The global energy challenge MCC Conference, 29th June 2023 | Slide 2 31 % 23 % 20 % 19 % 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 March 2022) 2. EPSRC Thermoelectric Network Roadmap (2018) Dr Jonathan Skelton
A comparative study Dr Jonathan Skelton GeSe GeTe SnSe SnTe 𝑃𝑛𝑚𝑎 ü ü ü ü 𝐶𝑚𝑐𝑚 ü 𝑅3𝑚 ü ü ü 𝐹𝑚0 3𝑚 ü ü MCC Conference, 29th June 2023 | Slide 5 𝑃𝑛𝑚𝑎 𝐶𝑚𝑐𝑚 𝑅3𝑚 𝐹𝑚* 3𝑚
Modelling thermal conductivity A. Togo et al., Phys. Rev. B 91, 094306 (2015) Dr Jonathan Skelton The simplest model for 𝜅"#$$ is the single-mode relaxation time approximation (SM-RTA) - a closed solution to the phonon Boltzmann transport equations 𝜿#$%% (𝑇) = 1 𝑁𝑉 . & 𝐶&(𝑇)𝒗& ⊗ 𝒗&𝜏&(𝑇) 𝐶% - phonon heat capacities 𝒗% - phonon group velocities 𝜏% - phonon lifetimes (inverse linewidths Γ% ) 𝑁 - number of 𝒒 in summation 𝑉 - unit cell volume MCC Conference, 29th June 2023 | Slide 6
Group velocities vs. lifetimes Dr Jonathan Skelton MCC Conference, 29th June 2023 | Slide 9 𝜿./00 ≈ 𝜏1234× 1 𝑁𝑉 2 5 𝜿5 𝜏5 = 1 𝑁𝑉 2 5 𝐶5 𝒗5 ⊗ 𝒗5 ×𝜏1234 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33, 164002 (2021) J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021)
Group velocities vs. lifetimes Dr Jonathan Skelton MCC Conference, 29th June 2023 | Slide 10 𝜿./00 ≈ 𝜏1234× 1 𝑁𝑉 2 5 𝜿5 𝜏5 = 1 𝑁𝑉 2 5 𝐶5 𝒗5 ⊗ 𝒗5 ×𝜏1234 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33, 164002 (2021) J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021)
Anharmonicity vs. “selection rules” Dr Jonathan Skelton MCC Conference, 29th June 2023 | Slide 15 𝜏: = 1 2𝜋Γ5 Γ5 ≈ 36𝜋 ℏ8 𝑁8 (𝒒5 , 𝜔5 )×𝑃5 and A. Togo et al., Phys. Rev. B 91, 094306 (2015) B. Wei, J. Flitcroft and J. M. Skelton, Molecules 27 (19), 6431 (2022)
Anharmonicity vs. “selection rules” Dr Jonathan Skelton MCC Conference, 29th June 2023 | Slide 16 𝑃𝑛𝑚𝑎 Other phases Other phases 𝑃𝑛𝑚𝑎 𝜏: = 1 2𝜋Γ5 Γ5 ≈ 36𝜋 ℏ8 𝑁8 (𝒒5 , 𝜔5 )×𝑃5 and
A. Walsh et al., Chem. Soc. Rev. 40, 4455 (2011) M. J. Smiles et al., J. Mater. Chem. A 9, 22440 (2021) Interpretation: anharmonicity Dr Jonathan Skelton MCC Conference, 29th June 2023 | Slide 20
Trends in structure type Dr Jonathan Skelton MCC Conference, 29th June 2023 | Slide 21 𝐶𝑚𝑐𝑚 SnSe: ? Low symmetry ü Large(-ish) cell (𝑛2 = 4) ü Sn constrained to a locally-symmetric environment 𝜋-cubic SnSe: ? High symmetry ü (Very) large cell (𝑛2 = 64) û Sn local geometry similar to 𝑃𝑛𝑚𝑎 phase R. E. Abutbul et al., CrystEngComm 18, 1918 (2016)
Summary Dr Jonathan Skelton The SM-RTA model provides insight into the 𝜅"#$$ at the level of individual phonon modes, which can be analysed to quantify the separate contributions of: o Group velocity vs. lifetimes - the CRTA model o Anharmonicity vs. selection rules - the constant interaction-strength model For a series of ten chalcogenides, we find that: o Low group velocities are favoured by complex structures with large unit cells o Strong phonon anharmonicity is favoured by structures where the tetrel atoms are constrained to locally-symmetric environments... o ... but less symmetric structures allow for a large number of allowed scattering pathways These competing factors are optimally balanced in 𝐶𝑚𝑐𝑚 SnSe, which has: o a larger and lower-symmetry unit cell compared to 𝑅3𝑚/𝐹𝑚0 3𝑚 phases... o ... but with the Sn atoms are constrained to a locally symmetric environment The trends in anharmonicity can be explained in terms of the revised lone pair model MCC Conference, 29th June 2023 | Slide 22
Acknowledgements Dr Jonathan Skelton MCC Conference, 29th June 2023 | Slide 23 ... plus other students, mentors and collaborators too numerous to mention
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