%0 Journal Article
%T Temperature Dependence of the Bragg Peak-Intensity Close to the -Incommensurate- Transition in Quartz
%A Hamit Yurtseven
%A Koray Kaymazlar
%J Journal of Solid State Physics
%D 2014
%R 10.1155/2014/538540
%X Quartz as a mineral has a stable crystalline phase at room temperature and atmospheric pressure; at low temperatures it is in the phase and when it is heated up, it transforms into the phase through the intermediate (incommensurate) phase within the temperature interval of nearly 1.3£¿K at around 847£¿K. The order parameter 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 - 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 for the order parameter (Bragg peak-intensity) for the -incommensurate (IC-) transition. Our values indicate that the -IC phase transition is of a second order and that the IC- phase transition is of a weak first order, as also reported in the literature. 1. Introduction Quartz (SiO2) is a mineral in crystalline form or amorphous [1] with various phases. At low temperatures in the phase with symmetry , it transforms into the phase with the symmetry [2] as the temperature increases. The transition temperature between the and phases is about 847£¿K. This crystalline structure was discovered by Le Chatelier in 1889 [3]. Since then, a great deal of work has been devoted to quartz. A review paper [4] and some studies on the - transition in quartz have been reported in the literature [5¨C9]. Measurements of the heat capacity [7¨C9] correlated with the thermal expansion have revealed the existence of an intermediate phase (incommensurate phase) in a small temperature interval of ~1.3£¿K between the and phases. We have analyzed the specific heat [10, 11] and we have examined the Pippard relations for the - transition in quartz [11] using the experimental data [8]. Spectroscopic studies on the - transition in quartz have also been reported in the literature. Some earlier Raman studies [12, 13] have investigated experimentally the soft mode behaviour of the 147£¿cm£¿1 and 207£¿cm£¿1 lattice modes close to the - transition in quartz. Neutron diffraction measurements [6, 7, 14, 15] have shown that the incommensurate phase is modulated. Change in the symmetry from the phase (low symmetry) to the phase (high symmetry) causes the order parameter in the phase to become zero in the phase. Ordering in the phase is due to a tilting of SiO4 tetrahedra around the threefold axis. It has been pointed out [16] that the symmetry change gives rise to the
%U http://www.hindawi.com/journals/jssp/2014/538540/