Chemistry Reference
In-Depth Information
2
ik
0
α
ν
ρ
ν
Q
rt
;
ν
μ
=
ρ
(2.55c)
ν
;
E
By means of these quantities three addenda have to be built similar to Equations
2.47a, 2.47b, and 2.47c, which may be called
X
t,
ν
,
X
r,
ν
, and
X
rt,
ν
. The fluores-
cence intensity to be measured by the detector can then be calculated by
I
fluo
;
ν
α
0
≅
I
n
c
x
;
ν
S
x
;
E
0
ε
det
T
air
A
ν
X
t
;
ν
α
ν
;
d
ν
X
r
;
ν
α
ν
;
d
ν
2
X
rt
;
ν
α
ν
;
d
ν
(2.56)
This rather complex expression has to be summed up for an element named
x
,
which is present in different layers. It is evident that a polychromatic instead of
a monochromatic excitation would further complicate this expression. It may
also be emphasized that the equation cannot be solved directly for any of the
possibly unknown parameters
c
x
,
v
,
ρ
v
,or
d
v
. The mass-fractions
c
x
,
v
are even
concealed in the mass-attenuation coefficients
μ
=
ρ
v
;
E
0
and (
μ
/
ρ
)
v
,
E
and not
only present as single factors.
One special and simplified case should be mentioned, namely, that of a
periodic multilayer. For this, only two different layers and consequently only
two different transfer matrices are relevant. Any period of a double layer is
characterized by one and the same characteristic matrix. On account of the
periodicity, the total multilayer with
N
periods is characterized by the
N
th
power of this matrix. All further calculations are considerably shortened under
this condition.
REFERENCES
1. Klockenkämper, R. (1997)
Total-ReflectionX-RayFluorescenceAnalysis
, 1st ed.,
John Wiley & Sons, Inc., New York.
2. Born, M. and Wolf, E. (1980).
PrinciplesofOptics
, 6th ed., (reprinted in 1993),
Pergamon Press: Oxford; 808 pp.
3. Röseler, A. (1990).
InfraredSpectroscopicEllipsometry
, Akademie Verlag: Berlin.
4. de Boer, D.K.G. (1991). Glancing incidence X-ray fluorescence of layered materials.
Phys.Rev.
,
B44
, 498-511.
5. de Boer, D.K.G. and van den Hoogenhof, W.W. (1991). Total-reflection X-ray
fluorescence of thin layers on and in solids.
Adv.X-RayAnal.
,
34
,35-40.
6. Kiessig, H. (1931). Interferenz von Röntgenstrahlen an dünnen Schichten.
Ann.
Phys.(Leipzig)
,
10
, 769-788.
7. de Boer, D.K.G., Leenaers, A.J.G., and van den Hoogenhof, W.W. (1995). Glanc-
ing-incidence X-ray analysis of thin-layered materials: a review.
X-RaySpectrom.
,
24
,91-102.
8. Huang, T.C. and Parrish, W. (1992).
Adv.X-RayAnal.
,
35
, 137-142.
9. Bedzyk, M.J., Bommarito, G.M., and Schildkraut, J.S. (1989). X-ray standing waves
at a reflecting mirror surface.
Phys.Rev.Lett.
,
62
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