Upgrade to Pro — share decks privately, control downloads, hide ads and more …

Understanding the thermal transport in Sn(S,Se)...

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
Tweet

More Decks by Jonathan Skelton

Other Decks in Science

Transcript

  1. Dr Jonathan Skelton Department of Chemistry, University of Manchester ([email protected])

    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