The Displacement Field Associated with the Freezing of a Melt and its Role in Determining Crystal Growth Kinetics

The atomic displacements associated with the freezing of metals and salts are calculated by treating crystal growth as an assignment problem through the use of an optimal transport algorithm. Converting these displacements into time scales based on the dynamics of the bulk liquid, we show that we can predict the activation energy for crystal growth rates, including activation energies significantly smaller than those for atomic diffusion in the liquid. The exception to this success, pure metals that freeze into face centred cubic crystals with little to no activation energy, are discussed. The atomic displacements generated by the assignment algorithm allows us to quantify the key roles of crystal structure and liquid caging length in determining the temperature dependence of crystal growth kinetics.