THE OSCILLATIONS OF THE VELOCITY AND CURVATURE OF THE AXIALLY-SYMMETRICAL PHASE BOUNDARY AT CRYSTALLIZATION IN AN OVERCOOLED MELT

Abstract

The gradient properties of the heat field on the phase boundary are studied at high-speed crystallization of a unicomponent overcooled melt. The increasing role of locally-nonequilibrium heat transfer at intensified overcooling is taken into account. The analytical transformations were carried out with the aid of a threedimensional orthogonal basis, which corresponded to the tangent, the main normal and the binormal of the phase boundary. Explicit expressions for the derivatives of the temperature and the heat flux vector are obtained. The origin of a lateral branch of a dendrite was simulated mathematically by the gradient catastrophe when the derivatives of the temperature and the heat flux vector become infinitely large. The tree reasons for the heat field destruction are indicated. Numerical calculations for the influence of time-periodical perturbations in the velocity and the curvature of the phase boundary affecting the structure of the heat field. The oscillation regimes at the dendrite top and in the distant zone are collated. The phase portraits for the system “melt – crystal” were built in the coordinates “velocity – curvature – temperature”, “velocity – curvature – heat flux” etc. All the calculations were carried out for the overcooled nickel melt.