Rotational invariants of network former and modifier cations in silicate glasses

The structure of oxide glasses is described in terms of the local atomic environment of cations, and a key role is played by cation-oxygen coordination numbers (CN) and coordination polyhedra. There are no preferred axes in an isotropic material like a glass, so the description of coordination polyhedra must be rotationally invariant. Here a new analysis is presented using the second order rotational invariant Q(l) which are based on the spherical harmonic coefficients C-lm of the coordination polyhedra. The Q(l) are related to crystal field strength parameters which are reported in the studies of rare earth luminescence. There are few previous studies of rotational invariants and they tend to focus on hard sphere and Lennard-Jones models, and to focus on Q(l) with l even. Here results are presented for Q(l) of Si, Na, Mg, Ca, Ba, and Eu cations in molecular dynamics models of silicate glasses including a 15,100 atom model of Eu-doped sodium silicate glass. For Si with CN = 4 the Q(l) are very similar to those for tetrahedra, and variations in tetrahedral distortion are apparent in different glasses. For Na with CN = 5 the Q(l) are similar to those for a random distribution, except for l = 1 and 2 where the non-overlap of neighbouring atoms prevents a truly random distribution. The values of Q(l) for Mg cations with CN = 4 and CN = 5 show similarities to those for Al cations with CN = 4 and Na cations with CN = 5 respectively. The values of Q(l) for Ca and Ba cations with CN = 6 differ from those for a random distribution for Q(l) with l <= 4. For Eu with CN = 6 the Q(l) are between those for octahedral and for a trigonal prism geometries. For all cations there are significant values for Q(l) with l odd. (C) 2014 Elsevier B.V. All rights reserved.