Thermal expansion at the incommensurate phase transition in [N(CH3)4]2ZnCl4-xBrx crystals

Abstract

The temperature dependence of the thermal expansion in the vicinity of the incommensurate phase transition in [N(CHa)4]2ZnC14-xBrx mixed crystals is found to deviate from that predicted within the Landau theory of phase transitions. It is shown that the dominant contribution to this deviation in the immediate vicinity of T~ is due to the presence of defects. The character of the deviation is found to be in qualitative agreement with the theoretically predicted behaviour in the presence of random field type defects. In some compounds (x = 0, 2.4, 2.9), the temperature dependence of the thermal expansion coefficient at T/> Ti + 3 K can be described by a z'-dependence with ct = 0.5. These values are in reasonable agreement with ~t = 0.5, corresponding to the fluctuation correction to the Landau theory. In solid solutions with a rather smeared paraelectric-incommensurate phase transition (x = 0.25, 0.45), the value of this exponent is found to be between 0.8 and 0.9. This suggests that the contribution to the thermal expansion due to the defects in these crystals is, even quite far from the phase transition, comparable to the contribution due to order parameter fluctuations.

Critical behaviour of optical birefringence near the normal–incommensurate phase transition in [N(CH3)4]2ZnCl4crystals under the influence of hydrostatic pressure

“…One can obtain evidence that the ξ(T ) curves are more gently sloping on the side of the asymmetric phase (τ < 0). It is worthwhile that similar asymmetry in the temperature dependence of derivatives of the relative linear thermal expansion 5 has earlier been noticed in the study [25] of solid solutions [N(CH 3 ) 4 ] 2 ZnCl 4−x Br x . As a result of the asymmetry, one gets the values G − ≈ 0.011 and G + ≈ 0.003 for TMAZC in the case of atmospheric pressure (see figure 5).…”

Analysis of temperature behaviour of refractive indices inK₂SO₄ and Rb₂SO₄ crystals in the vicinity of phase transition points

“…Хоча точність оцінки G у вихідній фазі обох кристалів була нижчою, згадану асиметрію спостерігали і в деяких попередніх експериментальних роботах (див. наприклад, [22]…”

“…Виходячи з цих міркувань, ми модифікували формули (1) до простішого вигляду (див. [22,25] Література…”