Chemistry Reference
In-Depth Information
the beam path between the sample and the detector. The sensitivity itself can be
further deduced from
S
x
;
E
0
g
x
ω
x
f
x
τ
=
ρ
(2.37)
x
;
E
0
where
g
x
is the relative emission rate of the element peak in its series;
ω
x
is the
fluorescence yield of the element
x
,
f
x
is its jump factor at the relevant
absorption edge and (
τ
/
ρ
)
x
,
E
0
is the photoelectric mass-absorption coefficient
at the primary photon energy
E
0
. This product of fundamental parameters is
independent of instrumentation or sample matrix and can be calculated for
each element
x
. Different sets of tables can be used for this calculation [39-41].
The foregoing derivation includes the absorption of the primary radiation as
well as the fluorescence radiation. Secondary fluorescence or enhancement is not
taken into account because it is a second-order process. It is rather complex and
may be neglected in the case of grazing incidence (but ought to be considered in
principle [4,32]). The angular divergence of the instrument, however, can easily
be taken into consideration. For that purpose, Equation 2.34 has to be convo-
luted by a triangle function of
α
0
with the width of the aperture.
The intensity dependence on the energy transfer (1
R
)
α
0
was derived
earlier in simple terms in Section 2.3.1. The matrix and the fundamental
parameter approaches have been introduced in the present section in order
to provide a more detailed description. Both formalisms can be expanded and
applied to single- and multiple-layer systems.
2.4.2AThinHomogeneousLayeronaSubstrate
A single layer with a thickness
d
1
may be deposited on a thick and flat substrate,
as demonstrated in Figure 2.25. Here
n
0
,
n
1
, and
n
s
shall denote the complex
Figure2.25.
Incoming, reflected, and refracted beams above, within, and below a thin layer,
respectively, deposited on a thick substrate.
n
0
,
n
1
, and
n
s
are the refractive indices. At any point
above and within the layer, there are two beams interfering with one another at an angle 2
α
0
or 2
α
1
,
respectively. In the substrate, there is only one refracted beam penetrating at an angle
α
s
. Figure
from Ref. [1], reproduced with permission. Copyright1996, John Wiley and Sons.
Search WWH ::
Custom Search