Experimental determination of extinction in crystals

In this paper we report the results of measurements on single crystals and powders undertaken to compare the observed diffracted intensities with those calculated for the traditional mosaic block model of a crystal. The mosaic block model was introduced by 1)arwin (1914) solely for mathematical convenience. Today we have an approximate idea of the structure of an imperfect crystal in terms of arrays of dish)cations but such a realistic case is mathematically untractal)le. I t behooves us, then, to pursue the crude mosaic block model since it may yield mathematical expressions which intrinsically contain the physics of the problem and are accurate enough for the bulk of the problems encountered by the X-ray physicist and crystallographer. In the mosaic block model a single crystal is divided into approximately equal small blocks (dimension to) with ncighboring blocks tilted with rcspect to each other so they do not simultaneously satisfy the Bragg conditions for any specific X-ray. Each mosaic block consists of a perfect array of atoms. The crystal is (tescribed, then, in terms of thc size of the bh)cks and the angular distribution between the blocks. For convenience the regions of misfit betwecn the blocks is considered void. In calculating the integratcd intensity of X-rays diffracted from a crystal one implicitly proceeds by calculating the diffraction from a frcc atom first. The amplitude of the scattered wave (in units of e2/mc 2) is commonly called the atomic scattering factor, f, and the intensity of scattered X-rays is proportional to J"~(e2/mc2) 2. When the atom becomcs part of a crystal the scattered amplitude of a unit cell of that crystal is called the structure factor, F(e'~/mc'Z), and is a sum of the atomic scattering factors of the atoms in the unit cell wcighted according to thcir phases. The calculation of the integrated intensity of a Bragg reflection of a crystal, however, can be beset with difficulties. Only in the limit of cxtremcly small mosaic blocks and very large angular tilts between the mosaic t)locks is the intcgratcd intensity proportional to F2(e-'/mc'Z) 2. For such a single crystal in symmetrical reflection the integrated intensity, E, of a Bragg reflection is independent of the size and angular distribution of the mosaic blocks and is given by