Geology Reference
In-Depth Information
POOR EXCITATION
IN MICROPROBE
4.0
20
'Major
elements'
0.1
K
α
Pb
3.0
ANALYTICAL
'WINDOW'
10
L
α
1
0.2
Fe
5.0
2.0
Ba
Sn
Ca
0.5
2.0
Zr
Si
1.0
1.0
Na
1.0
2.0
0.5
STRONG ABSORPTION OF X-RAYS
10
20
30
40
50
60
70
80
σ
K
σ
L
Atomic number
Z
Figure 6.6
Moseley's Law plotted in linear form (Appendix A and Exercise 6.4). Note that the vertical axis is graduated in
λ
−
1
2
(linear outer scale) and
λ
(inner scale). The unshaded area shows the range of wavelengths and elements attainable in
routine microprobe analysis of minerals and rocks.
of X-ray wavelengths that others (with atomic num-
bers of 43, 61, 72, 75, 85 and 87) still remained to be
discovered.
For plotting the Moseley Equation (6.1) in a graph, it
is convenient to express it in terms of the square roots
of each side:
peak intensities can be recorded by a relatively simple
X-ray detector driven mechanically to the approp-
riate angles. Alternatively the incoming X-ray beam
can be passed directly into a semiconductor detector
that can separate the spectral components according to
photon energy ('energy-dispersive' or 'ED' analysis).
How such a semiconductor detector works is explained
in Chapter 7.
It can be seen from Figure 6.6 that the long-wave-
length X-ray spectra from elements of atomic number
less than 10 are strongly absorbed, and this limits the
effectiveness of X-ray methods when analysing ele-
ments having atomic numbers lower than 10, although
improved spectrometer design has greatly extended
light-element performance in recent years.
05
.
1
(
)
.
kZ
σ
05
=
−
(6.2a)
λ
()
=
(
05
.
)
05
.
(
)
or
E
hck
Z
−
σ
(6.2b)
Plotting (1/λ)
0.5
or
E
q
0.
against
Z
will produce a
straight line with a gradient of
k
0.5
or (
hck
)
0.5
respec-
tively (Figure 6.6) and an intercept of
σ
on the
Z
axis.
Plotting 1/λ or
E
q
directly versus
Z
, on the other
hand, would have given a less useful curved line
(Appendix A).
The same equation can be used for predicting other
X-ray lines such as K
β
and L
α
for a particular element,
but the constants
k
and
σ
will have different values
(Figure 6.6).
The analysis of X-ray spectra can be carried out
in practice by one of two methods. A crystal of
known atomic spacing can be used as an X-ray
dif-
fraction
grating (Box 5.3) to disperse the various
wavelength components of the spectrum into a
series of peaks according to the Bragg equation
(called 'wavelength-dispersive' or 'WD' analysis);
Review
(a) The energy level structure in atoms (Figure 5.7),
together with the effect of increasing nuclear
charge, leads to a periodicity of chemical proper-
ties when elements are examined in atomic-
number order.
(b) The Periodic Table provides a concise means of
summarizing and predicting the variation of
chemical properties (such as electronegativity
and valency) among the known chemical
elements.
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