Use of Topotactic Phase Transformations to Obtain Solutions of the Crystal Structures of Highly Disordered Materials

Abstract

A straightforward procedure is outlined for prediction of the complete three-dimensional coordinate set for a highly disordered phase. For a mother and daughter phase, where one of the pair has an "unsolvable" structure, one needs only to (a) establish the topotaxy using previously published techniques, (b) obtain the topotactic transformation matrix, ρ, between the ordered and highly disordered phase, and (c) apply the transpose of ρ-1 to obtain a trial set of coordinates for refinement using the reflection data set of the highly disordered phase. For the inclusion compound [Fe(η-C5H5)]·3(NH2)2CS (1), which contains highly disordered ferrocene molecules above 160 K (polymorph 1-I), we found a more ordered structure at low temperature. At 135 K (polymorph 1-II), two ferrocene moieties are present in the thiourea channel in an approximately 1:1 ratio. One is nearly orthogonal (87.0°) to the channel axis, while the other is tipped 16.2° from that direction. Using steps (a-c) outlined above, a trial structure may be obtained for 1-I, and refinement leads to R1 = 4.25%. The structure of 1-1, containing 12-fold disordered ferrocene molecules, is similar to that found at temperatures below the phase transition, with a greater amount of the orthogonal orientation (55:45 vs 51:48), consistent with, but lower than, amounts found using solid-state NMR techniques. The low temperature polymorph is a trill, with an approximately 3:1:1 ratio of twin components. The exact alignment of the mother phase and the three daughters has been established using the methods of topotactic analysis described previously.