On the origin of the inhomogeneities and birefringence in the incommensurate phase of quartz

Abstract

It is shown that the incommensurate (IC) phase near the α ↔ β transition point in quartz (SiO 2 ) is an improper ferroelastic one and should be split into domains. The birefringence induced by such a ferroelastic phase is estimated, and it is shown that it can be as strong as is observed in experiments only if one accepts a new model for the IC transition in quartz.

Origin of the Opalescence at theα−βTransition of Quartz: Role of the Incommensurate Phase Studied by Synchrotron Radiation

“…This is not compatible with the present results. As the tripling of the elementary cell, proposed by Aslanyan et al [12], was observed neither in TEM [20] nor in the present x-ray experiments, we do not consider this model anymore. The third model, namely, the coexistence model [6], is based on the systematic observations of LS occurring in the -inc coexistence state: SAS is attributed to the nonequilibrium properties of the inc rotation domains in the vicinity of the phase boundary while LAS is attributed to the extensive presence of the transition domains of the phase (called Dauphiné twins in quartz), also perturbed by the presence of the phase boundary.…”

“…The origin of these LSs remained unexplained until the discovery of the incommensurate (inc) phase of quartz [9], predicted by Aslanyan and Levanyuk [10]. This opened the way to the LS models developed recently by SaintGrégoire et al [11] and Aslanyan et al [12], introducing the existence of different ferroelastic inc phases. A third model is based on the facts that the -inc transition is first order and that LS is observed only during the -inc coexistence [6].…”

“…Saint-Grégoire et al [11] first proposed that SAS is due to the ferroelastic properties of blocks of two dimensional periodic elongated triangles (2D-ELT), which they observed by TEM. This model was criticized by Aslanyan et al [12] who proposed the existence of another ferroelastic inc phase related to a new commensurate phase with a tripling of the elementary cell, necessary in their model to produce an intense LS. In both models, the new inc phases are considered as equilibrium phases, existing in a small temperature range above T c .…”

Light and X-Ray Scattering at the Incommensurate Transition of Quartz

“…In 1996, Saint-Grégoire et al [6] proposed that the quartz opalescence is due to the ferroelastic properties of an inc structure of elongated triangles (ELT), that they observed by transmission electron microscopy (TEM). More recently Aslanyan et al [7] developed another ferroelastic model, but with an inc phase around b*/3 (and not close to the centre of the Brillouin zone, as observed in all previous experiments). Finally, we have recently proposed that SAS is due to a structure of equilateral triangle (EQT) and that LAS is due to Dauphiné twins, both in non equilibrium strained states [5].…”

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

“…To solve these and other problems, a new model was proposed by Aslanyan et al, which claims that the appearance of u z is attributed to the higher order interactions between η and the TA 1 branch (lowest frequency phonon) such as η{[(∂η/∂x) 2 −(∂η/∂y) 2 ]u yz +2(∂η/∂x)(∂η/∂y)u xz } [6]. It is also claimed that the actual temperature interval of the IC phase is wider than [T c ,T i ], but in the interval [T i ,T x ] the diffraction satellites are not observed because of large phase fluctuation [7]. In this respect, it is important to investigate what kind of structure could be expected in quartz in the vicinity of α↔β transition from a microscopic point of view.…”