Array-type universal profile function for powder pattern fitting

An array-type universal profile function for powder-pattern fitting is described. It is defined as an array of unknown parameters representing the profile heights at discrete angular steps. The unknown parameters are determined during least-squares fitting together with the integrated intensity, the peak position, the peak width and background parameters. The function has been applied to profile fitting in a small 20 range, and has better R-factors than the pseudo-Voigt and Pearson VII functions. This new function has some important advantages: it can model any complex profile shape, which would be difficult to describe by a smoothly varying analytical-type function; it generally gives a better fit and thus more precise and accurate analysis than currently used analytical-type functions; and it can be applied to the data of all radiation sources including conventional X-rays, synchrotron radiation and time-of-flight and fixed-wavelength neutrons without changing the mathematical form. The optimized use of the function and the accuracy of deduced parameters are also discussed.