Modulated structure of the NC-type (N = 5.5) pyrrhotite, Fe_1-xS

The modulated structure of the NC-type pyrrhotite Fe1 - xS with x = 0.09 has been determined. The analysis is based on a four-dimensional space group, Wpna21qq1, and an anharmonic modulation model with 53 positional, two thermal, and eight occupational parameters including up to fourth-order harmonics, a = 11.952, b = 6.892, c = 5.744 Å. The final R for 404 observed reflections is 0.097. The modulation wave for occupation probability of Fe shows a strong anharmonicity and has a low value in a narrow range corresponding to successive Fe layers perpendicular to the c axis of the fundamental NiAs-type structure. From this and the four-dimensional symmetry, it is concluded that Fe vacancies are distributed spirally along the c axis. The relationship between the usual superstructure model and this four-dimensional description is discussed.