It was recalled that it had been argued that in the Frank-Bilby equation for the geometrical analysis of grain boundaries, and in o-lattice equations, a pseudo-inverse had to be used when the reduced displacement-field matrices were not invertible. An explicit expression was derived here, using a direct vector approach, for the pseudo-inverse of Frank’s formula. This was important, as the Frank-Bilby equation played a particularly important role in determining dislocation contents.

A Pseudoinverse for Frank’s Formula. A.Gómez, D.Romeu: Acta Crystallographica A, 2001, 57[1], 116-7