The incommensurate phase of

Abstract

The incommensurate state and the incommensurate - commensurate (IC - C) transition in a minimal Landau model for are investigated using rigorous analytical and numerical techniques. The Euler - Lagrange equations are solved numerically using parameters for ; the results differ significantly from those obtained using the constant-amplitude approximation. The minimal model predicts that the IC - C transition is first order, in agreement with experiment; the predicted discontinuity of the wavenumber q at the transition is 42% of the maximum q, rather than the measured 50%. The predicted temperature dependence of the IC wavenumber is too strong, and the predicted entropy change at the transition is too small, suggesting that the transition in is more strongly first order than predicted by the minimal model. Some general results for the asymptotic interaction of discommensurations are also obtained.

Effect of impurities on the successive phase transitions in (Cs1 xRbx)2ZnI4compounds

“…Since Cs 2 ZnI 4 is an improper ferroelastic the possible contribution of fluctuations in heat capacity anomalies should be noted. However at x = 0 the influence of fluctuations is negligible as was mentioned in [15,16]. In the substituted crystal one can expect an increase of the fluctuation contribution resulting from the decrease of the correlation radius of fluctuations far from the transition point (see e.g.…”

“…For n = 4 the anisotropy is not necessarily weak [19]. Cs 2 ZnI 4 is exactly the case of the middle anisotropy condition where r ∼ = 0.45 as was shown in [15,16]. In the studied series of the (Cs 1−x Rb x ) 2 ZnI 4 solutions the parameter r is varied between 0.50 and 0.33.…”

“…In the studied series of the (Cs 1−x Rb x ) 2 ZnI 4 solutions the parameter r is varied between 0.50 and 0.33. In that case the solution for the order parameter near Inc-C transition is neither solitonic nor truly sinusoidal [16]. The absence of the well formed narrow solitons near T L is a critical condition against the presence of a strong pinning by defects in this region.…”

“…The free energy functional, the order parameter and the spatial coordinate can be scaled as f = β 1 γ 4 f * , ρ = γρ * and x = κz * /δ, with γ = δ/ √ κβ 1 . The scaled energy density F(α * , r ) then depends on only two parameters, the anisotropy parameter r = β 2 /β 1 and the α * = κα/δ 2 [16].…”

“…To calculate the average free energy we have followed the variational method in which the average potential F is minimized with respect to both q and θ at given temperature, and yields their equilibrium values [16].…”