Study on the Influencing Factors of the Levenberg-Marquardt Algorithm for X-ray Diffraction Quantitative Phase Analysis

There are many traditional methods of X-ray Diffraction (XRD) quantitative analysis. The latest developed Levenberg-Marquardt (LM) algorithm has the obvious advantages over traditional methods. However, it is still unclear which, and how, influencing factors affect the reliability and accuracy of the computed results in practice. In order to improve the accuracy and processing efficiency, the authors discuss influences of the choice of diffraction intensity, pattern background and sample numbers on phase quantitative analysis based on the LM method and Matlab program. A series of mixed minerals, which consist of corundum, quartz, calcite and albite, or bulk samples mixed with corundum under different proportions, were designed to examine the influences. The computed results from the sum of integral intensities of the top three peaks have improved accuracy over these by the integral intensity of the strongest peak. Some random errors are eliminated through the sum of integral intensities of the top three peaks effectively to some extent. The accuracies of the computed results were improved by background correction. Because of the differences in crystal structure and diffraction characteristics, the influences of background on the calculation results were different. The sample size also affects the accuracy of quantitative analyses using the LM method. Increasing samples can improve accuracy significantly if the number of samples is less than the threshold value, however, there is no obvious change if the number of samples is more than threshold value.