Direct methods in superspace. II. The first application to an unknown incommensurate modulated structure

The direct method previously proposed [Hao, Liu & Fan (1987). Acta Cryst. A43, 820-824] has been used to determine the incommensurate modulation in the structure of ankangite by using the h0l electron diffraction pattern. Ankangite is a newly discovered mineral which belongs to the priderite group with chemical composition Ba_0.8(Ti, V, Cr)₈O₁₆. The h0l electron diffraction pattern shows sharp satellite reflections which correspond to a one-dimensional incommensurate modulation along the c axis. Direct phasing of the h0l satellite reflections based on the known phases of the main reflections led to a three-dimensional hyperprojection along the a₂ direction of the four-dimensional electron potential distribution, revealing clearly occupational and positional modulations of the Ba atoms. Positional modulation of other atoms has also been observed.