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Variance apparent particle sizes for cylinders, prisms and hemispheres

Variance apparent particle sizes for cylinders, prisms and hemispheres Apparent particle sizes corresponding to the slope and intercept of the variance‐range curve are interpreted geometrically; the analytical results of Lele & Anantharaman for cylinders and certain prisms are confirmed. The slope apparent particle size is half the harmonic mean of hsec ϕ and bcsc ϕ, where h is the height of the cylinder or prism, b is the breadth of a rectangle having an area equal to that of its top face and a width equal to that of its radiation shadow, and ϕ is the angle between its axis and the diffraction vector. For cylinders, but not in general for prisms, the intercept apparent particle size is 1/√2 times the geometric mean of the same quantities. For a hemisphere of diameter d the slope apparent particle size is given by d/(1 + cos ϕ), where ϕ is the angle between the diffraction vector and the normal to the plane face, and the intercept apparent particle size is the square root of πd2csc 2ϕ. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Crystallography Wiley

Variance apparent particle sizes for cylinders, prisms and hemispheres

Wilson, A. J. C.
Journal of Applied Crystallography , Volume 2 (4) – Oct 2, 1969
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References (1)

  • A. Wilson, C. Holbrow (1963)

    X-Ray Optics

    American Journal of Physics, 31

Publisher
Wiley
Copyright
Copyright © 1969 Wiley Subscription Services, Inc., A Wiley Company
ISSN
1600-5767
eISSN
1600-5767
DOI
10.1107/S0021889869006893
Publisher site
See Article on Publisher Site

Abstract

Apparent particle sizes corresponding to the slope and intercept of the variance‐range curve are interpreted geometrically; the analytical results of Lele & Anantharaman for cylinders and certain prisms are confirmed. The slope apparent particle size is half the harmonic mean of hsec ϕ and bcsc ϕ, where h is the height of the cylinder or prism, b is the breadth of a rectangle having an area equal to that of its top face and a width equal to that of its radiation shadow, and ϕ is the angle between its axis and the diffraction vector. For cylinders, but not in general for prisms, the intercept apparent particle size is 1/√2 times the geometric mean of the same quantities. For a hemisphere of diameter d the slope apparent particle size is given by d/(1 + cos ϕ), where ϕ is the angle between the diffraction vector and the normal to the plane face, and the intercept apparent particle size is the square root of πd2csc 2ϕ.

Journal

Journal of Applied Crystallography – Wiley

Published: Oct 2, 1969

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