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The chemical ordering transition in a binary alloy is examined using classical density functional theory for a binary mixture. The ordered lattice is assumed to be obtained from the disordered lattice by a volume change only, as in L1_2 ordering from an face centered cubic chemically disordered crystal. Using the simplest possible approach, second order truncation of the expansion, non-overlapping Gaussian distributions at the sites, and expansion of the correlation functions about the sites, a very tractable expansion is obtained. Under these assumptions the expansion consists of the same terms as the lattice gas formalism where the lattice is implicitly taken as fixed, plus additional interaction terms, and an additional entropy term. This additional entropy term represents a lowest order approximation to the vibrational entropy change.
Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with respect to
Many features of granular media can be modelled as a fluid of hard spheres with {em inelastic} collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations. At low-density, a fundamental
A previous analysis of scaling, bounds, and inequalities for the non-interacting functionals of thermal density functional theory is extended to the full interacting functionals. The results are obtained from analysis of the related functionals from
The Jeans stability criterium for gravitational collapse is examined for the case of an inert binary mixture in local equilibrium, neglectinq dissipative effects. The corresponding transport equations are established using kinetic theory within the E
High-entropy alloys (HEAs), which have been intensely studied due to their excellent mechanical properties, generally refer to alloys with multiple equimolar or nearly equimolar elements. According to this definition, Si-Ge-Sn alloys with equal or co