![]() ![]() These two works form the basis of the interaction of the incident wave and the crystal. Ewald (1916, 1917 ) and Laue (1931 ) took this further and introduced the polarizability of the electron density by the incoming electromagnetic wave by considering the crystal as a series of dipoles (Ewald) and a distributed electron density (Laue). This led to the diminution of the incident beam and explained the width of the profile. Soon after Bragg published his explanation, Darwin (1914 ) recognized that the scattering from a set of parallel planes introduces re-scattering from the underside of planes above. This explanation assumes that all the atoms aligned in these planes concentrate their amplitudes at one position and can be simply interpreted, or that the amplitude diminishes from the peak due to size effects (James, 1962 Authier, 2001 ) etc., which is the shape transform. The dominating features in a diffraction pattern are the strong peaks that Bragg (1913 ) associated with specular (mirror) reflections from crystal planes. Also, any unforeseen microstructure features may confuse the interpretation. All the amplitudes will be coherently related which makes the inverse problem of estimating the structure from the diffraction pattern a difficult challenge. The most complete description of diffraction should include all the scattered amplitudes from all the atoms at all detection positions, including atomic vibrations and re-scattering. Also, the reliability of the measured data can only be estimated with confidence if a complete interpretation of the diffraction pattern is available. It is therefore crucial to ensure that the derived structural model closely resembles reality, which can only be achieved if the description of diffraction is sufficiently complete. X-ray diffraction analysis has relied to an increasing extent on the accuracy of intensity measurements to reveal important structural information in complex molecules, e.g. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. By applying the idea that the higher-order peaks are due to path lengths of n λ, it is shown that `systematically absent' reflections in the conventional theory may not be absent. ![]() This `enhancement' effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This article takes the concepts of the `new diffraction theory' and examines the implications for the interpretation of experimental results and the estimation of structure factors.
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