THE TREATMENT OF WEAK INTENSITIES OF REFLEXION

A. Wilson

Though weak intensities present special problems in crystal-structure determination, they convey at least as much information as strong intensities, and should not be ignored /1,2,3,4,5/. Since an intensity is estimated as the difference between counts on peak and counts on background, and each count is subject to statistical (Poisson) fluctuations, a reflexion that is actually zero or small may be measured as negative ; the probability distribution of the difference is given by a modified Bessel function /2,6/ for the fixed-time counting technique. With some approximation, Bayesian methods /3/ may be used to estimate the likely positive value in such cases. The statistical fluctuations, however, result in a bias when the square-root of the intensity is taken in order to obtain the structure factor. Correction of the bias is easy when the intensity is moderate /7/, but gives problems for weak intensities /8,4/. Precision, the statistical reproducibility of a determination, must be distinguished from accuracy, the extent to which a determination approaches the true value of the quantity sought. When systematic errors or defects in the structural model are appreciable, the accuracy of a determination may be much less than its precision (/9/ ; compare also /4/ and /10/) ; the common procedure of 'adjusting the weights' is of dubious statistical legitimacy.

Domaines: Articles anciens

A. Wilson. THE TREATMENT OF WEAK INTENSITIES OF REFLEXION. Journal de Physique Colloques, 1986, 47 (C5), pp.C5-7-C5-16. ⟨10.1051/jphyscol:1986502⟩. ⟨jpa-00225819⟩