSe 15-20 % S
21. Reducing 𝒗𝜆 I: alloying Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 21 Dr Jonathan M. Skelton 54.2 % ↓ Sn(S0.1875 Se0.8125 ) SnSe J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021)
22. Reducing 𝒗𝜆 II: discordant doping Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 22 Dr Jonathan M. Skelton H. Xie et al., J. Am. Chem. Soc. 141 (47), 18900 (2019)
23. Reducing 𝜏𝜆 I: “rattler” TEs Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 23 Dr Jonathan M. Skelton Schwartz and Walker, Phys. Rev. B 155, 959 (1967) E. S. Toberer et al., J. Mater. Chem. 21, 15843 (2011) J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) “One phonon” model for resonant scattering: 𝜏−1 = ෍ 𝑖 𝑐𝑖 𝜔2𝑇2 𝜔𝑖 2 − 𝜔2 2 + 𝛾𝑖 𝜔𝑖 2𝜔2
24. Reducing 𝜏𝜆 II: hybrid TEs (?) Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 24 Dr Jonathan M. Skelton A. Gold-Parker et al., PNAS 115 (47), 11905 (2018)
25. Workflow Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 25 Dr Jonathan M. Skelton 𝜿latt (𝑇) Τ 𝜿 𝜏CRTA 𝜏CRTA ഥ 𝑁2 ෨ 𝑃 𝑺(𝑛, 𝑇) 𝝈(𝑛, 𝑇) 𝜿el (𝑛, 𝑇) Phonopy + Phono3py AMSET 𝑍𝑇(𝑛, 𝑇) A. Togo and I. Tanka, Scr. Mater. 108, 1 (2015) A. Togo et al., Phys. Rev. B 91, 094306 (2015) A. M. Ganose et al., Nature Comm. 12, 2222 (2021)
26. Predicting 𝒁𝑻 Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 26 Dr Jonathan M. Skelton J. M. Flitcroft et al., Solids 3 (1), 155 (2022)
27. Challenges and opportunities Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 27 Dr Jonathan M. Skelton D. W. Davies et al., Chem 1 (4), 617 (2016)
28. Challenges and opportunities Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 28 Dr Jonathan M. Skelton W. Rahim et al., J. Mater. Chem. A 8, 16405 (2020) W. Rahim et al., J. Mater. Chem. A 9, 20417 (2021) K. Brlec et al., J. Mater. Chem. A 10, 16813 (2022) 𝛼-Bi2 Sn2 O7 𝑛 = 1.73 × 1019 cm-3 𝑍𝑇 = 0.36 (385 K) Ca4 Sb2 O / Ca4 Bi2 O 𝑝 = 4.64 / 2.15 × 1019 cm-3 𝑍𝑇 = 1.58 / 2.14 (1000 K) Y2 Ti2 O5 S2 𝑛 = 2.37 × 1020 cm-3 𝑍𝑇 = 1.18 (1000 K)
29. Challenges and opportunities Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 29 Dr Jonathan M. Skelton
30. Challenges and opportunities Nanoscale Energy Harvesting, 24th Aug 2022 | Slide 30 Dr Jonathan M. Skelton Some questions to consider (definitely not exhaustive...): 1. Is there a “killer” application of TEs that we should target? 2. If so, what are the parameters? • Operating temperature and target 𝑍𝑇? • Target cost per device? • Constraints on elemental composition? • Constraints on synthesis/device fabrication for scale up? 3. How can theory and experiment best work together? • Is modelling in a position to provide actionable suggestions to improve 𝑍𝑇? • Would it be possible(/useful) to use modelling to screen candidates to narrow the focus of experiments? • Are existing theoretical techniques sufficient, or is more development needed (e.g. faster, cheaper, easier to use, capability to model new things ...)?
31. https://bit.ly/3AjphfB These slides are available on Speaker Deck: