Development the Fourier analysis method of x-ray diffraction to calculate variables in crystal structure as well as calculation of some lattice parameters

Abstract

The Fourier method was developed to calculate other important variables in the crystalline structure, such a strain, which is equal to 7.4828 x 10−3 instead of the mean square strain and the energy density of the strain, which is equal to 2799614.7 dyne / cm2 and the stress equal to 7.4828 x 108 dyne/cm2. The results obtained from the Fourier method for calculating other parameters of the manganese oxide lattice for each peak of x-ray diffraction peaks such as the texture coefficient, its mean value equal to 0.99999 and the micro strains, which its mean value equal to 4.47 × 10−3 dislocation density, its mean value are equal to 37.3 (lines .m−2) and the specific surface area its mean value is equal to 19,58432 of crystalline volume. A comparison was also made between the values of the square of strain and the apparent strain.

Sequential structural degradation of red perovskite quantum dots and its prevention by introducing iodide at a stable gradient concentration into the core–shell red perovskite quantum dots

“…QD/0.8APTES showed similar XRD patterns corresponding to the (001), (011), and (002) planes belonging to the cubic Pm3m symmetry group. The peak positions of (001) and (002) planes for QD/0.8APTES shifted from 14.6 (6.1 Å) to 14.3° (6.2 Å) and from 29.5 (3.0 Å) to 29.0° (3.1 Å), respectively, as compared to those observed for pristine perovskite QDs, leading to c -axis expansion (lattice distance was calculated from the XRD data using the Scherrer equation (eqn (2))): 47 …”

Effects of calcination and sintering processes on structural profile parameters of modified BNKT-based ferroelectric ceramics

“…During the grain growth of the micro/nanoparticles, they experience a lot of compression and relaxation in the lattice, resulting in deviation in the lattice constant as well as an overall deviation in the lattice volume. On the other hand, the displacements of the atoms with respect to the neighboring lattice position result in strain broadening [25]. Micro-strains of all samples are calculated using the following formula based on Scherrer's equation [40].…”

“…Examining the distinctive diffraction order dependence makes it possible to distinguish the influences of crystallite size and lattice strain on peak broadening. Standard X-ray diffraction profile analysis procedures, such as assessing the full width at half maximum (FWHM), integral breadths, and Fourier coefficient of the profiles yield information about apparent crystallite size and lattice strain [24][25][26]. Crystallite size measures the size of coherently diffracting domains.…”