The phase diagram for a three-phase equilibrium was derived using van der Waals (vdW) equation of state (EOS) with respect to pressure. Aside from the typical liquid-gas vdW EOS, a new solid-gas vdW EOS was introduced. The new vdW EOS had the same functional form as the original equation of state and only the van der Waals coefficients were different. The thermodynamic EOSs were integrated to obtain the internal energy and the integral constants were given explicitly. The calculated phase diagram was consistent with that for argon and the Lennard-Jones system.

The melting entropy values of argon at constant volume (Δ_vS) as a function of density were calculated using molecular dynamics simulations. These calculations employed cells with N = 864 molecules. The resulting entropy of melting per particle, Δ_vS/N, was found to be essentially constant (with some slight effect of the crystal form) and nearly equal to 0.5 k, where k is the Boltzmann constant. The melting entropy values at constant pressure (Δ_pS) were also determined and it was observed that Δ_pS > Δ_vS. In addition, variations in the vibrational frequency in the liquid were compared with fluctuations in the solid near the melting point as a means of further investigating the melting entropy.

Adding a polarization function to a basis set for molecular orbital calculation is frequently useful for producing accurate representations of chemical bonding. This article explains practical training that could greatly promote intuitive understanding of the general idea of adding a 3d-type polarization function in a π-type molecular-orbital function. In the training, by using Microsoft Excel, students draw contour plots of the molecular orbitals supplemented with and without the polarization function in ethylene (CH₂ = CH₂), and visualize the effect of the addition.

Radioactive substances are diffused by meteorological effects and soil property or underground water. The movements affect the ambient dose rate slowly and with smoothing in the long term. We detect the phenomena at monitoring posts in Fukushima. The monitoring post measures the flux from radionuclides; therefore, we discuss relations between the flux and mass density. Time-decreasing of the flux is a function of convection-diffusion of carriers of the nuclides. At the same time, it is also a decay function of radionuclides. We discuss product of the two functions, and get an expression for the time series of radioactive contaminated grounds. By using the expressions, we research changes of typical contaminants in Fukushima. This indicates movements of radionuclides.