From Crystals to Nanocrystals: Semiconductors and Beyond

  • Valeri Petkov
  • Simon J. L. Billinge
Part of the Fundamental Materials Research book series (FMRE)


Knowledge of the atomic-scale structure is an important prerequisite to understand and predict the physical properties of materials. In the case of crystals it is obtained from the positions and the intensities of the Bragg peaks in the diffraction data1. However, many materials of technological importance are not perfectly crystalline but contain significant disorder at the atomic scale. The diffraction patterns of such materials show only a few Bragg peaks, if any, and a pronounced diffuse component. This poses a real challenge to the usual techniques for structure characterization. The challenge can be met by employing the so-called atomic pair distribution function (PDF) technique. The atomic PDF gives the number of atoms in a spherical shell of unit thickness at a distancerfrom a reference atom. It peaks at characteristic distances separating pairs of atoms and thus describes the structure of materials. The PDF, G(r)=4πr[ρ(r)−ρ 0 ], is the sine Fourier transform of the so-called total scattering structure factorS(Q)
$$ G(r) = (2/\pi )\int\limits_{Q = 0}^{{Q_{\max }}} {Q[S(Q) - 1]\sin (Qr)dQ,} $$


Bragg Peak Pair Distribution Function National Synchrotron Light Source Tetrahedral Network Experimental Structure Factor 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Valeri Petkov
    • 1
  • Simon J. L. Billinge
    • 1
  1. 1.Physics & Astronomy DeptMichigan State UniversityEast LansingUSA

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