Displacive feature and kinetics of the first-order β-Sn to γ-Sn transition under rapid compression
Phys. Rev. B 114, 194106 – Published 13 October, 2026
DOI: https://doi.org/10.1103/yzqf-mh8g
Abstract
A first-order structural phase transition is typically a displacive or reconstructive transformation. The latter has been considered a nondirect group–subgroup symmetry transition. However, with an alternative pathway, recent group-theoretical symmetry analysis predicts that such a reconstructive transition can be realized via a multistep displacive mode. So far, no direct observations of such a displacive transition pathway under pressure have been reported because of the lack of sufficient temporal resolution. Here, we present our experimental results on the phase transition of tin with a specially designed ultrafast time-resolved x-ray diffraction (tens of microseconds) combined with a series of rapid compressions (up to 51.5 TPa/s), revealing the missing region in both the time domain and compression-rate range between static and shock compression. The pressure-induced first-order phase transition from to γ-Sn(/mmm) without direct symmetry operation shows distinct displacive characteristics in the sequential x-ray diffraction measurements, and the transition time is observed to depend on the compression rate. The deficit of summed phase fraction of β-Sn and γ-Sn from unity directly derived from diffraction peak intensities during the phase transition shows a clear compression-rate-dependent profile, which indicates the existance of an intermediate phase. Solid-state nudged elastic band calculations confirm the collective displacive paths of all atoms during the transition, and the corresponding XRD simulated patterns show results consistent with the experimental time-resolved XRD observations. This dynamic structural evolution occurs on the microsecond time scale, which is orders of magnitude shorter than conventional high-pressure XRD experiments. Our results shed new light on the dynamics of the traditionally assumed reconstructive phase transition on the microsecond time scale.
