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Low cost descriptors for surrogate modelling of energy generation and storage

963f83cdd6c15fdba1fa247eaf448940?s=47 Dan Davies
February 28, 2021

Low cost descriptors for surrogate modelling of energy generation and storage

Departmental seminar given at STFCs SciML group at the Rutherford Appleton Labs, Didcot, UK.

963f83cdd6c15fdba1fa247eaf448940?s=128

Dan Davies

February 28, 2021
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  1. Low cost descriptors for surrogate modelling and screening of energy

    materials Dr Daniel Davies @danwdavies SciML Seminar September 2020 Department of Chemistry
  2. Context: Energy materials discovery / design hydrogen 1 H 1.00794

    lithium 3 Li 6.941 beryllium 4 Be 9.01218 sodium 11 Na 22.9898 magnesium 12 Mg 24.3050 potassium 19 K 39.0983 calcium 20 Ca 40.078 rubidium 37 Rb 85.4678 strontium 38 Sr 87.62 cesium 55 Cs 132.9055 barium 56 Ba 137.327 scandium 21 Sc 44.9559 titanium 22 Ti 47.867 vanadium 23 V 50.9415 chromium 24 Cr 51.9961 manganese 25 Mn 54.938 iron 26 Fe 55.845 cobalt 27 Co 58.9331 nickel 28 Ni 58.6934 copper 29 Cu 63.546 zinc 30 Zn 65.38 galium 31 Ga 69.723 germanium 32 Ge 72.64 aluminium 13 Al 26.9815 silicon 14 Si 28.0855 boron 5 B 10.811 carbon 6 C 12.0107 nitrogen 7 N 14.0067 oxygen 8 O 15.9994 phosphorus 15 P 30.9737 sulfur 16 S 32.065 arsenic 33 As 74.9216 selenium 34 Se 78.96 fluorine 9 F 18.9984 neon 10 Ne 20.1797 chlorine 17 Cl 35.453 argon 18 Ar 39.948 bromine 35 Br 79.904 krypton 36 Kr 83.798 thallium 81 Tl 204.3833 lead 82 Pb 207.2 indium 49 In 114.818 tin 50 Sn 118.710 antimony 51 Sb 121.760 tellurium 52 Te 127.60 bismuth 83 Bi 208.980 polonium 84 Po 209 iodine 53 I 126.904 xenon 54 Xe 131.293 astatine 85 At 210 radon 86 Rn 222 yttrium 39 Y 88.9059 zirconium 40 Zr 91.224 niobium 41 Nb 92.906 molybdenum 42 Mo 95.96 technetium 43 Tc 98 ruthenium 44 Ru 101.07 rhodium 45 Rh 102.9055 palladium 46 Pd 106.42 silver 47 Ag 107.8682 cadmium 48 Cd 112.411 hafnium 72 Hf 178.49 tantalum 73 Ta 180.9478 tungsten 74 W 183.84 rhenium 75 Re 186.207 osmium 76 Os 190.23 iridium 77 Ir 192.217 platinum 78 Pt 195.084 gold 79 Au 196.9666 mercury 80 Hg 200.59 helium 2 He 4.00260 Walsh Materials Design SMACT Periodic Table lanthanides actinides and other hard-to- pronounce elements +1,-1 +1 +1 +1 +1 +1 +2 +2 +2 +2 +2 +3 +3,+4 tt  +2,+3,+6 +2,+4,+7 +2,+3,+6 +2,+3 +2 +1,+2 +2 +3 tttttt  -3,+3,+5 -2 -1 +3 -4,+4 -3,+3,+5 -2,+2,+4 +6 -1,+1,+3 +5 +7 -1  t  +5,+7 +3 -4,+2,+4 -3,+3,+5 -2,+2,+4 +6 -1,+1,+3 +5 +7 +3 +4 +3,+5 +4,+6 +4,+7 t  +2,+3 +2,+4 +1 +2 +3 -4,+2,+4 -3,+3,+5 -2,+2,+4 +6 +4 +3,+5 t  +4,+6,+7 +4,+8 +3,+4 t  +1,+3 +1,+2 +1,+3 +2,+4 +3,+5 -2,+2,+4 -1,+1 tin 50 Sn 118.710 -4,+2,+4 common oxidation states atomic mass elemental symbol atomic number elemental name +2,+6 +2,+4,+6 +2 Energy Materials PV absorbers TCOs / TCMs PEC materials Thermoelectrics Battery cathodes Solid electrolytes …
  3. We can compute a lot… https://www.top500.org/lists/ https://www.archer.ac.uk/status/codes/ • Higher throughput

