International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. C, ch. 6.4, p. 610

Zachariasen (1967) introduced the concept of using the kinematic result in the smallcrystal 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). Xray optics. London: Methuen.
Zachariasen, W. H. (1967). A general theory of Xray diffraction in crystals. Acta Cryst. 23, 558–564.