Monte Carlo modeling of dopant segregation

On Linear Analysis of the Movement of the Interface under Directed Crystallization

“…Layer non-equilibrium solution gives yields a value of distribution coefficient close to unity but less than unity. However, there are several works, such as [26] [27], in which it is shown that the dependence of ( ) k eff on V can be an increasing function. Consequently, in the case of non-equilibrium layer, a small adsorption effect leads to the values of the distribution coefficient is more than unity.…”

An analytical model for complete solute trapping during rapid solidification of binary alloys

“…The probability that an atom will be trapped into a crystal depends on the ratio of the distance that the interface advances during this time to the distance that the atom can diffuse during this time [1][2][3]. The distance L which a solute atom can move by diffusion during time t is L¼(Dt) 1/2 .…”

“…Much of the current detailed understanding of rapid solidification of binary alloys under nonequilibrium conditions has been developed based on Monte Carlo computer simulations, which employ a detailed picture of the solid-liquid interface [1][2][3], and on local nonequilibrium diffusion model (LNDM) [4][5][6][7], which takes into account deviation from local equilibrium of solute diffusion in the bulk liquid. The most obvious manifestation of the deviations from equilibrium during rapid solidification is solute trapping which reduces the segregations at the solid-liquid interface.…”

“…The degree of solute trapping is usually quantified by the partition coefficient K, defined as the ratio of the concentration of solute in the solid to that in the liquid at the interface. The effect of solute trapping has been investigated both theoretically and experimentally [1][2][3][5][6][7][8][9][10][11][12][13][14][15]. The most outstanding question in all these studies is transition to complete solute trapping K(V)¼1 at high interface velocity V. Conventional modes of solute trapping result in K(V)-1 only at V-N. LNDM predicts complete solute trapping K¼ 1 at a finite interface velocity [5][6][7].…”

“…Moreover, rapid solidification of binary alloys is of fundamental interest to physicists in the general context of the evolution of dynamic systems far from local equilibrium. To address this issue, we will incorporate the LNDM approach [4][5][6][7] into the Jackson et al model [1][2][3] to take into account deviations from equilibrium both at the solid-liquid interface and in the bulk liquid.…”