Droplet model for central phonon peaks

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 $\frac{1}{{(T-T_c)}^2}$ 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 $\frac{1}{(T-T_0^{\prime })}$ where $T_0^{\prime }$ 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 $T_c+4\mathrm{}$ is in agreement with the measurements of Töpler, 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.