Disorder in layered hydroxides: DIFFaX simulation of the X-ray powder diffraction patterns of nickel hydroxide

Layered metal hydroxides exhibit non-uniform broadening of lines in their X-ray powder diffraction (XRPD) patterns, which cannot always be explained on the basis of crystallite size effects. In the case of hexagonal solids such as nickel hydroxide, DIFFaX simulations of the XRPD patterns show that: (1) stacking faults and turbostratic disorder at low (<30%) incidence selectively broaden the h0l reflections; (2) turbostratic disorder at high (>40%) incidence causes asymmetric broadening of the hk0 reflections and a complete extinction of the hk1 reflections while leaving 001 unchanged; (3) interstratification selectively broadens the non-hk0 reflections; and (4) cation vacancies reduce the relative intensity of the 100 reflection. In contrast, a reduction in the thickness of the crystallites along the stacking direction of the layers selectively broadens the 001 reflections while a reduction in the disc diameter causes the progressive broadening and extinction of the hk0 reflections. Comparison with experimental data shows that several kinds of disorders have to be invoked to account for the observed broadening. DIFFaX simulations enable the quantification of the different kinds of disorder.