Dr Jonathan Skelton Department of Chemistry, University of Manchester ([email protected]) Controlling the heat transport in thermoelectric materials 

Acknowledgements Dr Jonathan Skelton ... plus other students, mentors and collaborators too numerous to mention MC16, 6th July 2023 | Slide 2 

The global energy challenge MC16, 6th July 2023 | Slide 3 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 

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) MC16, 6th July 2023 | Slide 4 

The IV-VI chalcogenides Dr Jonathan Skelton L.-D. Zhao et al., Nature 508, 373 (2014) MC16, 6th July 2023 | Slide 5 

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 𝑃𝑛𝑚𝑎 𝐶𝑚𝑐𝑚 𝑅3𝑚 𝐹𝑚* 3𝑚 MC16, 6th July 2023 | Slide 6 

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!"## = 1 𝑁𝑉 & $ 𝜿$ = 1 𝑁𝑉 & $ 𝐶$ 𝒗$ ⊗ 𝒗$ 𝜏$ 𝐶% - phonon heat capacities 𝒗% - phonon group velocities 𝜏% - phonon lifetimes (inverse linewidths Γ% ) 𝑁 - number of 𝒒 in summation 𝑉 - unit cell volume MC16, 6th July 2023 | Slide 7 

A comparative study Dr Jonathan Skelton 𝜅𝐥𝐚𝐭𝐭 (𝑇 = 300 K) [W m-1 K-1] SnSe (𝐶𝑚𝑐𝑚) 0.96 SnTe (𝑃𝑛𝑚𝑎) 1.09 GeTe (𝑃𝑛𝑚𝑎) 1.32 SnSe (𝑃𝑛𝑚𝑎) 1.36 GeTe (𝐹𝑚+ 3𝑚) 1.57 GeSe (𝐹𝑚+ 3𝑚) 1.67 GeSe (𝑃𝑛𝑚𝑎) 2.36 SnTe (𝑅3𝑚) 4.18 GeTe (𝑅3𝑚) 4.36 SnTe (𝐹𝑚+ 3𝑚) 5.01 MC16, 6th July 2023 | Slide 8 

Group velocities vs. lifetimes Dr Jonathan Skelton 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) MC16, 6th July 2023 | Slide 9 

Group velocities vs. lifetimes Dr Jonathan Skelton 𝜅𝐥𝐚𝐭𝐭 [W m-1 K-1] ⁄ 𝜅𝐥𝐚𝐭𝐭 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] SnTe (𝑃𝑛𝑚𝑎) 1.09 0.27 3.98 GeTe (𝑃𝑛𝑚𝑎) 1.32 0.34 3.91 SnSe (𝑃𝑛𝑚𝑎) 1.36 0.35 3.89 GeSe (𝑃𝑛𝑚𝑎) 2.36 0.39 6.03 SnTe (𝑅3𝑚) 4.18 0.69 6.07 GeTe (𝑅3𝑚) 4.36 0.87 5.01 SnTe (𝐹𝑚+ 3𝑚) 5.01 1.07 4.67 SnSe (𝐶𝑚𝑐𝑚) 0.96 1.09 0.88 GeTe (𝐹𝑚+ 3𝑚) 1.67 2.99 0.56 GeSe (𝐹𝑚+ 3𝑚) 1.57 3.29 0.48 MC16, 6th July 2023 | Slide 10 

Group velocities vs. lifetimes Dr Jonathan Skelton 𝜅𝐥𝐚𝐭𝐭 [W m-1 K-1] ⁄ 𝜅𝐥𝐚𝐭𝐭 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] GeSe (𝐹𝑚+ 3𝑚) 1.57 3.29 0.48 GeTe (𝐹𝑚+ 3𝑚) 1.67 2.99 0.56 SnSe (𝐶𝑚𝑐𝑚) 0.96 1.09 0.88 SnSe (𝑃𝑛𝑚𝑎) 1.36 0.35 3.89 SnTe (𝑃𝑛𝑚𝑎) 1.32 0.34 3.91 SnTe (𝑅3𝑚) 1.09 0.27 3.98 SnTe (𝐹𝑚+ 3𝑚) 5.01 1.07 4.67 GeTe (𝑅3𝑚) 4.36 0.87 5.01 GeSe (𝑃𝑛𝑚𝑎) 2.36 0.39 6.03 SnTe (𝑅3𝑚) 4.18 0.69 6.07 MC16, 6th July 2023 | Slide 11 

