Interatomic distances and atomic valences in NaZn_(13)

Abstract

The crystal structure of NaZn_(13) and of several homologous compounds AB_(13) was reported by Ketelaar and by Zintl & Hauke to be based on space group O_h^6-Fm3c, with 8 :Na in 8(a): ¼, ¼:, ¼; ... ; 8 Zn_I in 8(b): 0, 0, 0; .... ; and 96 Zn_(II) in 96(i): 0, y, z; ... . Approximate values were reported for the parameters a_0, y, and z; for NaZn_(13) Zintl & Hauke reported 12.27 Å, 0.178, and 0.122 for these three parameters. Each Zn_I is surrounded by twelve Zn_(II) at the vertices of a nearly regular icosahedron, and each Na by twenty-four Zn_(II) at the vertices of a snub cube. Our interest in the structure was largely concerned with the valences of the two different kinds of Zn atoms, it being presumptive that Zn_I has a larger valence than Zn_(II) because its icosahedral coordination requires it to be smaller than Zn_(II). Lines on new powder photographs of NaZn_(13) were measured and the intensities were estimated visually with as much precision as possible. Least-squares treatments were employed in order to obtain the best possible values for the three parameters; the values obtained are a_0 = 12.2836 ± 0.0003Å, y = 0.1806 ± 0.0003, and z = 0.1192 ± 0.0003. The uncertainties given are calculated standard deviations. Analysis of the interatomic distances yields a selfconsistent interpretation in which Zn_I is assumed to be quinquevalent and Zn_(II) quadrivalent, while Na may have a valence of unity or one as high as 1¼, the excess over unity being suggested by the interatomic distances and being, if real, presumably a consequence of electron transfer. A valence electron number of approximately 432 per unit cell is obtained, which is in good agreement with the value 428.48 predicted on the basis of a filled Brillouin polyhedron defined by the forms {444}, {640}, and {800}.