Efficient methods for accurately calculating thermoelectric properties – electronic and thermal transport

1. Efficient methods for accurately calculating thermoelectric properties – electronic and thermal transport Anubhav Jain Lawrence Berkeley National Laboratory MRS Fall meeting, Nov 2022 Slides (already) posted to hackingmaterials.lbl.gov

2. There are many efforts to identify new thermoelectric materials through calculations 2 Urban, J. J.; Menon, A. K.; Tian, Z.; Jain, A.; Hippalgaonkar, K. New Horizons in Thermoelectric Materials: Correlated Electrons, Organic Transport, Machine Learning, and More. Journal of Applied Physics 2019, 125 (18), 180902.

3. Such screening studies are typically limited to using approximate models for estimating zT 3 Electron mobility Thermal conductivity Figure of merit 1. Constant / uniform relaxation time approximation 2. Semi-empirical models[1] 1. Glassy limit thermal conductivity models[2] 2. Semi-empirical models[1] 1. Combining previous models for electron and thermal conductivity (optimize for doping, T) 2. Descriptors that implicitly optimize[1] for doping, T !=constant [1] Yan, J.; Gorai, P.; Ortiz, B.; Miller, S.; Barnett, S. A.; Mason, T.; Stevanović, V.; Toberer, E. S. Material Descriptors for Predicting Thermoelectric Performance. Energy Environ. Sci. 2015, 8 (3), 983–994 [2] D. G. Cahill, S. K. Watson, R. O. Pohl, Phys. Rev. B 1992, 46, 6133-6140 ; D. G. Cahill, R. O. Pohl, Ann. Rev. Phys. Chem. 1988, 39, 93-121. 3 fitted parameters (A0, B, s) Band effective mass based on DOS effective mass and valley degeneracy 2 fitted parameters (A1, A2) Later extended to include coordination number effects

4. For example, we previously calculated a large amount of transport data under cRTA 4 ~50,000 crystal structures and band structures from Materials Project are used as a source F. Ricci, et al., An ab initio electronic transport database for inorganic materials, Sci. Data. 4 (2017) 170085. We compute electronic transport properties with BoltzTraP and atomate About 300GB of electronic transport data is generated. All data is available free for download https://contribs.materialsproject.org/projects/carrier_transport/ All data is available free for download via Materials Project or direct download from journal article.

5. We used this data to identify materials with decent figure-of-merit, but no breakthroughs 5 • Calculations: trigonal p- TmAgTe2 could have power factor up to 8 mW/mK2 • requires 1020/cm3 carriers experiment computation • Calculations: p-YCuTe2 could only reach PF of 0.4 mW/mK2 • SOC inhibits PF • if thermal conductivity is low (e.g., 0.4, we get zT ~1) • Expt: zT ~0.75 – not too far from calculation limit • carrier concentration of 1019 • Decent performance, but unlikely to be improved with further optimization • Expt: p-zT only 0.35 despite very low thermal conductivity (~0.25 W/mK) • Limitation: carrier concentration (~1017/cm3) • likely limited by TmAg defects, as determined by followup calculations • Later, we achieved zT ~ 0.47 using Zn-doping TmAgTe2 YCuTe2 Collaborations w/Jeff Snyder & M.A. White

6. How to bring the field forward? • Approximate and semi-empirical techniques used in high-throughput screening studies typically suffer from two issues • The first (and obvious) one is accuracy • The second one is information content • In addition to being less accurate, approximate techniques give you much less information than full theoretical techniques • Can we retain accuracy and information content, while minimizing computational cost and retaining automation for future studies? 6

7. Outline • Electronic properties using the AMSET method • Phonon and thermal properties by efficient data fitting 7

8. The Boltzmann transport equation determines carrier transport properties 8 group velocity (easy) lifetime (hard)

9. τ ... DFPT AMSET ∝ DOS–1 / semi- empirical constant lifetime A model to explicitly calculate scattering rates while remaining computationally efficient Aim: accuracy comparable to EPW at 1/100th – 1/1000th computational cost AND with rich information content AMSET is a new framework for calculating transport properties including e- lifetimes

10. primary input: uniform k-mesh band structure calculation Step 1: Band structure (probably DFT)

