Elasticity of the olivine and spinel polymorphs of Ni2SiO4

Abstract

The single-crystal elastic moduli, cij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni2SiO4 olivine: c11=3.40(2), c22=2.38(2), c33=2.53(2), c44=0.71(1), c55=0.87(1), c66=0.78(1), c12=1.09(2), c13=1.10(4), c23=1.13(3), Ni2SiO4 spinel: c11=3.66(3), c44=1.06(1), c12=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c11>c33>c22, regardless of composition. The moduli c55 and c66 are approximately equal, and greater than c44. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO4 tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of \(\bar c_{12} > \; = (c_{12} + c_{13} + c_{23} )/3\) and \(\bar c_{44} = (c_{44} + c_{55} + c_{66} )/3\). When transition-metal cations are six-coordinated by oxygen \(\bar c_{12} > \bar c_{44}\), and when alkaline-earth cations are six-coordinated \(\bar c_{44} > \bar c_{12}\).