The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination

Abstract

The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the hkl dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.

Strength can be controlled by edge dislocations in refractory high-entropy alloys

“…The resulting Zener anisotropies, (NbTaTiV) and 0.596 (CrMoNbV), a regime where peak broadening is particularly sensitive to dislocation character (see below). The observed peak broadening during subsequent deformation is analyzed, using the quantitative state-of-the-art Convolutional Multiple Whole Profile (CMWP) method 25 . Note that the CMWP procedure has been widely applied to determine dislocation densities, slip modes, and Burgers vector character in face-centered-cubic (FCC), BCC, and hexagonal-close-packed (HCP) crystals 25 , 26 .…”

“…The observed peak broadening during subsequent deformation is analyzed, using the quantitative state-of-the-art Convolutional Multiple Whole Profile (CMWP) method 25 . Note that the CMWP procedure has been widely applied to determine dislocation densities, slip modes, and Burgers vector character in face-centered-cubic (FCC), BCC, and hexagonal-close-packed (HCP) crystals 25 , 26 . In addition to the instrumental response, HEAs have a peak broadening in the undeformed state due to local deviations of atoms from the perfect lattice positions.…”

Towards quantitative inference of nanoscale defects in irradiated metals and alloys

“…More recently, the convolutional multiple whole profile (CMWP) X-ray diffraction Line Profile Analysis (XLPA) method [67,68] has been developed to characterize dislocation loops in irradiated materials [69,70]. Through calculation of the broadening of X-ray diffraction (XRD) peaks, the type, density, and size distribution of dislocation loops can be determined.…”

Validating x-ray line-profile defect analysis using atomistic models of deformed material

“…The above brief explanation neglects much complexity and subtlety in the approach and we refer the reader in particular to Ungar et al [33] and Ribarik et al [35] for more detailed accounts. For our purposes we need only consider some small details of the behaviour of the profile functions associated with dislocations.…”