Small-single-crystal diffractometry with monochromated synchrotron radiation – the wavelength-dispersion minimum condition for Bragg reflection profile measurement

Abstract

The interaction of a synchrotron beam incident on a 'perfect' monochromator crystal, M, and then on a small single crystal, c, is examined and the resultant 2D shape in Δω, Δ2θ space of Bragg reflections from c is deduced. This allows (a) identification of the components intrinsic to M which contribute to the shape, namely its effective aperture and angular bandpass, and (b) prediction of the change of shape with θc. Projection of the 2D shape onto the Δω axis yields the corresponding 1D 'counter' profile and shows that, for Gaussian-like components, the full width at half maximum (FWHM) of the profile is [p2 + q2(t --tmin)2]1/2 where p and q are constants, t = tan θc/tan θM and tmin corresponds to the minimum dispersion condition. It is suggested that, for similar conditions, the relationship determining scan range should be of a similar functional form rather than the conventional linear relationship.