Institute of Metals Division - The Intersections of [112] Twins in Bcc Crystals (TN)

THE existence of mechanical twins in bcc metals has long been known. With recent intensive interest in the mechanism of twin formation and its role in plasticity and crack initiation, a study of the general Characteristics of twin intersection appears pertinent. The scope of the present note will be limited to the crystallography of the twin intersections of (112) twins, without consideration of its mechanism, movement of atoms, crystal structure, or the strain energy involved at such an intersection. The twinning elements of (112) twins are considered to be K1 = {112}, n1 = (111) and K2 = {112}, n2 = (111) with a twin shear of 0.707. The crystallographic features of twin intersections have been worked out in detail by Cahn.1 The present work applies the general principles postulated by Cahn to the intersections of (112) twins. The basic conditions for the twin intersection are: 1) The trace of crossing (A) and the secondary (C) twins in the planes of the crossed twin (B) must be parallel. 2) The direction (n1) and magnitude (s) of shear must be identical in the crossing and secondary twins. Also the sense of shear must be the same. These two conditions have to be fulfilled in order to maintain geometrical continuity at the twin interfaces. Fig. 1 shows the perspective representation of how these two conditions are fulfilled at the intersection. This type of intersection will be named Type-I. It is the purpose of this note to point out the existence of another type of intersection, Type-II, as shown in Fig. 2. In this type of intersection, the crossing twin A remains straight and the crossed twin B has been bent. The two conditions laid down by Cahn must also be met. This leads to the following corollary conditions: 1) The interface between twins B and C must be parallel to the twin habit of crossing twin A. 2) n1c must be parallel to n1A. 3) The twin shear (s) of twin C must be exactly equal to and in the same sense as that of crossing twin A. Thus, in order for the Type-II intersection to take place, the twining elements of secondary twin C must fulfill the above three conditions with respect to crossing twin A. Let K1 of crossed twin B be (112). All indices of the matrix can therefore be converted into new in-