The structure of Ksub(1.33)Mn8O16 and cation ordering in hollandite-type structures

Crystal data: Msub(r)=747.5, tetragonal, I4/m, a=9.866(3), c=2.872(1) A, V=279.6(2) A3, Z=8(Ksub(0.167)MnO2), Dsub(x)=4.442 g cm-3, lambda(Ag Kα, graphite monochromator)=0.56005 A, μ=49.9 cm-1, F(000)=353.5, T=295 K, final R=1.9% for 436 unique reflections. In this mixed-valence compound Ksub(x)Mn4+sub(x8)Mnsub(x)3+O16(x=1.33) the channel cation position (K+) is not at 001/2 but at 00z with z=0.375. It is shown that the symmetry of hollandite-type structures (Asub(x)B8O16) is determined by the relative sizes of the framework (B) and the channel (A) cations. Single-crystal rotation photographs around c show extra diffuse levels between reciprocal-lattice planes perpendicular to c. These extra levels, attributed to channel-cation ordering, have spacings which indicate that, in a given channel, the order involves three unit cells in the c direction. The presence of vacancies in the channels allows a relaxation of the K+ cations and a minimization of the K-K electrostatic repulsion via a displacement of the K+ cations from the centers of their square-prismatic channel sites toward the neighboring vacancies. It seems likely that either diffuse or superstructure reflections should occur in most Asub(x)B8O16 hollandite-type compounds studied so far. In the former case long-range ordering occurs among the A cations and vacancies along a given channel without a correlation between adjacent channels, as in Ksub(1.33)Mn9O16 where the K ordering is one-dimensional. In the latter case the ordering is accompanied by a strong correlation between channels leading to a three-dimensional ordering. (orig.)