Analysis of migration paths in fast-ion conductors with Voronoi–Dirichlet partition

Abstract

In terms of the Voronoi-Dirichlet partition of the crystal space, definitions are given for such concepts as ;void', ;channel' and ;migration path' for inorganic structures with three-dimensional networks of chemical bonds. A number of criteria are proposed for selecting significant voids and migration channels for alkali cations Li+-Cs+ based on the average characteristics of the Voronoi-Dirichlet polyhedra for alkali metals in oxygen-containing compounds. A general algorithm to analyze the voids in crystal structures has been developed and implemented in the computer package TOPOS. This approach was used to predict the positions of Li+ and Na+ cations and to analyze their possible migration paths in the solid superionic materials Li3M2P3O12 (M=Sc, Fe; LIPHOS) and Na1+xZr2SixP3-xO12 (NASICON), whose framework structures consist of connected M octahedra and T tetrahedra. Using this approach we determine the most probable places for charge carriers (coordinates of alkali cations) and the dimensionality of their conducting sublattice with high accuracy. The theoretically calculated coordinates of the alkali cations in MT frameworks are found to correlate to within 0.33 A with experimental data for various phases of NASICON and LIPHOS. The proposed method of computer analysis is universal and suitable for investigating fast-ion conductors with other conducting components.

Sulfur‐ and Selenium‐Containing Compounds Potentially Exhibiting Al Ion Conductivity

“…To evaluatee ach void in each compound,t he two principles of determination and comparison need to be evaluated. [33] First, all voids with solid angles to non-X atoms larger than 5% and 4% in the case of Sa nd Se, respectively,w ereo mitted. Compounds without any voids left were taken out, yielding {45/13} compounds.S econd, all voids with r SD values smaller than the data-minedv alue minus three times its standard deviation, rounded down (1.51 (S), 1.68 (Se)), were deleted.T he reason for this is described in the DFT section: we suspect even lower-size Al ions to be stable in these chalcogenide environments because of the decreased electrostatic interactions between the Al ion and its chemical environment through the polarisation of the chalcogenides, the decreasing absolute values of the valence charges of the non-Al-cations and anions and increasingi nteratomic distances in the system we observed in the DFT calculations.…”

“…To evaluate each void in each compound, the two principles of determination and comparison need to be evaluated . First, all voids with solid angles to non‐X atoms larger than 5 % and 4 % in the case of S and Se, respectively, were omitted.…”

Alkali Metal Cation and Proton Conductors: Relationships between Composition, Crystal Structure, and Properties

“…The radii of circumspheres centered at Voronoi polyhedra vertices characterize the size of inter-site voids, while the radii of circumcircles centered at the polyhedra edges characterize the bottleneck size for the channels connecting voids. Originally, VT was used to study atomic arrangements in amorphous systems [78,79], but was then further developed for locating and characterizing voids (cavities) and channels in amorphous [80,81] and crystalline structures [82][83][84][85] and in isolated macromolecules [86,87]. However, it should be pointed out that, for atomic structures where the components are significantly different in size, a simple bisecting partitioning based only on the position of atomic centers results in an unphysical picture, with Voronoi polyhedra faces lying within larger atoms.…”

“…Finally, the resultant conductivity graph is analyzed in terms of dimensionality, connectivity of fragments, radius of cavities circumsphere, bottleneck radius, pathway length, and so on. Software developed specifically for the analysis of crystal or molecular space includes Voro3D [91], PROVAT [92], and MOLE [93], all of which focus on the analysis of voids and channels in biomolecules, and also TOPOS [82,94], which was designed for the analysis of periodic crystal structures.…”

Mechanism of structural phase transitions in the Li4GeO4-ZnGeO4 system: Computer modeling and identification of invariant nanocluster structures in Li4GeO4, LISICON Li6Zn(GeO4)2, and Li4Zn2(GeO4)2 (γ phase)

“…This work continues studies into the geometrical and topological analysis of solid electrolyte structures [13][14][15][16] and modeling of self organization processes in chemical systems [17][18][19][20][21][22]; this work employs advanced computer assisted methods of crystal struc ture analysis like those employed in the cluster analysis of tetrahedral zeolite structures [23].…”