Symmetrized multipole analysis of coupled orientation-translation distributions

Mikko Kara

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1 Citation (Scopus)

Abstract

Symmetrized multipole formalism, in diffraction studies of orientationally disordered molecular crystals, is generalized to include coupling between orientations and translations of a rigid body and anharmonicity in the center-of-mass motion. This generalized formalism is intended for use with direct multipole analysis of the observed form factors. In the relationships between the radial multipole coefficients of the dynamic and static density, correlations cause a mixing in the multipole order. In the dynamic form factor the parameters describing the coupling are linear combinations of the multipole expansion coefficients of the corresponding rigid-body distribution. Parameters describing anisotropy are directly the multipole expansion coefficients of the rigid-body center-of-mass distribution. As an example of the formalism, neutron diffraction data from cubic KCN, NaCN, KOD, NaOD and CBr4 and rhombohedral RbNO3 are reanalyzed with direct multipole analysis. In these examples the importance of coupling seems to grow with the complexity of the crystal.
Original languageEnglish
Pages (from-to)274 - 285
Number of pages12
JournalActa crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography
Volume38
Issue number2
DOIs
Publication statusPublished - 1982
MoE publication typeNot Eligible

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Neutron Diffraction
Anisotropy
multipoles
Molecular crystals
Neutron diffraction
Crystal orientation
rigid structures
Diffraction
Crystals
formalism
center of mass
form factors
coefficients
expansion
11-keto-9(E),12(E)-octadecadienoic acid
mass distribution
crystals
neutron diffraction
anisotropy
causes

Cite this

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title = "Symmetrized multipole analysis of coupled orientation-translation distributions",
abstract = "Symmetrized multipole formalism, in diffraction studies of orientationally disordered molecular crystals, is generalized to include coupling between orientations and translations of a rigid body and anharmonicity in the center-of-mass motion. This generalized formalism is intended for use with direct multipole analysis of the observed form factors. In the relationships between the radial multipole coefficients of the dynamic and static density, correlations cause a mixing in the multipole order. In the dynamic form factor the parameters describing the coupling are linear combinations of the multipole expansion coefficients of the corresponding rigid-body distribution. Parameters describing anisotropy are directly the multipole expansion coefficients of the rigid-body center-of-mass distribution. As an example of the formalism, neutron diffraction data from cubic KCN, NaCN, KOD, NaOD and CBr4 and rhombohedral RbNO3 are reanalyzed with direct multipole analysis. In these examples the importance of coupling seems to grow with the complexity of the crystal.",
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Symmetrized multipole analysis of coupled orientation-translation distributions. / Kara, Mikko.

In: Acta crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, Vol. 38, No. 2, 1982, p. 274 - 285.

Research output: Contribution to journalArticleScientificpeer-review

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N2 - Symmetrized multipole formalism, in diffraction studies of orientationally disordered molecular crystals, is generalized to include coupling between orientations and translations of a rigid body and anharmonicity in the center-of-mass motion. This generalized formalism is intended for use with direct multipole analysis of the observed form factors. In the relationships between the radial multipole coefficients of the dynamic and static density, correlations cause a mixing in the multipole order. In the dynamic form factor the parameters describing the coupling are linear combinations of the multipole expansion coefficients of the corresponding rigid-body distribution. Parameters describing anisotropy are directly the multipole expansion coefficients of the rigid-body center-of-mass distribution. As an example of the formalism, neutron diffraction data from cubic KCN, NaCN, KOD, NaOD and CBr4 and rhombohedral RbNO3 are reanalyzed with direct multipole analysis. In these examples the importance of coupling seems to grow with the complexity of the crystal.

AB - Symmetrized multipole formalism, in diffraction studies of orientationally disordered molecular crystals, is generalized to include coupling between orientations and translations of a rigid body and anharmonicity in the center-of-mass motion. This generalized formalism is intended for use with direct multipole analysis of the observed form factors. In the relationships between the radial multipole coefficients of the dynamic and static density, correlations cause a mixing in the multipole order. In the dynamic form factor the parameters describing the coupling are linear combinations of the multipole expansion coefficients of the corresponding rigid-body distribution. Parameters describing anisotropy are directly the multipole expansion coefficients of the rigid-body center-of-mass distribution. As an example of the formalism, neutron diffraction data from cubic KCN, NaCN, KOD, NaOD and CBr4 and rhombohedral RbNO3 are reanalyzed with direct multipole analysis. In these examples the importance of coupling seems to grow with the complexity of the crystal.

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