Integrated Intensities of the Diffracted and Transmitted X-rays due to ideally Perfect Crystal (Laue Case)

The analytical expressions of the integrated reflecting power and transmitting power of X-rays for absorbing perfect crystals are obtained as follows: The diffracted wave: {aligned} {RH}ʸ{=}e^{-μ₀t}{·}π/2[2∑_{n{=}0}∞J₂ₙ₊₁(2A)+I₀(h)-1]. {aligned} The transmitted wave: {aligned} {RT}ʸ{=}e^{-μ₀t}{·}(-2π)[∑_{m{=}1}∞mcos mβ Iₘ(h)]-{RH}ʸ. {aligned} In these formulae {aligned} h{=}2A√{k²+g²} β{=}tan⁻¹k/g. {aligned} J m is the first kind Bessel function of m -th order and I m is the modified Bessel function of m -th order, and the other notations are the same as those of Zachariasen's text-book on X-ray diffraction (1944). A practical method of obtaining the numerical values of R H y and R T y , and calculated results are shown.