Institute of Metals Division - On Coincidence Sites (TN)

HE recent papers of Aust and Rutter112 have again brought to mind the importance of certain "special" orientation relationships between the lattices of two fcc crystals on the mobility of the grain boundary separating them. No theoretical treatment of this problem has been offered till now. The only principle published so far that has given an indication why certain orientation relationships should be "special" is the counting of "coincidence sites" according to the suggestions by Kronberg and Wilson.3 The "coincidence plots" published by these authors show, for instance, that two fcc lattices rotated by 38 deg around a common (111)-axis have 1/7 of their lattice sites in common. Such an orientation relationship is also characteristic for high boundary mobility. The accuracy of the orientation relationship needed for high mobility is not too rigid. Deviations up to 10 deg from the ideal orientation seem to be tolerable as can be gathered from the experimental data.'j4 The auestion arises, then. how the density of coincidence sites will be affected by a deviatioi from mathematical accuracy. This can be checked by a simple model. Two sieves are prepared, the arrangement of the holes corresponding to lattice sites on a (111)-plane in a fcc crystal. They are placed upon each other, Fig. 1. One is kept fixed, the other is rotated around an axis pushed through one hole in common to both. The light falling through holes of both sieves is then a measure for the density of coincidence sites. If the diameter of the holes is very small, light intensity is contributed only by holes the centers of which coincide "exactly." If the diameter of the holes is rather large, some intensity will be contributed by