Electron swarm technique

Momentum-transfer cross sections are normally determined by the electron swarm technique. A detailed discussion of the drift and diffusion of electrons in gases under the influence of electric and magnetic fields is beyond the scope of this book and only a brief summary will be given. The book by Huxley and Crompton (1974) should be consulted for a full description of the experimental methods and analysis procedures. 

Mayhew, C.A. Critchley, A.D.J. Howse, D.C. Mikhailov, V. Parkes, M.A. Measurements of thermal electron attachment rate coefficients to molecules using an electron swarm technique. Eur. Phys. J. D 2005,35, 307-312. 

The transport coefficients depend on a balance between the rates of acquiring energy from acceleration in the field and losing it in collisions. Since this balance can be made very close the swarm technique is particularly suited for providing cross-section data at low electron energies. 

Figure 6.1 Plots of ECD and electron swarm data as In KTm versus 1,000/r for molecular oxygen. The ECD data with the higher P region were published in [18], while the other data appeared in [17]. The electron swarm data derive from [16]. This shows the equivalence of the ECD and electron swarm data. The calculated curve through the ECD data gives an AEa of 1.07 eV as determined by three techniques [111-113].

The electron beam and electron swarm experiments [13] can also be used to determine attachment rate constants. However, these are determined as a function of energy and can then be extrapolated to thermal energy. Other techniques used to... 

The experimental Ea for 02 are assigned to bound states. The VEa for these states range from 0.9 eV to —0.75 eV. The activation energies for thermal electron attachment determined from the ECD data range from 0.05 eV to 1.9 eV. The frequencies observed in solids and the Morse parameters obtained from PES, ECD, electron swarm, and other techniques can be used to approximate the intemuclear distance and frequency of the predicted states. These give six M 2) curves (EDEA < 0, and Ea and VEa > 0) and six M( 1) curves (only Ea > 0). The PES Ea, with values of 0.430, 0.450 0.002 eV, is the most precise Ea and the Born... 

Figure 5 Left panel Rate constants k for electron attachment to as a function of the mean collisional energy. (From Ref. 118.) (O) The results obtained using the pulse radiolysis microwave cavity technique combined with microwave electron heating ( ) previous results by Shimamori et al. [J. Chem. Phys. 1993, 99, 7789] ( ) electron swarm [Spyrous and Christophorou, J. Chem. Phys. 1985, 82, 1048] and (O) high-Rydberg atom beams [Marawar et al., J. Chem. Phys. 1988, 88, 2853]. Right panel Comparison of the cross section cr(s) for attachment to C5F5 as a function of the electron energy, (—) derived by unfolding the rate constants (From Ref. 118.) with the previous cross...

The electron attachment rate constant for SFg in nitrogen at ambient temperature and pressure showed a smooth decline with increasing E/N over the range of 0.39-0.78 Td [56]. As shown in Figure 13.7, the results obtained by IMS agree closely with those obtained by the well-established high-pressure swarm technique [57]. A further series of experiments with E/N from 0.05 to 0.9 Td confirmed this excellent agreement between the two methods [55]. 

Jarvis, G.K. Kennedy, R. A. Mayhew, C. A. Investigations of low energy electron attachment to ground state group 6B hexafluorides (SF, SeF, and TeF ) using an electron-swarm mass spectrometric technique. Int. J. Mass Spectrom. 2001, 205, 253—270. 

Traditionally, experimental values of Zeff have been derived from measurements of the lifetime spectra of positrons that are diffusing, and eventually annihilating, in a gas. The lifetime of each positron is measured separately, and these individual pieces of data are accumulated to form the lifetime spectrum. (The positron-trap technique, to be described in subsection 6.2.2, uses a different approach.) An alternative but equivalent procedure, which is adopted in electron diffusion studies and also in the theoretical treatment of positron diffusion, is to consider the injection of a swarm of positrons into the gas at a given time and then to investigate the time dependence of the speed distribution, as the positrons thermalize and annihilate, by solving the appropriate diffusion equation. The experimentally measured Zeg, termed Z ), is the average over the speed distribution of the positrons, y(v,t), where y(v,t) dv is the number density of positrons with speeds in the interval v to v + dv at time t after the swarm is injected into the gas. The time-dependent speed-averaged Zef[ is therefore... 

The technique involves high precision measurements of characteristic transport properties, the transport coefficients, of an ensemble or swarm of electrons as they drift and diffuse through a gas at pressure ranging from a few torr to many atmospheres. The most commonly measured transport coefficients are the drift velocity W, which is defined as the velocity of the centroid of the swarm in the direction of the applied uniform electric field E, the ratio Dt/p (where Dt is the diffusion coefficient perpendicular to the electric field and p is the electron mobility, defined as W E) and, when a magnetic field B transverse to the electric field E is present, the ratio (where is the drift velocity at right angles to E and B). For a... 

The complementary techniques for determining rate constants for thermal electron attachment, detachment, and dissociation are the flowing afterglow, the microwave technique, the ion cyclotron resonance procedures, the swarm and beam procedures, the shock tube techniques, the detailed balancing procedures, the measurement of ion formation and decay, and the high-pressure mass spectrometer procedures. In all cases the measurement of an ion or electron concentration is made as a function of time so that kinetic information is obtained. In the determination of lifetimes for ions, a limiting value of the ion decay rate or k is obtained. 

Beam collision measurements represent the ideal for us in terms of potential quality of data, but they are the most scarce in terms of quantity. Many early beam measurements were of relative cross sections nevertheless, they are useful when used in conjunction with calculations or swarm measurements. Ab initio calculations of electron impact cross sections for complex molecules, as discussed by Winstead and McKoy (1999), have become very sophisticated but require enormous computational resomces for large molecules. The third technique has been in use for some three decades. There is a very large body of literature reporting on measurements and interpretations of electron transport or swarm coefficients in many of the same gases in which we are currently interested. This is an excellent technique, as I describe below, for estimating cross sections when no other data are available. 

The utility of such techniques can be seen in Fig. 6, where I have plotted various measured and swarm-derived cross sections for electron impact dissociation of molecular nitrogen. Winters (1966) and Cosby (1993) have measured the cross section for dissociation of N2 in electron collisions. Winters measured the total dissociation cross sections [as we have seen previously in the Winters and Inokuti (1982) measurements of dissociation of C2F6] and subtracted the... 

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