Metastability and dynamics of the shock-induced phase transition in iron

The shock-induced α(bcc)→ɛ(hcp) transition in iron begins at 13 GPa on the Hugoniot. In the two-phase region above 13 GPa, the Hugoniot lies well above the equilibrium surface defined by ${\mathrm{G}}_{\mathrm{\alpha }}$ =${\mathrm{G}}_{\mathrm{\varepsilon }}$ , with G the Gibbs free energy. Also, the phase transition relaxation time τ is uncertain, with estimates ranging from <50 ns to ≈180 ns. Here we present an extensive study of these important aspects, metastability and dynamics, of the α-ɛ transition in iron. Our primary theoretical tools are (a) accurate theoretically based free energies for α and ɛ phases of iron and (b) accurate calculations of the wave evolution following planar impacts. We define metastable surfaces for forward and reverse transitions by the condition that the thermodynamic driving force ${\mathrm{G}}_{\mathrm{\alpha }}$ -${\mathrm{G}}_{\mathrm{\varepsilon }}$ is just balanced by an opposing force resulting from elastic stresses, and we calibrate the forward surface from the Hugoniot and the reverse surface from the phase interface reflection feature of shock profiles. These metastable surfaces, corresponding to α⇆ɛ transitions proceeding at a rate of tens of nanoseconds, are in remarkable agreement with quasistatic diamond cell measurements. When the relaxation time τ is calibrated from the rise time of the P2 wave, our calculated wave profiles are in good agreement with VISAR data. The overall comparison of theory and experiment indicates that (a) τ depends on shock strength and is approximately 60→12 ns for shocks of 17→30 GPa, and (b) while τ expresses linear irreversible-thermodynamic relaxation, some nonlinear relaxation must also be present in the shock process in iron.