Fluctuations of the diffracted beam intensity resulting from the finite number of diffracting crystallites is called "crystallite statistics". This source of measurement uncertainty is more important that the "counting statistics" for crystallite size larger that one or few micrometers. Nevertheless, hitherto existing investigations of this effect are scarce [1] - [4].
          Quantitative input data for quantifying the crystallite statistics are variation of peak intensity I_i observed when the powder sample is rotated or oscillated in step-like manner. The recorded values I_i (i = 1, ... n) are autocorrelated because each diffracting crystallite contributes to a few subsequent data points.
          The proper statistical procedures for proceeding the autocorrelated data were given only recently [5], [6], [7]. Standard deviation of the single observation s and standard deviation of the mean s_mean are related  by the formula s_mean = s /(n_eff)^1/2 in which n_eff is the effective number of observations [6] smaller than the number of experimental points n. The value of n_eff  can be estimated from the experimental autocorrelation function. The proper formula for the unbiased estimator for the variation of the mean reads s² _mean = [( SUM (x_i - x_mean)² ] / [n(n_eff  - 1)]  [7].
          For crystallite statistics effect standard deviation s represents the uncertainty of the diffraction peak intensity for the fixed sample position and s_mean quantifies the effect of averaging due to oscillation or rotation of the sample. Experimental examples are given for both measurement geometries. For Al₂O₃ sample with 30 micrometer grain size its oscillating in the range +/- 1 deg causes a decrease of the relative standard deviation from 6,6% to 1,2%. Spinning of the other exemplary sample decreases the effect by the factor  (n_eff)^1/2 = 6.
          This uncertainty of peak intensity propagates directly into uncertainty of the phase content in multiphase sample. It also affects the accuracy of atomic positions in structural analysis. On the other hand quantyfying the crystallite statistics effect makes possible a rough estimate of the crystallite size. This method is effective for grain size range for which the line broadening method cannot be used. 

[1]   L. Alexander, P. K. Harold, E. Kummer.  J. Appl. Phys. 19 (1948) 742.
[2]   P. M. De Wolff, J. M. Taylor, W. Parrish. J. Appl. Phys. 30 (1959) 63.
[3] N. J. Elton, P. D. Salt, Powder Diffraction 11 (1996) 218.
[4] D. K. Smith, Powder Diffraction 16 (2001) 186.
[5] Dorozhovets M., Warsza Z. L. Pomiary Automatyka Robotyka, no. 1/2007, p. 18. In Polish with English Summary and Figure Captions.
[6] N. F. Zhang, Metrologia 43 (2006) S276.
[7] A. Zięba. Materials of the conference: Basic Problems of Metrology (PPM'08), Sucha Beskidzka, 11-14 May 2008. In Polish with English Summary and Figure Captions.

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