On the use of pseudo-Voigt function in the variance method of size-strain analysis

Conference: 2022: 72nd ACA Annual Meeting
PRABAL DASGUPTA Poster Author
Konnagar
 
Endale Abeba Gudeta Additional Author
Jimma University
Jimma, Oromiya 
 
07/31/2022: 5:30 PM - 7:30 PM
Poster Session 
Portland Marriott Downtown Waterfront 
Room: Exhibit Hall 

Description

Although pseudo-Voigt(p-V) function is widely used to describe an experimentally observed powder XRD line, mainly due to ease with which its mathematical calculations could be tackled, Dasgupta[1,2] has shown that under certain conditions fitting of an observed profile with a p-V function, may lead to erroneous results, in case of Warren-Averbach[3] analysis. Pseudo-Voigt functions may be fitted with experimentally observed X-ray powder diffraction profiles and subsequently be subjected to variance method of size-strain analysis to extract particle size and root mean square strain of a crystallite. This work mathematically shows that for spherical crystallite and also for h00 reflections of a cubic crystallite and hho reflections of an octahedron shaped crystals (for which taper parameter L=0), Cauchy content η must be less than 0.328, otherwise no meaningful results in terms of particle size and root-mean-square (r.m.s) strain could be extracted from such profiles. We have made use of variance equation for pseudo-voigt profile deduced by Sanchez-Bajo and Cumbrera[4] and expression for intercept of a sample related variance, W0 given by Klug & Alexander[5] .Taper parameter values were taken from Wilson's paper[6].
References:
1. P. Dasgupta,. Fizika A (Zagreb) 9, 61 (2000)
2..P.Dasgupta,.J..Appl.Cryst 35,267(2002) https://doi.org/10.1107/S0021889801021203
3. B.E. Warren and B.L.Averbach, J.Appl.Phys. (1952) 23, 497https://doi.org/10.1063/1.170223
4. F.Sanchez-Bajo, & F.L Cumbrera,. J.Appl.Cryst.30,427.(1997)
https://doi.org/10.1107/S0021889801021203
5. H.P. Klug H.P & Alexander L.E In: X-ray diffraction procedure for polycrystalline and amorphous materials, (John Wiley, New York) .(1974)
6. A.J.C. Wilson, Proc.Roy.Soc. 80, 286 (1962)