Structure and elastic properties of quartz at pressure

Abstract

Unit cells and crystal structures were determined on a single crystal of quartz at seven pressures from I atm to 61.4 kbar. Unit-cell parameters are a:4'916(l) and c : 5.a054(4)A at I atm, and a: 4.7O22(3) and c : 5.2561Q)A at 61.4 kbar. Structural changes observed over this pressure range include a decrease in the Si-O-Si angle ftom 143.73(7) to 134.2(l)' a decrease in the average Si-O bond distance from 1.6092(7) to 1.605(l)A, and an increase in distortion ofthe silicate tetrahedron. Several O-O distances show very large changes (ll7a) that can be related to the unit-cell-edge compression. As pressure is increased, the geometry of the SiO, (quartz) structure approaches that of the low-pressure GeO, (quartz) structure. The structural changes that take place with increased temperature are not the inverses of those that occur with increased pressure; changes in the Si-O-Si angle and the tetrahedral tilt angle control thermal expansion, whereas smaller changes in the Si-O-Si angle and tetrahedral distortion control isothermal compression. By constraining the zero-pressure bulk modulus to be equal to that calculated from acoustic data [K, : 0.371(2) Mbar], the pressure derivative of the bulk modulus at Tnro pressure tKi : 6.2(l)l has been calculated by fitting the P-V data to a Birch-Murnaghan equation of state. The anomalously low value of Poisson's ratio in quartz can be explai-ned by the low ratio of the off-diagonal shear moduli to the pure-shear moduli. This small ratio reflects the easily expandin! or contracting spirals of tetrahedra that behave like coiled springs.