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Statistical Factors Affecting the Intensity of X‐Rays Diffracted by Crystalline Powders

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3 Author(s)
Alexander, Leroy ; Department of Research in Chemical Physics, Mellon Institute, Pittsburgh 13, Pennsylvania ; Klug, Harold P. ; Kummer, Elizabeth

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The Laplacian probability equation can be used to predict the reproducibility of the intensities of x-rays diffracted by crystalline powders. If absorption is neglected, and N is the number of particles irradiated, p the proportion of particles which are oriented so as to diffract, and q=1 - p, the relative mean deviation to be expected in repeated intensity measurements is given by Um=0.798 (q/Np)½. When absorption and the actual distribution of particle sizes are taken into account, the expression becomes

Um=0.798(qμve/pA)
 1 
 2 
,
where μ is the linear absorption coefficient of the material, ve the effective volume per particle, and A the cross-sectional area of the incident beam. The theory is confirmed by measurements on four size fractions of quartz powder using a Norelco Geiger-counter x-ray spectrometer. For typical experimental conditions and powders of medium absorbing power for x-rays, it is demonstrated that good reproducibility can be expected only if the effective particle dimension is less than approximately five microns.

Published in:

Journal of Applied Physics  (Volume:19 ,  Issue: 8 )