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The Determination of Crystallite Size and Size Distribution from Broadened X-Ray Diffraction Lines

Published online by Cambridge University Press:  06 March 2019

H. F. Quinn  and
P. Cherin
H. F. Quinn
Affiliation:
International Business Machines Corporation, Oswego, New York
P. Cherin
Affiliation:
International Business Machines Corporation, Oswego, New York
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Abstract

Magnesium oxide crystallites having mean dimensions in the range of 25–1000 A can be prepared by controlled thermal decomposition of the carbonate.

Following some earlier investigations of Birks and Friedman, we have determined the mean size and size distribution of several such MgO samples from the broadened X-ray diffraction lines which they exhibit. Contrary to the procedure of the above investigators, the harmonic analysis due to Stokes has been used to correct for instrumental broadening and values of mean-size and size-distribution functions obtained from the Fourier coefficients by the methods of Warren and Averbach.

The results obtained are compared with average sizes and distributions obtained by direct examination of the samples in an electron microscope.

A composite sample has been prepared by mixing known quantities of the sample previously studied. The distribution function obtained by harmonic analysis of one diffraction line of the composite sample is compared with the function calculated from the distributions of its components.

Conclusions are drawn concerning the significance of the results obtained by the Warren technique: in particular, the average sizes obtained by this method are compared with those given by the approximate method used by Birks and Friedman.

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 5: Tenth Annual Conference on Applications of X-ray Analysis, August 7-9, 1961 , 1961 , pp. 94 - 103
Copyright
Copyright © International Centre for Diffraction Data 1961

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References

1. Warren, B. E. and Averbach, B. L., “The Effect of Cold-Work Distortion on X-Ray Patterns,” J. Appl. Phys., Vol. 21, 1950, p. 595.Google Scholar
2. Stokes, A. R., “A Numerical Fourier Analysis Method for the Correction of Widths and Shapes of Lines on X-Ray Powder Photographs,” Proc. Phys. Soc. (London), Vol. 61, 1948, 1. 382.Google Scholar
3. Birks, L. S. and Friedman, H., “Particle Size Determination from X-Ray Line Broadening,” J. Appl. Phys., Vol. 17, 1946, p. 687.Google Scholar
4. Warren, B. E., “X-Ray Studies of Deformed Metals,” Ch. 3 in Progress in Metal Physics, Vol. 8, Pergamon Press, New York, 1959.Google Scholar