Reciprocal Space Mapping

  • Paul F. Fewster
Part of the NATO ASI Series book series (NSSB, volume 357)


Crystals that are highly perfect will diffract over a very small angular range and therefore require very high angular resolution x-ray techniques to extract detailed structural information. The aim of this paper is to discuss the use of reciprocal space mapping or diffraction space mapping as a route to extracting very detailed structural information from high quality crystals. In fact much information is obscured by standard diffraction profile analysis methods unless significant assumptions are made to interpret the data. Reciprocal space mapping has not been confined to highly perfect crystals but has yielded detailed understanding of polycrystalline samples, (Fewster and Andrew, 1996). The conventional “powder diffraction” methods yield little detailed information because of the swamping effects of the ill-defined diffraction probe. The well defined probe of the high resolution diffractometer to be described is important for analysing ill-defined samples. Only when the analysist is sure of the assumptions about the structure should a less well defined probe be used. The aim of this paper though is to show how an enormous quantity of structural information from multiple crystal diffractometric methods can be extracted using reciprocal space mapping. The relationship between the resultant diffraction pattern and the real structure will be discussed and how with the aid of additional tools it is possible to come closer to a truer picture of the structure. This paper will be confined to high angular resolution techniques. Low resolution diffraction space mapping has its advantages for mapping very large areas of reciprocal space and for very imperfect samples (Fewster and Andrew, 1996, 1993a).


Reciprocal Lattice Reciprocal Space Diffraction Plane High Angular Resolution Axial Divergence 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bartels, W.J., 1983, Characterization of thin layers on perfect crystals with a multipurpose high resolution X-ray diffractometer, J. Vac. Sci. Technol. B, 1:338CrossRefGoogle Scholar
  2. Bond, W.L., 1960, Precision lattice constant determination, Acta Cryst 13:814CrossRefGoogle Scholar
  3. Bonse, U. and Hart, M., 1965, Tailless X-ray single crystal reflection curves obtained by multiple reflection, Appl. Phys. Lett. 7:238ADSCrossRefGoogle Scholar
  4. Compton, A.H., 1917, The reflection coefficient of monochromatic X-rays from rock salt and calcite, Phys. Rev. 10:95Google Scholar
  5. DuMond, J.W.M., 1937, Theory and use of more than two succssive X-ray crystal reflections to obtain increased resolving power, Phys. Rev. 52:872ADSCrossRefGoogle Scholar
  6. Fewster, P.F., 1985, Alignment of double-crystal diffractometers, J. Apl. Cryst. 18:334CrossRefGoogle Scholar
  7. Fewster, P.F., 1989, A high-resolution multiple-crystal multiple-reflection diffractometer, J. Appl. Cryst. 22:64CrossRefGoogle Scholar
  8. Fewster, P.F., 1991a, Combining high resolution X-ray diffractometry and topography, J. Appl. Cryst 24:178CrossRefGoogle Scholar
  9. Fewster, P.F., 1991b, Multicrystal X-ray diffraction of heteroepitaxial structures, Appl. Surf. Science 50:9ADSCrossRefGoogle Scholar
  10. Fewster, P.F., 1992, The simulation and interpretation of diffraction profiles from partially relaxed layer structures, J. Appl. Cryst. 25:714CrossRefGoogle Scholar
  11. Fewster, P.F., 1993, Review article: X-ray diffraction from low dimensional solids, Semicond. Sci. Technol. 8:1915ADSCrossRefGoogle Scholar
  12. Fewster, P.F., and Andrew, N.L., 1993a, Diffraction from thin layers, in Proceedings of the second European Powder Diffraction Conference, R. Delhez and E.J. Mittemeijer, Ed., TransTech Publications, SwitzerlandGoogle Scholar
  13. Fewster, P.F., and Andrew, N.L., 1993b, Determining the lattice relaxation in semiconductor layer systems by X-ray diffraction, J. Appl. Phys. 74:3121ADSCrossRefGoogle Scholar
  14. Fewster, P.F., and Andrew, N.L., 1993c, Interpretation of the diffuse scattering close to Bragg peaks by X-ray topography, J. Appl. Cryst. 26:812CrossRefGoogle Scholar
  15. Fewster, P.F., and Andrew, N.L., 1995a, Applications in multiple-crystal diffractometry, J. Phys. D 28:A97ADSCrossRefGoogle Scholar
  16. Fewster, P.F., and Andrew, N.L., 1995b, Absolute lattice-parameter measurements, J. Appl. Cryst., 28:451CrossRefGoogle Scholar
  17. Fewster, P.F., and Andrew, N.L., 1996 reciprocal space mapping and ultra high resolution diffraction of polycrystalline materials, Microstructure Analysis from Diffraction, R.L. Snyder, H. Bunge and J. Fiala, Ed., Oxfors University Press, in preparationGoogle Scholar
  18. IIda, A. and Kohra, K., 1979, Seaparate measurements of dynamical and kinematical X-ray diffractions from silicon crystals with a triple crystal diffractometer, Phys. Stat. Solidi A, 51:533ADSCrossRefGoogle Scholar
  19. Kato, N., 1980, Statistical dynamical theory of crystal diffraction. I. General formulation, Acta Cryst. A 36:763CrossRefGoogle Scholar
  20. Takagi, S., 1962, Dynamical theory of diffraction applicable to crystals with any kind of small distortions, Acta Cryst. 15:1311CrossRefGoogle Scholar
  21. Takagi, S., 1969, A dynamical theory of diffraction for a distorted crystal, J. Phys. Soc. Japan 26:1239ADSCrossRefGoogle Scholar
  22. Taupin, D., 1964, Théorie dynamique de la diffraction des rayons X par les cristaux déformés, Bull. Soc. Fr. Minéral Cristallogr. 57:467Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Paul F. Fewster
    • 1
  1. 1.Philips Research LaboratoriesRedhillUK

Personalised recommendations