Abstract
Phenomenal profiling functions were applied for the simulation of an X-ray diffraction (XRD) pattern of pyrite ash bioprocessed in Acetobacter aceti contained growth media. The full width at half maximum (FWHM) values were estimated for each pattern of pyrite ash, and the Bragg equation was used to determine the atomic layer spacing, as well crystallite size and strain broadening were accomplished by applications of Scherrer and Williamson-Hall equations. Errors in line broadening were correlated with the FWHM equations of the generalised profiling functions, and the microstrain (<i>ε</i>) was estimated with the relation between the integral breadth (<i>β</i><sub>i</sub>) and cos<i>θ</i>. Furthermore, the XRD pattern of a discrete peak was 3D simulated using Gaussian, Lorentzian, Pearson VII, pseudo-Voigt, and Voigt functions. The Gaussian function with a round top peak was designated the most suitable profile simulation by offering the maximum peak height, <i>I</i><sub>max</sub> and tails comparable to the experimental peak.
Highlights
Phenomenal simulation functions were applied to X-ray diffraction (XRD) patterns to better understand the empirical outcomes of crystal structures and simulate the peak profiles
The individual peak of the XRD pattern of pyrite ash bioprocessed in A. aceti contained growth media was 3D simulated, as illustrated in Figs. 10 and 11, applying fundamental approximation functions such as Gaussian, Lorentzian, Pearson VII, pseudo-Voigt, and Voigt equations
Error approximations sourced from the standard deviation (σ) associated full width at half maximum (FWHM) of Gaussian (FWHMG), Lorentzian (FWHML), Pearson VII (FWHMP), pseudo-Voigt (FWHMV), and Voigt (FWHMPV) functions are presented in Fig. 3 to compare the FWHM values of each profiling peak; the FWHM value of the Voigt function (FWHMV) was found to be the highest
Summary
Phenomenal simulation functions were applied to X-ray diffraction (XRD) patterns to better understand the empirical outcomes of crystal structures and simulate the peak profiles. The essentials of diffractometer system techniques are based on the formation of incident X-rays at several wavelengths; the rays interact with the electrons of the atoms in the crystal, and the diffracted beams pattern of X-rays from the crystal lattice at relevant angles produce peaks of diffraction intensity. The peak profile is shaped relatively with the angle of the diffracted rays enduring essential structures. 1.1 Profiling functions The X-ray waves are diffracted by electrons of the atoms, and the wavelength and angle of the diffracted X-ray beams are defined as the intrinsic parameters used to describe the shape profiling of a diffraction peak. The equation of Bragg’s Law verifies the atomic structure of crystals and describes the reflection of the X-ray beams by the crystals at certain angles of frequency.
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