GEOMETRY OF SINGLE CRYSTAL-PLANE SCATTERING IN DYNAMICAL THEORY OF X-RAY DIFFRACTION. D.S. de Vasconcelos, W.A. Keller and Marek Urbanski, Instituto de Fisica, Universidade Federal da Bahia, Salvador, Brazil

X-ray diffraction from a crystal plane with zero thickness (two-dimensional problem) filled up by scattering electrical charge which can be treated as either a continuous or discrete distribution, has been calculated in analytical and numerical ways, respectively. The crystal plane scattering was regarded as due to radiation from classical dipoles activated in one case, only by the external electrical field, and in the second case, by the external field plus field due to other dipoles in the plane, determined self-consistently. In the first solution we consider the situation of a single plane wave, incident at the [[theta]] glancing angle, as the source of a field forcing the dipole oscillations. In the second, self-consistent solution, we also include fields of neighbouring radiating dipoles. It is then possible to show by using either analytical or numerical methods that the combined dipole radiation takes the form of two plane waves leaving symmetrically the crystal plane at [[theta]] angles which give rise to reflected and forward scattered waves. The resultant dipole waves calculated for the first mode of activation (external field only) have a phase shift equal to +[[pi]]/2 in relation to the incident wave, a result which is known to violate conservation of energy. It is shown here that, the two methods of calculation (analytical and numerical) agree on the shift, they desagree on the minimum distance xP at which the resultant dipole waves are formed as plane waves. The analytical evaluation requires only xP>0, while the numerical one gives an approximate value xP=0.5-1.0[[lambda]], for distance between dipoles which are encountered in common diffraction experiments. In the self-consistent mode, once again the analytical and numerical methods yield the same values as above. More importantly, in this mode, which considers cooperative effects between scatterers, energy is conserved. The calculated phase shift is shown to be greater than [[pi]]/2 by exactly the amount necessary to conserve energy.