We report neutron inelastic scattering on single crystal 0.68Pb(Mg1/3Nb2/3O3)-0.32PbTiO3 (PMN-0.32PT), a relaxor ferroelectric material that lies within the compositional range of the morphotropic phase boundary (MPB). Data were obtained between 100 K and 600 K under zero and non-zero electric field applied along the cubic [001] direction. The lowest energy, zone-center, transverse optic phonon is strongly damped and softens slowly at high temperature; however the square of the soft mode energy begins to increase linearly with temperature as in a conventional ferroelectric, which we term the soft mode "recovery," upon cooling into the tetragonal phase at TC. Our data show that the soft mode in PMN-0.32PT behaves almost identically to that in pure PMN, exhibiting the same temperature dependence and recovery temperature even though PMN exhibits no well-defined structural transition (no TC). The temperature dependence of the soft mode in PMN-0.32PT is also similar to that in PMN-0.60PT; however in PMN-0.60PT the recovery temperature equals TC. These results suggest that the temperature dependence and the energy scale of the soft mode dynamics in PMN-xPT are independent of concentration on the Ti-poor side of the MPB, but scale with TC for Ti-rich compositions. Thus the MPB may be defined in lattice dynamical terms as the concentration where TC first matches the recovery temperature of the soft mode. High-resolution x-ray studies show that the cubic-to-ferroelectric phase boundary shifts to higher temperatures by an abnormal amount within the MPB region in the presence of an electric field. This suggests that an unusual instability exists within the apparently cubic phase at the MPB.
Length-scale dependent average structures, piezoelectricity enhancement and depolarization mechanisms in a non-MPB high-performance piezoelectric alloy system PbTiO3-Bi(Zr1/2Ni1/2)O3
Shear Banding in Amorphous Solids as a Nonlinear Screened Soft Mode Instability
Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Sino-Europe Complex Science Center, School of Mathematics, North University of China（中北大学数学学院中欧复杂科学中心）；Department of Chemical Physics, the Weizmann Institute of Science（魏茨曼科学研究所化学物理系）
