The calculation of solid-liquid interface free energies from biased atomistic simulations

Abstract

The orientation dependence of the solid-liquid interface (SLI) free energy is an important parameter which determines orientation selection and the evolution of dendritic morphologies during the solidification of metallic melts. Atomistic simulations complemented with well-tempered metadynamics has been carried out to compute SLI free energies for the (100), (110) and (111) crystal interfaces of pure aluminium modelling using the empirical potential model of Mendelev and coworkers.

The orientation dependence of the SLI free energy is known to be small, on the order of about 2%, and therefore great care was taken to quantify the accuracy of the metadynamics technique. It can be shown that significant reduction of the error can be achieved by averaging the free energy surfaces from many independent metadynamics runs. The supercell sizes considered in this work are sufficiently small to cause the observed melting temperature to deviate from the bulk melting temperature. Since the metadynamics method is susceptible to systematic errors caused by the latter temperature deviations, the interface-pinning method of locating melting points was used to locate the supercell-size dependent melting temperature and thereby eliminate this source of error.

Sufficient accuracy has been achieved to resolve the finite-size contributions towards the estimated value of the SLI free energy caused by the finite dimensions of the supercells used; the values of SLI free energy obtained were found to depend strongly on both the supercell cross section and length. Attempts have been made to rationalise these finite-size effects based on the logarithmic scaling relations of Binder and Schmitz and coworkers. Estimates for the anisotropy ratio are obtained and compared with literature.

Difficulties relating to the formation of twinned regions was encountered when applying the metadynamics technique to (111)-orientated supercells. The imposition of an appropriate restraining wall was found to inhibit the formation of these twins and thus allow the SLI free energy to be computed successfully. It is anticipated that the results of this study will provide an invaluable framework in any future attempt to estimate SLI free energies from small simulation cells which is a requirement perhaps necessitated by ab initio simulation.