Saha equation

The ionization constant can be calculated from the Saha equation. ... 

The mass action law or Saha equation for thermal ionisation of seed atoms is... 

More precisely, the inverse of the average decay constant of the various isotopes, weighted by their abundance according to the Saha equation expressed roughly by Eq. (6.21). 

If an electron absorbs sufficient energy, equal to its first ionization energy, it escapes the atomic nucleus and an ion is formed. In the ICP the major mechanism by which ionization occurs is thermal ionization. When a system is in thermal equilibrium, the degree of ionization of an atom is given by the Saha equation ... 

Degree of ionization as a funetion of first ionization energy calculated using the Saha equation. 

Spectrographic studies were also made to det the temp densities. The plasma temp and particle densities were also detd by using the relative intensities of two adjacent lines of die same species and applying the Saha equation... 

Thus, the intensity of the random source involves three terms, each corresponding to one of the pair of processes (direct and inverse), defining the change in the concentrations. In the state of complete equilibrium (i.e., if a Saha equation is valid), the first and second terms in each bracket of (5.19) become equal. 

Many attempts have been made to quantify SIMS data by using theoretical models of the ionization process. One of the early ones was the local thermal equilibrium model of Andersen and Hinthome [36-38] mentioned in the Introduction. The hypothesis for this model states that the majority of sputtered ions, atoms, molecules, and electrons are in thermal equilibrium with each other and that these equilibrium concentrations can be calculated by using the proper Saha equations. Andersen and Hinthome developed a computer model, C ARISMA, to quantify SIMS data, using these assumptions and the Saha-Eggert ionization equation [39-41]. They reported results within 10% error for most elements with the use of oxygen bombardment on mineralogical samples. Some elements such as zirconium, niobium, and molybdenum, however, were underestimated by factors of 2 to 6. With two internal standards, CARISMA calculated a plasma temperature and electron density to be used in the ionization equation. For similar matrices, temperature and pressure could be entered and the ion intensities quantified without standards. Subsequent research has shown that the temperature and electron densities derived by this method were not realistic and the establishment of a true thermal equilibrium is unlikely under SIMS ion bombardment. With too many failures in other matrices, the method has fallen into disuse. 

In addition to the statistical mechanical temperatures, a distribution temperature, called the ionization temperature, and defined by the Saha equation, is frequently referred to (D2, S3). In its simplest form—for a monatomic gas—the Saha equation states that the equilibrium established between the species present [positive ions (+), electrons (e), and neutral atoms (0) ] is a function of temperature,... 

The term Et/kT can also be written in the equivalent form, H°/RT.) Ei is not a constant at high temperatures. Its diminution has been estimated by Unsold (Ul) to be AEt = 7.0 X 10 7 ne% volt. For very high temperatures, the exponential term in the Saha equation should read... 

Determination of ionization temperatures requires solution of the Saha equation [ (8) or (9) ]. As an example, consider a monatomic gas (A) partially ionized according to the reaction, + e. For a... 

If we assume in an orientation calculation with the Saha equation (21) that all the species have the same ionization potential (I) and a temperature of 2000 K, the fraction of species charged is given by ... 

Table II. Fraction of Ionized Particles as a Function of Their Diameter (Da) and Electron Concentration n ), Computed by Using the Saha Equation...

However, the latter is also given by the well-known Saha equation. With the aid of wave mechanics and through differentiation of the Boltzmann equation, the Saha function in terms of the partial pressures can also be expressed as ... 

The Saha equation is only valid for a plasma which is in local thermal equilibrium, where the temperature in the equation is then the ionization temperature. When this condition is not fullfilled, the equilibrium between the different states of ionization is given by the so-called Corona equation [16],... 

When the plasma is not in local thermal equilibrium (LTE), the electron number densities cannot be determined on the basis of the Saha equation. Irrespective of the plasma being in local thermal equilibrium or not, the electron number density can be derived directly from the Stark broadening of the Hg line or of a suitable argon line. This contribution to broadening is a result of the electrical field of the quasi-static ions on one side and the mobile electrons on the other side. As described in Ref. [17] it can be written as ... 

From Eqs. (63) and (64), which give the intensity of a line, and from the Saha equation [Eq. (68)], it can be understood that for each spectral line emitted by a plasma source there is a temperature where its emission intensity is maximum. This is the so-called norm temperature. In a first approximation [18], it can be written as ... 

The ionization temperature is relevant for all phenomena involving equilibria between analyte atoms, ions and free electrons in plasmas. In the case of thermal equilibrium, it occurs in the Saha equation [Eqs. (66, 68)] and can be determined from the intensity ratio of an ion and an atom line of the same element. In all other cases ionization temperatures can be determined from the ne value obtained from Stark broadening [see Eqs. (74, 77)]. 

If the gas is partially ionized, which is the case close to the stellar surface, then it is necessary to solve the Saha equation to determine the distribution of ions for every element. 

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