Droplet model for central phonon peaks

Abstract

The central phonon peaks which have been observed at first- and second-order structural phase transitions are studied using a droplet model based on pairwise, nonlocal interactions. For second-order structural transitions, the peak is found to diverge as $\frac{1}{{(T\ensuremath{-}{T}_{c})}^{2}}$ in which $T$ is the temperature and ${T}_{c}$ is the measured critical point. Long-range order is suppressed by antiphase fluctuations between the temperatures ${T}_{I}$ and ${T}_{c}$ where ${T}_{I}$ is the critical point according to mean-field theory. The divergence of the central peak for first-order transitions is not as strong, behaving as $\frac{1}{(T\ensuremath{-}{T}_{0}^{\ensuremath{'}})}$ where ${T}_{0}^{\ensuremath{'}}$ is the coherent transformation temperature. The relatively slow atomic movements resulting from the growth and collapse of embryos for first-order transitions and antiphase domains for second-order transitions control the width of the central peak in frequency space. A calculation of the peak width for SrTi${\mathrm{O}}_{3}$ at ${T}_{c}+4$ is in agreement with the measurements of T\"opler, Alefeld, and Kollmar. When a substantial volume or shape change is associated with the first-order phase transition, the heterophase fluctuations which give rise to the central peak will be suppressed.