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1-D Paracrystalline Model to Simulate a Bragg Reflection: Computation of Crystallite Size and Lattice Strain

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A simple and elegant method to simulate single order reflection profile based on 1-D paracrystalline model has been proposed here. For variety of polymer films this approach has been applied to compute microcrystalline parameters like crystallite size and lattice strain. Other metallic oxide compounds are also analysed using this approach. Employing this model, X-ray diffraction patterns from various polymer samples have been analysed and corresponding microstructure parameters have been reported in this article.
Cite this paper
Prakash, M. , Urs, G. , Ananda, H. and Somashekar, R. (2014) 1-D Paracrystalline Model to Simulate a Bragg Reflection: Computation of Crystallite Size and Lattice Strain. Crystal Structure Theory and Applications, 3, 48-55. doi: 10.4236/csta.2014.32006.
 

[1] Zernike, F. and Prins, J.A. (1927) Die Beugung von Rontgenstrahlen in Flussigkeiten als Effekt der Molekulanordnung. Zeitschrift fur Physik, 41, 184-194.
http://dx.doi.org/10.1007/BF01391926
[2] Warren, B.E. (1969) X-Ray Diffraction. Addison-Wesley, Reading.
[3] Hosemann, R. and Bagchi, S.N. (1962) Direct Analysis of Diffraction by Matter. North-Holland, Amsterdam.
[4] Hall, I.H. and Somashekar, R. (1991) The Determination of Crystal Size and Disorder from the X-Ray Diffraction Photograph of Polymer Fibres. 2. Modelling Intensity Profiles. Journal of Applied Crystallography, 24, 1051.
http://dx.doi.org/10.1107/S0021889891007707
[5] Balzar, D. (1993) X-Ray Diffraction Line Broadening: Modeling and Applications to High-Tc Superconductors. Journal of Research of the National Institute of Standards and Technology, 98, 321.
http://dx.doi.org/10.6028/jres.098.026
[6] Delhez, R., de Keijser, Th.H., Langford, J.L., Louer, D., Mittemeijer, E.J. and Sonneveld, E.J. (1993)
[7] Langford, J.I. and Lour, D. (1982) Diffraction Line Profiles and Scherrer Constants for Materials with Cylindrical Crystallites. Journal of Applied Crystallography, 15, 20-26.
http://dx.doi.org/10.1107/S0021889882011297
[8] Scardi, P. and Leoni, M. (2002) Whole Powder Pattern Modeling. Acta Crystallographica Section A. Foundations of Crystallography, 58, 190-200.
http://dx.doi.org/10.1107/S0108767301021298
[9] Nandi, R.K., Kuo, H.K., Schlosberg, W., Wissler, G., Cohen, J.B. and Crist Jr., B. (1984) Single-Peak Methods for Fourier Analysis of Peak Shapes. Journal of Applied Crystallography, 17, 22-26.
http://dx.doi.org/10.1107/S0021889878012662
[10] Klug, H.P. and Alexander, L.E. (1974) X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials. 2nd Edition, Wiley, New York.
[11] Kuzel Jr., R. and Klimanek, P. (1989) X-Ray Diffraction Line Broadening Due to Dislocations in Non-Cubic Crystalline Materials. III. Experimental Results for Plastically Deformed Zirconium. Journal of Applied Crystallography, 22, 299-307.
http://dx.doi.org/10.1107/S0021889889001585
[12] Rietveld, H.M. (1969) A Profile Refinement Method for Nuclear and Magnetic Structures. Journal of Applied Crystallography, 2, 65-71.
http://dx.doi.org/10.1107/S0021889869006558
[13] Young, R.A. (1995) The Rietveld Method. Oxford University Press, Oxford, 132-166.
[14] Ungar, T., Gubicza, J., Ribarik, G. and Borbely, A. (2001) Crystallite Size Distribution and Dislocation Structure Determined by Diffraction Profile Analysis: Principles and Practical Application to Cubic and Hexagonal Crystals. Journal of Applied Crystallography, 34, 298-310.
http://dx.doi.org/10.1107/S0021889801003715
[15] Snyder, R.J., Fiala, J. and Bunge, H.J. (1999) Defect and Microstructure Analysis by Diffraction. Oxford University Press, Oxford.
[16] Somashekar, R., Hall, I.H. and Carr, P.D. (1989) The Determination of Crystal Size and Disorder from X-Ray Diffraction Photographs of Polymer Fibres. 1. The Accuracy of Determination of Fourier Coefficients of the Intensity Profile of a Reflection. Journal of Applied Crystallography, 22, 363-371.
