Solving the crystal structures of zeolites using electron diffraction data. II. Density-building functions

A density‐building function is used to solve the crystal structures of zeolites from electron diffraction data using both two‐ and three‐dimensional data sets. The observed data are normalized to give unitary structure factors |Uh|obs. An origin is defined using one to three reflections and a corres...

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Veröffentlicht in:Acta crystallographica. Section A, Foundations of crystallography Jg. 64; H. 2; S. 295 - 302
Hauptverfasser: Gilmore, Christopher J., Dong, Wei, Dorset, Douglas L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.03.2008
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Schlagworte:
Crystal structure
Crystallography
density building
Diffraction
electron crystallography
Entropy
entropy maximization
Fourier transforms
Zeolites
ISSN:0108-7673, 1600-5724, 2053-2733
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Zusammenfassung:A density‐building function is used to solve the crystal structures of zeolites from electron diffraction data using both two‐ and three‐dimensional data sets. The observed data are normalized to give unitary structure factors |Uh|obs. An origin is defined using one to three reflections and a corresponding maximum‐entropy map, qME(x), is calculated in which the constraints are the amplitudes and phases of the origin‐defining reflections. Eight strong reflections are then given permuted phases and each phase combination is used to compute P(δq) = ∫Vδq(x)2/qME(x)dx, where δq(x) is the Fourier transform of |Uh|obsexp(i) − |Uh|MEexp(i), is the permuted phase for reflection h and is the phase angle for reflection h predicted from the Fourier transform of qME(x). The 64 phase sets with minimum values of P(δq) are subjected to entropy maximization and, following this procedure, those with the five highest log‐likelihood gains are examined. Sometimes auxiliary potential histogram information is also used. The method worked routinely with seven zeolite structures of varying complexity and data quality, but failed with an eighth structure.
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ISSN:0108-7673
1600-5724
2053-2733
DOI:10.1107/S0108767307058631