Plane analytical geometry has been used to derive formulas of peak shifts due to specimen geometry and beam divergence of X-ray diffractometers in a Seemann–Bohlin configuration. When the attenuated diffraction below the specimen surface is not considered, peak shifts depend on Bragg angle (θ), incident beam divergence (2α), curvature radius of the specimen surface (r), and the tilt angle of the specimen (ψ). Numerical results show that at any fixed Bragg angle value, the peak shift increases with 2α whatever the combination of r and ψ values are. Moreover, at any fixed value of both Bragg angle and beam divergence, the peak shift depends directly on |ψ| and inversely on |r|. Shifts of peaks have been compared on both goniometer circle (Δ2θS) and focusing circle (Δ2θP). The results show that when ψ>0, then (Δ2θS) is less than (Δ2θP). On the contrary, when ψ<0, then (Δ2θS) is greater than (Δ2θP). Both (Δ2θS) and (Δ2θP) increase when the Bragg angle is decreased under the same fixed set of ψ, 2α, and r values. These peak shifts are so high that lattice strains may be masked at either high values of |ψ| and 2α, or small |r| values.
Influence of incident beam divergence on the intensity of diffuse streaks