Dr Jonathan Skelton Department of Chemistry, University of Manchester ([email protected]) Understanding and controlling the heat transport in thermoelectric materials
Overview TYC Seminar, 26th Jan 2023 | Slide 3 Dr Jonathan Skelton o Thermoelectric power and the global energy challenge o Modelling lattice thermal conductivity o Models for understanding 𝜅latt : • CRTA model - 𝒗λ vs. 𝜏λ • Constant 𝑃λ model - ഥ 𝑁2 (𝜔) vs. ෨ 𝑃 o Strategies for controlling 𝜅latt : • Reducing 𝒗λ - alloying and doping • Reducing 𝜏λ - “rattler” TEs o Modelling the thermoelectric figure of merit o Recent highlights and current work http://bit.ly/3H3ys7x
The global energy challenge 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) TYC Seminar, 26th Jan 2023 | Slide 4 Dr Jonathan Skelton
Modelling thermal conductivity 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 TYC Seminar, 26th Jan 2023 | Slide 6 Dr Jonathan Skelton
Modelling thermal conductivity 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 TYC Seminar, 26th Jan 2023 | Slide 8 Dr Jonathan Skelton
Modelling thermal conductivity J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) TYC Seminar, 26th Jan 2023 | Slide 9 Dr Jonathan Skelton
J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A 𝒗𝜆 vs. 𝜏𝜆 : SnS/SnSe TYC Seminar, 26th Jan 2023 | Slide 12 Dr Jonathan Skelton SnS SnSe
Workflow 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) TYC Seminar, 26th Jan 2023 | Slide 21 Dr Jonathan Skelton
Reducing 𝒗𝜆 I: alloying 54.2 % ↓ Sn(S0.1875 Se0.8125 ) SnSe J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021) TYC Seminar, 26th Jan 2023 | Slide 23 Dr Jonathan Skelton
Reducing 𝜏𝜆 I: “rattler” TEs J. W. Schwartz and C. T. Walker, Phys. Rev. B 155, 959 (1967) E. S. Toberer et al., J. Mater. Chem. 21, 15843 (2011) “One phonon” model for resonant scattering: 𝜏−1 = 𝑖 𝑐𝑖 𝜔2𝑇2 𝜔𝑖 2 − 𝜔2 2 + 𝛾𝑖 𝜔𝑖 2𝜔2 TYC Seminar, 26th Jan 2023 | Slide 25 Dr Jonathan Skelton
Reducing 𝜏𝜆 I: “rattler” TEs TYC Seminar, 26th Jan 2023 | Slide 26 Dr Jonathan Skelton J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) 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
Reducing 𝜏𝜆 I: “rattler” TEs TYC Seminar, 26th Jan 2023 | Slide 27 Dr Jonathan Skelton J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) We can define a rattling frequency ሚ 𝑓𝑥 for the noble gas fillers X based on the 𝑫 XX, 𝐪 = Γ : 𝑫 XX, 𝐪 = Γ = 1 𝑚X 𝑙′ 𝚽 X0, X𝑙′ What happens to 𝜅latt if we artificially change the 𝑚X while keeping the 𝚽 fixed?
Summary o The SM-RTA can give quantitative predictions of the 𝜅latt of a wide range of materials o The contributions of individual phonon modes can be used to obtain microscopic insight into how the 𝜅latt “works”: • CRTA model: 𝒗λ vs. 𝜏λ • Constant 𝑃λ model: ഥ 𝑁2 vs. ෨ 𝑃 o Modelling on Si allotropes shows that low 𝜅latt is favoured by: 1) Large primitive cells 2) Lower crystal symmetry o With reference to existing TEs, the CRTA model can be used to suggest strategies for reducing the 𝜅latt : • 𝒗λ - alloying and discordant-atom doping • 𝜏λ - introducing “ratters”, small molecules may be particularly effective o These ideas are being explored in our current work -- watch this space! TYC Seminar, 26th Jan 2023 | Slide 34 Dr Jonathan Skelton
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