Predicting short-range order and correlated phenomena in disordered crystalline materials

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Science Advances  28 Aug 2020:
Vol. 6, no. 35, eabc2758
DOI: 10.1126/sciadv.abc2758
  • Fig. 1 Neutron total scattering data collected from disordered MgAl2O4.

    (A) Experimental neutron diffraction pattern (black circles) of MgAl2O4 modeled with the disordered spinel structure (red line). (B) Experimental pair distribution function (PDF; black circles) of MgAl2O4 compared with a simulated PDF calculated from the model refined from the diffraction pattern (red) and one simulated directly from application of Pauling’s first rule (blue) with Shannon’s ionic radii.

  • Fig. 2 Schematic representation of the eight possible combinations of oxygen environments in the A2+B3+2O−42 spinel structure with their electrostatic valence bond strengths calculated from Pauling’s second rule.

    In this representation, the thinner solid line above the oxygen anion (symbolized as solid red circle) represents the single bond with the tetrahedral site, and the three thicker solid lines below oxygen represent the bonds with the octahedral sites. The orange and dark blue bonds are with A2+ and B3+ cations, respectively. Only one of the eight possible arrangements produce an electrostatic valence bond strength equal and opposed to that of the oxygen anion satisfying Pauling’s valence rule (the normal spinel arrangement, top left).

  • Fig. 3 Schematic illustration of cation coordination.

    (A) before and (B) after the motion of an oxygen anion from the 48f to the 8a Wyckoff equipoint in the pyrochlore structure. The dark brown polyhedra are eight-coordinated, the light brown polyhedra are seven-coordinated, and the green polyhedra are six-coordinated. The viewing direction is [100]Fd-3m.

  • Fig. 4 Two cation layers comprise the layer stacking model (32) that describes the pyrochlore structure.

    The fundamental building blocks contained within these two layers comprising the layer stacking model, (A) an A3B layer and an (B) AB3 layer, are shown (C) before and (D) after the motion of an oxygen anion from the 48f to the 8a Wyckoff equipoint. The cation coordination scheme is compared with (E) the DFT-relaxed weberite-type arrangement of Ho2Zr2O7. The dark brown polyhedra are eight coordinated, the light brown polyhedra are seven coordinated, and the green polyhedra are six coordinated. The viewing directions for (A) and (B) are [1 1 1]Fd-3m, [0 −1 1]Fd-3m for (C) and (D), and [0 1 0]C21/m for (E).

  • Fig. 5 The locally ordered weberite-type (red diamonds) versus global, disordered, anion-deficient fluorite phase fractions (black squares), obtained from small-box and Rietveld refinements of neutron total scattering data, respectively, from Ho2Ti2−xZrxO7 pyrochlore.

    Dashed lines are included to guide the eye.

  • Fig. 6 Schematic illustration of atomic arrangements in ordered (left) and disordered (right) ionic materials.

    The red circles represent anions, and the different blue and green circles represent unique cation species. When a material that appears structurally disordered over longer length scales is studied at the atomic-scale, the actual atomic configuration and accompanying structural distortions obey Pauling’s rules. The rules are labeled for the length scales over which they are primarily applicable.

Supplementary Materials

  • Supplementary Materials

    Predicting short-range order and correlated phenomena in disordered crystalline materials

    Eric C. O’Quinn, Kurt E. Sickafus, Rodney C. Ewing, Gianguido Baldinozzi, Joerg C. Neuefeind, Matthew G. Tucker, Antonio F. Fuentes, Devon Drey, Maik K. Lang

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    • Tables S1 to S4

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