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Theory-Led Control of Heat Transport in Thermoelectric Materials

Theory-Led Control of Heat Transport in Thermoelectric Materials

Presented at the International Conference on Frontier Materials (IFCM) 2022.

Jonathan Skelton

May 30, 2022
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  1. Dr Jonathan 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 ICFM 2022, 30th May 2022 |

    Slide 2 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) Dr Jonathan Skelton
  3. Thermoelectric materials Dr Jonathan Skelton 𝑍𝑇 = 𝑆!𝜎 𝜅"#" +

    𝜅#$% 𝑇 𝑆 - Seebeck coefficient 𝜎 - electrical conductivity 𝜅!"! - electronic thermal conductivity 𝜅"#$ - lattice thermal conductivity G. Tan et al., Chem. Rev. 116 (19), 12123 (2016) ICFM 2022, 30th May 2022 | Slide 3
  4. Lattice thermal conductivity Phonons are generated at the hot side

    of the material and transport energy to the cold side Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 4
  5. Modelling thermal conductivity A. Togo et al., Phys. Rev. B

    91, 094306 (2015) 𝜿#$%% (𝑇) = 1 𝑁𝑉& . ' 𝐶'(𝑇)𝒗' ⊗ 𝒗'𝜏'(𝑇) Dr Jonathan Skelton The simplest model for 𝜅"#$$ is the single-mode relaxation time approximation (SM-RTA) - a closed solution to the phonon Boltzmann transport equations Modal heat capacity Mode group velocity 𝜕𝜔% 𝜕𝐪 Average over phonon modes λ Phonon MFP Mode lifetime 𝜏% = 1 2Γ% 𝚲& 𝑇 = 𝒗& 𝜏& 𝑇 ICFM 2022, 30th May 2022 | Slide 5
  6. Modelling thermal conductivity Dr Jonathan Skelton ICFM 2022, 30th May

    2022 | Slide 6
  7. Modelling thermal conductivity A. Togo et al., Phys. Rev. B

    91, 094306 (2015) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 7
  8. Phonon glass electron crystal 𝑍𝑇 = 𝑆!𝜎 𝜅"#" + 𝜅#$%

    𝑇 𝑆 - Seebeck coefficient 𝜎 - electrical conductivity 𝜅"#$ - lattice thermal conductivity 𝜅!"! - electronic thermal conductivity Phonon scattering by “rattler” filler atoms Electron transport through crystalline host framework G. A. Slack in CRC Handbook of Thermoelectrics (1995) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 8
  9. Filled Skutterudites Composition 𝒁𝑻 CoSb3 0.05 (773 K) Ni0.3 Co3.7

    Sb12 0.52 (773 K) Na0.48 Co3 Sb12 1.25 (800 K) Sr0.16 Tb0.03 Co4 Sb11.82 1.32 (850 K) Ba0.08 La0.05 Yb0.04 Co4 Sb12 1.7 (850 K) Yb0.2 Ba0.1 Al0.1 Ga0.1 In0.1 La0.05 Eu0.05 Co4 Sb12 1.2 (800 K) Ce0.12 Fe0.71 Co3.29 Sb12 0.8 (750 K) D. T. Morelli et al., Phys. Rev. B 51, 9622 (1995) Y. Lei et al., J. Mater. Sci. Mater. Electron. 30, 5929 (2019) Y. Z. Pei et al., Appl. Phys. Lett. 95, 042101 (2009) S. Q. Bai et al., Appl. Phys. A 100, 1109 (2010) X. Shi et al., J. Am. Chem. Soc. 133, 7837 (2011) S. Zhang et al., J. Alloys Compd. 814, 152272 (2020) X. F. Tang et al., J. Mater. Sci. 36, 5435 (2001) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 9
  10. 𝜿𝐥𝐚𝐭𝐭 of pristine CoSb3 J. Tang and J. M. Skelton,

    J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 10
  11. A “toy model” for filled CoSb3 Filler 𝒎𝐗 [amu] 𝒓𝐗

