Analysis of interface kinetics: solutions of the Gibbs-Thomson-type equation and of the kinetic rate theory

A Salhoumi,P K Galenko

doi:10.1088/1757-899x/192/1/012014

Abstract

Rapidly moving solid-liquid interface is treated analytically and numerically. Derivation and qualitative analysis of interface propagation kinetics is presented. Quantitative predictions of solutions, which follow from the Kinetic Rate Theory and the solution of Gibbs-Thomson-type equation, are compared with Molecular Dynamics simulation data (MD-data) on crystallization and melting of fcc-lattice of nickel. It is shown in the approximation of a linear behavior of the interface velocity versus undercooling that the Gibbs-Thomson-type equation and kinetic rate theory describe MD-data well enough, in the range of small growth velocity and within the range of relatively small undercooling, with a relative error for the obtained values of kinetic coefficient of the order 1.1%. Within the small-and long range of undercooling, in nonlinear behavior of the interface velocity versus undercooling, the kinetic rate theory disagrees sharply with MD-data, qualitatively and quantitatively, unlike to the Gibbs-Thomson-type equation which is in a good agreement with MD-data within the whole range of undercooling and crystal growth velocity.

Highlights

Methods of atomistic simulation represent the robust quantitative techniques, which serve to obtain equilibrium and kinetic properties of phase interfaces
We have found that, for the Kinetic Rate Theory, the better correspondence to the simulated Molecular Dynamics simulation data (MD-data) is obtained for the kinetic coefficient β(T ) = 0.711 m/(s·K)
The phase field equation, Eq (22), shows that the interface velocity V gradually deviates from the linear law to smaller values as the undercooling increases. Such a behavior in crystal growth kinetics has been found by MD-simulations of elemental systems [1], qualitatively confirmed in our work [20] and presently confirmed in quantitative comparison of Eq (22) with the MD-data of Hoyt et al [5]

Summary

Introduction

Methods of atomistic simulation represent the robust quantitative techniques, which serve to obtain equilibrium and kinetic properties of phase interfaces. Among the other important results of the dynamic boundary condition Eq (21) for the rapidly moving curved interface which includes both velocity and acceleration of the interface and can move by mean curvature and due to the driving force given by a deviation of temperature and concentration from their equilibrium values, the following should be mentioned: (i ) a generalization for the well-known velocity dependent Gibbs-Thomson relation, and (ii ) a generalized Born-Infeld equation for the hyperbolic motion by mean curvature and under driving force in the traditional Cartesian coordinates. Small range of undercooling and overheating we compare the predictions of the equations from kinetic rate theory [9] and the nonlinear solution of the phase field model [20] with MD-data of computer simulation of Mendelev et al [4] These data was obtained for relatively small values of the undercooling 0 < ∆T (K) < 50 and overheating −55 < ∆T (K) < 0 at the solid-liquid interface of the nickel crystal. It is seen clearly that Eq (5) and Eq (22) describe these well enough and even if we take into account the exponential equation of the kinetic rate theory, namely Eq (4), only a very slight difference in comparison with the linearized equation; Eqs. (5) appears

50 MD Simulation

Conclusions