Three kinds of Cu-13.7Al-4.0Ni (mass%) alloy single crystals have been prepared by rapid (R.Q.) and normal (N.Q.) quenching from 1273 K and by aging at 523 K after the N.Q. treatment (A.), the martensites formed in them being the β′
1, a mixture of the β′
1 and γ′
1 and the γ′
1, respectively. They have then been subjected to training cycling, which consists of cooling below
Mf, bending of 2.6% strain in maximum and heating up above
Af, up to 1000 cycles. As a result, the two-way shape memory effect (TWSME) was found to appear in Sps. R.Q. and N.Q., but not in Sp. A., indicating that the appearance of TWSME depended on the crystal structures of martensites in specimens. The martensites in Sp. N.Q. on quenching changed to only the β′
1 on the way of the training cycling. Fairly reproducible microstructures of the β′
1 was observed in Sp. R.Q. even in the non-trained condition, and the reproducibility increased with the number of training cycles. Meanwhile, no reproducibility of microstructures of the γ′
1 was observed in Sp. A. at all both in the non-trained and trained conditions. Thus, the β′
1 was found to be the martensite phase responsible for the appearance of TWSME. This difference in the appearance of TWSME between the β′
1 and γ′
1 was elucidated in terms of some difference in the number of dislocations introduced during the training cycling and in the nucleation and growth characteristics of the martensites nucleated at the dislocations.
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