Mechanical and dielectric energy loss related to viscous motion and freezing of domain walls

Three dielectric loss (D) and/or three mechanical loss (Q(-1)) peaks (P-1,P-2,P-3) and corresponding susceptibilities for ferroelectric KDP and TGS, and ferroelastic LNPP crystal and Cu-Al-Zn-Ni alloy have been investigated in the kHz range. P-1 and P-2 almost overlap for first order phase transitions. P-1, a very narrow peak, is attributed to the dynamic domains due to fluctuations near T-C. P-2 is recognized to be related to domain walls (DWs). The formulas of Q(-1) and D caused by the viscous motion of DWs are derived, being fairly coincident with the experimental data of P-2. The viscous coefficient, pinning force constant of DW and the spontaneous shear strain have been calculated for Cu-Al-Zn-Ni. The susceptibility, epsilon' or Delta J/J, always shows a high plateau below T-C and drops down rapidly nearly consistent with the low temperature side of P-3 peak for poly-domain TGS, KDP and Cu-Al-Zn-Ni. P-3 is thought to originate from the freezing of DWs of high density due to a collective pinning of randomly distributed defects, similar to the pinned-vortex glass model suggested for high T-C superconductors.