The shape formed in the melt of the crystals depends on the growth conditions (overheating and supercooling liquid heat removal direction, and other impurities) and the metal nature. In conditions close to equilibrium, properly cut crystals are formed. They grow slowly; their surface is smooth, although it contains steps necessary for the construction of faces. If the impurities are small and the temperature of the liquid increases with the distance from the surface of the crystal, the zone advanced for some reason or another enters the zone with the higher temperature and the growth slows down. Under these conditions, the faces with the densest packing of atoms having a minimum surface energy are predominantly developed. In the direction perpendicular to the less densely packed face, growth occurs faster, as a result of which it wedges out and the crystal acquires an equilibrium shape characterized by the minimum of the thermodynamic potential. In such crystal, the faces are removed from the center by distances proportional to their interfacial surface tension.
According to the Gibbs-Curie-Wulff rule
γ1/h1= γ2/h2= γ3/h3…,
where h — the distance of the face from the center of the crystal;
у — the surface tension.
Thus, the equilibrium shape of the crystal is polyhedral: the faces intersect at the vertices and edges, which, according to L.D Landau, are slightly rounded.
With the acceleration of the cooling, along with the close-packed ones, the faces with the less dense packing appear, dendritic, lamellar and needle crystals are formed. The spherical crystals composed of thin radically directed needles are also created. In these cases, the shape of the crystal is far from equilibrium.
The forms of growth are associated with the structure of the crystallization front. The interface between the crystal and the liquid is particularly sensitive to supercooling and impurity content. From relatively smooth, with low steps, the interfacial surface becomes uneven, wrinkled with increasing supercooling of the liquid. A lot of cells are found on the surface of the crystal, the middle part of which slightly protrudes with growth into the melt, and the edges lag behind. The appearance of the cellular structure is associated with impurities present in the technical metals. The 0.01% admixture is enough to create the cellular structure. If the impurity is slightly soluble in the crystal, it accumulates in the liquid ahead of the crystallization front, then reaching the cell boundaries.
Upon cooling through the solidified metal, the crystal acquires the columnar shape elongated in the direction of the heat sink. In the cross section of such crystals, the cells are seen whose walls in the longitudinal section look like thin parallel lines. The crystal grown under these conditions resembles the bundle of pencils, the lateral surfaces of which correspond to impurity-enriched cell boundaries. The average cell diameter (d) depends on the growth rate of the crystal (Up) and the temperature gradient in the liquid (ΔT):
d~1∕ Up ΔT.