The Crystallographic Aspect of the Mechanical Twinning in Metals

In order to investigate twinning dislocations of metals, a simple crystallographical calculation is done, assuming that atomic movements are periodic as the twinning plane moves, that there is no diffusion, and that atoms come to new twin lattice sites from the most neighbouring original lattice sites of them. The shear strain S , Burgers vector b t and its associated atomic movements U , and the structure of twin boundary are obtained for any crystallographic plane. It is shown that U may be easily demonstrated by using a "modified lattice" in which b t diminishes to zero. Compared with various twinning planes, the observed twinning planes have the following characteristic: their S is the smallest, but their | b t | and | U | are not. And when their S is equal to others, the twinning planes which have smaller | b t | are liable to twin. There are several twinning planes, which are possible to twin, e.g. {431} of β-Sn, and {100}, {531}, {221} of Bi type. In {1011} of Mg, S =0.353, and K 2 , plane is such a one as (1320) which is somewhat rotated around the axis normal to (1011).