Continuous growth model for interface motion during alloy solidification

Atomistic and continuum modeling of dendritic solidification

“…In 2000, Celestini and Debierre [154] used a forced velocity MD technique to investigate solute trapping in LJ mixtures with equal atomic sizes. In both the LJ binary study and the aforementioned Yu et al investigation of Si-Ge the segregation coefficient as a function of interface velocity was found to be modeled well by the continuous growth model of Aziz and Kaplan [155] and Aziz [156].…”

“…However, they are not for a mesoscopic width. Kaplan and Aziz [155] and Aziz [156] have argued that significant solute trapping occurs when the interface velocity approaches a characteristic value, V d , given by V d ¼ D l =d where d is the interplanar spacing. For diffuse interface models the trapping velocity becomes V d ¼ D l =W and therefore a larger W will lead to an abnormally large amount of trapping.…”

Parameter-free test of alloy dendrite-growth theory

“…As the velocity increases, the liquidus and solidus lines approach each other and coincide in the case k(V)ϭ1. 8 …”

“…3,6 Kinetically suppressed partitioning at the interface is well described by the continuous growth model for solute trapping of Aziz and coworkers. [7][8][9] In the dilute concentration limit of alloys the velocity (V) dependence of the partition coefficient (k) is given by k͑V ͒ϭ…”

Supersaturating silicon with transition metals by ion implantation and pulsed laser melting

“…To achieve supersaturation, the solidification speed v must be high enough, compared to the diffusive speed v D of the solute, for deviations from local interfacial equilibrium to cause significant solute trapping. [8][9][10][11] Ion implantation and PLM have been used to synthesize single-crystalline silicon supersaturated with a range of dopants from group III-group VI and their diffusive speeds have been well characterized. [10][11][12][13][14][15] Transition metals, however, have proven challenging; early attempts at non-equilibrium doping of Si with transition metals resulted in complete segregation out of the solid during resolidification.…”