Parallel intergrowths in cronstedtite-1T: determination of the degree of disorder

Abstract

The study presents a simple method for determining the degree of disorder of crystals affected by stacking faults and out of step domains due to polytypism. The method is demonstrated on the 1 T polytype of the 1: 1 layer silicate cronstedtite. The structure of cronstedtite-1 T (trigonal, P 31 m, a = 5.494, c = 7.090 A) contains stacking faults so that domains of the original 3D periodic structure can be shifted by ( a 2 - a 1 )/3 or ( a 1 - a 2 )/3, so-called OD parallel intergrowths. The effect manifests itself in the diffraction pattern so that reflections with h-k = 3 n (the family reflections) are always sharp, whereas remaining reflections (the characteristic polytype reflections) may be weaker and smeared out parallel to c * . The intensities of the latter are thus underestimated during diffractometer measurements and as a result, ghost peaks in Fourier maps can appear. These peaks can be avoided by assigning separate scale factors to the polytype and family reflections. Two functions are defined: (i) the q function represents the square of the ratio of scale factors of polytype and family reflections for structures with various amounts of shifted domains, (ii) the q * function represents the square of the ratio of scale factors as obtained from refinements (with real data sets) of artificial “imposed” structure models with various proportions of shifted domains, ignoring the actual content of these domains in the crystal. The structure model can be considered as appropriate, if q = q * . The solution in the simplified double intergrowth model (with only one kind of shifted domains considered) is presented. The solution in the triple intergrowth model is not unambiguous, as the same value of q can be obtained for various combinations of two kinds of shifted domains. The procedure is demonstrated on refinements of four data sets acquired from crystals with somewhat different degree of disorder. Of possible factors affecting the accuracy of the method, the influence of extinction is discussed.