Research ArticleChemistry

Thermodynamic limit for synthesis of metastable inorganic materials

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Science Advances  20 Apr 2018:
Vol. 4, no. 4, eaaq0148
DOI: 10.1126/sciadv.aaq0148
  • Fig. 1 A schematic Gibbs free energy (G) versus temperature (T) diagram typically used to explain polymorphic systems (52).

    Free energies of three crystalline polymorphic phases (A, B, and C) and the amorphous phase are shown relative to the ground-state crystal. Although a deviation from the projection of liquid free energies to lower temperatures is expected, the amorphous phase is depicted as a continuation of the liquid phase as often assumed. At T = 0 K, GE (internal energy), as pressure-volume contributions to enthalpy are negligible near ambient pressure for condensed phases.

  • Fig. 2 Assessing the crystalline synthesizability in 41 material systems in the “stability skyline” defined by the amorphous limits.

    (A) Energies of inorganic amorphous materials (horizontal bars, amorphous limits in bold) are compared to the crystalline polymorphs available in the Materials Project. Synthesizability ranges defined by the amorphous limits are shaded in gray. Circles and triangles correspond to polymorphs with and without existing ICSD entries, respectively. A circle is open if the ICSD-acquired polymorph is above the amorphous limit and falls under at least one of the exception categories described in the text. (B) Corresponding PDFs for ICSD (in blue) and non-ICSD (in red) crystalline polymorphs, compared to amorphous polymorphs (histogram). ICSD structures that have been associated with “high-pressure” synthesis are further tagged with a solid black circle. Units of PDFs are atom per electron volt.

  • Fig. 3 Performance of constant heuristic limits in capturing synthesized metastable materials (“sensitivity”) and excluding the “unsynthesizable ranges.”

    The sensitivity is defined as the percentage of known synthesized materials in a system that are within a given constant heuristic energy limit from the ground state. Sensitivities of heuristic limits for individual systems are also plotted in the background (thin lines) as a guide for the eye. The unsynthesizable range is defined for a system when a heuristic limit is greater than its amorphous limit, as the excess energy range between these two limits, averaged over these systems at each heuristic limit value.

  • Fig. 4 Amorphous limit sampling error as a function of sample size estimated for four different systems.

    The values of amorphous limits are also given in parentheses in electron volts per atom for comparison with the errors. The error in the amorphous limit due to limited sampling is mostly independent of the value of the amorphous limit. The error is “fail-safe” for materials discovery applications because it is guaranteed to be in only one direction, that is, the actual amorphous limit can only be lower than the limit found by a sample size of n, which prevents excluding potentially revolutionary functionality that is still synthesizable. See Supplementary Text and fig. S84 for further details.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaaq0148/DC1

    Supplementary Text

    figs. S1 to S42. Radial distribution functions of amorphous configurations.

    figs. S43 to S83. Bond-angle distribution functions of amorphous configurations.

    fig. S84. Amorphous limit sampling probability.

    fig. S85. Snapshots of atomic structures of amorphous materials.

    fig. S86. Probability of finding the correct, observed ground states.

    fig. S87. PDFs from aggregated uncertainties in the amorphous limit classification of crystalline polymorphs.

    table S1. The amorphous limits for the synthesizability of polymorphs.

    database S1. Energies of amorphous configurations.

    References (5363)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • figs. S1 to S42. Radial distribution functions of amorphous configurations.
    • figs. S43 to S83. Bond-angle distribution functions of amorphous configurations.
    • fig. S84. Amorphous limit sampling probability.
    • fig. S85. Snapshots of atomic structures of amorphous materials.
    • fig. S86. Probability of finding the correct, observed ground states.
    • fig. S87. PDFs from aggregated uncertainties in the amorphous limit classification of crystalline polymorphs.
    • table S1. The amorphous limits for the synthesizability of polymorphs.
    • Legend for database S1
    • References (53–63)

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    Other Supplementary Material for this manuscript includes the following:

    • database S1 (.json format). Energies of amorphous configurations.

    Files in this Data Supplement:

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