Inversion of convergent-beam electron diffraction patterns

The problem of recovering the structure factors that contribute to a zone-axis convergent-beam diffraction pattern is discussed. It is shown that an automated matching procedure that minimizes the sum-of-squares difference between experimental and simulated patterns is effective whether one is refining accurate structure factors in a known crystal or attempting ab initio structure determination. The details of the minimization method are analysed and it is shown that a quasi-Newton method that uses analytically derived gradients is particularly effective when several structure factors are varied. The inversion method for ab initio structure determination is tested on the [110] axis of GaP, using simulated patterns as ideal 'experimental' data.