International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 6.4, p. 610

## Section 6.4.5. Primary extinction

T. M. Sabinea

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### 6.4.5. Primary extinction

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Zachariasen (1967) introduced the concept of using the kinematic result in the small-crystal limit for σ, while Sabine (1985, 1988) showed that only the Lorentzian or Fresnellian forms of the small crystal intensity distribution are appropriate for calculations of the energy flow in the case of primary extinction. Thus, where is the kinematic integrated intensity on the k scale , , and T is the volume average of the thickness of the crystal normal to the diffracting plane (Wilson, 1949). To include absorption effects, which modify the diffraction profile of the small crystal, it is necessary to replace T by TC, where To determine the extinction factor, E, the explicit expression for [equation (6.4.5.1)] is inserted into equations (6.4.4.3) and (6.4.4.4), and integration is carried out over Δk. The limits of integration are and . The notation and is used for the extinction factors at 2θ = 0 and 2θ = π rad, respectively.

After integration and division by it is found that and In these equations, and y = μD.

### References

Sabine, T. M. (1985). Extinction in polycrystalline materials. Aust. J. Phys. 38, 507–518.
Sabine, T. M. (1988). A reconciliation of extinction theories. Acta Cryst. A44, 368–373.
Wilson, A. J. C. (1949). X-ray optics. London: Methuen.
Zachariasen, W. H. (1967). A general theory of X-ray diffraction in crystals. Acta Cryst. 23, 558–564.