New-corrected functions of X-ray powder diffraction

X-ray powder diffraction is an indispensable technique to study material structure, phase transition and so on. It is necessary for high quality diffraction data to get high-precision diffraction angle. This work proposed four corrected functions of X-ray powder diffraction angle. Two methods, linearization method and modified Levenberg-Marquardt iteration method, are given to solve the function parame-ters, and the modified Levenberg-Marquardt method has fast convergent speed and stable solution. Two methods can give closed parameters, including those of Lu, Liu, and Chu functions and polyno-mial. New-corrected functions were used to fit the diffraction angle error of the tetragonal rutile poly-crystalline TiO₂ mixed with Gd_0.45Y_2.55Sc₂Ga₃O₁₂ as a standard sample, and the computation result indi-cates that these functions can characterize the diffraction error very well. In some cases, the new-cor-rected functions can describe the diffraction angle error better than the reported corrected functions. At the same time, the lattice parameter of Gd_0.45Y_2.55Sc₂Ga₃O₁₂ was computed with two methods. When the corrected function parameters and lattice parameters were solved by the least square method, the interaction of the function parameters and lattice parameters would result in great error. However, when the X-ray diffraction angles were corrected by corrected functions using a standard sample, the au-thentic lattice parameters can be obtained by the least square fitting.