Non-equilibrium phase transformations

An analytical model for non-equilibrium segregation during crystallization

“…(44) formalizes the reasonable expectation that the growth and melting should be reversible below and above the T 0 temperature for diffusionless transformation, that is, where the transformation proceeds very rapidly compared to the rate of chemical diffusion. This is in accord with Monte Carlo results at this limit [26].…”

“…The non-equilibrium k-value is derived directly from the equations which describe the growth process. This new analytical model has been developed based on extensive Monte Carlo modeling of alloy solidification [26][27][28][29]. The magnitude of the nonequilibrium effect depends on a parameter which was derived from fitting the Monte Carlo modeling results.…”

Monte Carlo modeling of dopant segregation

“…The Monte Carlo computer simulation results [10][11][12] suggest that the non-equilibrium k-value which can be used to describe the phenomenon known as solute trapping, depends on the growth rate, on the free energy driving the transformation, and on the diffusion coefficient as combined in the dimensionless growth parameter b:…”

“…In this case, freezing and melting occur, respectively, below and above the T 0 temperature of the alloy [10], which is where the free energies of the two phases of the alloy are equal. The dependence of the nonequilibrium segregation coefficient on growth rate, orientation, and liquid diffusivity in Monte Carlo simulations of rapid solidification of silicon doped with bismuth [11][12][13] are in substantial agreement with the experiment.…”

“…This model has been extended [9][10][11][12][13] to study the solidification of binary alloys under non-equilibrium conditions. Fig.…”