Advertisement

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

  • P. Coppens
  • V. Petříček

Abstract

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.

Keywords

Acta Cryst Molecular Crystal Main Reflection Incommensurate Phasis Translational Displacement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. M. De Wolff, The Pseudo-symmetry of modulated crystal structures, Acta Cryst. A30:777 (1974).Google Scholar
  2. 2.
    A. Janner and T. Janssen, Symmetry of periodically distorted crystals, Phys.Rev. BI5:643 (1977).ADSGoogle Scholar
  3. 3.
    P. M. De Wolff, T. Janssen, and A. Janner, The superspace groups for incommensurate crystal structures with a one-dimensional modulation, Acta Cryst. A37:625 (1981).Google Scholar
  4. 4.
    Modulated Structures, J. M. Cowley, J. B. Cohen, M. B. Salamon, and B. J. Wuensch (Eds), EIP Conference Proceedings, No. 53, American Institute of Physics, New York (1979).Google Scholar
  5. 5.
    J. L. Baudour and M. Sanquer, Structural phase transition on polyphenyls. VIII. The modulated structure of phase III of biphenyl (T 20K) from neutron diffraction data, Acta Cryst. B39:75 (1984).Google Scholar
  6. 6.
    H. Cailleau, Ch. 12 in: “Incommensurate Phases in Dielectric 2”, R. Blinc and A. P. Levanyuk, eds; Elsevier (1986);Google Scholar
  7. H. Cailleau, J. C. Messager, F. Moussa, F. Bugaut, C. M. E. Zeyen, and C. Vettier, Main characteristic properties of incommensurate biphenyl, Ferroelectrics 67:3 (1986).CrossRefGoogle Scholar
  8. 7.
    V. Heine and E. H. Simmons, Correct choice of superspace group for an incommensurate phase transition, Acta Cryst. A43:289 (1987).Google Scholar
  9. 8.
    F. Denoyer and R. Currat, Modulated phases in thiourea, Ch. 14 in: “Incommensurate Phases in Dielectrics 2”, R. Blinc and A. P. Levanyuk (Eds), Elsevier (1986).Google Scholar
  10. 9.
    V. Petiícek, P. Coppens, and P. Becker, Structure analysis of displacively modulated molecular crystals, Acta Cryst. A41:478 (1985).Google Scholar
  11. 10.
    V. Petrícek and P. Coppens, Structure analysis of displacively modulated molecular crystals. V. Symmetry restrictions due to special positions, (to be published).Google Scholar
  12. 11.
    P. C. W. Leung, T. J. Emge, M. A. Beno, H. H. Wang, J. M. Williams, V. Petiícek, and P. Coppens, Novel structural modulation in the ambient-pressure sulfur-based organic superconductor ß-(BEDT-TTF)2I3: Origin and effects on its electrical conductivity, J.Am.Chem.Soc. 107:6184 (1985).CrossRefGoogle Scholar
  13. 12.
    N. Laukhin, E. E. Kostyuchenko, Yu. V. Sushko, I. F. Shchegolev, and E. B. Yagubskii, Effect of pressure on the superconductivity of ß-(BEDT-TTF)2I3, JETP Lett. 41:68 (1985).Google Scholar
  14. 13.
    K. Murata, M. Tokumoto, H. Anzai, H. Bando, G. Saito, K. Kajimura, and T. Ishguro, Superconductivity with the onset at 8K in the organic conductor ß-(BEDT-TTF)213 under pressure, J.Phys.Soc.Jap. 54:1236 (1985).ADSCrossRefGoogle Scholar
  15. 14.
    A. J. Schultz, M. A. Beno, H. H. Wang, and J. M. Williams, Neutron diffraction evidence for ordering in the high-T phase ofß-di[bis(ethyl-enedithio)tetrathiafulvalene]triiodide, fi(E)2 I3’ Phys. Rev.B 33:7823 (1986).ADSCrossRefGoogle Scholar
  16. 15.
    Y. Gao, M. Gajhede, P. Mallinson, V. Petiícek, and P. Coppens, Structure analysis of modulated molecular crystals II: The modulated phase of thiourea as described by a molecular displacement model, Phys.Rev. B: in press.Google Scholar
  17. 16.
    L. Solomon, Thiourea, a new ferroelectric, Phys.Rev. 104:1191 (1956).ADSCrossRefGoogle Scholar
  18. 17.
    Y. Shiozaki, Satellite X-ray scattering and structural modulation of thiourea, Ferroelectrics 2:245 (1971).CrossRefGoogle Scholar
