The Δω, Δ2Θ two-dimensional nature of Bragg X-ray reflexions from a small single crystal: its influence on the assessment of structure factors

By its two-dimensional nature, the Δω, Δ2θ intensity distribution of a Bragg X-ray reflexion has greater angular resolution and greater information content than the corresponding one-dimensional Δω reflexion profile. It allows for the measurement of integrated intensity, exactly and equally truncated, over the full range of θ. Also, it is potentially correctable point by point for extinction and simultaneous diffraction. Consequently, it has inherent capabilities for the estimation of structure-factor values with improved accuracy. To realize this potential, it is necessary to identify and appreciate the various factors which, convoluted together, determine the 2D distribution. Among these factors, important ones are the crystal mosaic/fragment distribution, μ, the X-ray source emission distribution and the wavelength distribution. By first treating the situation for a hypothetical point source, the relation of the reflectivity (or 'level of interaction') with the μ distribution is highlighted. Extension to a real source indicates the probable need for deconvolution in practical cases to extract meaningful estimates of the μ distribution and hence the reflectivity distribution, the most significant measured quantity for accurate structure-factor evaluation. The 2D distribution is discussed in relation to single (H) scattering, multiple (H.) scattering (extinction) and simultaneous (H. K) scattering.