Abstract-Free growth of a dendrite crystal in a stationary multicomponent melt is investigated. A mathe matical model of the process is developed and its analytic solution is constructed. A stability criterion is obtained for a 2D parabolic dendrite and the refined relation is derived for the growth rate of the dendrite tip taking into account the anisotropy of surface tension at the solid phase-melt interface. It is shown that the accumulation of impurity in the front of a dendrite makes it tip thinner and reduces its velocity. The theory contains limiting transitions to the familiar dendrite growth criteria for one component and binary systems.
Abstract-An analytical solution is found for the problem of the growth of an isolated dendrite in a convective binary melt with allowance for the Soret and temperature dependent diffusion effects. Nonlinear impurity transport is shown to radically change the impurity concentration in front of the growing crystal and, corre spondingly, the concentration supercooling, which is responsible for the condition of choosing the dendrite tip growth rate.
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