Incommensurate phase of quartz : I. Elastic neutron scattering

Abstract

We report on elastic neutron scattering results showing that the intermediate phase of quartz existing in a 1.3 K range between the α and β phases is in fact incommensurate. Six satellites are observed around most Bragg peaks along the three [100] directions of reciprocal space. The modulation corresponds to the superposition of sinusoidal plane waves as no higher order harmonics are observed. With decreasing temperature the modulation vector decreases from 0.033 to 0.029 reciprocal units. Premonitory diffuse scattering is observed in the β phase a few degrees above Ti = 847.2 K, the incommensurate transition temperature. The results are discussed in relation with the current theories of incommensurate phases and are in many respect analogous to the situation of NaNO2

Numerical analysis of atomic motion in the incommensurate phase of quartz (SiO 2 ) in the vicinity of phase transition

“…Temperature T i corresponds to a certain critical value of the phase correlation time. The existence of u z agrees with the observed satellite pattern [1]. If the gradient coupling between OP and TA(C 66 ) is the sole origin of IC structure, the freezing of pure TA(C 66 ) mode would not give the acoustic displacement u z in the modulation pattern.…”

“…The diffraction intensity is proportional to (Gu) 2 . In the diffraction pattern at G=(300), the satellites at (3±k,0,0) corresponding to pure displacements u x were absent [1]. If there were no acous-tic z-component, there should be only four satellites observable near G=(022) as well.…”

“…In diffraction experiments [1], the β↔IC transition is detected by sharp increase in the intensity of satellite peaks around the Bragg peaks below a certain pressure-dependent temperature T i , which is about 850 K at normal pressure. On further cooling, the IC↔α transition takes place at T c , when the satellite peaks vanish.…”

α-β Transition in Quartz: Temperature and Pressure Dependence of the Thermodynamic Quantities for β-Quartz and β-Cristobalite as Piezoelectric Materials

“…If an electric field is applied to NaNO 2 the INC phase disappears and there is a direct transition from the paraelectric to the ferroelectric phase [8]. For quartz, the effect of the field conjugate to the other parameter can be studied.…”

A closed-shell furnace for neutron single-crystal diffraction

“…The flexible thermocouple was fixed with ceramic glue to the aluminium foil. The experiment was conducted on the four-circle diffractometer D9 at ILL in Grenoble in the vicinity of the ct-incommensurate(INC)-fl phase transitions (see, for example, Dolino, Bachheimer, Berge & Zeyen, 1984). A position-sensitive detector (Lehmann, Kuhs, McIntyre, Wilkinson & Allibon, 1989) was used to study the positions and intensities of the satellite reflections in the INC phase, which is stable between 845.9 and 847.2 K. The INC-fl transition was found to be reproducible at a thermocouple reading of 845.9 (1) K (on heating), the INC-7 transition at 844.5 (1) K (on cooling), in satisfactory agreement with the literature values.…”