New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution

The analytical solution of the problem of X-ray spherical-wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect. It is shown that if a thickness increase takes place at the side of the reflected beam, the related reflected wave amplitude is calculated as a sum of three terms, two of which are complex. If all three terms have a comparable modulus, it can lead to an increase in the reflected beam intensity by up to nine times due to interference compared with the value for a plane parallel shape of the crystal. The equation for the related transmitted wave amplitude contains only two terms. Therefore, the possibility to increase intensity is smaller compared with the reflected beam. The analytical solution is obtained after a solution of the integral equations by means of the Laplace transformation. A general integral form of the Takagi equations derived earlier is used. The results of relative intensity calculations by means of analytical equations coincide with the results of direct computer simulations.