Kinetics of the bct–bcc phase transformation in tin revealed by ultrafast x-ray diffraction

Understanding structural phase transitions is crucial for predicting the macroscopic behaviors of materials under shock compression. In this study, we employed in situ x-ray diffraction to investigate the crystal structures of tin along the Hugoniot. Our results demonstrate that the bct–bcc phase boundary shifts to a higher pressure under shock compression compared to static compression. This shift addresses the observed discontinuity in the relationship between shear strength and shock pressure, anchoring the dynamic bct–bcc phase boundary at 34.7 ± 2.5 GPa. To elucidate the mechanisms behind the shift, we propose a nucleation model that emphasizes the roles of surface free energy and chemical potential difference in determining the energy barrier for nucleation and the kinetics of phase transformation. This straightforward yet generalized model accounts for hysteresis effects during compression and decompression, particularly when the chemical potential differences approach zero. Additionally, it explains how phase boundaries shift under shock compression, considering competition among various phase transformation pathways. These results underscore the critical role of phase transformation kinetics in interpreting the dynamic properties of materials under shock compression, providing insights that go beyond traditional static phase diagrams.