An improved transformation procedure for radial distribution function analysis

Various methods of reducing the effect of termination error on radial distribution functions are briefly reviewed. A new approach is introduced in which the RDF is calculated by generating the Fourier transform at predetermined points. The resulting sampled transform is relatively free of termination ripple and the spacing of the points reflects the true resolution of the method for the particular, experimentally limited, S_max. The optimum choice of sampling points is determined in relation to special data terminations such as at a zero value of the interference functions or at a peak or trough position. The effectiveness of the sampled transform routine in reducing termination error is demonstrated by applying it to prematurely truncated interference functions derived from scattering data from atactic polystyrene. The advantage of the sampled transform approach to RDF analysis is that it prevents a termination discontinuity in the interference function, such as is often unavoidable even when special care is taken to apply precise corrections to the data, from causing an obscuring ripple on the RDF. In fact, in the extreme, it enables generation of useful RDF's of glassy polymers from data which have been neither corrected nor normalized.