Chemistry Reference
In-Depth Information
s-s
0
W
s
0
b
2
/sin
q
b
1
s
b
2
b
1
FIGURE 7.6 Angular window of instrument from the incident beam convergence.
where b ¼ b
1
¼ b
2
is for the case that incident beam divergences in both directions
are the same.
In the above equation, the angular window is calculated only with the contribution
of the incident beam divergence. The sampling statistics increases with increasing
incident beam divergence. However, there is a limit on the beam divergence. The
angular window introduces an instrumental broadening effect on the Bragg peak,
which convolutes with the other part of broadening effect. The divergence angle
of the incident beam should be smaller than the required 2u resolution. We have so
far ignored the mosaicity of the crystallites. The angular window with contribu-
tions from both the instrumental window and crystallite mosaicity should be given as
W ¼ðb
1
þ eÞðb
2
=
sin uþ eÞ
ð7
:
26Þ
where e is the FWHM of the rocking angle due to the crystallite mosaicity.
7.4.3 Virtual Oscillation
For XRD
2
, the angular window is not only determined by the incident beam
divergence, but also significantly increased by g-integration. When g-integration is
used to generate the diffraction profile, it actually integrates the data collected in a
range of various diffraction vectors. Figure 7.7 shows the relation between the
g-integration range, Dg, and the angle between two extreme diffraction vectors within
the g-integration range. The incident beam vector is s
0
. The diffracted beams at the
two extremes of the g-integration range are s
1
and s
2
, respectively, and the two
diffraction planes are defined by the incident beam s
0
and the diffracted beams s
1
and
s
2
. The angle between the two diffraction planes is Dg. The angle between the two
extreme diffraction vectors is given by
Dc ¼ 2 arcsin½cos u sinðDg=
2Þ
ð7
:
27Þ
Since the effect of g-integration on sampling statistics is equivalent to the angular
oscillation on the c axis in a conventional diffractometer, the effect is referred to as
