Various possibilities for formation of incommensurate superstructure near the α-β transition in quartz

Aslanyan, T. A.; Levanyuk, A. P.; Vallade, M.; Lajzérowicz, J.

doi:10.1088/0022-3719/16/35/004

Cited by 80 publications

(60 citation statements)

References 12 publications

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“…As a result, a triple point of a new type, called the Lifshitz-type (LT) point, appears on the T-P phase diagrams. This point was previously predicted theoretically [5]. The LT-point can be observed in the T-P phase diagram at a given wave number q=q TL .…”

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confidence: 78%

Theoretical Approach to Constructing Temperature-Pressure Phase Diagrams for TMA-Family Crystals

2003

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The main theoretical concepts of phenomenological approach to constructing temperature -pressure phase diagrams for TMA -family crystals are presented. The phase diagram is calculated successfully for {N(CH 3 ) 4 } 2 CuCl 4 .Keywords: Phase diagram; Devil's staircase; incommensurate phase A theoretical method is developed for a constructing the temperature-pressure (T-P) phase diagrams of different crystals of tetramethylammonium tetrahalogenometalic compounds, {N(CH 3 ) 4 } 2 MX 4 , where M and X are divalent metals and halogens, respectively (see, e.g. reviews [1-3]).The method is based on the phenomenological description of a Devil's staircase [4]. We assume that all phases, observed on the T-P phase diagram in experiment for each crystal, are produced by a single soft optical branch of the normal vibration spectrum of the crystal. This branch in TMA-crystals has, in some range of parameters, two minima:the first at the center and the second at an arbitrary point of the Brillouin zone (Fig. 1). Due to this special feature, the TMA crystals differ from other crystals with the same space group D 2h 16 of the initial phase C, such as, e.g., K 2 SeO 4 , SC(NH 2 ) 2 , BCCD, the soft optical branch for which has only one minimum. As a result, a triple point of a new type, called the Lifshitz-type (LT) point, appears on the T-P phase diagrams. This point was previously predicted theoretically [5]. The LT-point can be observed in the T-P phase diagram at a given wave number q=q TL . At qq TL the C-IC phase transition occurs (IC is the incommensurate phase). Thus, the LT-point separates the transitions from the C phase to the C 0/1 and IC phases. The Lifshitz (L) point separates the same transitions [6]. But the L-point can be observed on the T-P phase diagrams at q=0.Therefore a specific feature of the T-P phase diagrams for the TMA-crystals is just the absence of the L-point.We use two theoretical approaches for description of the sequence of phase transitions

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confidence: 78%

Theoretical Approach to Constructing Temperature-Pressure Phase Diagrams for TMA-Family Crystals

2003

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“…While the notion of an interface with a negative energy is at the first glance paradoxical, similar concepts were previously used for description of incommensurate ferroic phases [37][38][39][40][41] , intercalation compounds 42,43 , crystallographic shear phases 44 and charge density waves. Essentially, an intrinsic wall instability predicts transition to the modulated phase where interfaces are uniformly distributed in space (that is, emergence of the long-range modulated phase as the thermodynamic ground state of the system), as opposed to formation of two-phase mixtures [45][46][47] . In particular, it was argued that the direct gradient coupling between the order parameters could lead to the oscillatory solutions and non-uniform pattern formation 47 .…”

Section: Discussionmentioning

confidence: 99%

Atomic-scale evolution of modulated phases at the ferroelectric–antiferroelectric morphotropic phase boundary controlled by flexoelectric interaction

Borisevich

Eliseev

Morozovska³

et al. 2012

Nat Commun

154

118

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“…This model was first set up in a purely phenomenological way based on an expansion of the Landau free energy (Aslanyan and Levanyuk 1979;Aslanyan et al 1983). It was then transformed somewhat and given more physical substance in terms of RUMs by Berge et al 1986, andDolino et al 1989.…”

Section: Introduction and Theoretical Reviewmentioning

confidence: 99%

“…Also, we are only concerned with Fourier components q along the a* direction (Aslanyan et al 1983 have considered the more general case of an arbitrary q in the x y plane). Then, using the hexagonal symmetry, G L becomes GL (t] If one eliminates the displacement variables by requiring them to adjust to a given value of the order parameter so as to minimize the free energy, this leads to a Landau free energy up to second order of the form…”

Section: Introduction and Theoretical Reviewmentioning

confidence: 99%

Rigid unit modes in the molecular dynamics simulation of quartz and the incommensurate phase transition

et al. 1991

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Abstract.A molecular dynamics simulation of quartz at different temperatures both in the e and in the/~ phase has been conducted. The e-/~ phase transition could be observed. A phonon analysis of the/%phase confirms and rounds out in a quantitative way the origin of the incommensurate (ic) modulated phase. In particular it traces the optic soft mode at Y becoming (to a good approximation) a so-called rigid unit mode (RUM) at q ~ 0, and elucidates its coupling to the transverse acoustic mode which precipitates the incommensurate transition. This success underpins and illuminates the concept of RUMs and their role in structural phase transitions.

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Various possibilities for formation of incommensurate superstructure near the α-β transition in quartz

Cited by 80 publications

References 12 publications

Theoretical Approach to Constructing Temperature-Pressure Phase Diagrams for TMA-Family Crystals

Theoretical Approach to Constructing Temperature-Pressure Phase Diagrams for TMA-Family Crystals

Atomic-scale evolution of modulated phases at the ferroelectric–antiferroelectric morphotropic phase boundary controlled by flexoelectric interaction

Rigid unit modes in the molecular dynamics simulation of quartz and the incommensurate phase transition

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