Dependence on the Growing Conditions of the Degree of Successful Growth and Orientation in Single Crystals Grown from the Melt

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For the solidification process, the thermal factor, in particular, temperature gradients in solid and in liquid at their interface, G_<s0> and G_<lo> crystallographic factor or directions of preferred crystal growth, and impurity factor or constitutional supercooling, as dependent on the crystallization velocity, R_i, and furnace temperature gradient, G_f, are discussed. It is shown that the conditions necessary for growing successfully single crystals from the melt are the high purity of the material and high value of the ratio G_f/R_i, as already known empirically. Next, since it may be considered that single crystals grow only when G_<lo> is positive and that the degree of successful growth, Q, is higher as G_<lo> is larger, if Q is taken to be proportional to G_<lo> to the first approximation, we get the following relation for Q : -Chemical formula where Chemical formula Here Q_o is the value of Q for R_i→O, A and S the cross-sectional area and circumference of the specimen (their variations accompanied with solidification are neglected for simplicity), k_l and k_s the thermal conductivities of liquid and solid, σ_l and σ_s the thermal missivities of liquid and solid, ρ_s the density of solid, and L the latent heat of solidification, This expresses the empirical rule that Q is higher as G_f/R_i is larger. Finally, it is shown that, if the orientation distribution of single crystals grown from the melt is determined mainly by the competition between crystallographic and thermal factors of the solidification process, the probability of single crystal growth is the same for all orientations for small R_i/G_f and, as R_i/G_f becomes larger, it becomes larger for crystals with orientations along the preferred directions of growth, which accords with the observed facts.
東北大学の論文

Dependence on the Growing Conditions of the Degree of Successful Growth and Orientation in Single Crystals Grown from the Melt

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