Structural relaxation along solid solutions: from the crystal field theory to the polyhedral bond valence approach

The degree of structural relaxation due to the isovalent substitution of cations along a solid solution can be evaluated by means of the structural relaxation coefficient, ε. This coefficient, defined as the measure of the mismatch between average and local bond distances at the crystallographic site where the substitution takes place, can vary between 0 and 1 (Urusov, 1992), i.e. from absent to total relaxation. Electronic absorption spectroscopy is one of the most common technique used in mineralogy to obtain local bond distances. Deconvolution of electronic spectra allows to calculate the crystal field strength (10Dq) that, according to the crystal field theory, is proportional to the inverse fifth power of the mean distances from XRD (Langer, 2001). In a recent work (Ardit et al., 2014) it is unequivocally demonstrated, at least for Al↔Cr substitutions at octahedral site, that ε inversely scales with the absolute difference between crystal field strengths of solid solution end-members. On the other hand, it is not always possible to obtain a complete solid solution, and the linear extrapolation of structural and optical parameters up to one of the end-members may lead to incorrect values. In light of this, a new approach based on the bond-valence method (Brown 2002) has been developed to evaluate the lattice strain associated to different local arrangement of ligands at a coordination site (Dondi et al., 2014). In detail, it has been demonstrated that the BVsumobs/ BVsumcalc ratio linearly scales with 10Dq (i.e. with the local bond distances of the involved crystallographic site). This ratio entails the observed bond-valence sum of polyhedra which share the oxygens coordinating a doped site (BVsumobs) with respect to the bond-valence sum calculated from ideal bond distances for each polyhedron (BVsumcalc). In this contribution, the aspects of above will be discussed through different case studies (i.e. the effect of Cr3+ and Co2+ at octahedral and tetrahedral sites, respectively) and by a comparison of structures having a different atomic arrangement (i.e. the case of II-NaMP2O7 pyrophosphates).