Analysis of structural phase transitions by computer simulation

Abstract

This paper presents the results from molecular-dynamics calculations on a lattice-dynamical system which undergoes a structural phase transition. The characteristics of the model system used for the calculations are described in detail; the model is two dimensional, has an antiferro-distortive structural change, and is in the category of displacive structural transitions. The following results are obtained from the molecular-dynamics calculations. First, some equilibrium properties are shown, including the static correlation function, to establish that the system has a second-order phase transition. Second, the results for the time-dependent order parameter or soft-mode correlation function are given. Near the transition the spectral function for this correlation function exhibits a very narrow and intense central peak, in addition to the soft-mode peak. The temperature dependences of the soft-mode frequency and the central-peak width are given. The results obtained here are very similar to experimental observations, particularly on SrTi${\mathrm{O}}_3$, and they are used to argue that only intrinsic anharmonic mechanisms are needed to explain the origin of central peaks. Third, extensive results are given for the temperature and wave-vector dependence of the displacement correlation function, which give the wave-vector dependence of the central-peak characteristics. In a small temperature interval around the transition and in a small region of wave-vector space around but not including the soft-mode wave vector, the central peak is found to split so that the maximum is not exactly at zero frequency. Lastly, results for the energy-density correlation function are given for wave vectors around the soft-mode wave vector and for temperatures above the transition. Near the transition the corresponding spectral function is found to develop a pronounced high-frequency peak.