    [pm] He 4.0026 31 Ne 20.180 38 Ar 39.948 71 Kr 83.798 88 Xe 131.29 108 Noble gases are chemically inert (closed shell, unlikely to reduce/oxidise host framework) and are likely closest it is possible to get to a “hard sphere” filler J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 11
  12. 𝜿𝐥𝐚𝐭𝐭 of filled XCo8 Sb24 Filler 𝜅𝐥𝐚𝐭𝐭 (𝑇 = 300

    K) [W m-1 K-1] - 9.98 He 9.11 (-9 %) Ne 8.86 (-11 %) Ar 9.17 (-8 %) Kr 8.77 (-12 %) Xe 8.49 (-15 %) J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 12
  13. How do the fillers suppress 𝜿𝐥𝐚𝐭𝐭 ? Consider again the

    SM-RTA model for 𝜿"#$$ : 𝜿"#$$ (𝑇) = 1 𝑁𝑉+ ; & 𝐶& (𝑇)𝒗& ⊗ 𝒗& 𝜏& (𝑇) Two mechanisms through which rattlers can affect 𝜅"#$$ : 1. Reduction of 𝑣& - avoided crossings 2. Reduction of 𝜏& - resonant scattering These are not necessarily mutually exclusive - both can be active in the same material E. S. Toberer et al., J. Mater. Chem. 21 (40), 15843 (2011) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 13
  14. 𝒗6 vs. 𝜏6 : the CRTA model Consider again the

    SM-RTA model: 𝜿"#$$ = 1 𝑁𝑉+ ; & 𝜿& = 1 𝑁𝑉+ ; & 𝐶& 𝒗& ⊗ 𝒗& 𝜏& Replace the 𝜏& with a constant lifetime (relaxation time) 𝜏,-./ defined as follows: 𝜿"#$$ 𝜏,-./ = 1 𝑁𝑉+ ; & 𝜿& 𝜏& = 1 𝑁𝑉+ ; & 𝐶& 𝒗& ⊗ 𝒗& 𝜿"#$$ ≈ 1 𝑁𝑉+ ; & 𝐶& 𝒗& ⊗ 𝒗& ×𝜏,-./ HA AH HA AH J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 14
  15. 𝒗6 vs. 𝜏6 : the CRTA model Replace the 𝜏&

    with a constant lifetime (relaxation time) 𝜏,-./ defined as follows: 𝜿"#$$ ≈ 1 𝑁𝑉+ ; & 𝐶& 𝒗& ⊗ 𝒗& ×𝜏,-./ J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 15
  16. Tuning the filler mass We can define a rattling frequency

    @ 𝑓0 for the noble gas fillers X based on the 𝑫 XX, 𝐪 = Γ : 𝑫 XX, 𝐪 = Γ = 1 𝑚1 ; 2! 𝚽 X0, X𝑙3 What happens to 𝜅"#$$ if we artificially change the 𝑚1 while keeping the 𝚽 fixed? J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 16
  17. Tuning the filler mass Lowering the @ 𝑓1 into the

    acoustic region reduces the 𝜏% and the group velocities → considerably larger reduction of 𝜅"#$$ J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 17
  18. Whalley et al., Phys. Rev. B 94, 220301(R) (2016) Gold-Parker

    et al., PNAS 115, 11905 (2018) Intrinsic anharmonicity: MAPbI3 Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 18
  19. Intrinsic anharmonicity: MAPbI3 Dr Jonathan Skelton A. Gold-Parker et al.,

    PNAS 115 (47), 11905 (2018) GaAs MAPbI3 ICFM 2022, 30th May 2022 | Slide 19
  20. The phonon lifetime 𝝉𝝀 Γ! = # !4!44 Φ"!!4!44 #×{

