Physical background

Shmueli, U.; Wilson, A. J. C.

doi:10.1107/97809553602060000554

International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

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International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 191 | 1 | 2 |

Section 2.1.2.2. Physical background

U. Shmueli^a ^* and A. J. C. Wilson^b ^‡

^a School of Chemistry, Tel Aviv University, Tel Aviv 69 978, Israel, and ^bSt John's College, Cambridge, England
Correspondence e-mail: ushmueli@post.tau.ac.il

2.1.2.2. Physical background

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The preceding section has used mathematical arguments. From a physical point of view, the radiation diffracted by atoms that are resolved will interfere destructively, so that the resulting intensity will be the sum of the intensities diffracted by individual atoms, whereas that from completely unresolved atoms will interfere constructively, so that amplitudes rather than intensities add. In intermediate cases there will be partial constructive interference. Resolution in accordance with the Rayleigh (1879) criterion requires that $[s = (2\sin \theta)/\lambda]$ should be greater than half the reciprocal of the minimum interatomic distance in the crystal (Wilson, 1979); full resolution requires a substantial multiple of this. This criterion is essentially equivalent to that proposed from the study of a special case of the second process in the preceding section.

References

Rayleigh, Lord (1879). Investigations in optics with special reference to the spectroscope. Philos. Mag. 8, 261–274.Google Scholar

Wilson, A. J. C. (1979). Problems of resolution and bias in the experimental determination of the electron density and other densities in crystals. Acta Cryst. A35, 122–130.Google Scholar

International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 191