Thermoelectric materials for energy harvesting new modelling tools with predictive power

Transcription

1 Thermoelectric materials for energy harvesting new modelling tools with predictive power Ole Martin Løvvik 1,2 1 SINTEF Materials Physics, Norway 2 University of Oslo, Norway

2 Thermoelectric generators 2

3 Space applications NASA s Mars Rover, Curiosity, is powered by a thermoelectric generator (TEG)

4 Off-grid power

5 Future potential: enormous 5

6 ~60% of all energy heat 6

7 Conversion efficiency: depends on DT, typically 5-10 % Thermoelectric generators (TEG) Seebeck effect: The conversion of heat DT to electricity DV : DV adt Thermoelectric figure of merit (electrical conductivity s, thermal conductivity k, Seebeck coefficient a): zt a 2 s k T A TEG device is coupled thermally in parallel and electrically in series

8 Thermoelectric efficiency: Trade-off between transport coefficients Insulator Semiconductor Semimetal Metal Figure of merit: zt a 2 s k T ZT Seebeck effect - Conversion of heat DT to electricity DV : DV adt Charge carrier concentration

9 Separation between electronic and nuclear degrees of freedom Electron-phonon scattering is next level 9

10 Figure of merit zt Development of new materials is crucial Current generation: Expensive Toxic Rare Half-Heusler (p,n) (HfZrTi)NiSn LAST (AgPb 18 SbTe 20 ) Bi 2 Te 3 (p,n) Mg 2 (Si,Sn) (n) Limited temperature range Not very efficient Next generation: 0.5 Significantly cheaper Non-toxic Broad temperature range Not necessarily more efficient, but more bang for the buck Temperature (K) State-of-the-art TE materials; current and some future. We are working on the black compounds.

11 Two main challenges in the field Electron transport: too expensive to perform highaccuracy calculations (hybrid, GW, etc.) The k p method Phonon transport: too expensive to perform highaccuracy calculations (three-phonon scattering) The TDEP method

12 Crystal structure Electronic properties from Boltzmann's transport equation (BTE) n, carrier concentration Band structure S 2 s, Power factor (PF) Optimized PF Ole Martin Løvvik Materials and Chemistry

13 A main challenge: Fermi velocities Energy k y Electrical conductivity tensor: Fermi velocity: k x Ole Martin Løvvik Materials and Chemistry

14 The extended k p method One-particle Schrödinger eq: Physics based interpolation Adds a correction term to improve fit Extrapolates from several k points K. Ole Berland, Martin Løvvik C. Persson, Materials Comp. and Chemistry Mater. Sci. 134 (2017)

15 HfPtPb ZrPtPb ZrPtSn HfPtSn ZrPdPb HfRhBi HfPdPb ZrNiPb HfNiPb ZrPdSn HfNiSn TiPtSn HfPdSn ZrNiSn ZrRhBi HfRhSb ZrIrBi TiPdSn TiNiSn HfIrSb TiIrSb ZrRhSb TiRhSb ZrIrSb TiIrAs ZrIrAs TiCoSb ZrCoBi HfCoSb ZrCoSb Power factor Optimized power factor S 2 s from GGA and hybrid calcs. (p-doped) PBE (GGA) T = 800 K HSE (Hybrid) t = s p-doping spin-orbit coupling

16 Lattice thermal conductivity from Boltzman transport equation Crystal structure Dispersion relation ++ Ole Martin Løvvik Materials and Chemistry

17 Boltzmann transport equation within the relaxation time approximation: Specific heat Phonon group vel. Phonon lifetime

18 Standard approach: the "frozen phonon" Very high accuracy is required Many calculations are needed Ole Martin Løvvik Materials and Chemistry

19 The temperature dependent effective potential (TDEP) method: use force/displacement data from MD Model potential energy U as function of displacements u from ideal positions: 2 nd order interatomic force constants 3 rd order interatomic force constants Hellman Ole Martin Løvvik et al., PRB Materials 84, (R) and Chemistry (2011)

20 TDEP in practice: Excellent quantitative correspondence Thermal resistivity of PbS, PbSe, and PbTe (lines) for +1% lattice constant (expt). Reducing accuracy slightly can reduce cost significantly

21 Very low ZrNiSn Virtual crystal approximation (VCA) + mass disorder YNiBi Minimum T=300 K Ingeborg T. Røe et al., In prep. HfNiSn TiNiSn LaNiBi ScNiBi

22 Thermal conductivity with various 800 K Thermal conductivity (W/mK) TiIrAs ZrCoSb HfIrSb TiCoSb ZrRhSb HfCoAs HfRhSb ZrIrSb ZrCoBi TiPtSn ZrNiSn TiRhSb HfPtSn TiIrSb ZrPtSn TiNiSn HfNiPb ZrPdSn HfPdSn ZrIrAs ZrNiPb ZrIrBi ZrRhBi HfRhBi ZrPdPb TiPdSn ZrPtPb HfPdPb HfNiSn 14 Alloy scattering: 12.5% mix on the X site Boundary scattering: MFP<50 nm Anharmonic 12 T = 800 K Anharm+alloy 10 Anharm+alloy+grain boundary

23 ZrIrAs HfPtPb ZrRhBi HfIrSb HfRhBi ZrIrBi ZrPtPb ZrIrSb TiIrAs HfPtSn ZrPdPb ZrNiPb ZrRhSb HfNiPb ZrPtSn HfPdPb HfRhSb HfNiSn ZrCoBi TiIrSb ZrNiSn TiPdSn ZrPdSn HfCoSb HfPdSn TiNiSn TiCoSb ZrCoSb TiRhSb ZT Optimized figure of 800 K T = 800 K optimal p-doping t = s 12.5% alloy: "Ti" = (Ti 87.5 Hf 12.5 ), etc. Crystallite size: 50 nm

24 Combining high-throughput modeling and experiments with machine learning

25 Take home: Efficient electron transport with the k p method Possible to predict thermoelectric properties ab initio Efficient phonon transport with the TDEP method Machine learning can speed up discovery further Ole Martin Løvvik Materials and Chemistry

26 Acknowledgements Funding: Attention: through several projects Computing resources: Ole Martin Løvvik Materials and Chemistry

27 Power factor Power factor S 2 s from hybrid calcs. (p) T = 800 K t = s p-doping spin-orbit coupling p-doping (cm -3 ) Ole Martin Løvvik Materials and Chemistry

28 A main challenge: Fermi velocities BoltzTraP: 48 Ole Martin Løvvik Materials and Chemistry

29 This can be improved with the extended k p method BoltzTraP: The extended k p method: 48 K. Berland, C. Persson, Comp. Mater. Sci. 134 (2017) Ole Martin Løvvik Materials and Chemistry