PMID- 2322430
OWN - NLM
STAT- MEDLINE
DCOM- 19900524
LR  - 20190516
IS  - 0108-7673 (Print)
IS  - 0108-7673 (Linking)
VI  - 46 ( Pt 4)
DP  - 1990 Apr 1
TI  - Exact random-walk models in crystallographic statistics. V. Non-symmetrically 
      bounded distributions of structure-factor magnitudes.
PG  - 241-6
AB  - Derivations of exactly formulated Fourier-series representations of probability 
      density functions (p.d.f.'s) of the magnitude of the structure factor are based 
      on the fact that the structure factor and its real and imaginary parts are 
      bounded. In some situations the bounds of the real and imaginary parts of the 
      structure factor are different, and this gives rise to modified forms of the 
      p.d.f.'s. Three physical examples that call for such modifications are 
      investigated: (i) effect of dispersive scatterers on the p.d.f. of a 
      centrosymmetric structure factor, (ii) effect of the presence of a 
      centrosymmetric fragment in the asymmetric unit of a non-centrosymmetric space 
      group, and (iii) effect of heavy scatterers in special positions of a 
      non-centrosymmetric space group, where the imaginary part of the trigonometric 
      structure factor for these special positions vanishes by symmetry. The general 
      form of an exact Fourier p.d.f., taking account of such modifications, is 
      derived, and expressions for Fourier coefficients are obtained for selected 
      examples of the above three situations. It is seen that the effects of 
      pseudocentrosymmetry may be most pronounced and those of dispersion are 
      significant mainly in the range of small values of the structure factor.
FAU - Shmueli, U
AU  - Shmueli U
AD  - School of Chemistry, Tel Aviv University, Tel Aviv, Israel.
FAU - Rabinovich, S
AU  - Rabinovich S
FAU - Weiss, G H
AU  - Weiss GH
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
PT  - Research Support, U.S. Gov't, Non-P.H.S.
PL  - United States
TA  - Acta Crystallogr A
JT  - Acta crystallographica. Section A, Foundations of crystallography
JID - 8305825
SB  - IM
MH  - *Data Interpretation, Statistical
MH  - *X-Ray Diffraction
EDAT- 1990/04/01 00:00
MHDA- 1990/04/01 00:01
CRDT- 1990/04/01 00:00
PHST- 1990/04/01 00:00 [pubmed]
PHST- 1990/04/01 00:01 [medline]
PHST- 1990/04/01 00:00 [entrez]
AID - 10.1107/s0108767389011438 [doi]
PST - ppublish
SO  - Acta Crystallogr A. 1990 Apr 1;46 ( Pt 4):241-6. doi: 10.1107/s0108767389011438.