The modern theory of crystallization and the Hansen-Verlet rule

摘要: A cluster expansion of an order parameter distribution function is introduced into the recent theory crystallization classical fluids. This allows us to demonstrate purely geometric origin empirical Hansen-Verlet rule (max. S(k) ⋍ 2·85 or c(k 0·65 with = (1 - c(k)-1). Using moment expansions (whose convergence assumed), we find that minimum value for which bifurcation a crystalline solution same thermodynamic potential as coexisting fluid possible within our perturbation scheme corresponds c(k) 0·69 f.c.c. structure and 0·59 b.c.c. k equal smallest reciprocal lattice vector corresponding cubic structure. To this end have considered limit where fractional density change fluid's compressibility vanish in such way their ratio remains constant guarantee first character transition. work out withou...