Research ArticleMATERIALS SCIENCE

The thermodynamic scale of inorganic crystalline metastability

See allHide authors and affiliations

Science Advances  18 Nov 2016:
Vol. 2, no. 11, e1600225
DOI: 10.1126/sciadv.1600225
  • Fig. 1 Influence of chemistry on thermodynamic scale of metastability.

    (A) Cumulative distribution functions of crystalline metastability for the most-represented chemistries in the Materials Project. Manual investigation reveals that the 20% highest-energy structures in the ICSD do not correspond to observed, crystalline polymorphs. (B) Bivariate sample density maps of metastability versus cohesive energy for group VI compounds. Chemistries with higher electronegativities, χ, exhibit stronger bonds, resulting in greater median cohesive energies and higher accessible crystalline metastabilities. (C) Energy scale of metastability for various chemistries, ordered vertically by the median cohesive energy. Left vertex, median metastability; right vertex, 90th percentile. Within a periodic group, greater lattice cohesivity yields greater crystalline metastability, as strong bonds can lock more metastable crystal structures.

  • Fig. 2 Influence of composition on thermodynamic scale of metastability.

    (A) Computed energy landscape of the ternary Fe-Al-O system with example polymorphic (red stars) and phase-separating (purple triangles) metastable compounds. For example, γ-Fe2O3 is a metastable polymorph, whereas FeAlO3 is metastable with respect to phase separation into Fe2O3 + Al2O3 (energies of metastable phases not drawn to scale). (B) Gaussian kernel density estimates of metastability distributions given the number of different elements in a compound. Dark- and light-shaded regions correspond to phase-separating and polymorphic entries, respectively. Relative areas of the shaded regions correspond to number of entries per category. Top number, median for all entries; bottom number, polymorphs only.

  • Fig. 3 Evaluating the synthesizability of metastable predicted compounds.

    (A) Metastability distributions of ICSD-observed (blue) and Data-Mined Structure Predictor (DMSP)-predicted (red) binary oxide polymorphs. (B) Energetic distribution of hypothetical polymorphs among the observed phases for five common binary oxides spanning oxidation states from +2 to +6. There is a large distribution of unobserved, low-energy hypothetical polymorphs within the energy spectrum of the observed polymorphs. (HP, high pressure; HT, high temperature). (C) The metastable β-phase is a ‘remnant’ of applied thermodynamic conditions where it was once the most stable phase. Low-energy polymorphs (red X) are potentially unsynthesizable if they cannot be stabilized under some thermodynamic condition.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/11/e1600225/DC1

    Supplementary Methods

    Dataset construction, validation, and provenance

    fig. S1. Convex hull in the binary A-B system.

    fig. S2. Phonon density of states for lattice-stable low-energy predicted Fe2O3 polymorphs.

    fig. S3. Phase stability errors should be referenced to adjacent phases in a convex hull, rather than the elemental states.

    fig. S4. Fraction of metastable phases in a convex hull with formation energies jittered by 24 meV/atom random Gaussian variable.

    fig. S5. Probabilities of attaining same stable phases or same stable compositions under a convex hull jittered by random DFT error.

    fig. S6. Cumulative distribution of volume changes in the Materials Project.

    fig. S7. Cumulative distribution of bond length changes in the Materials Project.

    fig. S8. Large change in bond length between the ICSD and computed entry for Ba2CoO4.

    fig. S9. Large change in bond length between the ICSD and computed entry for SnF2.

    fig. S10. Energy distribution of metastable binary oxide polymorphs in the Materials Project, sorted by provenance.

    fig. S11. Gaussian kernel distribution of the formation energies of both stable and metastable ICSD entries in the Materials Project.

    table S1. Data Table for Fig. 1: Metastability by Chemistry

    table S2. Data Table for Fig. 2: Metastability by Composition

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Methods
    • Dataset construction, validation, and provenance
    • fig. S1. Convex hull in the binary A-B system.
    • fig. S2. Phonon density of states for lattice-stable low-energy predicted Fe2O3 polymorphs.
    • fig. S3. Phase stability errors should be referenced to adjacent phases in a convex hull, rather than the elemental states.
    • fig. S4. Fraction of metastable phases in a convex hull with formation energies jittered by 24 meV/atom random Gaussian variable.
    • fig. S5. Probabilities of attaining same stable phases or same stable compositions under a convex hull jittered by random DFT error.
    • fig. S6. Cumulative distribution of volume changes in the Materials Project.
    • fig. S7. Cumulative distribution of bond length changes in the Materials Project.
    • fig. S8. Large change in bond length between the ICSD and computed entry for Ba2CoO4.
    • fig. S9. Large change in bond length between the ICSD and computed entry for SnF2.
    • fig. S10. Energy distribution of metastable binary oxide polymorphs in the Materials Project, sorted by provenance.
    • fig. S11. Gaussian kernel distribution of the formation energies of both stable and metastable ICSD entries in the Materials Project.
    • table S1. Data Table for Fig. 1: Metastability by Chemistry
    • table S2. Data Table for Fig. 2: Metastability by Composition

    Download PDF

    Files in this Data Supplement:

Navigate This Article