Association

3.4. Ex situ characterization techniques 47
Figure 3.11.: The measurement geometry of
a two-axis X-ray diffraction. In the
Bragg-Brentano geometry, the focus of
the X-ray tube, the detector and the
sample are situated on a focussing circle
with a radius scaling down with
larger diffraction angles.
Coherent areas of the reciprocal space can be recorded with two-dimensional reciprocal space
maps (RSM). In the neighborhood of a selected diffraction peak, a series of ω–2θ scans is
conducted such that a two-dimensional area is scanned by the stepwise variation of ω. The
coordinates in reciprocal space q are expressed as
q ‖ = R Ewald
(
cosω − cos(2θ − ω)
)
(3.7)
q ⊥ = R Ewald
(
sinω + sin(2θ − ω)
)
, [q] = rlu = reciprocal lattice units (3.8)
where R Ewald = 2π/λ Cu K α
= 40.7 nm −1 is the radius of the Ewald’s sphere. We obtain an interpretation
of structural deviations from a perfect crystal by reflex broadening with respect to
the scattering vector q (see Fig. 3.12). Moreover, a quantitative evaluation of parallel and perpendicular
lattice components i with respect to the surface can be obtained, if the reciprocal
Figure 3.12.: Reciprocal space mapping. (a) An asymmetric reflex provides information of q ‖ as well
as q ⊥ . (b) Broadening effects of an asymmetric reflex and its structural interpretation. 135