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Navigating the combinatorial materials space

Navigating the combinatorial materials space

Presented at the CECAM workshop on accelerating materials discovery in Liverpool (UK) in July 2019. Various low-cost, high-throughput screening approaches are covered.

Dan Davies

July 10, 2019
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  1. Navigating the combinatorial materials
    space using chemical heuristics,
    machine learning and first-principles
    calculations
    Dan Davies
    @danwdavies

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  2. Overview
    1. Combinatorial composition space
    Bottom-up materials discovery
    2. Tiered screening
    Cheap filters to narrow down the search space
    3. Automated first-principles calculations
    High-throughput DFT

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  3. Overview
    1. Combinatorial composition space

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  4. Counting materials
    What proportion of the composition space
    for materials is represented by known
    materials?

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  5. 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
    403 species of
    interest
    The building blocks

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  6. The combinatorial perspective
    r Aw
    Bx
    Aw
    Bx
    Cy
    Aw
    Bx
    Cy
    Dz
    nCr
    81,003 107 109
    With
    stoichiometry
    106 109 1012
    n = 403 species
    Aw
    Bx
    Cy
    Dz
    w,x,y,z ≤ 8

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  7. Applying heuristic limits
    n = 403 species
    Aw
    Bx
    Cy
    Dz
    w,x,y,z ≤ 8
    1. Charge neutrality:
    wqA + xqB + yqC + zqD = 0
    2. Electronegativity order:
    Cation < Anion

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  8. Scale of the composition space
    “Computational screening of all stoichiometric inorganic
    materials”, Chem, 2016

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  9. SMACT
    Github.com/wmd-group/smact

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  10. Overview
    2. Tiered screening

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  11. Hierarchy of screening steps
    LOW COST
    HIGH COST
    Sustainability
    Band gap
    Electron energies
    (Hybrid) DFT
    Structure
    assignment
    Compositional
    filters
    (Global optimization)
    Ionic substitution
    Automated
    calculations
    PV absorbers, TCOs, photocatalysts…

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  12. Band gap screening

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  13. SSE to screen 160k chalcohalides
    VASP:
    HSE06
    K-points 0.242 Å-1
    cutoff 520 eV
    “Computer-aided design of metal chalcohalide semiconductors: from
    chemical composition to crystal structure”, Chem. Sci., 2018
    M. Gaultois et al.,
    Chem. Mater., 25,
    2911 (2013)

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  14. SSE accuracy
    Band gap of 35 ternary semiconductors
    RMSE = 0.66 eV

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  15. SSE for other chemistries
    IP of oxides
    BaO -4.97 eV
    SiO2
    -9.90 eV
    Al2
    O3
    -12.42 eV
    Range = 4.9 eV
    SD = 1.44 eV
    Band gap of 800 oxides

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  16. Supervised learning
    x: composition
    y: GLLB-sc band gap
    800 oxides
    Hackingmaterials.github.io/matminer
    Castelli et al., Adv. Energy. Mat., 2015, 5, 1400915
    ML
    model
    New
    data
    Output
    Training
    data
    training
    prediction
    Predicted
    band gap
    1.1M oxides
    x: composition

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  17. Gradient boosting regression
    Band gap of 800 oxides
    (10-fold cross validation)
    RMSE = 0.95 eV
    +
    Error
    +
    Number of trees
    “Data-driven discovery of photoactive quaternary oxides using first-
    principles machine learning”, submitted, available on ChemRxiv

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  18. Oxide bandgaps
    Distribution of GLLB-sc band gaps
    for 800 oxides
    8%
    Distribution of PBE band gap
    range for oxide compositions
    “Data-driven discovery of photoactive quaternary oxides using first-
    principles machine learning”, submitted, available on ChemRxiv

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  19. Using oxidation state data
    I. Langmuir, J. Am. Chem. Soc, 41, 868-934, 1919

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  20. Oxidation state filter
    “Materials discovery by chemical analogy: role of oxidation states in
    structure prediction”, Faraday Discussions, 2019
    species with
    anion
    metal with
    anion

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  21. Overview
    3. Automated first-principles calculations

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  22. Hierarchy of screening steps
    LOW COST
    HIGH COST
    Sustainability
    Band gap
    Electron energies
    (Hybrid) DFT
    Structure
    assignment
    Compositional
    filters
    (Global optimization)
    Ionic substitution
    Automated
    calculations
    PV absorbers, TCOs, photocatalysts…

    View full-size slide

  23. Hierarchy of screening steps
    LOW COST
    HIGH COST
    Sustainability
    Band gap
    Electron energies
    (Hybrid) DFT
    Structure
    assignment
    Compositional
    filters
    (Global optimization)
    Ionic substitution
    Automated
    calculations
    PV absorbers, TCOs, photocatalysts…

    View full-size slide

  24. Hierarchy of screening steps
    LOW COST
    HIGH COST
    Sustainability
    Band gap
    Electron energies
    (Hybrid) DFT
    Structure
    assignment
    Compositional
    filters
    (Global optimization)
    Ionic substitution
    Automated
    calculations
    PV absorbers, TCOs, photocatalysts…
    Known New Relaxed

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  25. Structure assignment
    USPEX: Max. two FU/unit cell, 60 structures/generation, 20% random,
    50% heredity, 10% permutation, 10% soft mutation, 10% lattice mutation
    Ionic
    substitution

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  26. Stability and properties
    DFT
    Thermodynamic stability
    Kinetic stability
    Hybrid DFT
    Band structure
    Carrier effective mass
    IP/EA
    Materialsproject.github.io/fireworks
    Atomate.org

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  27. Automated calcs in the cloud

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  28. Building hybrid workflows
    Combining:
    Databases,
    Statistical models,
    Heuristic rules,
    First principles methods
    ChemRxiv 2019, github.com/WMD-group/Solar_oxides_data

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  29. Summary
    • The inorganic composition space – even as defined
    within strict limits – is vast and hardly explored.
    • Compositions screening structure DFT can
    work but requires relevant compositional descriptors.
    • Simple applications of ML can open new screening
    pathways.

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  30. Acknowledgements
    Aron Walsh
    Keith Butler
    Jonathan Skelton
    Adam Jackson
    Ben Morgan
    Artem Oganov
    Conwei Xie
    Olexandr Isayev
    WMD-group.github.io

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