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

Rapid Multicomponent Alloy Solidification with Allowance for the Local Nonequilibrium and Cross-Diffusion Effects

“…Today, ultrashort energy sources allow rapid melting of layers as thin as several nanometers with re-solidification occurring on a time scale of picoseconds [ 39 ]. The corresponding solid–liquid interface velocity during re-solidification may exceed 1 m/s, which significantly suppresses the equilibrium partitioning of the species [ 19 , 25 , 26 , 27 , 30 ]. Figure 1 schematically shows the moving interface during re-solidification of a thin metal layer after ultrashort pulse laser melting.…”

“…Depending on the laser excitation strength, melting occurs roughly on a picosecond timescale followed by re-solidification with fast moving solid–liquid interface. In such a case solute diffusion in the bulk liquid occurs under local nonequilibrium diffusion conditions [ 18 , 19 , 25 , 26 , 27 , 31 , 32 ] and the generalization of the classical Fick law with allowance for the diffusional interaction between different solutes is given by [ 14 , 18 ] where t is time and is the relaxation time of the diffusion flux of component i .…”

“…At such velocities, solute diffusion in the liquid phase occurs under far from local equilibrium conditions and classical diffusion equation of parabolic type is not adequate for describing space–time evolution of solute concentrations [ 14 , 17 , 18 , 19 ]. To consider the deviation from local equilibrium of solute diffusion the liquid phase under rapid solidification conditions, the local nonequilibrium diffusion model (LNDM) [ 25 , 26 , 27 ] has been introduced by using diffusion equation of hyperbolic type, which is not based on the local equilibrium assumption. It has been demonstrated that the local nonequilibrium effects change drastically the diffusion field in the bulk liquid leading to a sharp transition from diffusion-controlled growth to kinetic-controlled growth with complete solute trapping [ 25 , 26 , 27 ].…”

“…To consider the deviation from local equilibrium of solute diffusion the liquid phase under rapid solidification conditions, the local nonequilibrium diffusion model (LNDM) [ 25 , 26 , 27 ] has been introduced by using diffusion equation of hyperbolic type, which is not based on the local equilibrium assumption. It has been demonstrated that the local nonequilibrium effects change drastically the diffusion field in the bulk liquid leading to a sharp transition from diffusion-controlled growth to kinetic-controlled growth with complete solute trapping [ 25 , 26 , 27 ]. The transition occurs when the interface velocity passes through the critical point , where is the solute diffusive velocity, i.e., velocity of propagation of diffusive disturbances.…”

“…The transition occurs when the interface velocity passes through the critical point , where is the solute diffusive velocity, i.e., velocity of propagation of diffusive disturbances. This implies that the transition to diffusionless and partitionless solidification is a purely diffusive phenomenon—it occurs independently of the interface solidification kinetics as soon as the interface velocity reaches [ 25 , 26 , 27 ]. The LNDM has been also used to study various phenomena pertinent to rapid alloy solidification, for example, nonequilibrium kinetic phase diagrams [ 10 , 28 ], dendrite solidification [ 29 , 30 ], transient effects [ 19 , 31 ].…”