The termination effect for amorphous patterns

Termination of the experimental intensity curve and the use of a convergence factor leads to an uncorrected radial distribution function which is equal to the true distribution function convoluted with a termination factor of the form sin x/x, and with a convergence factor of exponential form. Although the convolution factors are known, a deconvolution of the uncorrected curve to obtain the true radial distribution function is not possible by the usual methods. However, for the case of moderately sharp peaks on a slowly varying background, an approximate method can be developed. For each peak of the uncorrected curve, we introduce a Gaussian A exp [-a²r²] whose convolution with the termination and convergence factors has the same width and height as the peak. These Gaussians are then used for the first step in a deconvolution of the uncorrected curve. Although it is approximate, the resulting curve is closer to the true distribution function than the original uncorrected curve, and the termination ripples have been eliminated. The method is completely objective, and free from all arbitrary adjustments.