    calculations • Higher quality calculations
  4. We can compute a lot… but not everything D. W.

    Davies et al., Computational screening of all stoichiometric inorganic materials, Chem, 2016 First 100 elements in their known charge states, stoichiometry limit of 8 How many compositions could there be for… • Ay Bz • Ax By Cz • Aw Bx Cy Dz … ensuring charge neutrality and a few other rules about electron distribution?
  5. If you want to know more about SMACT

  6. The DFT bottleneck 1010 quaternary compounds ⏳ > 200,000 years

    ??? Compounds that are (i) stable and (ii) have useful properties
  7. Overview LOW COST HIGH COST • Automated first- principles calculations

    Q 1: What is worth calculating from first principles? Q 2: What is worth making? Surrogate models: • Heuristic screening • ML
  8. Overview PART 1: What is worth calculating from first principles

    - Estimating properties of solar energy materials - Estimating conductivity in energy storage materials PART 2: What is worth making - Calculating stability from first principles
  9. PART 1: What materials are worth calculating from first principles

  10. We can compute many properties for solar materials accurately but

    at a cost A. Ganose et al., Beyond methylammonium lead iodide: prospects for the emergent field of ns2 containing solar absorbers, Chem. Commun., 2016
  11. We can roughly estimate bandgap in milliseconds A. H. Nethercot,

    prediction of fermi energies and photoelectric threshold based on electronegativity concepts, Phys. Rev. Lett 1974 W. A. Harrison, Electronic structure and the properties of solids, 1980 B. D. Pelatt et al., Atomic solid state energy scale, JACS, 2011 • Solid state energy (SSE) scale derived from IP and EA of various binary semiconductors “The solid state energy (SSE) scale is obtained by assessing an average EA (for a cation) or an average IP (for an anion) for each atom by using data from compounds having that specific atom as a constituent. For example, the SSE for Al (-2.1 eV) is the average EA for AlN, AlAs, and AlSb.”
  12. We can roughly estimate bandgap in milliseconds A. H. Nethercot,

    prediction of fermi energies and photoelectric threshold based on electronegativity concepts, Phys. Rev. Lett 1974 W. A. Harrison, Electronic structure and the properties of solids, 1980 B. D. Pelatt et al., Atomic solid state energy scale, JACS, 2011 • Solid state energy (SSE) scale derived from IP and EA of various binary semiconductors • Used to screen a space of 160k chalcohalide compositions for water splitting materials D. W. Davies et al., Computer-aided design of metal chalcohalide semiconductors: from chemical composition to crystal structure, Chem. Sci., 2018
  13. We can roughly estimate bandgap in milliseconds sometimes IPs of

    oxides are not good “training data” (e.g. BaO: -5.0 eV, SiO2 : -9.9 eV, Al2 O3 : -12.4 eV…) Input data from Castelli et al., New Light-Harvesting Materials Using Accurate and Efficient Bandgap Calculations, Adv. Energy. Mat., 2015 How to improve on this? Better representation of materials? More sophisticated model? µ(𝝌) Max(𝝌) Min(𝝌) µ(rion ) … y 2.2 3.4 0.9 4.3 … 3.6 3.5 5.3 0.3 3.3 … 5.6 85 compositional features + + Number of trees Error Gradient boosting regression algorithm
  14. A simple machine learning approach offers a solution RMSE =

    0.95 eV D. W. Davies et al., Data-Driven Discovery of Photoactive Quaternary Oxides Using First-Principles Machine Learning, Chem. Mater., 2019 IPs of oxides are not good “training data” (e.g. BaO: -5.0 eV, SiO2 : -9.9 eV, Al2 O3 : -12.4 eV…) RMSE = 0.95 eV is approaching the limit of accuracy without structural information
  15. Descriptors for energy storage materials Insulating Metallic TiO MgO In2

    O3 Fe2 O3 Interest in battery cathodes…
  16. Modelling charge transport beyond the effective mass approximation L. D.

