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The time dependence of the crystallization rate at crystal pulling to the cold zone with a velocity that has a sinusoidal component has been investigated within a one-dimensional time-dependent model of solidification of a diluted binary melt by the net method. It is shown that the regularities that were obtained previously by the analytical method for pulling rates with small oscillations are repeated in many respects when considering oscillations of larger amplitudes. At significant oscillation amplitudes, the time-averaged values of impurity concentration at the interface for the stationary and vibrational crystallization modes may differ by several dozen percent.

The time dependence of the crystallization rate V(t) in the transient process that occurs during crystal pulling into a cold zone at a constant rate W has been investigated within the one-dimensional time-dependent model of binary melt solidification using numerical and analytical approaches. It is shown that the character of the dependence V(t) in this process is mainly determined by the parameter B w = V c /W, where V c is the crystallization rate at which the constitutional supercooling zone is formed in the melt. At B w ≥ 1, the function V(t) monotonically approaches its steady-state value W, while at B w < 1 V(t) is generally nonmonotonic. The nonmonotonic character of V(t) can manifest itself both as aperiodic damping and in the form of damping oscillations. At B w ∼ 0.1, the vibrational amplitude of the crystallization rate in the initial transient process may reach several tens of a percent of W.

The dependence of the critical crystallization rate on the initial impurity concentration in melt is derived by determining the condition at which a nonplanar solution to the stationary diffusion problem arises. It is suggested that the conditions at which defects arise at the interface differ from those obtained when crystallization becomes stationary. The initial transient process of binary melt solidification under crystal pulling at a constant rate has been studied numerically within a 1D model. It is shown that the character of the time dependence of the crystallization rate is determined by the ratio of the crystal pulling rate to solidification rate Vc, when a constitutional supercooling zone is formed in the melt.

The stationary task of impurity diffusion in a melt has been solved within a two-dimensional crystallization model in a second-order approximation with respect to the amplitude of deviation from a smooth crystallization front. The dependence of the surface tension Γ at the interface on the impurity concentration C is taken into account in the form Γ = Γ0 + ζ d C, where Γ0 and ζ d are constants. The variational method is used to obtain the condition for the transition from a smooth crystallization front to a cellular one. It is shown that calculated cell sizes are in agreement with the experimental data in the literature only when the parameter ζ d ≠ 0. For binary systems with distribution coefficients k 1, ζ d should be positive and negative, respectively.

This paper reports on the results obtained during the development of the technological process of growth of sapphire crystals for optoelectronics through horizontal directional crystallization in a gaseous argon medium at a pressure of 800 mmHg. The sapphire crystals intended for the use in optoelectronics have been grown from purified molten alumina according to the authors’ technology. It has been demonstrated that, under conditions of a high temperature gradient across the crystallization front and at a low content of reducing components (H2, CO) in the growth medium, it is possible to grow sapphire crystals satisfying the requirements of optoelectronics.

The stability of the flat crystallization front of a dilute binary melt is investigated within the two-dimensional model of solidification taking into account the latent heat of fusion and the difference between thermal conductivities of the solid and liquid phases by the method of integral functionals with an unknown region of integration. The stationary problem of impurity diffusion in a crystallizing melt and heat propagation in a limited region Ω is solved within the second-order approximation in the amplitude of deviation from a flat crystallization front. An expression for the functional is obtained whose value is proportional to the energy dissipated in the region Ω owing to heat and mass transfer processes. The results obtained are compared with the literature data on the stability of the flat crystallization front of a binary melt.

The variational method is applied to the study of crystal growth from melt under the condition that the boundary between the liquid and solid phases has a cellular structure. The surface energy of the interface is taken into account.