Chemistry Reference
In-Depth Information
The intensity of any characteristic line of a target element can be expressed
in number of photons emitted per unit time or second. For lines in the primary
X-ray spectrum, for example, produced by electrons of an X-ray tube, this
intensity can be given by an empirical formula:
kIg
ij
ω
i
?
E
m
min
E
0
=
E
min
m
N
line
E
ij
1
(1.8)
where
N
line
(
E
ij
) is the number of photons with
E
ij
,
k
is a constant,
I
is the
electron current,
g
ij
is the emission rate of the respective line,
i
,initsseries,
j
,
ω
i
is the fluorescence yield of the target material,
E
0
is the accelerating
potential of the X-ray tube, and
E
min
is the critical excitation energy for the
appropriate spectral series. The exponent,
m
, usually has a value below 2. It
maybe5/3for
E
min
<
E
0
<
2
E
min
, and slowly decreases to 1.0 for
E
0
values
>
5
E
min
. This equation for target lines is rather simple compared to
the formula for a secondary X-ray spectrum produced by X-ray fluorescence
of a sample.
There are some exceptions to the aforementioned selection rules. First,
there are emission peaks that do not correspond to permitted transitions
and therefore are called“forbidden”peaks. Second, there are additional
peaks that arise from a double ionization by a simultaneous impact of
photons or electrons on two inner electrons of the atom. As the energy
levels of the doubly ionized atom slightly differ from those of the singly
ionized atom, somewhat different peaks occur, which are called“satellite”
peaks. Forbidden and satellite peaks are always weak, and satellites mainly
appear in the K-spectra of lighter elements. Nevertheless, they must not be
ignored in trace analysis if they are generated by a major component at
energies close to small peaks of trace elements. Consequently, both
forbidden and satellite peaks are alsoincludedintablesorstoredin
computers.
According to their energy position, the characteristic X-ray peaks are
independent of the chemical bonding or state of the atoms. This advantage
exists as long as only electrons from inner shells are involved in the X-ray
emission process and as long as these electrons are not affected by the chemical
vicinity of the atoms. In practice, this is the normal situation for the detection of
higher photon energies and heavier elements. However, exceptions can appear
for lower energies and lighter elements. If an electron from a valence or a near
valence band is involved in the emission process, the respective energy level of
the atom and the energy transition will be affected by the chemical state.
Consequently, the characteristic peaks may be shifted for elements in different
compounds. As the effect is in the range of a few electronvolts, it can be
measured and used to get information on chemical bonding. However, other
spectroscopic techniques are more efficient in this respect. For the usual X-ray
spectrometrical practice, peak shifts are an exception but may be taken into
account to avoid systematic errors.
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