Ionization efficiency curves

Ionization efficiency curve. Shows the number of ions produced as a function of energy of the electrons, photons, or particles used to produce ionization. 

Figure 2. Ionization efficiency curves in the Cermak-Herman operation of an ion source. Relative ion intensity normalized at 40 volts for CHA+ and CH +. Voltage between filament and ionization chamber constant at 8 volts...

This reaction was considered the only reaction channel because it is the only known channel which is exothermic with ground state CH4+ ions. Reactions yielding C2H5+ and C2H4 + have been observed and are the least endothermic of the possible reactions of CH4+ with CH4. However, ionization efficiency curves establish CH3 + rather than CH4 + as the reactant ion. Reaction 14 ... 

Indeed, by using soft El ionization, we have been able to unambiguously detect products from all five reaction pathways (2a)-(2e), determine their branching ratio and characterize their dynamics.34 Here we discuss some of the results that we have obtained on this reaction, which well exemplify the power of soft El ionization. First of all, from measurements of the El efficiency curves at various to/e ratios (15, 42, and 43), we have found that the parent ion at m/e = 43 (CH2CHO+, corresponding to one of the main reaction channels, the vinoxy radical,) is not stable, so measurements of angular and TOF distributions were carried out at m/e = 42. Incidentally, from the El ionization efficiency curve at m/e = 42 we have obtained some direct information on the IE of the vinoxy radical, for which no such information was available till now. The IE should be <11 eV. 

Figure 1. Sketch of the ionization efficiency curves and the "70 eV" mass spectrum for the electron impact ionization of carbon monoxide.

A multitude of semiempirical and semiclassical theories have been developed to calculate electron impact ionization cross sections of atoms and atomic ions, with relatively few for the more complicated case of molecular electron impact ionization cross sections. One of the earlier treatments of molecular targets was that of Jain and Khare.38 Two of the more successful recent approaches are the method proposed by Deutsch and Mark and coworkers12-14 and the binary-encounter Bethe method developed by Kim and Rudd.15,16 The observation of a strong correlation between the maximum in the ionization efficiency curve and the polarizability of the target resulted in the semiempirical polarizability model which depends only on the polarizability, ionization potential, and maximum electron impact ionization cross section of the target molecule.39,40 These and other methods will be considered in detail below. 

The parameter e0 was chosen for best agreement with the experimental data of Opal et al.52 at = 500 eV. Jain and Khare applied this equation to the calculation of ionization cross sections for C02, CO, HzO, CH4, and NH3 and achieved fairly good agreement with experiment for all cases except for CO, where the cross section was too low, though the ionization efficiency curve still exhibited the correct shape. The main limitation of this method, which it has in common with the BED theory, is the inclusion of the differential oscillator strengths for the target molecule which restricts the number of systems to which it can be applied. 

The interaction will become weaker as the electron wavelength becomes greater or less than the molecular diameter with a consequential decrease in the cross section. This leads to an expression for the ionization probability as a function of electron energy, giving the shape of the ionization efficiency curve,... 

This expression reproduces the experimentally measured ionization efficiency curves surprisingly well, considering the simplicity of the model on which it is based. There is a discontinuity in the function at the maximum (when X = Xmax) but this affects only a small region of the ionization efficiency curve, and satisfactory values of the cross section are still obtained over this region. A great advantage of this method is that it is very simple to apply, depending on only three parameters the molecular polarizability volume, the ionization potential, and the maximum electron impact ionization cross section. These can be measured or calculated values (from the ab initio EM method described above, for example). 

None of the three theories used to calculate electron impact ionization cross sections could be considered to render the others obsolete. The BEB method gives the best fit to the functional form of the ionization efficiency curve for small molecules, it provides a better fit to the experimental data closer to the ionization threshold than the other methods, but it underestimates the maximum ionization cross sections for heavier molecules. The DM method provides a better fit to the ionization efficiency curves for the heavier molecules, especially for electron energies greater than max, but it tends to overestimate the cross sections for heavier molecules and it underestimates E for lighter molecules. The EM method performs as well as the other methods for the value of amax for the light molecules but underestimates the cross sections for heavy molecules by a factor similar to the overestimation of the DM method. The polarizability method outperforms the BEB and the DM methods for the calculation of and when combined with the value from the EM calculation reproduces the ionization efficiency curve as well as the BEB method. 

It can be shown that ifH ,exp(A+/AB) is obtained by linear extrapolation of the ionization efficiency curve [64], the products have only the translational energy required to conserve momentum, and the relationship between d/icxp(A+/AB) (or ArH ) andH b(A+/AB) is... 

Fio. 7. Ionization efficiency curve for oxygen (a) obtained using monoenergetic electrons (= + 0-06 e.v.) from an electrostatic velocity selector. The positions of thresholds due to the ground state and vibrationally excited states of the 77g ion are indicated by the arrows (b). (Reproduced with permission from Brion, 1964.)... 

