A direct method for the determination of polytype structures. I. Theoretical basis

A direct method for the determination of polytype structures of SiC, ZnS and similar substances from X-ray data is described. It is based on the values of a Patterson-like function (the `Pattersonian') which only depends on the stacking of the translationally equivalent layers of the structure. The way of obtaining the Pattersonian function from the experimental intensities is described and an algorithm given by which the sequence of layers may be deduced. This sequence is conveniently characterized by the sequence of the digits of a binary number. The influence of experimental errors in the intensities on the possibilities of determining the real sequence is discussed.