Patterson Functions and Diffuse Scattering

  • Brent Fultz
  • James M. Howe

Abstract

Starting in Chapter 3, the kinematical theory of diffraction has been developed by calculating the diffracted wave from crystals with increasing amounts of disorder. The amplitude of the diffracted wave, Ψ), is the sum of phase factors of wavelets emitted from individual atoms. We have evaluated these sums analytically (as a geometric series, for example), graphically (with a phase-amplitude diagram), and numerically. These calculations of Ψ(∆k) were performed for crystals having only small departures from ideality, such as crystals of small size, crystals with strain distributions, or isolated defects imaged with a TEM. In many respects these calculations were extensions of the calculation of wave interference from atoms in a perfect crystal. Recall that the phase information in Ψ(∆k) includes details of atom positions, which can be obtained by inverse Fourier transformation, F-1 Ψ.

Keywords

Milling Coherence Expense Autocorrelation Convolution 

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Further Reading

The contents of the following are described in the Bibliography

  1. J. M. Cowley: Diffraction Physics, 2nd edn. (North—Holland Publishing, Amsterdam 1975).Google Scholar
  2. C. Barrett and T. B. Massalski: Structure of Metals, 3rd edn. (Pergamon Press, Oxford 1980).Google Scholar
  3. A. Guinier: X-Ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies (Dover, Mineola NY 1994).Google Scholar
  4. Harold P. Klug and Leroy E. Alexander: X-Ray Diffraction Procedures (Wiley—Interscience, New York 1974).Google Scholar
  5. M. A. Krivoglaz: Theory of X-ray and Thermal Neutron Scattering by Real Crystals (Plenum Press, New York 1969).Google Scholar
  6. L. H. Schwartz and J. B. Cohen: Diffraction from Materials (Springer—Verlag, Berlin 1987).CrossRefGoogle Scholar
  7. B. E. Warren: X-Ray Diffraction (Dover, Mineola, NY 1990).Google Scholar

Chapter 9 title image conveys the important concept of Fig. 9.2

  1. 9.1
    F. Ducastelle: Order and Phase Stability in Alloys (North-Holland, Amsterdam 1991) pp. 439–442. This ”relaxation energy“ is important for the thermodynamics of many alloys.Google Scholar
  2. 9.2
    B. E. Warren: X-Ray Diffraction (Dover, New York, 1990) pp. 178–193.Google Scholar
  3. 9.3
    B. E. Warren: X-Ray Diffraction (Dover, New York, 1990) pp. 206–250.Google Scholar
  4. 9.4
    L. H. Schwartz and J. B. Cohen: Diffraction from Materials (SpringerVerlag, Berlin 1987) pp. 407–409.CrossRefGoogle Scholar
  5. 9.5
    J. M. Cowley: Diffraction Physics, 2nd edn. (North-Holland Publishing, Amsterdam 1975) pp. 152–154.Google Scholar
  6. 9.6
    A. Williams: Atomic Structure of Transition Metal Based Metallic Glasses. Ph.D. Thesis, California lnstitute of Technology, California (1981).Google Scholar
  7. 9.7
    H. P. Klug and L. E. Alexander: X-Ray Diffraction Procedures (WileyInterscience, New York 1974) pp. 791–859.Google Scholar
  8. 9.8
    T. Egami: ‘PDF Analysis Aplied to Crystalline Materials’, in: Local Structure from Diffraction, ed. by S. J. L. Billinge and M. F. Thorpe (Plenum, New York 1998) pp. 1–21.Google Scholar
  9. 9.9
    A. Guinier: X-Ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies (Dover, New York 1994) pp. 344–349.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Brent Fultz
    • 1
  • James M. Howe
    • 2
  1. 1.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of Materials Science and EngineeringUniversity of VirginiaCharlottesvilleUSA

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