Chemistry Reference
In-Depth Information
Figure4.17.
Cross-section of an X-ray beam reflected by a flat sample under an angle
α
.
Incident and reflected beam interfere in a triangle with height
h
. It can simply be shown that
h
is
w
beam
/(2 cos
α
). For small angles,
h
is approximately
w
beam
/2 (relative deviation
<
0.06% for
angles
<
2
°
).
A first limitation is given by the geometry of excitation as illustrated in
Figure 4.17. The width of the primary beam
w
beam
is usually limited by a slit that
is less than 30
μ
m for X-ray tubes and less than 100
μ
m for synchrotron beam
lines. The height of the triangular region
h
triangle
where the standing wave field
appears is approximately
w
beam
/2 for grazing incidence. For that reason, the
thickness of a specimen should be restricted to several tens of micrometers.
The second reason for a restriction arises from the limited counting capa-
bility of the detector. A count rate of about 12 000 cps for a Si(Li) detector and
of 1 000 000 cps for an SDD is a maximum value where the dead time
percentage is 63%. This high count rate is achieved for a specimen amount
mainly depending on the matrix. Upper values have been determined exper-
imentally for three typical matrices characterized by their density
ρ
: organic
tissues (dried,
∼
0.2 g/cm
3
), mineral powders (
∼
1-2 g/cm
3
), and covers of metal
salts (
∼
2.5 g/cm
3
) or metallic smears (
∼
8 g/cm
3
). The upper limits,
m
max
, are
250
μ
g/cm
2
for organic tissues, 140
μ
g/cm
2
for mineral powders or salts, and 8
μ
g/
cm
2
for metallic smears. This is a rough estimate from unpublished measure-
ments and can differ by a factor of two for the different excitation modes
mentioned in Section 4.2.1.
The corresponding thickness
d
max
can be determined according to
d
max
m
max
=
ρ
(4.14)
provided that the carrier is uniformly covered. This quantity
d
max
is 12
μ
m for
organic tissues, 0.7
μ
m for mineral powders, and 10 nm for metallic smears.
4.4.3.1MassandThicknessofThinLayers
As already mentioned, a further limitation can be caused by a strong selective
X-ray absorption of the matrix for the analyte element. For a thin layer the
absorption can be expressed by Equation 4.1. It causes an intensity deficit,
which will remain below a certain permissible level
a
rel
in percent, if the
thickness of the specimen is restricted to a maximum value
d
max
. This further
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