A Crystallographic Alternative to the Coincidence Relationships in Copper

Abstract

The preferred orientation relationships between growing grains and strained (4–8 pct in tension) single crystal matrices of 99.999 pct purity copper were observed to be (001) 19° and (111) ~ 30°, identical to those previously found after secondary re-crystallization. Nearly all of the growing grains contained an annealing twin. By considering the orientation of the parent (or twinned) grains, the preferred relationships may be expressed, approximately, in terms of parallelism between the following pairs of orthogonal directions:

P-relationship:	Growing Grain	Matrix
	>001<	>111<
	>010<	>110<
	>100<	>112<
Q-relationship:	Matrix	Growing Grain

By considering the matrix during the secondary recrystallization in copper as (001)[100] and its four twin orientations, the present alternative suggests that it is the twin matrices, not the (OOl) [100] orientation, which support the growth of both (001) 19° and (111) 22° secondary grains. When the occurrence of annealing twins is rare, such as in aluminum, it is therefore expected that these two relationships should be absent, as observed experimentally. The findings of only two preferred relationships in the present investigation is in agreement with the alternative offered, but not with the coincidence model, which yields many relationships with a high coincidence density.