Heterogeneous nucleation model of twinned crystal growth from the melt
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of the chill face. In previous investigations 6's'13 attempts were made to determine the origin of twinned grains by sectioning the ingot transversely. It was observed that many twinned grains originated near the chill face, but the exact position of nucleation could not be determined because of difficulty in finding the initiation point. Therefore, in the present work, the origin of twinned grains was not fixed at one point, but was assumed to be at or near the chill face. (2) Nuclei have an asymmetric lenticular shape with the twin boundary at the center, as shown in Figure 1. In previous work H it was shown that a groove exists at the tip of a twinned grain. However, a twinned grain has a simple morphology at the initial stage of nucleation 14 and therefore the asymmetric lenticular nucleus is assumed. The analytical development is similar to that for current heterogeneous nucleation theory. ~5The free energy change, AG, for the formation of a solid with a twin boundary is given by AG = A G i -
[1]
AGp + AG,,
where AGi is the interface contribution, AGp is the volume contribution, and AG, is the twin boundary contribution. These terms are calculated from the following equations: AGi = 27rr2(1 -- c o s 0 ) T -
7rr 2 s i n 2 0 c o s 0 3,
= 7rr2(2 - 3 cos 0 + cos 3 0 ) y .
Heterogeneous Nucleation Model of Twinned Crystal Growth from the Melt H. KATO and J. R. CAHOON Growth twins often appear in continuously cast or unidirectionally solidified aluminum alloys and there are a number of investigations 1-~3 on the origin, the orientation relation, and the growth preference of these grains. According to previous reports twinned grains originate at a lattice defectTM or by growth accidents, 4 but there are conflicting conclusions on the role of the nucleation rate TM and the growth rate ~~ on the occurrence or the prevalence of twinned grains. At present the nucleation mechanism for twinned grains is not clear and a quantitative discussion is lacking. Twinned grains always coexist with normal columnar grains or equiaxed grains, and this indicates that twinned grains can nucleate under the same conditions as those of normal grains but that the rate of nucleation is far smaller than that of normal grains because of the existence of a twin boundary. In this communication the fraction of twinned grains is analyzed using current nucleation theory and compared semi-quantitatively with experimental results. The following assumptions are made in this analysis: (1) Twinned grains nucleate heterogeneously in the vicinity
AGp = (Tr/3)r3(2 - 3 cos 0 + cos 30)AGv.
[2b]
AG, = r2(O - sin 0 cos O)y,,
[2c]
where r is the radius of the solid-liquid interface, 0 is the contact angle, y is the solid-liquid interfacial energy per unit area, AGv is the free energy change from the liquid to the solid per unit volume, and y, is the twin boundary energy per unit area. AGp can also be represented as the work required to form the solid in the liquid, VAp, in which V is the volume and Ap is the pressure difference between the solid and
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