Effect of Dispersion and Geometric Intensity Factors on X-Ray Back-Reflection Line Profiles

At high diffraction angles the rapid variation of dispersion causes the center of gravity of the observed diffraction-line distribution of intensity versus 2τ to be displaced away from the Bragg angle τm corresponding to the mean value ρ̄λ̄ of the convolution of the distribution of lengths ρ of reciprocal-lattice vectors hkl with the distribution of x-ray wavelengths λ. The displacement has been calculated for the case of measurements both on individual Kα components and on unresolved Kα doublets. In a probable example of the latter case, with CuKα radiation, the displacement at 2τ=160° corresponds to a relative error in spacing measurement of 1 part in 104 and increases rapidly with increasing 2τ. The simple procedure is recommended of replotting the observed intensities against a scale of sine τ. The mean of the replotted distribution corresponds very closely to τm.