Evolution and destruction of the crystal growth line in a supercooled melt

The paper studies the macroscopic shape of the crystal growth line in a supercooled melt of a pure substance. The analysis focuses on the spatial heterogeneity of supercooling at the crystallization phase boundary. The paper shows that there is a threshold value of the heterogeneity parameter, and this threshold corresponds to the cellular structure of the crystallization front which is periodic along the coordinate transverse to the growth direction. The ratio of the structure period to the curvature radius of an individual cell is equal to $\pi$. The tip of the growth line is wedge-shaped on both sides of the threshold. When crossing the threshold, bifurcated situations are observed, since the cells are an intermediate structure between the flat front and the dendrites. The paper analyses the case when the small value of the first order of smallness is the angle between the normal and the symmetry axis of the growth line. Under this approximation, the growth equation has the form of the Burgers equation. A new physical interpretation is given to the exact solutions of this equation known in the literature, which allows considering the following processes: a disturbance wave caused by the curvature rupture; a destruction wave is a precursor of tip splitting; a rupture is a strong discontinuity of the sharpness angle; overturning of the growth line is a precursor to the tip neck introvolution. The paper comprehensively analyses stable and unstable ruptures of the growth line. It reveals that the differences between the blunting of the tip behind the rupture and overturning are explained by the direction of the transition through the threshold value of the heterogeneity parameter. The paper gives calculation examples illustrating the properties of the velocity of disturbance and destruction waves.