ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
The joint probability distributions for three structure factors whose subscripts add to zero, in the general case of unequal atoms, are expressed in an exponential form for space groups P1 and P{\bar 1}. The latter are representative of noncentrosymmetric and centrosymmetric space groups respectively. The exponential form possesses considerably improved convergence properties over those of the standard asymptotic series, although it too remains asymptotic. With the range of values ordinarily obtained for the normalized structure-factor magnitudes, the exponential forms are quite accurate. However, the accuracy deteriorates somewhat as these magnitudes approach their largest possible values. By altering the exponential form with the use of a result from the inequality theory, joint probability distributions are obtained which are accurate over the entire range of values for the structure-factor magnitudes and are most accurate at the largest values. Several probability measures of interest are derived from the joint distribution functions such as expected values, variances and the probability that a structure factor has a positive sign. Numerical tests indicate that the derived probability measures are very reliable and that their validity extends to higher space groups than P1 and P{\bar 1}.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739473001002
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