Global optimum of microstructure parameters in the CMWP line-profile-analysis method by combining Marquardt-Levenberg and Monte-Carlo procedures

Abstract

Line profile analysis of X-ray and neutron diffraction patterns is a powerful tool for determining the microstructure of crystalline materials. The Convolutional-Multiple-Whole-Profile (CMWP) procedure is based on physical profile functions for dislocations, domain size, stacking faults and twin boundaries. Order dependence, strain anisotropy, hkl dependent broadening of planar defects and peak shape are used to separate the effect of different lattice defect types. The Marquardt-Levenberg (ML) numerical optimization procedure has been used successfully to determine crystal defect types and densities. However, in more complex cases like hexagonal materials or multiple phases the ML procedure alone reveals uncertainties. In a new approach the ML and a Monte-Carlo statistical method are combined in an alternative manner. The new CMWP procedure eliminates uncertainties and provides globally optimized parameters of the microstructure.

Microstructure, Texture, and Strength Development during High-Pressure Torsion of CrMnFeCoNi High-Entropy Alloy

“…The measurements are done along the radius of the HPT discs, i.e., at positions where the shear strains are different. The line profiles are evaluated by using the convolutional multiple whole profile (CMWP) procedure [16]. The measured diffraction pattern is matched by the theoretically calculated and convoluted profile functions accounting for the effects of size, distortion, planar defects and instrumental effects, while the background is determined separately.…”

“…The parameters obtained by using the CMWP method characterizing the substructure are the area average crystallite (subgrain) size <x> area , dislocation density ρ, dislocation character q (edge versus screw), dislocation arrangement parameter M = R e √ ρ (R e = effective outer cut-off radius of dislocations), twin density β (number of twin boundary planes within hundred {111} lattice planes parallel to the twin boundary) and average distance between adjacent twin boundaries d Tw = 100 d {111} /β. The M parameter is closely related to the dipole character of the dislocation arrangements [16]. In plastic deformation there are usually equal numbers of plus and minus dislocations, where the plus-minus pairs form dislocation dipoles.…”

“…When the two dislocations in the pairs are close or far from each other the dipole character is strong or weak and the corresponding M parameter close to unity or considerably larger than one, respectively. The CMWP procedure can handle more than one phase [16]. This option is used to evaluate the dislocation, size and planar defect parameters in the FCC and HCP phases at the same time.…”

Microstructural Investigation of Nanocrystalline Hydrogen-Storing Mg-Titanate Nanotube Composites Processed by High-Pressure Torsion

“…In brief, the contribution of lattice strain and coherently scattering domains on peak broadening can be separated on the basis of their different diffraction order dependence. The applied profile functions are generated for each Bragg-reflection of each crystalline phase as the inverse Fourier transform of the product of the size and strain Fourier coefficients providing both the strain and size parameters of the microstructure [51]. In this model, it is assumed that the crystallites have a lognormal size distribution:…”

The Microstructure and strength of a V–5Cr–5Ti alloy processed by high pressure torsion

“…According to the kinematical theory of X-ray diffraction, small crystallite size and large lattice distortions are causing peak broadening in diffraction patterns [24]. The dislocation density and arrangement, the dislocation characters and the crystallite size have been evaluated by using the CMWP line profile analysis procedure [25][26][27]. The theoretical models of dislocation and crystallite size implemented in the CMWP are described briefly as follows.…”