Best Fit for Complex Peaks (BFCP) in Matlab® for quantitative analysis of in situ 2D X-Ray diffraction data and Raman spectra

Abstract

Large mineral grains that have undergone shock metamorphism or tectonic stress can exhibit plastic deformation. Using in situ micro X-Ray diffraction, such deformation is revealed in a 2D detector image by distortion of diffraction spots into an angular spread or ‘streaking’ along Debye ring or chi (χ) dimension; this can provide a quantitative measurement of plastic deformation via full width at half maximum (FWHMχ) measurement of the diffraction profile along χ. Often the X-ray intensity is not a single homogeneous streak, but is partitioned into discrete orientationally-related spots along the Deybe ring, called asterism. These complex peaks require more sophisticated fitting. This study introduces a user-friendly, high efficiency data fitting program, Best Fit for Complex Peaks (BFCP), executed within Matlab®. Using XRD data as examples, we fit the integrated complex peaks by a Pseudo-Voigt function and assess the BFCP fitting ability on arbitrarily-generated complex peaks simulating XRD peaks with and without observable noise. In addition, we test BFCP with representative highly-deformed terrestrial and meteoritic samples: quartz in the Concord Granite, olivine in ureilite meteorite Larkman Nunatak 04315, and plagioclase in martian meteorite Northwest Africa 8171. We further test BFCP on Raman spectra from a plagioclase clast in martian meteorite Northwest Africa 11220. Fitting results are monitored by the Normalized Root-Mean-Squared Error (NRMSE), the sum of full width at half maximum (∑(FWHM)) and Modified-∑(FWHM). BFCP is designed for XRD data where there is contribution from both Lorentzian and Gaussian components, but it can be applied where appropriate to peak-fitting of other intensity-versus-quantity data, including spectra.