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We extend the recently proposed Z method of estimating the melting temperature from a complete liquid and propose a modified Z method to calculate the melting temperature from a solid-liquid coexistence state. With the simulation box of rectangular parallelepiped, an initial structure of perfect lattice can run in the microcanonical ensemble to achieve steady solid-liquid coexistence state. The melting pressure and temperature are estimated from the coexistence state. For the small system with 1280 atoms, the simulation results show that the melting curve of copper has a good agreement with the experiments and is identical in accuracy with the results of the two-phase coexistence method with 24 000 atoms in the literature. Moreover, the method is conceptually simpler than the two-phase coexistence method.

We report continuous measurements of the sound velocity along the principal Hugoniot curve of α quartz between 0.25 and 1.45 TPa, as determined from lateral release waves intersecting the shock front as a function of time in decaying-shock experiments. The measured sound velocities are lower than predicted by prior models, based on the properties of stishovite at densities below ∼7  g/cm^{3}, but agree with density functional theory molecular dynamics calculations and an empirical wide-regime equation of state presented here. The Grüneisen parameter calculated from the sound velocity decreases from γ∼1.3 at 0.25 TPa to 0.66 at 1.45 TPa. In combination with evidence for increased (configurational) specific heat and decreased bulk modulus, the values of γ suggest a high thermal expansion coefficient at ∼0.25-0.65  TPa, where SiO_{2} is thought to be a bonded liquid. From our measurements, dissociation of the molecular bonds persists to ∼0.65-1.0  TPa, consistent with estimates by other methods. At higher densities, the sound velocity is close to predictions from previous models, and the Grüneisen parameter approaches the ideal gas value.

We examined the validity of the modified Z method to predict the high-pressure melting curve of the body-centered-cubic transition metals, e.g., tantalum, in the molecular dynamics simulations using an extended Finnis-Sinclair potential. A unique feature was observed that a solid system evolves into the steady interphase of the solid and the liquid. In spite of simple running processes, the melting curve extracted from the solid-liquid coexistence states composed of only 960 atoms reaches an excellent agreement with that of the two-phase method in the literature. The liquid microstructure at the melting curve is dominated by the icosahedral short-range order, almost independent of the pressure up to 400 GPa.

The shear viscosity of matter and efficient simulating methods in a wide range of temperatures and densities are desirable. In this study, we present the deep-learning many-body potential (the deep potential) method to reduce the computational cost of simulations for the viscosity of liquid aluminum at high temperature and high pressure with accurate results. Viscosities for densities of 2.35 g/cm3, 2.7 g/cm3, 3.5 g/cm3, and 4.27 g/cm3 and temperatures from melting points to about 50 000 K are calculated. The results agree well with the experiment data at a pressure near 1 bar and are consistent with the simulation of first-principles at high pressure and high temperature. We reveal the behavior of the shear viscosity of liquid Al at a range where the current experimental results do not exist. Based on the available experimental data and newly generated simulation data, we propose a modified Enskog–Dymond theory, which can analytically calculate the viscosity of Al at this range. This research is helpful for numerous potential applications.