Direct Methods for Modulated Structures

  • Fan Hai-fu
Part of the NATO ASI Series book series (NSSB, volume 274)


Modulated structures belong to that kind of crystal structure, in which the atoms suffer from certain occupational and/or positional fluctuation. If the period of fluctuation is commensurate with that of the three-dimensional unit cell then a superstructure results, otherwise an incommensurate modulated structure is obtained. Modulated phases have been found in many important inorganic and organic solids. In many cases, the transition to the modulated structure corresponds to a change of certain physical properties. Hence it is important to know the structure of modulated phases in order to understand the mechanism of the transition and properties in the modulated state. Up to the present most procedures used for solving modulated structures, especially those for solving the incommensurate ones, depend on some preliminary assumption to the form of modulation. It is worthwhile to find a straightforward way to solve this important kind of structures. Both commensurate modulated structure (superstructure) and incommensurate modulated structure possess pseudo-translational symmetry.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aalst, W. van, Hollander, J. den, Peterse, W.J.A.M. & Wolff, P.M. de (1976). Acta Cryst. B32, 47–58.CrossRefGoogle Scholar
  2. Boehme, R. (1982). Acta Cryst A38, 318–326.CrossRefGoogle Scholar
  3. Fan Hai-fu (1975). Acta Phys. Sin. 24, 57–60.Google Scholar
  4. Fan Hai-fu, He Luo, Qian Jin-zi & Lui Shi-xiang (1978). Acta Phys. Sin. 27, 554–558.Google Scholar
  5. Fan Hai-fu, Qian Jin-zi, Zheng Chao-de, Gu Yuan-xin Ke Heng-ming & Huang Sheng-hua (1990). Acta Cryst A46 (in the press).Google Scholar
  6. Fan Hai-fu, Yao Jia-xing, Main, P. & Woolfson, M. M. (1983). Acta Cryst A39, 566–569.CrossRefGoogle Scholar
  7. Fan Hai-fu, Yao Jia-xing & Qian Jin-zi (1988). Acta Cryst A44, 688–691.CrossRefGoogle Scholar
  8. Gramlich, V. (1975). Acta Cryst A31, S90.CrossRefGoogle Scholar
  9. Gramlich, V. (1978). Acta Cryst A34, S43.CrossRefGoogle Scholar
  10. Hao Quan, Liu Yi-wei & Fan Hai-fu (1987). Acta Cryst A43, 820–824.CrossRefGoogle Scholar
  11. Ito, T. (1973). Z. Krist 137, 399–411.CrossRefGoogle Scholar
  12. Ito, T. & Nowacki, W. (1974). Z. Krist 139, 85–102.CrossRefGoogle Scholar
  13. Prick, P.A.J., Beurskens, P.T. & Gould, R.O. (1983). Acta Cryst A39, 570–576.CrossRefGoogle Scholar
  14. Qian Jin-zi, Fu Ping-qui, Kong Yuo-hua & Gong Guo-hong (1982). Acta Phys. Sin. 31, 577–584.Google Scholar
  15. Sayre, D. (1952). Acta Cryst 5, 60–65.CrossRefGoogle Scholar
  16. Wolff, P.M. de (1977). Acta Cryst A30, 777–785.CrossRefGoogle Scholar
  17. Xiang Shi-bin, Fan Hai-fu, Wu Xiao-jing Li Fang-hua & Pan Qing (1990). Acta Cryst (submitted)Google Scholar
  18. Yamamotb, A. (1982). Acta Cryst A38, 87–92.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Fan Hai-fu
    • 1
  1. 1.Institute of PhysicsChinese Academy of SciencesBeijingP.R. China

Personalised recommendations