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Lineshape Analysis of X-ray Diffraction Profiles: Polyethylene and Model Copolymers

Published online by Cambridge University Press:  06 March 2019

Buckley Crist  and
Paul R. Howard
Buckley Crist
Affiliation:
Dept. of Materials Science & Engineering and Materials Research Center Northwestern University Evanston, IL 60208
Paul R. Howard
Affiliation:
Dept. of Materials Science & Engineering and Materials Research Center Northwestern University Evanston, IL 60208
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Extract

Studies of the shapes of X-ray diffraction peaks from synthetic polymers are still rather uncommon. One probable cause of this situation is the small peak-to-background ratio in most polymer diffraction experiments; it is difficult to achieve precise line profiles for quantitative analysis. Increased utilization of automated data collection/analysis systems and more intense X-ray sources should alleviate this restriction. We suspect, furthermore, that confusion about nomenclature has impeded the acceptance of lineshape analysis for polymers. The peak broadening mechanisms which are generally considered are finite coherence length or crystal size, lattice parameter fluctuation, and displacement disorder of the second kind. Both latter mechanisms have, unfortunately, been referred to as “strains” or “microstrains”. Metallurgists have traditionally expressed displacement disorder as a (length dependent) “microstrain”, and this convention has been adopted in some studies of polymer diffraction. Other work on polymers, however, has termed lattice parameter fluctuation as “microstrain“. The inconsistent use of this term can imply a nonexistent relation between two distinct phenomena.

Type
X. Crystallite Size/Strain Analysis
Information
Advances in X-Ray Analysis , Volume 34: Thirty-Ninth Annual Conference on Applications of X-ray Analysis, July 30 - August 3, 1990 , 1990 , pp. 519 - 529
Copyright
Copyright © International Centre for Diffraction Data 1990

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References

1. Bodor, G., X-Ray Lineshape Analysis. A Means for the Characterization of Crystalline Polymers, Adv. Polym. Sci. 67: 165 (1985).Google Scholar
2. Warren, B. E., X-Ray Studies of Deformed Metals, in: “Progress in Metal Physics”, Vol. 8, B. Chalmers and R. King, eds., Pergamon Press, New York, NY (1959), pp. 147 ff.Google Scholar
3. Buchanan, D. R. and Miller, R. L., X-Ray line Broadening in Isotactic Polystyrene, J. Appl. Phys. 37: 4003 (1966).Google Scholar
4. Wecker, S. M., Cohen, J. B. and Davidson, T., Study of Deformation in Polytetrafluoroethylene by X-ray Line Broadening, J. Appl. Phys. 45: 4453 (1974).Google Scholar
5. Vogel, W., Haase, J. and Hosemann, R., Analysis of X-ray Line Profiles for Microstrains and Paracrystalline Distortions by Fourier Transformation, Z. Naturforsch. 29a:1152 (1974).Google Scholar
6. Hosemann, R., Schmidt, W., Fischer, A. and Balta-Calleja, F. J., X-Ray Diffraction Line Profile Analysis in Microparacrystals, An. Fisica A 79: 145 (1983).Google Scholar
7. Crist, B. and Cohen, J. B., Fourier Analysis of Polymer X-Ray Diffraction Patterns, J. Polym. Sci.: Polym. Phys. Ed. 17: 1001 (1979).Google Scholar
8. Bertaut, E. F., Particle Sizes and their Statistics from Debye-Sherrer Lines, in: “International Tables for Crystallography”, Vol. 3, International Union of Crystallography, Birmingham, UK (1968), pp. 318–323.Google Scholar
9. Takehashi, H., Fourier Coefficients of Line Profiles of Debye-Scherrer Rings Broadened by Lattice Distortion, J. Phys. Soc. Japan 27: 708 (1969).Google Scholar
10. Guinier, A., “X-Ray Diffraction”, W. H. Freeman, San Francisco (1963), Chapt. 6.Google Scholar
11. Rothman, R. L. and Cohen, J. B., X-Ray Study of Faulting in BCC Metals and Alloys, J. Appl. Phys. 42: 971 (1971).Google Scholar
12. Guinier, A., loc. cit., Chapt. 9.Google Scholar
13. Cowley, J. M., Diffraction by Crystals with Planar Faults. I. General Theory, Acta. Cryst. A 32: 83 (1976).Google Scholar
14. Warren, B. E. and Averbach, B. L., The Separation of Cold-Work Distortion and Particle Size Broadening in X-Ray Diffraction Patterns, J. Appl. Phys. 23: 497 (1952).Google Scholar
15. Rothman, R. L. and Cohen, J. B., A New Method for Fourier Analysis of Shapes of X-Ray Peaks and its Application to Line Broadening and Integrated Intensity Measurements, in: “Advances in X-Ray Analysis”, Vol. 12, C. S. Barrett, J. B. Newkirk and G. R. Mallett, eds., Plenum Press, New York, NY (1969), pp. 203–235.Google Scholar
16. Howard, P. R. and Crist, B., Unit Cell Parameters in Model Ethylene - Butene-1 Copolymers, J. Polym. Sci.: Part B: Polym. Phys. 27: 2269 (1989).Google Scholar
17. Stokes, A. R., A Numerical Fourier Analysis Method for the Correction of Widths of Lines on X-ray Powder Photographs, Proc. Phys. Soc. London 61: 382 (1948).Google Scholar
18. Howard, P. R., “The Location of Ethyl Branches in Model Ethylene Copolymers”, Ph.D. Thesis, Northwestern University (1987).Google Scholar
19. Howard, P. R., Wissler, G. E. and Crist, B., X-Ray Lineshape Analysis of Polyethylene and Model Copolymers, J. Polym. Sci.: Part B: Polym. Phys. (submitted).Google Scholar