On freedom from extinction and the (universal) kinematical limit

Examination of the limiting relation of extinction and diffraction makes it clear that extinction is only zero, in an absolute sense, when diffracted power is identically zero. This latter condition is the proper operational identifier for the attainment of the kinematical limit and is valid irrespective of the state of perfection of the crystal medium. At the limit of zero diffracted power, the kinematical (single-scattering or first Born) approximation is asymptotically exact so that experiment and theory become strictly compatible. Experimental structure-factor values which are free from extinction effects can therefore be derived in this limit. In practice, the advantages of this approach have to be gained by greater attention to data collection. Typically, the method involves (i) determination of integrated reflectivity at a series of levels of interaction (attained by controlled variation of a suitable physical parameter) and (ii) extrapolation of an appropriate function of the measurements to zero level of interaction as identified by zero diffracted power. Various possible procedures for effecting this approach are discussed here in general terms. The approach proposed here has advantages over the earlier prescription of the kinematical limit [Bragg, Darwin & James (1926). Philos. Mag. 1, 897-922] based on the state of the crystal medium ('ideally imperfect'). It avoids any need for the necessarily approximate assumptions inherent in the Darwin-Zachariasen treatment of extinction. It also avoids dealing with the complications arising from idiosyncratic or anisotropic extinction effects since it refers all cases to zero level of interaction. The kinematical limit, as defined here, is a universal limit.