Structure Analysis of Modulated Molecular Crystals IV: Survey of our Recent Studies

  • P. Coppens
  • V. Petříček


There has been a considerable upsurge in interest in modulated crystal following the development of the multidimensional description of modulated solids by DeWolff, Janner and Janssen1,2,3. Modulations are quite common in minerals and inorganic solids 4 which often exhibit substitutional and displacive modulations at or above ambient temperatures. However, with the greater awareness of the occurrence of modulations and the wider accessibility of low temperature diffraction equipment suitable for routine use, the number of known modulated molecular solids is rapidly increasing. Among the most thoroughly studied are the low-temperature phase of biphenyl5,6,7 and the modulated phase of thiourea, which is stable over a narrow temperature range between 202 and 169K (ref. 8). Table 1 lists some known modulated molecular solids. In almost all studies which have been made, the atoms of a molecule are treated as individual entities, rather than as parts of a rigid covalently bonded framework. Since this can lead to unlikely distortions of the molecular geometry, we have introduced a molecular model in which the displacement of each atom is determined not by its own location, but by a point common to all atoms in a molecule or group, which is referred to as the phase reference point9. The molecular displacements are described in terms of rigid-body translations and rotations, thus greatly reducing the number of parameters of the model. A harmonic rigid-body description in general requires twelve parameters per molecule, which are to be determined from a usually large number of measurable satellite reflections.


Acta Cryst Molecular Crystal Main Reflection Incommensurate Phasis Translational Displacement 
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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • P. Coppens
    • 1
  • V. Petříček
    • 2
  1. 1.Department of ChemistryState University of New York at BuffaloBuffaloUSA
  2. 2.Institute of PhysicsCzechoslovak Academy of SciencesPraha 8Czechoslovakia

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