Geometrical limits and improvement of the diffraction optics in Gandolfi cameras

The Gandolfi technique is used to obtain powder diffraction patterns from a single-crystal by rotating it simultaneously around two axes. In order to maximize the number of possible orientations, the angle χ between the two axes should approach 90° but, for technical reasons, it must be smaller than 90° and some reflections will be lost. For an optimization of the technique, experiments have been realized for different χ values and equations have been established that allow the calculation of the limits (expressed in terms of fraction of missing orientations, q_m, and the maximum diffraction angle, 2θ_G, up to which no reflection is lost) of a given camera (characterized by χ and the ratio h/r between the height and radius of the film or detector). With χ = 70° and h/r = 16/57.3, for example, q_m = 6% and 2θ_G = 46°, which compares favourably with the conventional Gandolfi camera (χ = 45°, h/r = 14/57.3; q_m = 29%, 2θ_G = 19°). For practical purposes, 2θ_G = 46° means that the diffraction pattern will be complete for the whole range of spacings with d ≥ 1.96 Å (Cu Kα radiation, λ = 1.5406 Å). This is sufficient for the unambiguous identification of most crystalline solids but it is worth mentioning that a simple increase of the film height to h = 48 mm extends the complete pattern up to 2θ_G, = 140°, equivalent to 94% of the theoretically accessible d spacings at a given wavelength, i.e. the Gandolfi technique can be made as reliable as true powder diffraction.