Strictly speaking, every molecular species has an ionization efficiency curve of its own depending on the ionization cross section of the specific molecule. In case of methane, this issue has been studied repeatedly (Fig. 2.3). [18] The ionization cross section describes an area through which the electron must travel in order to effectively interact with the neutral and consequently, the ionization cross section is given in units of square-meters. Ionization cross section graphs are all of the same type exhibiting a maximum at electron energies around 70 eV (Chap. 5.1.3). 

Although the general shape of any function resembles the ionization efficiency curve to the left of the maximum, these must not be confused. At an excess energy close to zero, the rate constant is also close to zero but it rises sharply upon slight increase of the excess energy. However, there is an upper limit for the rate of a dissociation that is defined by the vibrational frequency of the bond to be cleaved. The fragments are not able to fly apart at a higher velocity than determined by their vibrational motion (Fig. 2.6). 

Numerous approaches have been published to improve the accuracy of IE data. However, the uncertainty of electron energy remains, causing the ionization efficiency curves not to directly approach zero at IE. Instead of being linear, they bend close to the ionization threshold and exponentially approximate zero. Even though the electron energy scale of the instrument has been properly calibrated against lEs of established standards such as noble gases or solvents, IE data obtained from direct readout of the curve have accuracies of 0.3 eV (Fig. 2.19a). 

To overcome the uncertainty of the actual onset of ionization, among several others, [80] the critical slope method has been developed. [25,81] It makes use of the fact that from theory realistic values of IE are expected at the position of the ionization efficiency curve where the slope of a semilog plot of the curve is... 

Fig. 2.19. Ionization efficiency curve of argon plotted on a linear scale (a) and as semilog plot (b). Extrapolation of the linear portion of a gives erroneous IBs, whereas the x-position of the tangent of an empirical critical slope to the sertrilog plot yields accuracies of 0.05 eV. Reproduced from Ref. [25] by permission. American Chemical Society, 1948.

The plateau of the ionization efficiency curve around 70 eV makes small variations in electron energy negligible in practice El works equally well at 60-80 eV. 

Fig. 5.4. Generalized ionization efficiency curve for El. The onset of ionization is marked by the IE of the respective compound. The curve shows a plateau around 70 eV. Adapted from Ref. [8] with permission. Springer-Verlag Heidelberg, 1991.

Fig. 4. Ionization efficiency curve s for SnCU. [Reprinted by permission from A. S. Buchanan, D. J. Knowles, and O. L. Swingler, J. Phys.Chem. 73,4394 (1969) copyright by the American Chemical Society.]...

Figure 2.33 Number of ions produced per cm free path length and per mmHg pressure in the ionization region of an electron ionization source as a function of electron energy. The ionization efficiency curves show a plateau between 50 and 80eV. (H. Kienitz (ed.), Massenspektrometrie (1968), Verlag Chemie, Weinheim. Reproduced by permission of Wiley-VCH.)...

Analysis of electron-impact-ionization efficiency curves. 

Additional details on some of these methods are described in other sections of this review. Attempts have also been made to determine excited-state populations in single-source mass-spectrometric experiments from an analysis of ionization efficiency curves.38ad There are several difficulties in applying such methods. For instance, it is now known from photoionization studies that ionization processes may be dominated by autoionization. Therefore, the onset of a new excited state is not necessarily characterized by an increased slope in the electron-impact ionization-efficiency curve, which is proportional to the probability of producing that state, as had been assumed earlier. Another problem arises because of the different radiative lifetimes that are characteristic of various excited ionic states (see Section I.A.4). 

Utilizing ionization efficiency curves to determine relative populations of vibrationally excited states (as in the photoionization experiments) is a quite valid procedure in view of the long radiative lifetime that characterizes vibrational transitions within an electronic state (several milliseconds). However, use of any ionization efficiency curve (electron impact, photon impact, or photoelectron spectroscopic) to obtain relative populations of electronically excited states requires great care. A more direct experimental determination using a procedure such as the attenuation method is to be preferred. If the latter is not feasible, accurate knowledge of the lifetimes of the states is necessary for calculation of the fraction that has decayed within the time scale of the experiment. Accurate Franck -Condon factors for the transitions from these radiating states to the various lower vibronic states are also required for calculation of the modified distribution of internal states relevant to the experiment.991 102... 

In the fragmentation of W(CO)6, competition can occur between different ionization and fragmentation processes, as shown by analysis of the electron-impact ionization efficiency curves (61). The ion W(CO)f can be formed by... 

Figure 7-7. (a) Electron ionization efficiency curve for CH3OH+ ion (m/z = 32) from an Ar/MeOH expansion. Arrow indicates energy corresponding to the first excited 4s state of Ar (11.55 eV). (b) Electron ionization efficiency curve for CH3OH+ ion (m/z = 32) from an He/MeOH expansion. Arrow indicates onset of ionization (10.8 eV). Reprinted with permission from Vaidyanathan et al. 1991b. Copyright 1991 American Institute of Physics. 

Figure 7-10. Electron ionization efficiency curves of Ar3+ ion in a neat argon expansion at different stagnation pressures (a) 1.2, (b) 2.0, (c) 2.5, and (d) 3.0 atm. Reprinted with permission from Vaidyanathan et al. 1992. Copyright 1992 American Chemical Society.

---