Low-frequency elastic properties of the incommensurate ferroelastic

Abstract

The low-frequency elastic properties of incommensurate ferroelastic crystals [N(${\mathrm{CH}}_{3}$${)}_{4}$${]}_{2}$${\mathrm{CuCl}}_{4}$ are studied in the vicinity of the incommensurate phase transitions using parallel-plate-stress and three-point-bending methods. The temperature dependences of the effective elastic constants (relative Young's modulus) along all principal crystal directions and the shear elastic compliance ${\mathit{S}}_{55}$=1/${\mathit{C}}_{55}$ were obtained. Similarly to the elastic properties at ultrasonic frequencies (10 MHz), the elastic anomalies at low frequencies (5 Hz) near the paraelastic-incommensurate transition (at ${\mathit{T}}_{\mathit{i}}$) are well explained in the framework of the plane-wave approximation. In the transition region from the incommensurate to the commensurate improper ferroelastic phase we apply soliton theory. From the experimental data it follows that the anomalous behavior of ${\mathit{S}}_{55}$ near the phase transition from incommensurate to commensurate improper ferroelastic phase has the same features as the dielectric constant in the vicinity of incommensurate-commensurate improper ferroelectric phase transition, including the Curie-Weiss-type anomaly for ${\mathit{S}}_{55}$(T) near ${\mathit{T}}_{\mathit{c}}$, thermal hysteresis phenomena, and similar changes in the character of the anomaly under applied static stress ${\mathrm{\ensuremath{\sigma}}}_{5}$. The last results are explained within the framework of soliton theory proposed by Holakovsky and Dvorak [J. Phys. C 21, 5449 (1988)]. \textcopyright{} 1996 The American Physical Society.