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Fractal Pores or a Distribution of Pore sizes: Alternative Interpretations of Power-Law Small-Angle Scattering

Published online by Cambridge University Press:  28 February 2011

Paul W. Schmidt
Paul W. Schmidt*
Affiliation:
Physics Department, University of Missouri, Columbia, MO 65203 USA
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Abstract

The intensity I(q) of the small-angle x-ray or neutron scattering has been calculated for a system of randomly oriented, independently scatter-ing pores with a number distribution of pore diameters which has the form of a power law. As has already been shown, [P. W. Schmidt, J. Appl. Cryst. 15, 567–569 (1982)], when the number distribution of the maximum diameters a of the pores is proportional to a−γ, I(q) is proportional to q−(7−γ), where q = 4πλ−1sin(θ/2), θ is the scattering angle, and λ is the wavelength. The coefficient of the power-law intensity has been expressed in terms of some of the constants which determine the diameter distribu-tion. Equations have been obtained for the scattered intensity I(q) at q values larger and smaller than those at which power-law scattering occurs. The intensity scattered by this system is compared with the intensity from a system of pores with fractal pore-boundary surfaces which have a fractal dimension D.

Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 73: Symposium H – Better Ceramics Through Chemistry II , 1986 , 351
Copyright
Copyright © Materials Research Society 1986

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References

REFERENCES

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