    𝑛!4 + 𝑛!44 + 1 𝛿 𝜔 − 𝜔!4 − 𝜔!44 + 𝑛!4 − 𝑛!44 𝛿 𝜔 + 𝜔!4 − 𝜔!44 − 𝛿 𝜔 − 𝜔!4 + 𝜔!44 } Decay Collision Three-phonon interaction strength (includes conservation of momentum) Conservation of energy Dr Jonathan Skelton A. Togo et al., Phys. Rev. B 91, 094306 (2015) ICFM 2022, 30th May 2022 | Slide 20
  21. Dr Jonathan Skelton A. Gold-Parker et al., PNAS 115 (47),

    11905 (2018) GaAs MAPbI3 𝑃! = 1 3𝑛$ # # !4!44 Φ!!4!44 # ICFM 2022, 30th May 2022 | Slide 21 MAPbI3 : phonon scattering
  22. MAPbI3 : phonon scattering Dr Jonathan Skelton ICFM 2022, 30th

    May 2022 | Slide 22
  23. MAPbI3 : phonon scattering A. Gold-Parker et al., PNAS 115

    (47), 11905 (2018) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 23
  24. Alloy TEs: SnSe L.-D. Zhao et al., Nature 508, 373

    (2014) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 24
  25. Alloy TEs: Sn(S1-x Sex ) C.-C. Lin et al., Chem.

    Mater. 29 (12), 5344 (2017) SnSe 15-20 % S Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 25
  26. Sn(S0.1875 Se0.8125 ): model J. M. Skelton, J. Mater. Chem.

    C 9, 11772 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 26
  27. Sn(S0.1875 Se0.8125 ): phonon spectrum SnS SnSe J. M. Skelton,

    J. Mater. Chem. C 9, 11772 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 27
  28. Sn(S0.1875 Se0.8125 ): phonon spectrum J. M. Skelton, J. Mater.

    Chem. C 9, 11772 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 28
  29. Sn(S0.1875 Se0.8125 ): 𝜿𝐥𝐚𝐭𝐭 54.2 % ↓ Sn(S0.1875 Se0.8125 )

    SnSe J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 29
  30. Optimising the 𝜿𝐥𝐚𝐭𝐭 in TEs 𝜅 [W m-1 K-1] ⁄

    𝜅 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] Si 136.24 5.002 27.24 SnS 2.15 0.718 3.00 SnSe 1.58 0.372 4.23 Sn(S0.1875 Se0.8125 ) 0.62 0.173 4.03 (est.) CoSb3 9.98 0.273 36.6 XeCo8 Sb24 8.49 0.239 35.6 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) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 30
  31. Summary Dr Jonathan Skelton The lattice thermal conductivity 𝜅"#$$ in

    thermoelectric materials can be modelled theoretically using the SM-RTA model The SM-RTA model calculates the macroscopic 𝜅"#$$ as a sum of microscopic contributions from individual phonon modes, which provides a large amount of insight into how 𝜅"#$$ “works” In CoSb3 , the filler “rattling frequency” depends on its mass and how strongly it interacts with the cage - calculations show that tuning this to around 1.5 THz can significantly reduce the 𝜅"#$$ through a combination of avoided crossings and resonant scattering In MAPbI3 , the ultra-low 𝜅"#$$ is due to very short phonon lifetimes, on the order of ps, which can be attributed to the phonon scattering introduced by the interaction of the MA+ cation with the PbI3 - framework In Sn(S0.1875 Se0.8125 ), alloying at the chalcogen site leads to a ~60 % reduction in the 𝜅"#$$ , which can be attributed to a “smearing out” of the dispersion reducing the group velocities Using the CRTA model to decompose the 𝜅"#$$ into a product of harmonic (group velocity) and lifetime terms can provide insight into what sort of engineering methods are appropriate for optimising the 𝜅"#$$ of current and new TEs ICFM 2022, 30th May 2022 | Slide 31
  32. Acknowledgements ... plus mentors and collaborators too numerous to mention

    Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 32
  33. https://bit.ly/3aoC7jv These slides are available on Speaker Deck: