Application of the Levenberg-Marquardt Algorithm to X-Ray Diffraction Quantitative Phase Analysis

The conventional X-ray diffraction quantitative phase analysis methods are over-reliant on pure standard substances, working curve and K value. If the phases are more than 3, the fitting results are not good by Rietveld method. In addition, the versatility of quantitative methods with large calculation and fussy operation also need to be expanded. A new non-standard quantitative phase analysis method based on nonlinear model parameters estimation method of 4 modular redundant systems that consist of Levenberg-Marquardt, Particle Swarm Optimization, Genetic Algorithm and Differential Evolution is proposed. Taking the content of 4 phases in 19 mixture powder as the original data, performing the whole process of computing in the Matlab environment, the experimental results show that the Levenberg-Marquardt algorithm is an effective tool with smaller computing complexity, faster convergence speed and better global searching capability and other advantages. It is no need to add reference phase to the samples, which overcomes the problems that all the samples must be determined more than one time, and the method with no need for K value which enlarges the applications and enhances the accuracy of the X-ray diffraction method for quantitative phase analysis of the mixture samples. Replacing the conventional specific single spectrum line intensity or intensity rations by the sum of the integrated intensity of the top three peaks can improve the precision of the X-ray diffraction quantitative phase analysis. With this method, the content of Corundum in 82 samples of Zhaosu section in Ili basin and 359 samples in ELJ drilling core of ICDP in Qinghai Lake are computed. The correlation coefficient of the match ratio and the calculated value of Corundum in Zhaosu section and ELJ drilling core have reached 0.83 and 0.63. Practice has proved that it is a feasible, effective, rapid and correct technique of quantitative analysis of minerals, and the stability is satisfactory. It can be used for quantifying the phases in more than 9-phase materials.