DYNAMICAL THEORY OF X-RAY-DIFFRACTION FOR THE STUDY OF CRYSTAL-SURFACES

The Darwin dynamical theory is extended to the asymmetric diffractions of the Bragg and Laue cases in a form suited for treating the crystal with a different structure on its surface by using the characteristic matrix method. For ideal crystals, the exact analytical solutions val id for any incidence condition are obtained as a function of the gener al expression of the deviation parameter within the two-beam approxima tion. It is shown that the exact expressions are reduced to the expres sions given by the conventional theories using the appropriate approxi mations in the cases of CTR (crystal truncation rod) scattering, specu lar reflectivity and Bragg reflection including the condition of a Bra gg angle of 90 degrees. Next the Darwin theory is extended to the copl anar three-beam case to study the effect of other beams on CTR scatter ing. It is shown that the reflectivity of CTR scattering obtained by t he two-beam approximation holds good except when the other beam satisf ies the Bragg condition, and the modulation in the reflectivity on suc h conditions is sensitive enough to get information of the surface str ucture.