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

Abstract

The shock-induced ␣͑bcc͒→͑hcp͒ 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 G ␣ ϭG , with G the Gibbs free energy. Also, the phase transition relaxation time is uncertain, with estimates ranging from Ͻ50 ns to Ϸ180 ns. Here we present an extensive study of these important aspects, metastability and dynamics, of the ␣transition in iron. Our primary theoretical tools are ͑a͒ accurate theoretically based free energies for ␣ and phases of iron and ͑b͒ 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 G ␣ ϪG 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 ␣↔ transitions proceeding at a rate of tens of nanoseconds, are in remarkable agreement with quasistatic diamond cell measurements. When the relaxation time 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 ͑a͒ depends on shock strength and is approximately 60→12 ns for shocks of 17→30 GPa, and ͑b͒ while expresses linear irreversible-thermodynamic relaxation, some nonlinear relaxation must also be present in the shock process in iron.

Semiempirical approach to the energetics of interlayer binding in graphite

“…[4][5][6][7][8] The DFT-LDA calculations for graphite have repeatedly given excellent results for the in-plane and even the c-axis lattice constants of graphite. [9][10][11][12][13][14][15][16] Some of these authors have also claimed that their predictions for the interlayer binding energy are reasonably well compared to experiments. [11][12][13]16 However, there has been confusion in quoting the experimental data given by Girifalco and Lad 17 and some corrections such as that due to thermal effect have been ignored in comparisons between theoretical predictions and experiments.…”

High pressure phase transformation in iron under fast compression

“…Iron was modeled using the two-phase equation of state of Ref. [28] (which reproduces accurately the α/ǫ phase boundary) , while Al and Al 2 O 3 were described by well calibrated equations of state in tabular form [29]. Neither Al nor Al 2 O 3 have any phase transformations in the P-T regime probed in these experiments.…”

“…Common approaches rely on simple representations of the phase transformation rates, e.g. depending linearly on the difference between the chemical potentials of the two phases [28], which reproduce some of the dynamic behavior observed in shock experiments but cannot explain more complex experimental features such as the negative acceleration loops recorded in these or the water experiments [18,19]. We adopt here the phenomenological but physical picture proposed by Kolmogorov and others [3], where well defined domains of the growing phase increase their size at the expense of the parent phase through the motion of an infinitely thin interface.…”

Ramp wave loading experiments driven by heavy ion beams: A feasibility study

“…The uranium beam intensities needed to generate pressures approaching 1 Mbar will become available with the completion of the high-current upgrade of SIS-18 in the year 2009. In RWL experiments with intense ion beams, the typical compression times from zero to the maximum pressure are about 20 ns for the aluminum and about 10 ns for the iron samples considered here, which is comparable with the dissipative relaxation times of aluminum and iron (Swegle & Grady, 1985;Boettger & Wallace, 1997). Resent laser-driven experiments (Smith et al, 2007) have demonstrated that at such short time scales there exists a stiffer response than had been expected from previous slower ramp compression experiments and from models relying on either static or shock-wave experiments.…”