http://dx.doi.org/10.1107/S0021889889004085
[17] Lee, K.G., Barton, R. and Schultz, J.M. (1995) Structure and Property Development in Poly(P-Phenylene Terephthalamide) during Heat Treatment under Tension. Journal of Polymer Science Part B: Polymer Physics, 33, 1-14.
http://dx.doi.org/10.1002/polb.1995.090330101
[18] Somashekar, R. and Somashekarappa, H. (1997) X-Ray Diffraction-Line Broadening Analysis: Paracrystalline Method. Journal of Applied Crystallography, 30, 147-152.
http://dx.doi.org/10.1107/S0021889896010023
[19] Balzar, D., Audebrand, N., Daymond, M.R., Fitch, A., Hewat, A., Langford, J.I., Le Bail, A., Lour, D., Masson, O., McCowan, C.N., Popa, N.C., Stephens, P.W. and Toby, B.H. (2004) Journal of Applied Crystallography, 37, 911-924.
http://dx.doi.org/10.1107/S0021889804022551
[20] Skoko, Z., Popovic, J., Dekanic, K., Kolbas, V. and Popovi, S. (2012) XBroad: Program for Extracting Basic Microstructure Information from X-Ray Diffraction Patterns in Few Clicks. Journal of Applied Crystallography, 45, 584-597.
http://dx.doi.org/10.1107/S0021889812014859
[21] Beyerlien, K.R., Snyder, R.L. and Scardi, P. (2011) Powder Diffraction Line Profiles from the Size and Shape of Nanocrystallites. Journal of Applied Crystallography, 44, 945-953.
http://dx.doi.org/10.1107/S0021889811030743
[22] Leonardi, A., Leoni, M., Siboni, S. and Scardi, P. (2012) Common Volume Functions and Diffraction Line Profiles of Polyhedral Domains. Journal of Applied Crystallography, 45, 1162-1172.
http://dx.doi.org/10.1107/S0021889812039283
[23] Stokes, A.R. (1948) A Numerical Fourier-Analysis Method for the Correction of Widths and Shapes of Lines on X-Ray Powder Photographs. Proceedings of the Physical Society, 61, 382-391.
http://dx.doi.org/10.1088/0959-5309/61/4/311
[24] Bhajantria, R.F., Ravindrachary, V., Harisha, A., Crasta, V., Nayak, S.P. and Poojary, B. (2006) Microstructural Studies on BaCl2 Doped Poly(Vinyl Alcohol). Polymer, 47, 3591-3598.
http://dx.doi.org/10.1016/j.polymer.2006.03.054
[25] Lakshmeesha Rao, B., Mahadevaiah, O., Sangappa, Y., Asha, S. and Somashekar, R. (2012) Microstructural Parameters in Electron Irradiated PVA Films by Wide Angle X-Ray Scattering Studies (WAXS). Advanced Materials Research, 585, 532-536.
http://dx.doi.org/10.4028/www.scientific.net/AMR.585.532
[26] Divakara, S., Siddaraju, G.N. and Somashekar, R. (2010) Comparative Study of Natural and Man-Made Polymers Using Whole Powder Pattern Fitting Technique. Fibres and Polymers, 11, 861-868.
http://dx.doi.org/10.1007/s12221-010-0861-7
[27] Sangappa, Demappa, T., Mahadevaiah, Ganesh, S., Divakara, S. and Somashekar, R. (2008) Microstructural Parameters in Electron-Irradiated Hydroxypropyl Methylcellulose Films Using X-Ray Line Profile Analysis. Journal of Applied Polymer Science, 109, 3983-3990.
http://dx.doi.org/10.1002/app.28495
[28] Divakara, S., Madhu, S. and Somashekar, R. (2009) Stacking Faults and Microstructural Parameters in Non-Mulberry Silk Fibres. Pramana, 73, 927-938.
http://dx.doi.org/10.1007/s12043-009-0159-8
[29] Divakara, S., Somashekar, R. and Roy, S. (2009) Correlation between Microstructure and Microrheological Parameters of Various Silk Fibres. Indian Journal of Fibre and Textile Research, 34, 168-174.
[30] Reddy, T., Roy, S., Prakash, Y., Somashekarappa, H., Ramesh, K., Divakara, S. and Somashekar, R. (2011) Stress-Strain Curves and Corresponding Structural Parameters in Mulberry and Non-Mulberry Silk Fibers. Fibers and Polymers, 12, 499-505.
http://dx.doi.org/10.1007/s12221-011-0499-0
[31] Niranjana, A.R., Divakara, S. and Somashekar, R. (2011) Characterization of Field Grown Cotton Fibres Using Whole Powder Pattern Fitting Method. Indian Journal of Fibre and Textile Research, 36, 9-17.
[32] Abhishek, S., Samir, O.M., Annadurai, V., Gopalkrishne Urs, R., Mahesh, S.S. and Somashekar, R. (2005) Role of Micro-Crystalline Parameters in the Physical Properties of Cotton Fibers. European Polymer Journal, 41, 2916-2922.
http://dx.doi.org/10.1016/j.eurpolymj.2005.06.005          eww141104lx

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