IUCr journals

Modular crystals as modulated structures: the case of the lillianite homologous series

Acta Cryst. (2008). B64, 684-701 (doi.org/10.1107/S0108768108031492)

[Results for heyrovskyite] (x, y) projection of the heyrovskyite structure (a), and continuous functions in superspace representing the x (b) and y (c) coordinates of the atoms in (a). Red (yellow) color represents S atoms at z = 0 (1/2) and black (gray) color represents Pb/Bi atoms at z = 0 (1/2).
Modular crystals, such as the heyrovskyite phase in the figure, consist of alternate stacking of two symmetry-related modules with internal approximate subperiodicity. Using the superspace formalism,originally developed for incommensurately modulated crystals, a whole series of commensurate modular structures can be described with atomic modulation functions almost independent of composition and given by few parameters. This superspace approach, with the remarkable zigzag form of the x component of the modulation functions, reveals an underlying misfit between different latent periodicities of cations and anions.

L. Elcoro, J. M. Perez-Mato, K. Friese, V. Petrí­cek, T.Balic-Zunic and L. A. Olsen