THE DISTORTION OF A CRYSTAL BY POINT IMPERFECTIONS

The distortion of a crystal lattice is discussed form the standpoint of calculations using the elastic displacement appropriate to a center of dilatation in an infinite medium. This displacement gives a nonzero stress at the surface of the solid. The treatment shows the necessity for additional image displacement in certain applications to insure that this stress vanishes. In particular, if image displacement is omitted the volume change due to one or more point singularities can be underestimated by a factor of 1.5 for metals or 1.8 for alkali halides. If the effects of the free boundary are ignored, any nonspherical body uniformly filled with point singularities would suffer a change of shape as well a change of size. When the boundary effect is considered, there is a change of volume without change of shape. Moreover, for this case, a calculation of the change of x-ray lattice constant gives a result consistent with the geometrical deformation only if the image displacements are included.