    Whalley, effmass: An effective mass package, Journal of Open Source Software, 2018 Effective mass Mobility n-type Conductivity p-type
  17. Electron and hole effective mass across metal oxides 5,548 metal

    oxides Electrons Holes  X M  Z R A Z −4 −2 0 2 4 6 8 Energy (eV) O (p) Sn (s) Sn (p) Sn (d) E.g. SnO2
  18. Moving from the band picture to thinking in terms of

    polarons P. A. Cox, Electronic Structure and Chemistry of Solids, 1987 Quasiparticles describing a charge carrier plus surrounding polarization of the lattice But polarons are currently impossible to model from first principles fully: • Large supercells required even for simple systems • DFT is a mean field theory • DFT relies on the Born- Oppenheimer approximation For latest efforts see: W. H. Sio, et al., Polarons from first principles, without supercells, PRL, 2019 W. H. Sio, et al., Ab initio theory of polarons: Formalism and applications, PRB 2019
  19. We can estimate polaron binding energy from effective mass and

    dielectric tensor S. Pekar, Local quantum states of electrons in an ideal ion crystal, J. Exp. Theor. Phys., 1946 H. Fröhlich, Electrons in lattice fields, Adv. Phys., 1954
  20. S. Pekar, Local quantum states of electrons in an ideal

    ion crystal, J. Exp. Theor. Phys., 1946 H. Fröhlich, Electrons in lattice fields, Adv. Phys., 1954 We can estimate polaron binding energy from effective mass and dielectric tensor
  21. We can estimate polaron binding energy from effective mass and

    dielectric tensor 214 metal oxides Type I Type II Type III D. W. Davies et al., Descriptors for electron ahd nhole charge carriers in metal oxides, J. Phys. Chem. Lett., 2019
  22. We can estimate polaron binding energy from effective mass and

    dielectric tensor 214 metal oxides Formula e h PtO2 0.5 1.5 CuRhO2 0.5 2.2 LiAg3 O2 18 11 NaNbO2 5.9 2.9 Ca4 Bi2 O 12 14 YZnAsO 17 30 NaAg3 O2 14 17 LaZnAsO 7.9 19 YZnPO 13 19 LiNbO2 36 6.6
  23. PART 2: What is worth making

  24. The problem is stability… LOW COST HIGH COST • Heuristic

    screening • ML models • Automated first- principles calculations Q 1: What is worth calculating from first principles? Q 2: What is worth making? What is worth trying to make?
  25. Layered quinary materials as p-type TCs A2+ B3+ O Ch

    Cu A-B-O-Cu-Ch Prototype: [Cu2 S2 ][Sr3 Sc2 O5 ] • Eg = 3.1 eV • µhole = 150 cm2V-1s-1 • σundoped = 2.8 Scm-1 @ 1017 cm-3
  26. Five elements à tunable electronic properties [Cu2 Ch2 ]2- [A3

    B2 O5 ]2+ Cu 3d – Ch 2p mixing in VBM à favourable band dispersion and delocalized holes. Large band gap due to perovskite- like layer. A2+ B3+ O Ch Cu A-B-O-Cu-Ch
  27. Widening the search for interesting compositions A2+ B3+ O Ch

    Cu A-B-O-Cu-Ch A = Sr, Ca, Ba, Mg B = Sc, Al, Ga, In, Y, La O S Cu 24 materials
  28. Widening the search for interesting compositions A2+ B3+ O Ch

