Computer simulation of thermal expansion of non-cubic crystals: forsterite, anhydrite and scheelite

Abstract

The thermal expansion of non-cubic crystal structures may be simulated by a geometric least-squares refinement of the known structure after predicting the thermal expansions of various coordination polyhedra. This method has been applied to forsterite, Mg2SiO4, anhydrite, CaSO4, and scheelite, CaWO4. The expansions of different M-O bonds (M = Mg or Ca) are predicted by using an empirical relationship between the expansion cofficient, α, and bond-strength, s. The expansions of the polyhedral edges are approximated from the changes in the average M-O bond lengths. The rigid tetrahedral groups (SiO4, SO4 or WO4) were assumed to retain their size and shape during the process of thermal expansion. The structural changes are simulated at 300°C for forsterite and at 200°C for anhydrite and scheelite. Calculated changes in the position parameters for forsterite are generally in the same direction as those observed experimentally. The lattice parameters compare well and calculated values of the expansion coefficients along the three crystallographic axes show the same trend as the observed values namely αa < αc < αb. Thermal expansion behavior of anhydrite has been determined experimentally in the temperature range 20-275°C and the structure has been simulated at 200°C. The observed and calculated values of the expansion coefficients agree well; both show that αa > αc >> αb. The calculations on scheelite successfully reveal the characteristic anisotropic thermal expansion behavior of scheelite-type structures, which is αa < αc.