Solute Segregation to Phase Interfaces and Grain Boundaries: Studies by Analytical Electron Microscopy and Profile Deconvolution

摘要

Mathematical deconvolution of the observed composition profiles at the interface or boundary with the x-ray generation profile to determine the actual composition profile is a viable procedure for extracting compositional data on a spatial scale smaller than the inherent resolution of thin foil x-ray microanalysis. In sufficiently thin foils, the x-ray generation profile can be calculated with the single scattering model. In thicker foils, the x-ray generation profile can be calculated with Monte Carlo techniques. Explicit deconvolution is, in general, not possible mathematically, but it can be accomplished numerically through iterative convolutions. Convolution of the x-ray generation profile with the assumed actual composition profile allows for direct calculation of the expected composition profile. The convolution procedure using various assumed actual concentration profiles is repeated iteratively until the calculated profile and the observed profile correspond. This paper describes the convolution process and introduces a rapid graphical solution to the problem, compares the convolution process using the single scattering model and Monte Carlo techniques, and discusses the limitations of the deconvolution procedure. This study uses the recently reported data of Ti enrichment at grain boundaries in an Fe-Ni superalloy. (ERA citation 12:046778)