GraphT-T (V1.0Beta), a program for embedding and visualizing periodic graphs in 3D Euclidean space.

Following the work of Day & Hawthorne [Acta Cryst. (2022), A78, 212-233] and Day et al. [Acta Cryst.

Bond topology of chain, ribbon and tube silicates. Part II. Geometrical analysis of infinite 1D arrangements of (TO) tetrahedra.

In Part I of this series, all topologically possible 1-periodic infinite graphs (chain graphs) representing chains of tetrahedra with up to 6-8 vertices (tetrahedra) per repeat unit were generated. This paper examines possible restraints on embedding these chain graphs into Euclidean space such that they are compatible with the metrics of chains of tetrahedra in observed crystal structures. Chain-silicate minerals with T = Si (plus P, V, As, Al, Fe, B, Be, Zn and Mg) have a grand nearest-neighbour ⟨T-T⟩ distance of 3.

Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (TO) tetrahedra.

Chain, ribbon and tube silicates are based on one-dimensional polymerizations of (TO) tetrahedra, where T = Si plus P, V, As, Al, Fe and B. Such polymerizations may be represented by infinite graphs (designated chain graphs) in which vertices represent tetrahedra and edges represent linkages between tetrahedra. The valence-sum rule of bond-valence theory limits the maximum degree of any vertex to 4 and the number of edges linking two vertices to 1 (corner-sharing tetrahedra).

Bond-length distributions for ions bonded to oxygen: results for the transition metals and quantification of the factors underlying bond-length variation in inorganic solids.

Bond-length distributions are examined for 63 transition metal ions bonded to O in 147 configurations, for 7522 coordination polyhedra and 41 488 bond distances, providing baseline statistical knowledge of bond lengths for transition metals bonded to O. bond valences are calculated for 140 crystal structures containing 266 coordination polyhedra for 85 transition metal ion configurations with anomalous bond-length distributions. Two new indices, Δ and Δ, are proposed to quantify bond-length variation arising from bond-topological and crystallographic effects in extended solids.

Empirical Lewis acid strengths for 135 cations bonded to oxygen.

New and updated Lewis acid strengths are listed for 135 cations bonded to oxygen for use with published Lewis base strengths. A strong correlation between Lewis acid strength and ionization energy is shown, and correlation with electronegativity is confirmed.

Bond-length distributions for ions bonded to oxygen: alkali and alkaline-earth metals.

Bond-length distributions have been examined for 55 configurations of alkali-metal ions and 29 configurations of alkaline-earth-metal ions bonded to oxygen, for 4859 coordination polyhedra and 38 594 bond distances (alkali metals), and for 3038 coordination polyhedra and 24 487 bond distances (alkaline-earth metals). Bond lengths generally show a positively skewed Gaussian distribution that originates from the variation in Born repulsion and Coulomb attraction as a function of interatomic distance. The skewness and kurtosis of these distributions generally decrease with increasing coordination number of the central cation, a result of decreasing Born repulsion with increasing coordination number.

Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.

Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra. Values of the RMSD range from 0.033-2.