Symmetrized multipole analysis of coupled orientation-translation distributions

Mikko Kara

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


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
Issue number2
Publication statusPublished - 1982
MoE publication typeNot Eligible

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