Dr Jonathan Skelton Department of Chemistry, University of Manchester ([email protected]) Understanding the thermal transport in Sn(S,Se) alloys for thermoelectric applications
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)
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
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
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
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
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
Modelling alloys Build supercell Enumerate structures Optimise structures Thermodynamics + Properties Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 12
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
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
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
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
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
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)
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