Structure refinement of the layered composite crystal Sc₂B_1.1C_3.2 in a five-dimensional formalism

Abstract

The crystal structure of a layered compound Sc(2)B(1.1)C(3.2), scandium boride carbide (M(r) = 140.43), has been re-refined as a commensurate composite crystal using 1795 single-crystal X-ray diffraction intensities with I > 2 sigma(I) collected by Shi, Leithe-Jasper, Bourgeois, Bando & Tanaka [(1999), J. Solid State Chem. 148, 442--449]. The crystal is composed of two layered subsystem structures, i.e. Sc--C--Sc sandwiches and graphite-like layers of the composition B(1/3)C(2/3). The structure refinement was performed in a five-dimensional formalism based on the trigonal superspace group P3m1(p00)(0p0)0m0. The unit cell and other crystal data are a = b = 3.387 (1), c = 6.703 (2) A, V = 66.59 (1) A(3), sigma(1) = (9/7 0 0), sigma(2) = (0 9/7 0), Z = 1, D(x) = 3.501 Mg m(-3). Two different three-dimensional sections through the superspace were analyzed, corresponding to two different superstructure models, one with P3m1 and the other with P3m1. A random distribution of B and C was assumed in the graphite-like layer and 41 structural parameters were introduced. R(F)/wR(F) were 0.0533/0.0482 and 0.0524/0.0476, respectively, for the first and second models. Although the difference between these R(F) or wR(F) values was too fine to exclude one of the models definitely, the advantages of using a superspace group were obvious. It not only brought about better convergence of refinement cycles by virtue of fewer parameters, but also gave an insight into the problem of symmetry of the superstructure.