Research ArticleMATERIALS SCIENCE

The phase stability network of all inorganic materials

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Science Advances  28 Feb 2020:
Vol. 6, no. 9, eaay5606
DOI: 10.1126/sciadv.aay5606
  • Fig. 1 Network representation of T = 0 K materials phase diagrams.

    Stable phases and two-phase equilibria (tie-lines) in a phase diagram are represented as nodes and edges, respectively, to create the corresponding network: (A) Schematic A-B binary system represented as a typical two-dimensional convex hull of compound formation energies. (B) Ti-Ni-Al as an example ternary system, with the T = 0 K phase diagram shown as a Gibbs triangle. (C) Schematic A-B-C-D quaternary phase diagram shown as a Gibbs tetrahedron. (D) The 3d transition metal-chalcogen (i.e., 14-dimensional chemical space) materials network. No conventional visual representations of phase diagrams exist at higher than four dimensions. Node sizes shown are proportional to node degree.

  • Fig. 2 Overall structure and topology of the materials network.

    (A) The distribution of node degree in the materials network (gray circles) shows a heavy tail; i.e., a sizeable fraction of materials have tie-lines with nearly all other materials. A lognormal fit is shown as a solid gray line. (B) The mean local clustering coefficient 〈𝒞i〉 (green) decreases with node degree k, indicating that stable materials form local, highly connected communities. The mean neighbor degree 〈kNN〉 (red) also decreases with k, implying a weakly dissortative network behavior; i.e., materials with a large number of tie-lines connect with those with fewer tie-lines in the network. In both subplots, the vertical dashed line represents the total number of nodes (stable materials) in the network.

  • Fig. 3 Hierarchy in the materials network and underlying energetic considerations.

    (A) The mean node degree or average number of tie-lines 〈k〉 (green, open) decreases as a function of number of components 𝒩 (i.e., binary, ternary, and so on), which results from high-𝒩 materials having to compete with low-𝒩 materials for stability. The number of known stable 𝒩-ary materials (red) itself actually peaks at 𝒩 = 3 (ternaries). (B) Gaussian kernel density estimates of compound formation energies for all stable materials separated by number of components in the material. Dashed vertical lines indicate the respective median of each distribution. High-𝒩 materials need notably lower formation energies than low-𝒩 materials to become stable, e.g., −2.08 versus −0.47 eV per atom for quaternary and binary materials, respectively.

  • Fig. 4 Nobility index of all elements.

    The standard score, 𝒵n, derived in this work using material connectivity in the phase stability network, as a measure of nobility against solid-solid and solid-gas reactions. Nobility increases up the scale. Numerical values of elemental 𝒵n are given below the respective symbols.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/9/eaay5606/DC1

    Section S1. Calculation of the T = 0 K universal phase diagram

    Section S2. Degree distribution of the network of all materials

    Section S3. New information encoded in the nobility index

    Table S1. Sample compute times for calculating the existence of a tie-line between two phases.

    Fig. S1. Fitting node connectivity data to candidate distributions.

    Fig. S2. Comparison of nobility index versus common elemental properties.

    Fig. S3. Comparison of number of compounds formed by an element versus its node degree.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Calculation of the T = 0 K universal phase diagram
    • Section S2. Degree distribution of the network of all materials
    • Section S3. New information encoded in the nobility index
    • Table S1. Sample compute times for calculating the existence of a tie-line between two phases.
    • Fig. S1. Fitting node connectivity data to candidate distributions.
    • Fig. S2. Comparison of nobility index versus common elemental properties.
    • Fig. S3. Comparison of number of compounds formed by an element versus its node degree.

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