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Understanding the thermal transport in Sn(S,Se) alloys for thermoelectric applications

Understanding the thermal transport in Sn(S,Se) alloys for thermoelectric applications

Presented as a keynote talk at the 2021 MISE Finale Workshop.

Jonathan Skelton

June 18, 2021
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  1. Dr Jonathan Skelton Department of Chemistry, University of Manchester (jonathan.skelton@manchester.ac.uk)

    Understanding the thermal transport in Sn(S,Se) alloys for thermoelectric applications
  2. Thermoelectrics: motivation Dr Jonathan Skelton MISE Finale Workshop June 2021

    | 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)
  3. Thermoelectrics: 𝒁𝑻 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) Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 3
  4. Thermoelectrics: SnSe Dr Jonathan Skelton MISE Finale Workshop June 2021

    | Slide 4 L.-D. Zhao et al., Nature 508, 373 (2014)
  5. Sn(S1-x Sex ): thermal conductivity Dr Jonathan Skelton MISE Finale

    Workshop June 2021 | Slide 5 C.-C. Lin et al., Chem. Mater. 29 (12), 5344 (2017) SnSe 15-20 % S
  6. Lattice thermal conductivity Phonons are generated at the hot side

    of the material and transport energy to the cold side Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 6
  7. Modelling 𝜿𝐥𝐚𝐭𝐭 A. Togo et al., Phys. Rev. B 91,

    094306 (2015) 𝜿latt (𝑇) = 1 𝑁𝑉0 ෍ 𝜆 𝐶𝜆 (𝑇)𝒗𝜆 ⊗ 𝒗𝜆 𝜏𝜆 (𝑇) The simplest model for 𝜅latt is the relaxation time approximation (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 Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 7
  8. Modelling 𝜿𝐥𝐚𝐭𝐭 A. Togo et al., Phys. Rev. B 91,

    094306 (2015) J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16) 164002 (2021) Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 8
  9. Interpreting 𝜿𝐥𝐚𝐭𝐭 : the CRTA model Consider again the 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 Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 9
  10. Interpreting 𝜿𝐥𝐚𝐭𝐭 : the CRTA model SnS SnSe Dr Jonathan

    Skelton MISE Finale Workshop June 2021 | Slide 10 J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A
  11. Interpreting 𝜿𝐥𝐚𝐭𝐭 : the CRTA model Dr Jonathan Skelton MISE

    Finale Workshop June 2021 | Slide 11 𝜅 [W m-1 K-1] Τ 𝜅 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] 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 (2021), DOI: 10.1039/D1TC02026A J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16) 164002 (2021)
  12. Modelling alloys Build supercell Enumerate structures Optimise structures Thermodynamics +

    Properties Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 12
  13. Modelling alloys Build supercell Enumerate structures Optimise structures Thermodynamics +

    Properties 1 10 100 1,000 10,000 1.000 0.875 0.750 0.625 0.500 0.375 0.250 0.125 0.000 Number of Structures Se Fraction Total Unique Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 13
  14. The Snm (S1-x Sex )m system Dr Jonathan Skelton MISE

    Finale Workshop June 2021 | Slide 14 D. S. D. Gunn et al., Chem. Mater. 31 (10), 3672 (2019)
  15. The Snm (S1-x Sex )m system Dr Jonathan Skelton MISE

    Finale Workshop June 2021 | Slide 15 D. S. D. Gunn et al., Chem. Mater. 31 (10), 3672 (2019)
  16. The Snm (S1-x Sex )m system Dr Jonathan Skelton MISE

    Finale Workshop June 2021 | Slide 16 D. S. D. Gunn et al., Chem. Mater. 31 (10), 3672 (2019)
  17. The Snm (S1-x Sex )m system Dr Jonathan Skelton MISE

    Finale Workshop June 2021 | Slide 17 D. S. D. Gunn et al., Chem. Mater. 31 (10), 3672 (2019)
  18. Pnma Sn(S1-x Sex ): 𝜿𝐥𝐚𝐭𝐭 Dr Jonathan Skelton MISE Finale

    Workshop June 2021 | Slide 18 C.-C. Lin et al., Chem. Mater. 29 (12), 5344 (2017) SnSe 15-20 % S
  19. Pnma Sn(S0.1875 Se0.8125 ): phonons Dr Jonathan Skelton MISE Finale

    Workshop June 2021 | Slide 19 J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A SnS SnSe
  20. Pnma Sn(S0.1875 Se0.8125 ): phonons Dr Jonathan Skelton MISE Finale

    Workshop June 2021 | Slide 20 J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A
  21. Pnma Sn(S0.1875 Se0.8125 ): 𝜿𝐥𝐚𝐭𝐭 Dr Jonathan Skelton MISE Finale

    Workshop June 2021 | Slide 21 J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A 54.2 % ↓ Sn(S0.1875 Se0.8125 ) SnSe
  22. Pnma Sn(S0.1875 Se0.8125 ): 𝜿𝐥𝐚𝐭𝐭 “Model 1”: 39.2 % ↓

    “Model 2”: 54.9 % ↓ “Model 3”: 59.4 % ↓ Expt: ~60-70 % ↓ Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 22 J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A C.-C. Lin et al., Chem. Mater. 29 (12), 5344 (2017)
  23. Summary First-principles modelling of the lattice thermal conductivity can provide

    accurate predictions and useful insight into how the 𝜅latt of thermoelectric materials “works” The CRTA model separates the 𝜅latt of a material into harmonic (heat capacity/group velocity) and anharmonic (lifetime) components, and may be a useful metric for comparing different TE materials The 𝜅latt of SnS and SnSe are a balance of smaller group velocities and longer lifetimes in the selenide A theoretical model for the Snm (S1-x Sex )n system suggests: o close to ideal mixing behaviour; o volume variation in accordance with Vegard’s law; and o a predictable variation in the bandgap of Sn(S1-x Sex )2 with composition, covering the Shockley–Queisser limit Calculations predict a 40-60 % reduction in the 𝜅latt of the Sn(S0.1875 Se0.8125 ) compared to SnSe, which can be ascribed mainly to a “smearing” of the phonon dispersion and a consequent reduction in the mode group velocities Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 23
  24. Acknowledgements Dr Jonathan Skelton MISE Finale Workshop June 2021 |

    Slide 24
  25. These slides are available on Speaker Deck: https://bit.ly/3q4MT24