Ultrasonic study of the normal — incommensurate — commensurate phase transitions in [N(CH3)4]2ZnCl 4

Abstract
The shear elastic constants c44, c55, and c66 of single-crystal [N(CH3)4] 2ZnCl4 have been measured at 10 MHz near the normal-incommensurate transition at Ti ≃ 23°C, the incommensurate-ferroelectric commensurate lock-in transition at Tc ≃ 8°C, and the first-order ferroelectric-ferroelastic transition at T1 ≃ 4°C. A substantial variation in the velocity and attenuation of the c66-mode ultrasonic shear wave in the incommensurate phase can be understood qualitatively in terms of soliton-phonon coupling. The longitudinal attenuation α associated with the c11 mode was also studied as a function of frequency (10-70 MHz) near T i. The critical attenuation in the incommensurate phase could be well characterized by α ≃ f2(Ti - T)-0.9