  19. 18.
    A. Yamamoto, Modulated structure of thiourea [SC(NH2)2], Phys.Rev. B22:373 (1980).ADSGoogle Scholar
  20. 19.
    M. M. Elcombe and J. C. Taylor, A neutron diffraction determination of the crystal structures of thiourea and deuterated thiourea above and below the ferroelectric transition, Acta Cryst. A24:410 (1968).Google Scholar
  21. 20.
    P. Coppens, V. Petiícek, D. Levendis, F. K. Larsen, A. Paturle, Y. Gao, and A. D. LeGrand, Synchrotron-radiation study of the five-dimensional modulated phase of tetrathiafulvalene-tetracyanoquinodimethanide at 15K. Phys.Rev.Lett. 59:1695 (1987).ADSCrossRefGoogle Scholar
  22. 21.
    J. P. Pouget, S. K. Khanna, F. Denoyer, R. Comes, A. F. Gasrito, and A. J. Heeger, X-ray observation of 2kF and 4kgg scatterings in tetrathiafulvalene tetracyanoquinodimethane (TTF-T(;NQ), Phys.Rev.Lett. 37:436 (1976).ADSCrossRefGoogle Scholar
  23. 22.
    S. Kagoshima, in: “Extended Linear Chain Compounds”, J. S. Miller (Ed.), Plenum, New York (1982), Vol. 2, p. 303.Google Scholar
  24. 23.
    F. Denoyer, R. Comes, A. F. Garito, and A. J. Heeger, The X-ray diffuse scattering evidence for a phase transition in tetrathiafulvalene tetracyanoquinodimethan (TTF-TCNQ), Phys.Rev.Lett. 35:445 (1975).ADSCrossRefGoogle Scholar
  25. 24.
    S. Kagoshima, T. Ishiguro, and H. Anzai, X-ray scattering study of phonon anomalies and superstructures in TTF7TCNQ, J.Phys.Soc.Jap. 41:2061 (1976).ADSCrossRefGoogle Scholar
  26. 25.
    E. F. Rybaczewski, L. S. Smith, A. F. Garito, A. J. Ieeger, and B. G. Silbernagel, Carbon-13 knight shift in TTF-TCNQ (C): Determination of the local susceptibility, Phys. Rev. B14:2746 (1976)ADSGoogle Scholar
  27. Y. Tomkiewicz, A. R. Taranko, and J. B. Torrance, Spin susceptibility of tetrathiafulvalene tetracyanoquinodimethane, TTF-TCNQ, in the semiconducting regime: Comparison with conductivity, Phys.Rev. B15:1017 (1977).ADSGoogle Scholar
  28. 26.
    L. Forro, S. Bouffard, and J. P. Pouget, X-ray diffuse scattering study of 2kF and 4kF anomalies in strongly irradiated TTF-TCNQ, J.Physique Lettres 45: L543 (1984).CrossRefGoogle Scholar
  29. 27.
    S. Megtert, A. F. Garito, J. P. Pouget, and R. Comes, Lecture notes in physics, in: “Quasi One Dimensional Conductors I”, S. Barisic, A. Bjelis, J. R. Cooper, and B. Leontic (Eds), Springer-Verlag, Berlin (1980).Google Scholar
  30. 28.
    K. Yamaji, S. Megtert, and R. Comes, 2D displacement pattern in TSeFTCNQ model analysis of the 2kF diffuse lines, J.Physique 42:1327 (1981).CrossRefGoogle Scholar
  31. 29.
    F. E. Bates, J. E. Eldridge, and M. R. Bryce, High resolution polarized far-infrared vibrational spectra of semiconducting TTF-TCNQ and TSeF-TCNQ, Can.J.Phys. 59:339 (1981).ADSCrossRefGoogle Scholar
  32. 30.
    A. J. Shultz, G. D. Stucky, R. H. Blessing, and P. Coppens, Th1 gmperature dependence of the crystal and molecular structure of A -Bi1,3-dithiole[TTF]7,7,8,8-tetracyano-p-quinodimethane[TCNQ], J.Am. Chem.Soc. 98:3194 (1976).CrossRefGoogle Scholar
  33. 31.
    P. Bak and T. Janssen, Symmetry of modulated phases in tetrathiafulvalene tetracyanoquinodimethane (TTF-TCNQ): Four and five-dimensional superspace groups, Phys.Rev. B17:436 (1978).ADSGoogle Scholar
  34. 32.
    V. Petfl ek and P. Coppens, Structure analysis of modulated molecular crystals III: Scattering formalism and symmetry considerations: Extension to higher dimensional space groups, Acta Cryst.A: in press.Google Scholar
  35. 33.
    B. D. Silverman, in: “Crystal Cohesion and Conformational Energies”, R. M. Metzger (Ed.), Springer-Verlag, Berlin (1981), p. 108.Google Scholar

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

Personalised recommendations