An analytic model of the shear modulus applicable at temperatures up to melt and at all densities is presented. It is based in part on a relation between the melting temperature and the shear modulus at melt. Experimental data on argon are shown to agree with this relation to within 1%. The model of the shear modulus involves seven parameters, all of which can be determined from zero-pressure experimental data. We obtain the values of these parameters for 11 elemental solids. Both the experimental data on the room-temperature shear modulus of argon to compressions of $\sim 2.5,$ and theoretical calculations of the zero-temperature shear modulus of aluminum to compressions of $\sim 3.5$ are in good agreement with the model. Electronic-structure calculations of the shear moduli of copper and gold to compressions of 2, performed by us, agree with the model to within uncertainties.

We present a theory of the melting of elements as a dislocation-mediated phase transition. We model dislocations near the melt as noninteracting closed loops on a lattice. In this framework we derive simple expressions for the melting temperature and latent heat of fusion that depend on the dislocation density at melt. We use experimental data for more than half the elements in the periodic table to determine the dislocation density from both relations. Melting temperatures yield a dislocation density of $(0.61\mathrm{}\pm {0.20)b}^{-2},$ in good agreement with the density obtained from latent heats, $(0.66\mathrm{}\pm {0.11)b}^{-2},$ where b is the length of the smallest perfect-dislocation Burgers vector. Melting corresponds to the situation where, on average, half of the atoms are within a dislocation core.

The melting curve of the body-centered cubic (bcc) phase of Mo has been determined for a wide pressure range using both direct ab initio molecular dynamics simulations of melting as well as a phenomenological theory of melting. These two methods show very good agreement. The simulations are based on density functional theory within the generalized gradient approximation. Our calculated equation of state of bcc Mo is in excellent agreement with experimental data. However, our melting curve is substantially higher than the one determined in diamond anvil cell experiments up to a pressure of 100 GPa. An explanation is suggested for this discrepancy.

Molecular dynamics simulations of the initial stages of the spall process in single nanocrystals and polynanocrystals of copper are performed. The simulations show that void nucleation in copper polynanocrystals occurs predominantly along the grain boundaries, whereas voids are formed at stacking fault intersections in copper monocrystals. The calculated spall strengths of single-crystal copper at strain rates of $2-4\times {10}^9{\mathrm{s}}^{-1}$ are consistent with existing experimental data, and the polynanocrystal spall strength is found to increase rapidly at rates around ${10}^9{\mathrm{s}}^{-1}$ up to the theoretical ultimate spall strength of $22.5\mathrm{GPa}$ at about $3\times {10}^9{\mathrm{s}}^{-1}$.

We demonstrate the topological equivalence of the phase diagrams of molybdenum (Mo) and tungsten (W), Group 6B partners in the periodic table. The phase digram of Mo to 800 GPa from our earlier work is now extended to 2000 GPa. The phase diagram of W to 2500 GPa is obtained using a comprehensive ab initio approach that includes (i) the calculation of the $T=0$ free energies (enthalpies) of different solid structures, (ii) the quantum molecular dynamics simulation of the melting curves of different solid structures, (iii) the derivation of the analytic form for the solid–solid phase transition boundary, and (iv) the simulations of the solidification of liquid W into the final solid states on both sides of the solid–solid phase transition boundary in order to confirm the corresponding analytic form. For both Mo and W, there are two solid structures confirmed to be present on their phase diagrams, the ambient body-centered cubic (bcc) and the high-pressure double hexagonal close-packed (dhcp), such that at $T=0$ the bcc–dhcp transition occurs at 660 GPa in Mo and 1060 GPa in W. In either case, the transition boundary has a positive slope $dT/dP.$

The unified analytic melt-shear model that we introduced a decade ago is generalized to multi-phase materials. A new scheme for calculating the values of the model parameters for both the cold $(T=0)$ shear modulus $\left(G\right)$ and the melting temperature at all densities $\left(\rho \right)$ is developed. The generalized melt-shear model is applied to molybdenum, a multi-phase material with a body-centered cubic (bcc) structure at low $\rho$ which loses its dynamical stability with increasing pressure (P) and is therefore replaced by another (dynamically stable) solid structure at high $\rho$ . One of the candidates for the high- $\rho$ structure of Mo is face-centered cubic (fcc). The model is compared to (i) our ab initio results on the cold shear modulus of both bcc-Mo and fcc-Mo as a function of $\rho$ , and (ii) the available theoretical results on the melting of bcc-Mo and our own quantum molecular dynamics (QMD) simulations of one melting point of fcc-Mo. Our generalized model of $G(\rho ,T)$ is used to calculate the shear modulus of bcc-Mo along its principal Hugoniot. It predicts that G of bcc-Mo increases with P up to ∼240 GPa and then decreases at higher P. This behavior is intrinsic to bcc-Mo and does not require the introduction of another solid phase such as Phase II suggested by Errandonea et al. Generalized melt-shear models for Ta and W also predict an increase in G followed by a decrease along the principal Hugoniot, hence this behavior may be typical for transition metals with ambient bcc structure that dynamically destabilize at high P. Thus, we concur with the conclusion reached in several recent papers (Nguyen et al., Zhang et al., Wang et al.) that no solid-solid phase transition can be definitively inferred on the basis of sound velocity data from shock experiments on Mo. Finally, our QMD simulations support the validity of the phase diagram of Mo suggested by Zeng et al.