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.
Highlights
IntroductionThere are two different approaches for treating diffraction line broadening
Line profile analysis (LPA) of X-ray and neutron diffraction patterns has proven to be a powerful method for quantitative and qualitative characterization of lattice defects in crystalline materials [1,2,3,4,5,6,7].Formally, there are two different approaches for treating diffraction line broadening
The top-down approach uses closed-form profile functions, like Gaussian, Lorentzian, pseudo-Voight, or Pearson-VII, for fitting peak profiles [8,9,10,11]. Since these profile functions are of ad hoc mathematical character, it is difficult to establish a sound correlation between specific lattice defects and the parameters of these functions
Summary
There are two different approaches for treating diffraction line broadening. The top-down approach uses closed-form profile functions, like Gaussian, Lorentzian, pseudo-Voight, or Pearson-VII, for fitting peak profiles [8,9,10,11]. Since these profile functions are of ad hoc mathematical character, it is difficult to establish a sound correlation between specific lattice defects and the parameters of these functions. The bottom-up approach is based on physical profiles developed by using the physical properties of specific lattice defects [2,3,4,5,6,12,13,14,15]. Size profile calculation is based on optical principles [16]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
