Chemistry Reference
In-Depth Information
FIGURE 7.5 Diffraction pattern from corundum: (a) reflection mode diffraction with 5
incident angle; (b) transmission mode diffraction with perpendicular incident beam.
transmission mode. The diffraction rings and the integrated profile do not show the
defocusing effect. Therefore, the transmission pattern has significantly better 2u
resolution. Transmission mode diffraction has other advantages as well. For instance,
the air scattering from the primary beam is blocked by the sample from reaching the
detector; therefore, the background due to air scattering is lower for transmission
diffraction. However, the transmission mode diffraction data can only be collected
from samples with limited thickness. As given in Chapter 6, the maximum scattering
intensity is achieved at low 2u angles with the sample thickness of t ¼ 1=m, where m is
the linear absorption coefficient. The scattering intensity drops dramatically when the
thickness increases. Transmission mode diffraction becomes impractical for cases
where the samples cannot be fabricated with the required thickness.
7.4 SAMPLING STATISTICS
In powder X-ray diffraction, the number of crystallites contributing to each reflection
must be sufficiently large to generate reproducible integrated peak intensities. The
standard deviation of the integrated peak intensity due to the number of contributing
crystallites (N
s
) is given by
N
p
, assuming a Poisson distribution and equal intensity
contribution from all participant crystals. A more revealing expression of the
measurement precision can be given as the percent standard deviation
100
N
s
s
% ¼
p
%
ð7
:
18Þ
A larger number of contributing crystallites give better precision or sampling
statistics (also referred to as particle statistics). Sampling statistics are determined by
