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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.

Explicit functions are widely used to interpolate, extrapolate, and differentiate theoretical or experimental data on the equation of state ͑EOS͒ of a solid. We present two EOS functions which are theoretically motivated. The simplest realistic model for a simple metal, the stabilized jellium ͑SJ͒ or structureless pseudopotential model, is the paradigm for our SJEOS. A simple metal with exponentially overlapped ion cores is the paradigm for an augmented version ͑ASJEOS͒ of the SJEOS. For the three solids tested ͑Al, Li, Mo͒, the ASJEOS matches all-electron calculations better than prior equations of state. Like most of the prior EOS's, the ASJEOS predicts pressure P as a function of compressed volume v from only a few equilibrium inputs: the volume v 0 , the bulk modulus B 0 , and its pressure derivative B 1. Under expansion, the cohesive energy serves as another input. A further advantage of the new equation of state is that these equilibrium properties other than v 0 may be found by linear fitting methods. The SJEOS can be used to correct B 0 and the EOS found from an approximate density functional, if the corresponding error in v 0 is known. We also ͑a͒ estimate the typically small contribution of phonon zero-point vibration to the EOS, ͑b͒ find that the physical hardness Bv does not maximize at equilibrium, and ͑c͒ show that the ''ideal metal'' of Shore and Rose is the zero-valence limit of stabilized jellium.

High-precision, large-basis-set calculations, in the local-density approximation (LDA) (using the allelectron, full-potential, linear combination of Gaussian orbitals, fitting-function technique), of the cohesive properties and electronic states (bare Kohn-Sham energies) of the isolated AB dilayer of graphite are reported. They show that the dilayer interplanar spacing (c axis) differs little from the value for ABABAB . crystalline graphite (0.7%%uo expansion relative to one calculation, 2.5%%uo contraction relative to another, 2% expansion relative to experiment). This result, which differs significantly from a preliminary report of strong c-axis contraction, is related to the weak interplanar binding. The intraplanar lattice spacing (a axis) is virtually identical with the crystalline value for both the graphite dilayer and monolayer. The interplanar binding energy (obtained directly via optimization of the monolayer ground state with the same techniques) is in excellent (perhaps fortuitous) agreement with the experimental value for the crystal, in contrast with crystalline calculations, which are too large (in magnitude) by 40 -100% or more. The dilayer cohesive energy agrees well with the crystalline value from an allelectron calculation. Both exceed the experimental value in magnitude by over 1 eV/atom, a problem already known to arise from inadequacies in the LDA treatment of the multiplet structure of the isolated C atom. The dilayer uniaxial compressibility is much larger than calculated for the crystal, apparently another manifestation of weak interplanar binding. Dilayer Kohn-Sham eigenvalues are largely consistent with those calculated self-consistently for the crystal using the same LDA model. Both differ substantially from the non-self-consistent band structure commonly used to parametrize graphite optical properties of interest in astrophysics. Calculated values of the dilayer work function are larger by about 0.6-0.7 eV than the crystalline experimental results. The dilayer density of states at the Fermi level is predicted to be much smaller than for the crystal, while the occupied bandwidth is in reasonable agreement with crystalline experimental results.