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New measures of sharpness for symmetric powder diffraction peak profiles are proposed. Analytical expressions for typical model profile functions and theoretical size-broadening profiles with statistical size distribution are presented.

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The statistical properties of X-ray intensities measured with counting systems were experimentally investigated by repeated measurements based on Chipman's foil method. It is shown that the observed statistical variance can be well reproduced by a formula derived from an intermediately extended dead-time model for counting loss.
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