The effect of density change on crystal growth rates from the melt

When a liquid crystallizes, both its structure and its average density change. The former represents a nonconserved, and the later a conserved, order parameter. Including convective flow in the fluid leads to coupled equations for average density and structural order parameter that resemble those for nonconserved order parameters, and that allow steady-state solutions. We use a simple square-gradient free-energy functional to explore the solutions to these equations and relate them to experiments and computer simulations for the crystallization of atomic fluids such as argon, silicon, sodium, and lead. The effect of the density change on freezing is predicted to be small in most cases.