On variance as a measure of line broadening in diffractometry: effect of a distribution of sizes on the apparent crystallite size

If the crystallites making up a diffractometer specimen have a number-average size 〈p〉, and the distribution function of crystallite sizes has a variance Wp and skewness γp, the crystallite size obtained from the slope of the variance-range curve will be

and that obtained from the intercept will be

Even when Wp and γp are unknown these equations set an upper limit of p₂²/p₁ to 〈p〉; for Langford's submicron nickel this limit is 121 Å.