Saha-Langmuir equation

In general the production of positive ions relative to neutral species can be predicted from the Saha-Langmuir equation ... 

This is the famous Saha-Langmuir equation. In it, g+/g0 is the ratio of the statistical weights of the ionic and atomic states, is the work function of the surface, / is the first ionization potential of the element in question, k is the Boltzmann constant, and T is the absolute temperature. Note that gjg0 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 Vi. Attainment of thermodynamic equilibrium was assumed in the derivation of this equation, and it is applicable only to well-defined surfaces. 

The Saha-Langmuir equation has been used to obtain both ionization potentials [25] and work functions [26]. Measuring ion beam intensities at several different temperatures and plotting their logarithms vs. 1/7" yield a straight line whose slope is ( - f)/k. If either or / is known, the other is readily calculated. Hertel introduced a method of measuring ionization potentials that was independent of the work function of the surface, using instead as reference an element of known ionization potential he applied it in the determination of the first ionization potentials of the lanthanide elements [27]. 

This equation, which relates the Frenkel equation [Eq. (1.11)], the Saha-Langmuir equation [Eq. (1.5)], and the ratio of charge transfer probabilities, makes possible a detailed study of the thermal ionization process. 

This equation is now called the Saha-Langmuir equation. The constant, A, depends on the quantum energy levels of the element or molecule and of the ionizing filament material. Efficient production of positive ions occurs from filament... 

Vice versa, nonmetallic elements with high IE and metal oxides may form negative ions [33,34], The degree of ionization a" is then obtained from the modified Saha-Langmuir equation... 

The term surface ionization is frequently used to describe the process in which ionization takes place within some critical distance from the surface. A number of surface-dependent ionization methods, such as field desorption, fast atom bombardment, and laser desorption, are described as surface ionization methods. Another use of this term is more restricted surface ionization (SI) is defined as the ionization process, which can be interpreted by use of the Saha-Langmuir equation. 

In 1923, Kingdom and Langmuir [1] first observed SI (Fig. 1). This phenomenon consisted of desorption of cesium (Cs) atoms in the form of positive ions from the surface of a heated tungsten (W) filament. Subsequently, numerous studies of positive-ion SI have been conducted, since this effect opens interesting possibilities for analysis of chemical species with low ionization energy (IE), for ion production, and for the detection of molecular and atomic beams. After the Saha-Langmuir equation [2] was established and well defined, further studies have [3,4] been directed to the atoms of virtually all elements, which have a low ionization energy. Especially, SI was studied for suitability as a source of ions for precise isotope-ratio measurements [5] and isotope-dilution techniques. It is apparent, however, that its use has, until recently, been restricted to metals. 

Surface ionization is conventionally interpreted by the use of the Saha Langmuir equation (Eq. 1), which is based upon the assumption that thermal and charge equilibria are established between the species on the surface material and the surface material itself [2j. This equation describes the temperature dependence of the degree of ionization, a. 

M ions are observed only for M having not too high IE. Aniline is the typical example. Molecular surface ionization (MSI) is easier not only in the case of a lower IE, but also in the case where a dissociative surface reaction takes place very slowly since the ionization process competes with a pyrolytic surface reaction. The M intensity varies significandy with the work function of the emitter surface. According to this behavior, MSI is a process conveniently described by the Saha-Langmuir equation, no matter whether the MSI process occurs in an equilibrium or in a nonequilibrium. 

The consecutive process is more likely the formation of surface dissociative reaction product with a low ionization potential (IP) followed by the Saha-Langmuir model SI on the hot surface emitter with a high work function. In this mechanism, the ionization currents for [M — H] radical are determined not only by the ionization efficiency, given by the Saha-Langmuir equation, but also by the efficiency of the formation of this [M — X] product on the emitter surface [16], The large [M — H]+ ion peak from toluene can be explained by this process since the ionization potential of benzyl radical, 7.63 eV, is sufficiently low to be ionized [17],... 

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