Page 17 - Inorganic Mass Spectrometry - Fundamentals and Applications

Mass
T~e~al Io~i~~tion Spectrometry 7

W+/Wo = A exp [Ei - Ea - (I - @)]/kT (1.10)
To arrive at an expression for a it is necessary to multiply the charge transfer
probability by the probability of evaporation of ions and atoms. The Frenkel
equation [33] expresses the probability that the kinetic energy of a given ion or
atom will exceed the desorption energy:
W(E,) = w,(E,) exp E,/kT) = 1/~, (1.11)

where the subscript x is either i or a for ions and atoms, respectively; w(Ex) is the
desorption probability of the species; I, is the mean residence time for the given
species; and wOx is the frequency of exchange of the electron with the surface.
Kaminsky measured mean residence times of alkali metals on tungsten surfaces
[24]; they are on the order of second. To obtain an expression for the degree
of ionization, a, Eqs. (1.10) and (1.11) are multiplied together:

(1.12)

This equation, which relates the Frenkel equation [Eq. (1.1 l)], the Saha-Langmuir
equation [Eq. (1 S)], and the ratio of charge transfer probabilities, makes possiblt;
a detailed study of the thermal ionization process.
There is some doubt about the validity of Eq. (1.9). It assumes that the
atomic and ionic states of an adsorbed atom on a hot surface are distinguish able^ as
shown in Figure 1.3, AQ should be nonzero if this is so. If, on the other hand, AQ =
0, this equation reduces to

Ea - Ei = (I - @) (1.13)
Available experimental evidence, though scanty, suggests that AQ is within
experimental error of 0, at least for some elements [30].
To sumrnkze the surface ionization phenomenon, an atom on a hot filament
surface exchanges an electron with it at rates of 1010-1014 sec-l [34]. The
adsorbed species will desorb as an atom or a singly charged positive ion; the
probability is controlled by the desorption energies of the two species. It is
important to note that the Saha-Langmuir equation applies only to an atomic beam
impinging on a hot surface; it does not apply to the single-filament situation. It is
easy to see why: As the temperature is raised, the element in question evaporates
from the surface at a progressively faster rate, an effect not addressed by the
equation. To illustrate this point, the author has over the decades analyzed over 30
elements by positive thermal ionization using single filaments; in all cases but
those of the most refractory elements (e.g., Th), there is a temperature that if
exceeded will lead to evaporation so fast and complete that it is impossible to
recover and get a good analysis; this phenomenon has also been reported by
Heumann for iron [35]. Such observations are not predicted by the equation.