Thinking in Reciprocal Space

  • David B. Williams
  • C. Barry Carter


In the previous chapter, you’ve already encountered vectors k and g and seen that they have lengths with units Å−1 or nm−1. These vectors are referred to as reciprocal lattice vectors. Now we are going to discuss what this reciprocal lattice is. The reciprocal lattice is simply a lattice in reciprocal space. Note that this lattice is just as real as the “real lattice” in “real” space. It’s like a new world in Gulliver’s Travels but the relationship to “our” world is not a linear scaling factor but a reciprocal one. If something (an object or a length) is large in real space, then it’s small in reciprocal space.


Real Space Reciprocal Lattice Reciprocal Space Reciprocal Lattice Vector Bragg Condition 
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General References

  1. Cullity, B.D. (1978) Elements of X-ray Diffraction, Addison-Wesley, Reading, Massachusetts.Google Scholar
  2. James, R.W. (1965) The Optical Principles of the Diffraction of X-rays, The Crystalline State, II (Ed. W.L. Bragg ), Cornell University Press, Ithaca, New York (first published in 1948 ).Google Scholar
  3. Schwartz, L.H. and Cohen, J.B. (1977) Diffraction from Materials, Academic Press, New York.Google Scholar

Specific References

  1. Cruickshank, D.W.J., Juretschke, H.J., and Kato, N., Eds. (1992) P.P. Ewald and His Dynamical Theory of X-ray Diffraction, Oxford University Press, New York.Google Scholar
  2. Ewald, P.P. (1962) Fifty Years of X-ray Diffraction, N. V. A. Oosthoek’s Uitgeversmaatschappij, Utrecht, the Netherlands.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • David B. Williams
    • 1
  • C. Barry Carter
    • 2
  1. 1.Lehigh UniversityBethlehemUSA
  2. 2.University of MinnesotaMinneapolisUSA

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