Vibrational properties of vacancy in bcc transition metals using embedded atom method potentials

The embedded atom method (EAM) potentials, with the universal form of the embedding function along with the Morse form of pair potential, have been employed to determine the potential parameters for three bcc transition metals: Fe, Mo, and W, by fitting to Cauchy pressure (C ₁₂???C ₄₄)/2, shear constants $G_\textrm{v} =({C_{11} -C_{12} +3C_{44}})/5$ and C ₄₄, cohesive energy and the vacancy formation energy. The obtained potential parameters are used to calculate the phonon dispersion spectra of these metals. Large discrepancies are found between the calculated results of phonon dispersion using the EAM and the experimental phonon dispersion results. Therefore, to overcome this inadequacy of the EAM model, we employ the modified embedded atom method (MEAM) in which a modified term along with the pair potential and embedding function is added in the total energy. The phonon dispersions calculated using potential parameters obtained from the MEAM show good agreement with experimental results compared to those obtained from the EAM. Using the calculated phonons, we evaluate the local density of states of the neighbours of vacancy using the Green’s function method. The local frequency spectrum of first neighbours of vacancy in Mo shows an increase at higher frequencies and a shift towards the lower frequencies whereas in Fe and W, the frequency spectrum shows a small decrease towards higher frequency and small shift towards lower frequency. For the second neighbours of vacancy in all the three metals, the local frequency spectrum is not much different from that of the host atom. The local density of states of the neighbours of the vacancy has been used to calculate the mean square displacements and the formation entropy of vacancy. The calculated mean square displacements of the first neighbours of vacancy are found to be higher than that of the host atom, whereas it is lower for the second neighbours. The calculated results of the formation entropy of the vacancy compared well with other available results.     

Equation of state of long chain molecules and rings

An equation of state for long chain molecules has been proposed using statistical associating fluid theory (SAFT). The formalism derived here is based on the assumption that the chain is formed by the pairs of trimers. The equations of state for 48-mers and 192-mers are formulated and compared with Monte Carlo results. The theory has been developed to treat hard sphere molecules with two attraction sites to form a ring molecule. The equations of state for trimer, hexamer and 12-mer ring molecules have been formulated. There is excellent agreement with available Monte Carlo results. Second virial coefficients of tangent chain molecules and ring molecules have been determined numerically and compared with simulation results.