Nonlinear and Nonlocal Lattice Dynamical Effects in the Cubic-Tetragonal Improper Ferroelastic Phase Transition in Perovskites.
Perovskite compounds, ABX(,3), have been studied both experimentally and theoretically above and below the cubic-tetragonal improper ferroelastic phase transition. The second order elastic constants of Potassium Manganese Fluoride KMnF(,3) were measured as function of temperature in the cubic prototype phase. Along 100 and 110 the two longitudinal modes were measured from 190 K to 430 K, and the two independent transverse modes from 190 K to 350 K. Strong anomalies were observed near the phase transition (T(,c) = 186 K). The three independent pressure derivatives of the elastic constants were measured from 200 K to 400 K and also show anomalous behavior near T(,c). By means of second harmonic generation, the nonlinearity parameter was measured in 100 , 110 and 111 from 298 K to 348 K. In this temperature range, all six independent third order elastic constants have been determined. Above 320 K the second and third order elastic constants show linear temperature dependence. The values pertaining to the static crystal were obtained by linear extrapolation to T = 0 from the high temperature region where the effect of the phase transition has subsided. A Landau-Ginzburg continuum model for the interphase boundaries in the heterotype phase has been developed. It includes nonlinear local terms and nonlocal gradient terms for the three-component primary order parameter (the rotation angles of the BX(,6) octahedra). By means of group theoretical methods, the gradient coefficients have been expressed in terms of the nonlinear dispersion of the soft phonon mode near the R-point. Analytic and numerical kink-type soliton solutions for both antiphase and twin boundaries were obtained. According to this model, the symmetry in the center of the twin boundary should be trigonal (rather than cubic, as for a proper ferroelastic). Numerical application to Strontium Titanate, SrTiO(,3), shows that at T = 0 the domain wall thickness is 12 (ANGSTROM), and the domain wall energy density is 0.33 erg/cm('2). The wall thickness increases and the energy density decreases as the transition is approached with increasing temperature.
- Pub Date:
- September 1987
- Physics: Condensed Matter