Use of three-dimensional parameters in the analysis of crystal structures under compression

TY - CHAP

T1 - Use of three-dimensional parameters in the analysis of crystal structures under compression

AU - Balic Zunic, Tonci

PY - 2007

Y1 - 2007

N2 - Volume-related parameters of atomic coordinations are an important tool for the analysis of structural changes. Unlike usual tables of bond distances and angles they directly depict three-dimensional properties of coordination polyhedra, and in many instances give more profound structural information.Accurate determination of atomic coordinations is difficult in cases where a clear bond gap does not exist. In such instances the most reliable existing method is the determination of atomic domains in electron density, which can be performed even for experimental high-pressure crystal structure data through use of a procrystal model.For non-regular coordination polyhedra a determination of the point with the minimum variation of distances to the vertices (the centroid of coordination) is a necessary prerequisite for a calculation of the volume-related parameters. The three parameters that completely describe distortions of coordinations are the eccentricity, the asphericity Calculation of volumes of coordination polyhedra of any shape and their standard deviations can be programmed using the general expression for the volume of a tetrahedron based on the orthogonal coordinates of its vertices.For a complete understanding of structural changes, the behaviour of all coordination polyhedra plus the voids that separate them must be investigated. The structural voids in a framework are identified by a Voronoi tessellation. It can be performed e.g. on the anionic framework alone to find the centres of the coordination polyhedra of cations and the voids that separate them. Analysis of individual compressional characteristics of structural components gives clues for the strong and weak parts of structures under high pressures and paths for structural transformations. The expected behaviour of distortion parameters for a stable atomic coordination under compression is a decrease of the global distortion parameter (sum of eccentricity, asphericity and volume distortion). Discrepancies from this behaviour reveal the stability limits of crystal structures and reasons for phase transitions. and the volume distortion.

AB - Volume-related parameters of atomic coordinations are an important tool for the analysis of structural changes. Unlike usual tables of bond distances and angles they directly depict three-dimensional properties of coordination polyhedra, and in many instances give more profound structural information.Accurate determination of atomic coordinations is difficult in cases where a clear bond gap does not exist. In such instances the most reliable existing method is the determination of atomic domains in electron density, which can be performed even for experimental high-pressure crystal structure data through use of a procrystal model.For non-regular coordination polyhedra a determination of the point with the minimum variation of distances to the vertices (the centroid of coordination) is a necessary prerequisite for a calculation of the volume-related parameters. The three parameters that completely describe distortions of coordinations are the eccentricity, the asphericity Calculation of volumes of coordination polyhedra of any shape and their standard deviations can be programmed using the general expression for the volume of a tetrahedron based on the orthogonal coordinates of its vertices.For a complete understanding of structural changes, the behaviour of all coordination polyhedra plus the voids that separate them must be investigated. The structural voids in a framework are identified by a Voronoi tessellation. It can be performed e.g. on the anionic framework alone to find the centres of the coordination polyhedra of cations and the voids that separate them. Analysis of individual compressional characteristics of structural components gives clues for the strong and weak parts of structures under high pressures and paths for structural transformations. The expected behaviour of distortion parameters for a stable atomic coordination under compression is a decrease of the global distortion parameter (sum of eccentricity, asphericity and volume distortion). Discrepancies from this behaviour reveal the stability limits of crystal structures and reasons for phase transitions. and the volume distortion.

M3 - Book chapter

VL - 37/661(2)

SP - 157

EP - 184

BT - Transworld Research Network

A2 - Grzechnik, Andrzej

CY - Kerala, India

ER -