An exact solution for the shape of a crystal growing in a forced flow

Selection of stable growth conditions for the parabolic dendrite tip in crystallization of multicomponent melts

“…Criterion (21) can easily be generalized to the case of the multicomponent system: (22) where N is the number of the mixture components, m j = -∂F/∂C j , F = F(C 1 , C 2 , …), and C j , k j , and D j are the concentrations of the impurity, the coefficients of its distribution, and the diffusion coefficients for the jth component. A number of important features of the theory being developed are also worth noting.…”

“…For this reason, the Ivantsov solution is used as the zeroth approximation in analysis of sta ble growth in which the surface tension anisotropy parameter or the growth kinetic anisotropy parameter plays the role of the small parameter [20]. After the formulation of the criterion of stable growth of the dendrite tip in a one component stationary medium [19,20], the problem was extended to the case of con vective flow of the medium [21][22][23], to the case of dendrite growth in a binary system without convection [24], and to the case of dendrite growth in a binary sys tem with convection [25,26]. However, in many situ ations a comparative analysis of the dendrite growth taking into account the multicomponent nature of the system is required [27].…”

On the theory of dendritic growth: Soret and temperature-dependent diffusion effects

“…As a result, the concentra tion supercooling increases or decreases, respectively, and the dendrite tip growth rate changes respectively. To study this problem in detail, it is necessary to ana lyze the stability of dendritic growth with allowance for the Soret and temperature dependent diffusion effects in terms of works [18][19][20][21][22].…”

“…depends only on variable η), we rewrite the formula tion of the problem in the form (see [18]) (10) where the temperature in the melt at infinity is consid ered to be specified; that is, T → T ∞ at η → ∞. The integration of Eq.…”

“…Therefore, the Ivantsov solution is only used as a zeroth approximation to solve the problem of stable growth, where the role of a small parameter is played by surface tension anisotropy or growth kinetics anisotropy [16]. After finding the criterion of stable dendrite tip motion in a single component unmovable medium [15,16], the problem was extended to the cases of a convective medium flow [17][18][19], crystal growth in a binary (chemically two component) con vective free system [20], and dendritic growth in a binary liquid with convection [21,22].…”