    Cu A-B-O-Cu-Ch A = Sr, Ca, Ba, Mg, Na, K, Rb, Cs, Zn, Al, Ga, In, Sc, Y, La, Ti, Zr, Hf, Ge, Sn, Pb O Cu 24 materials à 1200 materials ?? 🤔 B = Sr, Ca, Ba, Mg, Na, K, Rb, Cs, Zn, Al, Ga, In, Sc, Y, La, Ti, Zr, Hf, Ge, Sn, Pb S, Se
  29. Heuristic design rules narrow down the search space a lot

    1. A and B chosen to be electropositive and closed shell 2. qA ≤ qB for perovskite-like framework 3. Goldschmidt tolerance factor for perovskite-like framework (0.7 – 1.0) 4. Charge neutrality t > 1 A too big t < 0.7 A and B similar in size 1200 704 496 154
  30. What kind of stability? A D E B + C

    Dynamic stability Kinetics Phonons Thermodynamic stability Internal/Free energy or
  31. First-principles calculations (using e.g. the VASP code), give access to

    DFT total energy == enthalpy Key parameter of interest: Energy above convex hull of composition phase diagram Materials Project Find competing phases 154 charge neutral PBEsol relaxations Thermodynamic stability Multiple magnetic orderings possible? Generate different spin- ordered supercells Y N 154 candidates 784 competing phases
  32. Materials Project Find competing phases 154 charge neutral PBEsol relaxations

    Thermodynamic stability Multiple magnetic orderings possible? Generate different spin- ordered supercells Y N 154 candidates 784 competing phases Key parameter of interest: Energy above convex hull of composition phase diagram First-principles calculations (using e.g. the VASP code), give access to DFT total energy == enthalpy
  33. Studying this many materials is possible with automated first-principles calculations

    Job script Input files Output files • Vim / Text editor • Bash / Python scripting • SSH & SCP Job script Input files Output files Processing Processing Before Now
  34. Mapping out thermodynamic stability Increasing size 87 possibly stable/metastable structures

    (Ehull < 90 meV/atom) Increasing size t > 1 A too big. t < 0.7 A and B similar in size
  35. Thermodynamic stability agrees with experiment so far Cu-S Cu-Se Sc

    0 0 In 0 0 Y 46 0 La 132 76 Ehull (meV/atom)
  36. Thermodynamic stability agrees with experiment so far Cu-S Cu-Se Ag-S

    Ag-Se Sc 0 0 2 0 In 0 0 8 0 Y 46 0 46 0 La 132 76 120 107 Ehull (meV/atom) Would a stricter (than < 90 meV/atom) Ehull threshold be more useful for this class of materials?
  37. Stability vs synthesizability • It is still not clear how

    first principles calculations can be used to predict the “synthesizability” of a compound accurately • A closer look at what is stable and what is unstable according to DFT is probably needed.
  38. Summary • We can use a range of descriptors to

    quickly and roughly predict properties of hypothetical energy materials • Predicting the stability of hypothetical compounds remains a challenge. We can do it for some well-known crystal structures but lack the tools to do it for much else. • Even with first-principles methods, thermodynamically stable =/= dynamically stable =/= synthesizable. The chemistry and structure type has a huge impact and this still needs unravelling. • Data-driven techniques have an important role to play in the prediction of the stability of new compounds.
  39. Tools and acknowledgements Electronic structure calculations • VASP (www.vasp.at) Everything

    else is open-source python • SMACT (smact.readthedocs.io) [WMD] • Sumo (sumo.readthedocs.io) [SMTG] • Pymatgen (pymatgen.org) • Atomate (atomate.org) • Jupyter (Jupyter.org) • Scikit-learn (scikit-learn.org) Acknowlegements: • David Scanlon & SMTG (esp. B. A. D. Williamson) • Aron Walsh and WMD group (ICL) • Geoff Hyett Gregory Limburn (Southampton) • MCC @danwdavies Thanks!
  40. We have a wide range of useful band gaps Increasing

    size Increasing size 87 fundamental band gaps (HSE06) ranging from 0 à 3.2 eV
  41. Property prediction is just one way ML is applied in

    chemistry and materials science Targeting discovery of new compounds Enhancing theoretical chemistry Assisting characterization Mining existing literature K. T. Butler et al., Machine learning for molecular and materials science, Nature, 2018