Derivation of conventional crystallographic descriptions of new phases from results of ab initio inorganic structure modelling

Abstract

The results of ab initio inorganic structure modelling are often in the form of Cartesian coordinates of atoms in a large, periodical and in general oblique simulation box containing hundreds to thousands of atoms. The contents of that box may correspond to a single crystal, a twin, a mixture of phases or a disordered block of matter. The problem of extracting corresponding crystallographic descriptions for single-crystal regions in the box, a necessary step in view of full quantum calculations and publication, is different from the familiar problem of extracting crystal symmetry and structure from experimental diffracted intensity data. The deductive computeraided method developed at the National Research Council of Canada over the years is based on eye identification of three pairs of atoms related by conjugate translations in the same single-crystal region on a stereo plot, followed by derivation of fractional coordinates for the atomic content of the corresponding primitive cell. Running this data through the MISSYM program discloses potential symmetry elements of the structure, with their corresponding crystallographic directions. These elements are then critically examined and accepted either as symmetry or pseudosyrnmetry on the basis of comparison of coordinate deviations between related atoms with the expected magnitude of thermal motion. All calculations described here can be performed with the NRCVAX system of programs.

Ab initioSimulation of Phase Transitions and Dissociation ofH2Sat High Pressure

“…2e) by geometry optimization at zero temperature. The optimized internal structure can be fit [18] to an orthorhombic lattice (a ഠ b 7.60, c 5.05 Å) with space group symmetry Cmc2 1 : S atoms at the positions 4a ͑1͞2, 0. What is most striking in the structure of phase VI (Fig.…”

“…2a and 2b for selected configurations. Within the same limitations underlined in our previous work on phase IV [10], we defined an average S sublattice of phase V, fitted[18] to an orthorhombic lattice (a 4.15, b 4.36, c 4.89 Å) with symmetry Pmn2 1 (space group 31) and S atoms at the 2a ͑0, 0.47, 20.13͒ and 2a ͑0, 0.01, 0.45͒ sites. This average structure…”

Static Structure and Dynamical Correlations in High PressureH2S

“…We compile first an average position for each S and fit this average lattice to a crystalline space group [26]. This yields the tetragonal I4͞mmm cell; we did not detect within our statistical errors any significant distortion into a lower symmetry space group.…”

Quantum software interfaced with crystal-structure databases: tools, results and perspectives

“…It also produces the origin shift and axial transformation that transform the original cell and its atomic content into the cell and with the origin that are conventional for the space group. This is in essence an automation of the method proposed in Le Page et al (1996). Trialand-error shows that the minimum tolerance for which a hexagonal structure is detected is 0.43 Å .…”