On the application of phase relationships to complex structures. XXVIII.XMYas a random approach to the phase problem

A random approach to the phase problem, a weighted XMY-function

It has become practice in direct methods to use a multisolution approach to the solution of the phase problem based on the initial refinement of random phases. The maximization of a function of phases proved to be very effective in obtaining correct phase sets. The expansion of this method leads to a method which is known under the name XMY, X minus Y and which is now an integral part of MULTAN90. Different weighting schemes are investigated in order to explore the possibility of still improving the actual XMY-method.

An extremal principle for the phase problem of structures consisting entirely of spherically symmetric non-overlapping parts

A simple extremal principle for the determination of the phases of the structure factors of a crystal is described. An empirical test is provided. An analytical theory of the extremal functions for phase determination is developed.