An empirical test of the crystal lattice strain model for rare-earth element partitioning into clinopyroxene

Abstract

The significance of crystallographic control over trace element incorporation into minerals is now widely recognized. Its most accepted parameterization – the crystal lattice strain model – is increasingly being applied with success in experimental and empirical petrology. The fundamental premise of the crystal lattice strain model is that isovalent trace element incorporation is governed mainly by two factors, the radius of the substituent cation and the elastic modulus of the substituent lattice site.This paper presents an empirical study that tests the premise of the crystal lattice strain model with a combination of high precision crystallographic and lanthanide data for the mineral clinopyroxene. Multiple aliquots of very small subgrains (ca. 50μm diameter) were exposed to repeat XRD analysis (Gandolfi camera) and subsequently chemically analyzed by low-blank miniaturized solution ICP-MS procedure. Additional in situ chemical analyses were also obtained by laser ablation ICP-MS. Using Rietveld analysis, the XRD data define the structural parameters of the crystal, including the exact geometry of the M2 and M1 sites. The lanthanide data, when normalized to an appropriate bulk rock composition, yield a normalized concentration with similar effectiveness to the distribution coefficient. The apex of the resulting Onuma diagram is centered over the ideal radius, which can be quantified using a plot of radius parameter versus the natural logarithm of the apparent distribution coefficient. The combined dataset thus yields two completely independent estimates for the effective radius of the M2 cation (and for two samples also the M1 cation), for which the lanthanides substitute.Comparison of the two independent estimates for the ideal radius yielded a robust positive correlation (r2=0.879) with a slope of 0.911 for 4 of the 5 studied specimens and even stronger agreement, when M1 data are included. This study thus provides very strong empirical evidence that adds to a growing database of experiments showing the validity of the crystal lattice strain model.