融液からする単結晶の製作における成功率および方位分布と製作条件との関係

Abstract

Firstly, the thermal factor or the temperature distribution, in particular, the temperature gradients in the solid and in the liquid at the solid-liquid interface, Gso and Glo, the crystallographic factor or the direction of preferential crystal growth, and the impurity factor or the constitutional supercooling, and their dependence on the crystallization velocity, Ri, and the furnace temperature gradient, Gf, are discussed for the case of solidification. It is shown that the conditions necessary for growing successfully single crystals from the melt are the high purity of the material and the high value of the ratio Gf⁄Ri as already known empirically. Secondly, the yield percentage, S, of growing single crystals from the melt as dependent on Ri and Gf is considered. It is found that single crystals grow practically only when Glo is positive and that S is higher as Glo is larger. If, as the first approximation, S is taken to be proportional to Glo, the relation between S and Glo is given by S = S_o [1 - D {1 - (S/A)^1/2(σ_l/k_l)^1/2}^-1(R_i/G_f)], where D = (A/S)^1/2 ρ_sL/{(k_l σ_l))^1/2 + (k_s σ_s)^1/2}. Here So is the value of S for Ri→0, A and S the cross-sectional area and circumference of the specimen (their variation accompanying solidification are neglected here for simplicity), respectively, kl and ks the thermal conductivities of the liquid and of the solid, respectively, σl and σs the thermal emissivities of the liquid and of the solid, respectively, ρs the density of the solid, and L the latent heat of solidification. This expression indicates that S is higher as Gf⁄Ri is larger, as is known empirically, and it agrees, in the relation between S and Ri, with the experimental results obtained preirously by the author and Watanabé in growing single crystals of zinc, bismuth, and white tin by the Bridgman method. Finally, it is shown that, if the orientation distribution of single crystals grown from the melt is determined mainly by the counterbalance of the crystallographic and thermal factors of the solidification process, the probability of single crystal growth is the same for all orientations for small Ri⁄Gf and, as Ri⁄Gf becomes larger, it becomes larger for crystals with orientations along the preferred directions of growth, which accords with the observed facts.