PMID- 2619966
OWN - NLM
STAT- MEDLINE
DCOM- 19900320
LR  - 20190516
IS  - 0108-7673 (Print)
IS  - 0108-7673 (Linking)
VI  - 45 ( Pt 3)
DP  - 1989 Mar 1
TI  - Explicit Fourier representations of non-ideal hypercentric P.D.F.'s of magnitude 
      of E.
PG  - 213-7
AB  - Explicit non-ideal hypercentric distributions of the magnitude of the normalized 
      structure factor have been derived and investigated for the space group P1. One 
      of the distribution types investigated arises when the asymmetric unit of P1 
      consists of several identical centrosymmetric motifs, interrelated by additional 
      non-crystallographic centres of symmetry. The ideal version of such distributions 
      was studied by Rogers & Wilson [Acta Cryst. (1953), 6, 439-449]. The other 
      distribution type studied originates from atomic arrangements in which the 
      asymmetric unit is composed of several unrelated centrosymmetric fragments that 
      may differ in their sizes and chemical compositions. Explicit non-ideal 
      probability density functions (p.d.f.'s) of the magnitude of the normalized 
      structure factor were formulated for both above types of distribution as Fourier 
      series, were evaluated numerically and were compared with appropriately simulated 
      distributions of magnitude of E. The computations were carried out for a range of 
      atomic compositions, and numbers of unrelated centrosymmetric fragments that 
      comprise the asymmetric unit; both of these factors have a significant influence 
      on the deviation of the hypercentric p.d.f.'s from the values predicted on the 
      basis of the central-limit theorem approximation.
FAU - Shmueli, U
AU  - Shmueli U
AD  - School of Chemistry, Tel Aviv University, Ramat Aviv, Israel.
FAU - Weiss, G H
AU  - Weiss GH
FAU - Wilson, A J
AU  - Wilson AJ
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  - *Crystallography
MH  - Fourier Analysis
MH  - Particle Size
EDAT- 1989/03/01 00:00
MHDA- 1989/03/01 00:01
CRDT- 1989/03/01 00:00
PHST- 1989/03/01 00:00 [pubmed]
PHST- 1989/03/01 00:01 [medline]
PHST- 1989/03/01 00:00 [entrez]
AID - 10.1107/s0108767388011043 [doi]
PST - ppublish
SO  - Acta Crystallogr A. 1989 Mar 1;45 ( Pt 3):213-7. doi: 10.1107/s0108767388011043.