Page 14 - Inorganic Mass Spectrometry - Fundamentals and Applications

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surface per unit area per second. On the assumption that a steady state is achieved,
the numbers of atoms impinging on the surface must equal the sum of the atoms
and ions leaving:
N = Na 4- Ni (1.4)
Langmuir and Kingdon used Saha’s original work [21], which was developed for
plasmas, as a starting point to derive an expression for a in terms of experimental
parameters. In the absence of an external electric field the equation is written

(1.5)
This is the famous Saha-Langmuir equation. In it, g+/g, is the ratio of the
statistical weights of the ionic and atomic states, @ is the work function of the
surface, I is the first ionization potential of the element in question, k is the
Boltzmann constant, and T is the absolute temperature. Note that g+/g, is close
to 1 for electronically complex elements; for simpler elements it can take on a
variety of values depending on how many electronic states can be populated in the
two species; for alkali atoms, for example, it is often %. Attai~ent of thermo-
dynamic equilib~um was assumed in the derivation of this equation, and it is
applicable only to well-defined surfaces.
Much experimental effort has been expended to confirm this equation. Early
work was compromised by the difficulty in obtaining a good enough vacuum.
Oxygen was the primary troublemaker; oxygen bonds with most metals, forming a
layer on the surface that has properties different from those of the pure metal and
that interacts with the im~ingin~ atoms. Figure 1.2 illustrates the situation; it takes
only a few seconds at torr for a monolayer of oxygen to form on tungsten
surfaces [22]. This effect has been experimentally investigated by Kawano et al.
[23]. Kaminsky measured residence times of alkali atoms on clean and gas-
covered tungsten surfaces and found that they were about 100 times longer on the
gas-covered surface [24]. Desorption energies for the ions were also affected by
gas coverage,
The Saha-L~gmuir equation has been used to obtain both ionization poten-
tials [25] and work functions [26]. Measuring ion beam intensities at several
different temperatures and plotting their logarithms vs. 1/T yield a straight line
whose slope is (0 - I)/k. If either 0 or I is known, the other is readily calculated.
Hertel introduced a method of measuring ionization potentials that was indepen-
dent of the work function of the surface, using instead as reference an element of
known ionization potential; he applied it in the dete~nation of the first ionization
potentials of the lanthanide elements [2’7].
Atoms adsorbed on a metal surface exchange electrons with it and, as a
result, may be desorbed as either atoms or ions. Only those ions and atoms with
enough energy to break the adsorption bond will leave the surface. The strength of
this bond is measured by the desorption energy, Ea and Ei, for atoms and singly