Voigt-function modeling in Fourier analysis of size- and strain-broadened X-ray diffraction peaks

Abstract

With the assumption that both size‐ and strain‐broadened profiles of the pure‐specimen function are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren–Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the `hook' effect occurs when the Cauchy content of the size‐broadened profile is underestimated. The ratio of volume‐weighted and surface‐weighted domain sizes can change from ~1.31, for the minimum allowed Cauchy content, to 2, when the size‐broadened profile is given solely by a Cauchy function. If the distortion Subscripts coefficient is approximated by a harmonic term, mean‐square strains decrease linearly with increasing the averaging distance. The local strain is finite only in the case of purely Gaussian strain broadening, because strains are then independent of averaging distance.

Compression Behavior of Zr-doped Nanoanatase

“…The diffraction spectrum of a CeO standard was used to determine the source emission profile and instrumental contribution to peak broadening. The effects of crystallite size and strain on the peak broadening were analyzed using the double-Voigt approach [42]. Integral-breadthbased volume-weighted mean column height L Vol IB of coherently diffracting domains as well as mean strain values e 0 [41] were obtained simultaneously, resulting in L Vol IB = 11.0(3) nm and e 0 = 22(1)%, while the residuals of the fit are Rwp = 1.370.…”

The effect of cooling rates on the microstructure and mechanical properties of thermo-mechanically processed Ti–Al–Mo–V–Cr–Fe alloys

“…Other factors such as dislocation density, slip activity [32], and the presence of stacking faults can also affect the shape and/or position of diffraction peaks [27]. Warren [39], Randle and Engler [40] developed the XRDLPA approach for the analysis of the microstructure, which was later followed by others [28,[41][42][43][44][45] with some modifications making it possible to determine the crystallite size and microstrain in materials reliably. Similarly to [16,23], the modified Rietveld [46] method has been used in order to characterise microstructures in this investigation.…”

X-ray diffraction peak profiles from threading dislocations in GaN epitaxial films

“…In many cases, the latter step is not sufficiently accurate, since it has to rely on a few Fourier coefficients obtained from noisy experimental data. Balzar 21,22 suggested to avoid this difficulty by directly fitting the peak profile to a convolution of a Lorentzian and a Gaussian, which is the Voigt function. The experimental peak profiles are not always described by the Voigt function and various other analytical functions were suggested on a purely phenomenological basis.…”