Stacking order and disorder in layered K₃Me(CN)₆ compounds studied by diffuse X-ray scattering: A realization of the ANNNI model?

Abstract

Layered crystalline materials like K₃Me(CN)₆ with Me=Cr, Mn, Fe, Co may often exist in various polytypic forms, due to a variety of choices of layer stacking modes. For cases where the interlayer constellations can be limited to only two energetically almost equivalent ways, the buildup of the crystal may be described by a spin-1/2 Ising-like model. For the system presently being studied one can rationalize the layer stacking to a four-valued choice (i.e., a 1D 4-state Potts case), or use an Ising-like two-sublattice model. Previous diffraction studies of K₃Me(CN)₆ indicated that two long-range ordered structures prevailed, an orthohombic one named MDO₁, with one double layer per repetition unit, and a monoclinic one, MDO₂, with two double-layer units. Our studies reveal a more complex situation: The Fe material is for the most part of the MDO₂ type. But in addition, in some crystal samples, a hitherto unobserved phase also appears, with six double-layer repetition units, in fact a hybrid of MDO₁ and MDO₂. The Co material is for the most part of the MDO₂ type, but contains in addition a considerable contribution of stacking disorder, as evidenced by the presence of diffuse X-ray scattering lines. The lines do, however, contain distinct maxima, indicating the presence of several layer stacking modes with preference of two, three, four, five, and seven double-layer correlations. The findings can be qualitatively discussed in terms of the ANNNI model.