Temperature Dependence of the Bragg Peak-Intensity Close to the α -Incommensurate- β Transition in Quartz

Quartz as a mineral has a stable crystalline phase at room temperature and atmospheric pressure; at low temperatures it is in the α phase and when it is heated up, it transforms into the β phase through the intermediate (incommensurate) phase within the temperature interval of nearly 1.3 K at around 847 K. The order parameter Q occurs due to a tilting of SiO4 tetrahedra around the threefold axis, which can be related to variation of the peak-intensity with the temperature in quartz. In this study, we analyze the temperature dependence of the Bragg peak-intensity measured through the α - β transition in quartz, as obtained from the literature according to a power-law formula. From our analysis, we deduce the values of the critical exponent β for the order parameter (Bragg peak-intensity) for the α -incommensurate (IC-) β transition. Our β values indicate that the β -IC phase transition is of a second order and that the IC- α phase transition is of a weak first order, as also reported in the literature.