The twinning orientation relationship between A and B martensite variants in a Cu-Zn-Al shape memory alloy

Abstract

It is known that in the Cu-Zn-Al shape memory alloy, the variants of thermoelastic martensites which are transformed from parent phase appear as a collection of the plate groups, each consisting of three fundamental combinations A : B, A : C and A : D type pairs [1–3]. All three of these combinations involve a twin orientation. Since their twin boundaries are mobile under applied stress, they are also regarded as deformation twin [4–6]. The A : C and A : D type pairs of plates which have intervariant boundary plane 1 2 8 and 1 0 1 0 respectively as a mirror reflection plane are classified as type I reflection twins [7]. However, the A : B type pair of plate which has no such boundary plane as a mirror reflection plane has been regarded as type II twin orientation in which two variants are related by a rotation of π about [10 9 1]β ′ 1 [8]. For type II twin, it can be deduced that plane (1 2 8)A and (1 0 1 0)A, which are perpendicular to [10 9 1]β ′ 1 , should be parallel to (1 2 8)B and (1 0 1 0)B exactly. That is, (1 2 8)A and (1 2 8)B spots should superimpose in the electron diffraction pattern. The twinning orientation relationship between A : B type pair, as well as A : C and A : D, is essential feature of martensites in shape memory alloys. Thus, an understanding of such relations is vital to further understanding of mechanism of self-accommodation between martensite plate variants and shape memory behavior. In this paper, direct evidence which shows that the A and B martensite variants are not related by a rotation of π about [10 9 1]β ′ 1 is provided. The orientation relationship between A and B martensite variants has been verified as secondary twin. The alloy studied in this work has a composition of 67.6 at % Cu, 22.1 at % Zn and 10.1 at % Al. The alloy was annealed for 1 h at 600 ◦C and cold-rolled from 2.0 mm to 1.1 mm strip. After mechanically thinning to 0.1 mm, the strip was punched into 3 mm diameter discs. The discs were jet-electropolished with a solution of H2NO3 : CH3OH= 2 : 1 at −30 to −50 ◦C; the resulting specimen was examined in a JEOL-2000 EX transmission electron microscope equipped with a doubletilt holder and operating at 160 kV. Lattice parameters of M18R martensite used for indexing of diffraction patterns and calculation of twins are a= 0.4553 nm, b= 0.5432 nm, c= 3.8977 nm and β = 87.5◦ [9]. Fig. 1a is an electron micrograph showing A and B martensite variant pair in Cu-Zn-Al shape memory alloy. The composite diffraction pattern taken from this area is shown in Fig. 1b. The orientation relationship derived from this diffraction pattern is [2 1 0]A//[2 9 2]B : (1 2 8)A//(1 2 8)B. It can be seen that 1 2 8 reflection spots from both component diffraction patterns do not overlap. One may argue this “splitting” might originate in long period stacking sequence or other source. In order to clarify this point, we have tilted the specimen about 50◦ to [8 0 1] zone where two variants A and B are in symmetry. Fig. 2 is its composite diffraction pattern in [8 0 1] zone. It is clear that two 1 2 8 spots are separated. This separation can be verified by observing 2 4 16 spots. The angle these two spots subtend is 3.5◦. From the fact that (1 2 8)A and (1 2 8)B spots do not superimpose, we can believe that A : B type pair is not type II twin. In this instance, we suggested that A : B type pair might be a secondary twin relationship. It is known that for reflection twin, the indices of a plane, (h k l), and a direction, [u v w], in the twin may be determined in terms of matrix by [10–14] h T kT lT  = T hk l  (1)