On the split Voigt profile and its use in the analysis of X-ray diffraction patterns
DOI:
https://doi.org/10.31349/RevMexFis.71.021004Keywords:
X-ray diffraction, split Voigt function, Line broadeningAbstract
The main properties (integral breadth, FWHM, Fourier transform) of the split Voigt function have been analysed. These are important in the study of the X-ray diffraction peaks. In this way, some X-ray diffraction lines of a sample of quartz and zirconia has been analysed by using single line methods, describing the instrumental-spectral asymmetric peaks by means of split Voigt functions.
References
H. C. van de Hulst and J. J. M. Reesinck, Line breadths and Voigt profiles, ApJ 106 (1947) 121
P. Suortti, M. Ahtee and L. Unonius, Voigt Function Fit of Xray and Neutron Powder Diffraction Profiles, J. Appl. Cryst. 12 (1979) 365
Th. H. de Keijser, J. I. Langford, E. J. Mittemeijer and A. B. P. Vogels, Use of the Voigt Function in a Single-Line Method for the Analysis of X-ray Diffraction Line Broadening, J. Appl. Cryst. 15 (1982) 308
D. Balzar and H. Ledbetter, Voigt-Function Modeling in Fourier Analysis of Size- and Strain-Broadened X-ray Diffraction Peaks, J. Appl. Cryst. 26 (1993) 97
J. I. Langford, A Rapid Method for Analysing the Breadths of Diffraction and Spectral Lines using the Voigt Function, J. Appl. Cryst. 11 (1978) 10
P. Thompson, D. E. Cox and J. B. Hastings, Rietveld Refinement of Debye-Scherrer Synchrotron X-ray Data from Al2O3, J. Appl. Cryst. 20 (1987) 79
M. M. Hall, V. G. Veeraraghavan, H. Rubin and P. G. Winchell, The approximation of symmetric X-ray peaks by Pearson type VII distributions, J. Appl. Cryst. 10 (1977) 66
J. Rodríguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Physica B 192 (1993) 55
B. H. Toby and R.B. Von Dreele, GSAS-II: the genesis of a modern open-source all purpose crystallography software package, J. Appl. Cryst. 46 (2013) 544
R. A. Young et al., The Rietveld Method (International Union of Crystallography, Oxford University Press, Oxford, 1993)
L. Lutterotti, Total Pattern Fitting for the Combined SizeStrain-Stress-Texture Determination in Thin Film Diffraction, Nucl. Instrum. Methods Phys. Res. B 268 (2010) 334
Y. H. Dong and P. Scardi, MarqX: a new program for wholepowder-pattern fitting, J. Appl. Cryst. 33 (2000) 184
R. W. Cheary and A. A. Coelho, Axial Divergence in a Conventional X-ray Powder Diffractometer. I. Theoretical Foundations, J. Appl. Cryst. 31 (1998) 851
E. Michalski, The Diffraction of X-rays by Close-Packed Polytypic Crystals Containing Single Stacking Faults. I. General Theory, Acta Cryst. A. 44 (1988) 640
H. Flores-Llamas, Asymmetries of the Voigt line shape, J. Appl. Cryst. 34 (2001) 136
M. J. Wojdyr, Fityk: A general-purpose peak fitting program, J. Appl. Cryst. 43 (2010) 1126
N. C. Halder and C. N. J. Wagner, Separation of particle size and lattice strain in integral breadth measurements, Acta Cryst. 20 (1966) 312
W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge University Press, New York, 1992)
M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions (Dover publications Inc., New York, 1972)
D. W. Posener, The shape of spectral lines: tables of the Voigt profile a π R +∞ −∞ [exp(−y 2 )dy/a2 + (v − y) 2 ], Aust. J. Phys. 12 (1959) 184
J. Pantoja-Cortes, F. Sánchez-Bajo and A. L. Ortiz, Evaluating nanocrystalline size distributions in doped and undoped nanocrystalline ceramics by X-ray diffractometry, Ceram. Int. 44 (2018) 22365
P. Scardi and M. Leoni, Whole powder pattern modelling, Acta Cryst. A A58 (2002) 190
G. K. Williamson and W. H. Hall, X-ray line broadening from filed aluminium and wolfram, Acta Metall. 1 (1953) 22
B. E. Warren and B. L. Averbach, The Effect of Cold-Work Distortion on X-Ray Patterns, J. Appl. Phys. 21 (1950) 595
Th. H. de Keijser, E. J. Mittemeijer and H. C. F. Rozendaal, The Determination of Crystallite-Size and Lattice-Strain Parameters in Conjunction with the Profile-Refinement Method for the Determination of Crystal Structures, J. Appl. Cryst. 16 (1983) 309
R. Delhez, Th. H. de Keijser and E. J. Mittemeijer, Determination of Crystallite Size and Lattice Distortions through X-ray Diffraction Line Profile Analysis, Fresenius Z. Anal. Chem. 312 (1982) 1
H. P. Klug and L. E. Alexander, X Ray Diffraction Procedures for Polycrystalline and Amorphous Materials (WileyInterscience Publication, 1974)
P. Dasgupta, On the intrinsic hook effect associated with pseudo-Voigt profiles, J. Appl. Cryst. 35 (2002) 267
R. K. Nandi, H. K. Kuo, W. Schlosberg, G. Wissler, J. B. Cohen and B. Crist Jr, Single-Peak Methods for Fourier Analysis of Peak Shapes, J. Appl. Cryst. 17 (1984) 22
A. L. Ortiz, F. Sanchez-Bajo, A. Hernández-Jiménez, F. Guiberteau and F.L. Cumbrera, X-ray line-broadening study of a liquid-phase-sintered silicon carbide, J. Eur. Ceram. Soc. 22 (2002) 2677
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 F. Sánchez-Bajo
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
