The exact dynamical wave fields for a crystal with a constant strain gradient on the basis of the Takagi-Taupin equations

From the Takagi-Taupin equations for two-beam cases, the exact wave fields for a spherical incident wave are obtained in the Laue case for a crystal having a constant strain gradient. Absorption is taken into account. Both direct and Bragg-reflected waves are essentially expressed in terms of confluent hypergeometric functions. Their characters depend on strain gradient, structure factor and crystal thickness. The wave fields tend to those obtained by Eikonal theory as the strain gradient decreases. For an extremely large strain gradient, the wave fields reduce to those predicted by the kinematical theory.