Dr Jonathan Skelton Department of Chemistry, University of Manchester ([email protected]) Theory-Led Control of Heat Transport in Thermoelectric Materials
The global energy challenge ICFM 2022, 30th May 2022 | 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) Dr Jonathan Skelton
Lattice thermal conductivity Phonons are generated at the hot side of the material and transport energy to the cold side Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 4
Modelling thermal conductivity A. Togo et al., Phys. Rev. B 91, 094306 (2015) 𝜿#$%% (𝑇) = 1 𝑁𝑉& . ' 𝐶'(𝑇)𝒗' ⊗ 𝒗'𝜏'(𝑇) Dr Jonathan Skelton The simplest model for 𝜅"#$$ is the single-mode relaxation time approximation (SM-RTA) - a closed solution to the phonon Boltzmann transport equations Modal heat capacity Mode group velocity 𝜕𝜔% 𝜕𝐪 Average over phonon modes λ Phonon MFP Mode lifetime 𝜏% = 1 2Γ% 𝚲& 𝑇 = 𝒗& 𝜏& 𝑇 ICFM 2022, 30th May 2022 | Slide 5
𝜿𝐥𝐚𝐭𝐭 of pristine CoSb3 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 10
A “toy model” for filled CoSb3 Filler 𝒎𝐗 [amu] 𝒓𝐗 [pm] He 4.0026 31 Ne 20.180 38 Ar 39.948 71 Kr 83.798 88 Xe 131.29 108 Noble gases are chemically inert (closed shell, unlikely to reduce/oxidise host framework) and are likely closest it is possible to get to a “hard sphere” filler J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 11
How do the fillers suppress 𝜿𝐥𝐚𝐭𝐭 ? Consider again the SM-RTA model for 𝜿"#$$ : 𝜿"#$$ (𝑇) = 1 𝑁𝑉+ ; & 𝐶& (𝑇)𝒗& ⊗ 𝒗& 𝜏& (𝑇) Two mechanisms through which rattlers can affect 𝜅"#$$ : 1. Reduction of 𝑣& - avoided crossings 2. Reduction of 𝜏& - resonant scattering These are not necessarily mutually exclusive - both can be active in the same material E. S. Toberer et al., J. Mater. Chem. 21 (40), 15843 (2011) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 13
𝒗6 vs. 𝜏6 : the CRTA model Consider again the SM-RTA model: 𝜿"#$$ = 1 𝑁𝑉+ ; & 𝜿& = 1 𝑁𝑉+ ; & 𝐶& 𝒗& ⊗ 𝒗& 𝜏& Replace the 𝜏& with a constant lifetime (relaxation time) 𝜏,-./ defined as follows: 𝜿"#$$ 𝜏,-./ = 1 𝑁𝑉+ ; & 𝜿& 𝜏& = 1 𝑁𝑉+ ; & 𝐶& 𝒗& ⊗ 𝒗& 𝜿"#$$ ≈ 1 𝑁𝑉+ ; & 𝐶& 𝒗& ⊗ 𝒗& ×𝜏,-./ HA AH HA AH J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 14
𝒗6 vs. 𝜏6 : the CRTA model Replace the 𝜏& with a constant lifetime (relaxation time) 𝜏,-./ defined as follows: 𝜿"#$$ ≈ 1 𝑁𝑉+ ; & 𝐶& 𝒗& ⊗ 𝒗& ×𝜏,-./ J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 15
Tuning the filler mass We can define a rattling frequency @ 𝑓0 for the noble gas fillers X based on the 𝑫 XX, 𝐪 = Γ : 𝑫 XX, 𝐪 = Γ = 1 𝑚1 ; 2! 𝚽 X0, X𝑙3 What happens to 𝜅"#$$ if we artificially change the 𝑚1 while keeping the 𝚽 fixed? J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 16
Tuning the filler mass Lowering the @ 𝑓1 into the acoustic region reduces the 𝜏% and the group velocities → considerably larger reduction of 𝜅"#$$ J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 17
Whalley et al., Phys. Rev. B 94, 220301(R) (2016) Gold-Parker et al., PNAS 115, 11905 (2018) Intrinsic anharmonicity: MAPbI3 Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 18
Sn(S0.1875 Se0.8125 ): phonon spectrum SnS SnSe J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 27
Sn(S0.1875 Se0.8125 ): 𝜿𝐥𝐚𝐭𝐭 54.2 % ↓ Sn(S0.1875 Se0.8125 ) SnSe J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021) Dr Jonathan Skelton ICFM 2022, 30th May 2022 | Slide 29
Summary Dr Jonathan Skelton The lattice thermal conductivity 𝜅"#$$ in thermoelectric materials can be modelled theoretically using the SM-RTA model The SM-RTA model calculates the macroscopic 𝜅"#$$ as a sum of microscopic contributions from individual phonon modes, which provides a large amount of insight into how 𝜅"#$$ “works” In CoSb3 , the filler “rattling frequency” depends on its mass and how strongly it interacts with the cage - calculations show that tuning this to around 1.5 THz can significantly reduce the 𝜅"#$$ through a combination of avoided crossings and resonant scattering In MAPbI3 , the ultra-low 𝜅"#$$ is due to very short phonon lifetimes, on the order of ps, which can be attributed to the phonon scattering introduced by the interaction of the MA+ cation with the PbI3 - framework In Sn(S0.1875 Se0.8125 ), alloying at the chalcogen site leads to a ~60 % reduction in the 𝜅"#$$ , which can be attributed to a “smearing out” of the dispersion reducing the group velocities Using the CRTA model to decompose the 𝜅"#$$ into a product of harmonic (group velocity) and lifetime terms can provide insight into what sort of engineering methods are appropriate for optimising the 𝜅"#$$ of current and new TEs ICFM 2022, 30th May 2022 | Slide 31
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