Re-Refinement of Composite Modulated Nb₂Zr_x-2O_2x+1 (x = 8) Using Synchrotron Radiation Data

The crystal structure of Nb₂Zr_x-2O_{2x + 1}, x = 8, has been re-refined as a composite modulated structure using synchrotron radiation data measured at energies below the Zr K absorption edge. The structure comprises one-atom thick layers of two substructures stacked alternately along the b direction. The two component substructures are, in general, mutually incommensurable along their common a-axis directions and are referred to as the metal substructure (M), space group Amma, a_M = 5.1348 (2), _bM = 4.9590 (2), c_M = 5.2908 (3) Å, and the oxygen substructure (O), space group Imam, a_O = 2.4164, b_O = b_M = b, c_O = c_M = c, respectively. The four basis vectors used to index reciprocal space, based on the more strongly scattering metal substructure, are a, b*, c* and q_M. The primary modulation wavevector q_M = - 2a + b* - 1/8 a + b* for x = 8. The overall superspace-group symmetry is Amma(10)0s0. Two sets of intensity data recorded at room temperature, 8 eV ( = 0.6892 Å) and 1450 eV ( = 0.7492 Å) below the Zr K absorption edge, were refined to an overall R() = 0.0377 and R() = 0.0439. The displacive modulation wave amplitudes obtained from these refinements agree well with those previously obtained for an x = 12 member. Difference Fourier maps show that metal-atom ordering is virtually negligible.