3 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 ( = 1) are considered industrially viable 1. Provisional UK greenhouse gas emissions national statistics (published June 2020) 2. EPSRC Thermoelectric Network Roadmap (2018)

+ lat - Seebeck coefficient - electrical conductivity lat - lattice thermal conductivity ele - electronic thermal conductivity Phonon scattering by “rattler” filler atoms Electron transport through crystalline host framework MCCM Jan 2021 | Slide 6 G. A. Slack in CRC Handbook of Thermoelectrics (1995)

Ni0.3 Co3.7 Sb12 0.52 (773 K) Na0.48 Co3 Sb12 1.25 (800 K) Sr0.16 Tb0.03 Co4 Sb11.82 1.32 (850 K) Ba0.08 La0.05 Yb0.04 Co4 Sb12 1.7 (850 K) Yb0.2 Ba0.1 Al0.1 Ga0.1 In0.1 La0.05 Eu0.05 Co4 Sb12 1.2 (800 K) Ce0.12 Fe0.71 Co3.29 Sb12 0.8 (750 K) D. T. Morelli et al., Phys. Rev. B 51, 9622 (1995) Y. Lei et al., J. Mater. Sci. Mater. Electron. 30, 5929 (2019) Y. Z. Pei et al., Appl. Phys. Lett. 95, 042101 (2009) S. Q. Bai et al., Appl. Phys. A 100, 1109 (2010) MCCM Jan 2021 | Slide 7 X. Shi et al., J. Am. Chem. Soc. 133, 7837 (2011) S. Zhang et al., J. Alloys Compd. 814, 152272 (2020) X. F. Tang et al., J. Mater. Sci. 36, 5435 (2001)

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 MCCM Jan 2021 | Slide 8 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter (accepted), DOI: 10.1088/1361-648X/abd8b8

B 91, 094306 (2015) latt () = 1 0 () ⊗ () The simplest model for latt is the relaxation time approximation (RTA) - a closed solution to the phonon Boltzmann transport equations Modal heat capacity Mode group velocity λ Average over phonon modes λ Phonon MFP Mode lifetime λ = 1 2Γλ = MCCM Jan 2021 | Slide 9

again the RTA model for latt : latt = 1 0 ⊗ Two mechanisms through which rattlers can affect latt : 1. Reduction of - avoided crossings 2. Reduction of - resonant scattering These are not necessarily mutually exclusive - both can be active in the same material MCCM Jan 2021 | Slide 12 E. S. Toberer et al., J. Mater. Chem. 21 (40), 15843 (2011)

as a linewidth (inverse lifetime) derived from a model for “one-phonon scattering due to force-constant changes” of the form: −1 = 22 2 − 2 2 + 22 MCCM Jan 2021 | Slide 15 Schwartz and Walker, Phys. Rev. B 155, 959 (1967)

1 X ′ X0, X′ The phonon frequencies are obtained by constructing and diagonalising the dynamical matrix () for a given phonon wavevector A good conceptual definition of “rattling” is to consider the filler atom moving inside a rigid host framework at = Γ = 0 0 0 The frequency can be obtained by diagonalising a 3 × 3 () from the “self” force constants Filler [amu] [eV Å-2] ෨ [THz] He 4.0026 1.005 5.960 Ne 20.180 2.316 4.022 Ar 39.948 6.410 4.745 Kr 83.798 8.643 3.798 Xe 131.29 12.35 3.613 MCCM Jan 2021 | Slide 16

rattling frequencies ሚ X suggest that most of the fillers introduce states among the CoSb3 optic modes These account for ~20 % of the overall latt in CoSb3 , so the impact of these fillers is somewhat limited - max. reduction of 15 % in XeCo8 Sb24 MCCM Jan 2021 | Slide 20

frequency for the noble gas fillers X based on the XX, = Γ : XX, = Γ = 1 X ′ X0, X′ What happens to latt if we artificially change the X while keeping the fixed? MCCM Jan 2021 | Slide 21

glass electron crystal” materials Noble-gas filled XCo8 Sb24 systems (X = He-Xe) are a good “toy model” to investigate how fillers suppress the thermal transport Possible to calculate a rattling frequency ሚ X from the harmonic force constants - shows a competition between the mass of the filler atoms and how strongly they interact with the framework A CRTA decomposition of the latt shows that the main impact of the fillers is on the group velocity λ of the optic modes, leading to a maximum reduction of 15 % Further “thought experiments” show that reducing the ሚ X to the acoustic mode frequencies leads to a sharp reduction in latt by reducing the λ ሚ X appears to be a good predictor of the effect of the filler on the latt - possibly useful for screening Currently looking at whether the alternative phonon scattering mechanism in MAPbI3 could potentially work for Skutterudites with molecular fillers MCCM Jan 2021 | Slide 30