AB-INITIO SOLUTION OF MISFIT LAYER STRUCTURES BY AUTOMATIC PATTERSON AND DIRECT-METHODS

A procedure is presented for the automatic solution of composite (misf it) layer compounds, for the case when the composite crystal structure consists of two types of layer, each of which can be approximately de scribed as a three-dimensional periodic structure with, however, mutua lly incommensurate lattices and hence mutually induced incommensurate modulations. The composite structure can be described as a periodic st ructure in four-dimensional superspace [van Smaalen (1992), Mater. Sci . Forum, 100&101, 173-2221. From reflection data indexed with four int eger indices HKLM, the phase problem is solved as follows. The basic s tructures of layers 1 and 2 are solved by routine application of autom ated Patterson interpretation and Fourier recycling using the main ref lections only and ignoring the modulation effects. The two layers are brought to a common origin by a shift function based on correlating F( obs) and F(calc) using the main reflections common to both layers. All other reflections, which are the (usually weaker) satellite reflectio ns, are phased from the known phases of the main reflections of either layer by application of the Sayre equation in four-dimensional supers pace [Hao, Liu & Fan (1987), Acta Cryst. A43, 820-824; Fan, van Smaale n, Lam & Beurskens (1993), Acta Cryst. A49, 704-7081. The procedure is performed by the program MISFIT, which is embedded in the DIRDIF syst em.