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Low cost descriptors for surrogate modelling of energy generation and storage

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.

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

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  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

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  3. We can compute a lot…
    https://www.top500.org/lists/ https://www.archer.ac.uk/status/codes/
    • Higher throughput calculations
    • Higher quality calculations

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  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?

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  5. If you want to know more about SMACT

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  6. The DFT bottleneck
    1010 quaternary compounds
    ⏳ > 200,000 years
    ??? Compounds that are (i)
    stable and (ii) have useful
    properties

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  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

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  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

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  9. PART 1: What materials are worth calculating from first principles

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  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

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  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.”

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  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

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  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

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  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

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  15. Descriptors for energy storage materials
    Insulating Metallic
    TiO
    MgO In2
    O3
    Fe2
    O3
    Interest in battery cathodes…

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  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

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  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

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  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

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  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

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  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

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  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

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  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

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  23. PART 2: What is worth making

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  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?

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  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

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  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

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  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

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  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

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  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

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  30. What kind of stability?
    A
    D
    E
    B + C
    Dynamic stability
    Kinetics
    Phonons
    Thermodynamic stability
    Internal/Free energy
    or

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  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

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  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

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  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

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  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

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  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)

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  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?

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  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.

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  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.

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  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!

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  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

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  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

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