Anharmonicity vs. “selection rules” Γ5 = 36𝜋 ℏ8 2 5&5&& Φ955&5&& 8×{ 𝑛5& + 𝑛5&& + 1 𝛿 𝜔 − 𝜔5& − 𝜔5&& + 𝑛5& − 𝑛5&& 𝛿 𝜔 + 𝜔5& − 𝜔5&& − 𝛿 𝜔 − 𝜔5& + 𝜔5&& } 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) MC16, 6th July 2023 | Slide 12 

Anharmonicity vs. “selection rules” Dr Jonathan Skelton 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) MC16, 6th July 2023 | Slide 13 

Anharmonicity vs. “selection rules” Dr Jonathan Skelton 𝑃𝑛𝑚𝑎 Other phases Other phases 𝑃𝑛𝑚𝑎 𝜏: = 1 2𝜋Γ5 Γ5 ≈ 36𝜋 ℏ8 𝑁8 (𝒒5 , 𝜔5 )×𝑃5 and MC16, 6th July 2023 | Slide 14 

Anharmonicity vs. “selection rules” Dr Jonathan Skelton 𝝉𝐂𝐑𝐓𝐀 [ps] ; 𝑷× 𝟑𝒏𝒂 𝟐 [eV2] ⁄ ; 𝑵𝟐 𝟑𝒏𝒂 𝟐 [THz-1] SnTe (𝑃𝑛𝑚𝑎) 3.98 9.07 × 10-9 1.70 × 10-2 SnSe (𝑃𝑛𝑚𝑎) 3.89 1.20 × 10-8 1.31 × 10-2 GeTe (𝑃𝑛𝑚𝑎) 3.91 1.35 × 10-8 1.15 × 10-2 GeSe (𝑃𝑛𝑚𝑎) 6.03 1.36 × 10-8 7.44 × 10-3 SnTe (𝑅3𝑚) 6.07 5.20 × 10-8 1.93 × 10-3 GeTe (𝑅3𝑚) 5.01 8.97 × 10-8 1.36 × 10-3 SnTe (𝐹𝑚+ 3𝑚) 4.67 1.09 × 10-7 1.20 × 10-3 SnSe (𝐶𝑚𝑐𝑚) 0.88 1.46 × 10-7 4.74 × 10-3 GeTe (𝐹𝑚+ 3𝑚) 0.56 1.31 × 10-6 8.35 × 10-4 GeSe (𝐹𝑚+ 3𝑚) 0.48 2.24 × 10-6 5.69 × 10-4 Calculate an averaged number of scattering pathways from 𝜏'()* and 7 𝑃: 8 𝑁+ = ℏ! ,+-! . /0"#$% MC16, 6th July 2023 | Slide 15 

Trends in structure type Dr Jonathan Skelton 𝑃𝑛𝑚𝑎 𝐶𝑚𝑐𝑚 𝑅3𝑚 𝐹𝑚* 3𝑚 Lower 𝒗1 : smaller ⁄ 𝜅"#$$ 𝜏'()* Stronger anharmonicity: larger 7 𝑃 → shorter 𝜏'()* Larger scattering phase space: larger 8 𝑁+ → shorter 𝜏'()* MC16, 6th July 2023 | Slide 16 

Interpretation: group velocities Dr Jonathan Skelton http://www-personal.umich.edu/~alberliu/writing/condensedmatter/1dlatticenormalmodes.pdf MC16, 6th July 2023 | Slide 17 𝑣% ≈ 𝑎 𝑘 𝑚 𝑣% ≈ 2𝑎 𝑘×𝑔 2𝑚(𝑘 + 𝑔) 𝑘 𝑔 𝑎 2𝑎 𝑘 Equiv. bonds (𝑔 = 𝑘) Broken chain (𝑔 = 0) 𝑚 𝑚 𝑚 𝑚 𝑚 𝑚 𝑚 𝑚 

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 MC16, 6th July 2023 | Slide 18 

Trends in structure type Dr Jonathan Skelton 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) MC16, 6th July 2023 | Slide 19 

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 scattering phase space 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 group velocity can be explained in terms of bonding inhomogeneity The trends in anharmonicity can be explained in terms of the revised lone pair model MC16, 6th July 2023 | Slide 20 

bit.ly/3JFclWU These slides are available on Speaker Deck: