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Model for solute diffusion during rapid solidification of binary alloy in semi-infinite volume

On the basis of local nonequilibrium approach, the one-dimensional model of the solute diffusion during rapid solidification of the binary alloy in the semi-infinite volume is considered. Within the scope of the model it is supposed that mass transport is described by the telegrapher equation. The basic assumption concerns the behavior of the diffusion flux and the solute concentration at the interface. Under the condition that these quantities are given by the superposition of the exponential functions the solutions of the telegrapher equation determining the flux and the solute distributions in the melt have been found. On the basis of these solutions different regimes of the solidification in the near surface region and the behavior of the partition coefficient have been investigated. The concentration profiles in the solid after complete solidification are analyzed depending on the model parameters.