11. Fourier interpolation of eigenvalues and group velocities (there is some custom resampling to get even more accurate integrations) Step 2: Interpolation of band structure to dense mesh

12. lifetimes calculated using scattering equations that depend on first-principles inputs Step 3: Use band structure and scattering equations to determine scattering rates

13. calculate mobility, conductivity, Seebeck & thermal conductivity Step 4: Transport properties by solving BTE

14. Acoustic deformation potential (ad) deformation potential, elastic constant Ionized impurity (ii) dielectric constant Piezoelectric (pi) dielectric constant, piezoelectric coefficient Polar optical phonon (po) dielectric constant, polar phonon frequency Scattering rates determined by DFT inputs *note: scalar equations shown, these are generalized to tensor forms

15. • All first principles inputs • Nothing fit or tuned to experimental data • Rich information content • scattering mechanisms • E & k-dependent scattering rates • Short runtime • ~60 mins of DFT calculations on 64 cores • Plus ~40 mins of time to run AMSET AMSET predicts switch from impurity to polar phonon scattering in GaN Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.; Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering Rates from First Principles. Nat Commun 2021, 12 (1), 2222.

16. • Anisotropy is also captured by AMSET • Allows for analyzing non- cubic systems and getting direction- dependent properties AMSET can also calculate the anisotropic transport properties of realistic materials Crystal structure image from: Pletikosić, Ivo et al. (2017). Band structure of a IV- VI black phosphorus analogue, the thermoelectric SnSe. Physical Review Letters. 120. Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.; Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering Rates from First Principles. Nat Commun 2021, 12 (1), 2222. SnSe

17. AMSET shows close agreement to experiment for the mobility and Seebeck coefficient across many materials Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.; Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering Rates from First Principles. Nat Commun 2021, 12 (1), 2222.

18. Timing for calculations are very reasonable and easily within reach of most groups Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.; Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering Rates from First Principles. Nat Commun 2021, 12 (1), 2222. Total calculation times are ~500X faster than DFPT+Wannier The AMSET portion of the calculation scales well with system size

19. Docs: https://hackingmaterials.lbl.gov/amset/ Support: https://matsci.org/c/amset Paper: installation pip install amset usage amset run --static-dielectric 10 ... Can be controlled through the command line or python interface, integration with atomate2 for automatic workflows Ganose, A. M.; Park, J.; Faghaninia, A.; Woods-Robinson, R.; Persson, K. A.; Jain, A. Efficient Calculation of Carrier Scattering Rates from First Principles. Nat Commun 2021, 12 (1), 2222. AMSET is an open source python package that you can run today, and has already been used in many downstream studies

20. Outline • Electronic properties using the AMSET method • Phonon and thermal properties by efficient data fitting 20

21. Calculating thermal properties of materials • The vibrational thermal properties of materials are determined by phonon behavior • In lattice dynamics, we typically tailor expand the phonon interactions by atomic displacements: And differentiate to solve for the interatomic force constants 21

22. After obtaining the force constants to various orders, one can calculate materials properties 22 Harmonic term (Φ2) Second order: phonon dispersion, phonon DOS, free energy, heat capacity (Cv), entropy Anharmonic terms (Φ3, Φ4) Φ 2 ( h a r m o n i c ) Fourth order: thermal expansion, more accurate thermal conductivity & free energies Third order: Gruneisen parameter, thermal conductivity More Thermal Properties Higher Physical Accuracy Computational Feasibility 4 th order of IFC 3 rd order of IFC 2 nd order of IFC … φ 4 Φ3 (anharm onic) …

23. The problem – obtaining force constants can require many DFT calculations 23 To obtain 2nd order IFCs To obtain 3rd order IFCs 2 displacements in a supercell (# of supercells needed: 1000s-10000s) … 1 displacement in a supercell (Usually <5 supercells needed) Finite-displacement method IFCs extracted from HiPhive To obtain any order of IFCs (2nd, 3rd,…) in one shot … displace each atom in a supercell (Only need 5~10 supercells in total!) • Traditionally, one performs systematic displacements, each of which only has a few atom movements and solves only a small portion of the IFC matrix • For higher-order terms, the IFC matrix contains many distinct terms and many calculations are needed • Primitive cells with reduced symmetry and many atoms can easily require 1000 or more calculations • The scaling goes something like: O(Nn) where N is the number of sites and n is the order of IFC you want. Not scalable!

