Original paper
An X-ray study of the temperature dependence of the quartz structure
Kihara, Kuniaki
European Journal of Mineralogy Volume 2 Number 1 (1990), p. 63 - 78
31 references
published: Feb 14, 1990
manuscript accepted: Sep 25, 1989
manuscript received: Feb 27, 1989
DOI: 10.1127/ejm/2/1/0063
Abstract
Abstract The structure analysis of a natural transparent quartz crystal was carried out using X-ray diffraction amplitudes at temperatures ranging from 298 K to 1126 K. The temperature dependence of the atomic probability density function (PDF), the mean-square displacement (MSD) and the orientation of thermal-motion ellipsoids was analysed in detail and shown to be useful for discussing the ß-quartz structure. There is no obvious X-ray diffraction evidence supporting a disordered model for ß-quartz as previously suggested by neutron diffraction work. Instead, a more weakly disordered or even ordered model seems to be in better agreement with the observations. The characteristic feature of our model is that oxygen atoms practically undergo librational motion around the Si-Si lines, being correlated with silicon atoms oscillating along the two-fold axes in〈100〉. In this model, the motion of SiO4 tetrahedra is not rigid, but is associated with considerable bending of the O-Si-O angles. By contrast, the Si-O-Si bonding planes are kept rigid. At 848 K, the Si-O bond length is 1.62 Å and the Si-O-Si angle is 145°, whereas the O-Si-O angles range from 100 to 118°. The MSDs for oxygen and silicon atoms in the directions closely related to the displacement vectors of the α-ß transition show an anomalous temperature dependence ; with increasing temperature, there is a decrease of MSD immediately after the transition, and then a gradual change to increasing values at around 950 K.
Keywords
quartz structure • thermal vibrations • temperature dependence • phase transition • probability density function • X-ray diffraction