Equation Of State For Crystals Research Articles

Three simple scenarios for high-dimensional sphere packings.

Based on results from the physics and mathematics literature which suggest a series of clearly defined conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: in scenario A, crystallization is impeded and the glass phase constitutes the densest packing; in scenario B, crystallization from the liquid is possible, but takes place much beyond the dynamical glass transition and is thus dynamically implausible; and in scenario C, crystallization is possible and takes place before (or just after) dynamical arrest, thus making it plausibly accessible from the liquid state. In order to assess the underlying conjectures and thus obtain insight into which scenario is most likely to be realized, we investigate the densest sphere packings for dimension d=3-10 using cell-cluster expansions as well as numerical simulations. These resulting estimates of the crystal entropy near close packing tend to support scenario C. We additionally confirm that the crystal equation of state is dominated by the free-volume expansion and that a meaningful polynomial correction can be formulated.

A new equation for period vectors of crystals under external stress and temperature in statistical physics: mechanical equilibrium condition and equation of state

Starting with the rigorous derivation of the work done on the center cell by external forces, a new equation is derived for the period vectors (cell edge vectors) in crystals under external stress and temperature. Since the equation is based on the principles of statistical physics, it applies to both classical and quantum systems. The existing theory for crystals under external pressure is covered as a special case. The new equation turns out to be the mechanical equilibrium condition and the equation of state for crystals under external stress and temperature. It may be used to predict crystal structures and to study structural phase transitions and crystal expansions. For linear elastic crystals, it takes the microscopic and temperature-dependent form of the generalized Hooke’s law, and may therefore be used to calculate the corresponding elastic constants. It should be helpful in studying piezoelectric and piezomagnetic materials, as the period vectors change with external stress. It is also consistent and can be combined with the previously derived corresponding one for Newtonian dynamics.

Calculation of concentrational dependence of equilibrium lattice parameters for the alloys Al-Cu and Al-Ag

We fit the Animalu model potential by using the crystal equation of state. We give the fitted parameters for 25 metals that have a cubic lattice. We calculate the concentrational dependence of the lattice parameters for the alloys Al-Cu and Al-Ag. The derivative da/dc in these alloys agrees well with the experimental data.

Pressure-volume-temperature relations for crystalline benzene

It is shown that a modified Bridgman sylphon method can be used to directly measure PVT data of reorientational solids. PVT properties of crystalline benzene are determined from −20 to 51°C to pressures up to 500 MPa (5 kbar). Isochoric paths of solid benzene are found to be linear and parallel in this range. Their mean slope value is in very good agreement with that we previously predicted from Raman spectroscopy experiments. From these results, it can be concluded that thermodynamic behaviour of reorientational crystalline benzene may be described in terms of a cubic crystal equation of state.