24. The solution – perform non-systematic displacements • Instead of performing systematic displacements, perform non-systematic displacements in which many IFC terms are “mixed up” • Then, perform a best fit procedure to fit the IFC matrix elements to the observed data • Typically undetermined, so regularization is important • This method has been suggested by several groups, for now we focus on the implementation in the HiPhive code (Erhart group, Chalmers University of Technology) 24 IFCs extracted from HiPhive To obtain any order of IFCs (2nd, 3rd,…) in one shot … displace each atom in a supercell (Only need 5~10 supercells in total!) Monte Carlo rattle penalizes displacements that lead to very small interatomic distances

25. HiPhive has been shown to give very good accuracy with few calculations, but can require parameter selection / tuning 25 HiPhive is itself not fully automatic. Things that need to be tuned include: • Number of training structures • Training structure supercell size and atom displacement strategy • Interaction cutoff distance • Method of regularization Fransson, E.; Eriksson, F.; Erhart, P. Efficient Construction of Linear Models in Materials Modeling and Applications to Force Constant Expansions. npj Comput Mater 2020, 6 (1), 135.

26. We have been testing parameters to determine “high-throughput” • Supercell size: 150 – 600 atoms, >= 18 Å in dimension • Training structures: 3 – 15 (depending on lattice symmetry) • Feature selection: Recursive feature elimination • Cutoffs (Å) – initial cutoffs below, these are increased to hit convergence 26 Period 2nd order 3rd order 4th order 1 5.0 3.0 2.5 2 6.0 3.5 3.0 3 7.0 4.5 3.5 4 8.0 5.5 4.0 5 9.0 6.0 4.5 6 10.0 6.5 5.0 7 11.0 7.0 5.5

27. We’ve also been automating physical considerations Highly ionic compounds require incorporation of non-analytical corrections 27 Dynamically unstable compounds Cubic SrTiO3 (Tc=105K) 100K 200K Wave vector Wave vector Frequency (THz) Frequency (THz) Wave vector vector Frequency (THz) NaCl no NAC w/NAC

28. We are wrapping all of these into automated workflows for high-throughput 28 VASP DFT relaxation VASP (Large displaced) Complete Φ Imaginary modes? Stable Phonon INPUT Bulk modulus ShengBTE Boltzmann Transport • Free Energy • Entropy • Heat Capacity • Gruneisen • Thermal Expansion • Lattice Thermal Conductivity Yes No • Phase transition • Thermoelectric zT Renormalization at T > 0 K Renormalized Φ • Corrected Free Energy HiPhive Harmonic Φ2 HiPhive Anharmonic Φ3, Φ4 etc VASP (Small displaced)

29. Testing and parameter selection is ongoing, but we see major speedups compared to standard methods 29 10x speedup 100x speedup 1000x speedup All 5 testing systems show a 100-500x speedup based on DFT computations, due to the very few supercells needed for HiPhive method. Expecting fully automated workflows in 2023

30. Conclusions • The community has already done a lot of great work with approximate methods of electronic and thermal conductivity • We are developing methods intended to be automatic and also >100X faster, while also retaining accuracy and information content • Looking ahead, we hope such methods will also lead to accurate databases of calculated electronic and thermal properties in resources like The Materials Project 30

31. Acknowledgements AMSET • Alex Ganose • Alireza Faghaninia • Junsoo Park 31 Funding provided by: • U.S. Department of Energy, Basic Energy Science, Early Career program • U.S. Department of Energy, Basic Energy Science, Materials Project program Slides (already) posted to hackingmaterials.lbl.gov Phonons • Zhuoying Zhu • Junsoo Park • Alex Ganose Alex Ganose Alireza Faghaninia Junsoo Park Zhuoying Zhu

Efficient methods for accurately calculating thermoelectric properties – electronic and thermal transport

Esté a ler uma amostra.

Confira estes a seguir

Efficient methods for accurately calculating thermoelectric properties – electronic and thermal transport

Mais Conteúdo rRelacionado

Semelhante a Efficient methods for accurately calculating thermoelectric properties – electronic and thermal transport (20)

Mais de Anubhav Jain (20)

Mais recentes (20)