Statistical dynamical theory of crystal diffraction. I. General formulation

The statistical dynamical theory is reformulated as an extension of the previous theory [Kato (1976). Acta Cryst. A32, 453-457, 458-466] by taking a more general form of the correlation function of the lattice phase factor. A 'static' Debye-Waller factor E and short-range correlation length τ are introduced for characterizing crystalline media. The fundamental equations consist of a set of differential equations for the averaged (coherent) wave fields {(D_o),(D_g)} and a set of differential equations for the incoherent part of the intensity fields {_Iⁱo, Iⁱ_g}. They are connected through the transformation to the incoherent beams from the coherent waves. In non-absorbing crystals, energy conservation holds for the total intensities {I^c_o + Iⁱ_o, I^c_g + Iⁱ_g}, where I^c_o = |(D_o)|² and I^c_g = |(D_g)|². The theory can be applied to the diffraction phenomena of the crystalline materials of any degree of perfection.