Pulsed Townsend Technique Research Articles

Thermal electron attachment to halogenated silanes in the gas phase.

Silane derivatives play a crucial role in industrial plasma processes for the fabrication of various electronic devices such as lighting devices, solar cells, and displays. Accurate quantitative data are essential for modeling technological plasmas. This study reports the rate coefficients (k) and activation energies (Ea) for thermal electron attachment to Si2Cl6, Si (CH3)3CHF2, and SiCl (CH3)2Si(CH3)3, which are key parameters for understanding the underlying processes in plasmas. The results obtained for other silane derivatives were also analyzed and discussed. The measurements were conducted using the pulsed Townsend technique. In this technique, electrons generated by a laser under an electric field travel to the anode, inducing a charge on it. In the presence of a scavenger gas, electrons are captured, leading to a decrease in the rate of charge increase over time. The kinetic parameters were deduced from the shape of the pulse. The G4 method was used to obtain bond dissociation energies (BDEs). This study determined the kinetic parameters for thermal electron attachment to Si2Cl6, Si (CH3)3CHF2, and SiCl (CH3)2Si(CH3)3 for the first time. The rate coefficients at 298 K were found to be 2.17 ±0.04 × 10-9cm3s-1, 2.01 ±0.09 × 10-12cm3s-1, and 8.05 ±0.07 × 10-12cm3s-1, respectively. The corresponding activation energies were determined to be 0.37 ±0.04 eV, 0.29 ±0.03 eV, and 0.21 ±0.01 eV for Si2Cl6, Si (CH3)3CHF2, and SiCl (CH3)2Si(CH3)3, respectively. The experiment was conducted over the temperature range of 298-378 K. The findings of this study provide significant new insights into fundamental parameters such as rate coefficients and activation energies for thermal electron capture by chlorinated and fluorinated silane derivatives. These data contribute to advancing our understanding of thermal electron interactions with chlorosilanes, which can be utilized for controlling important species in the plasmas of various modern technologies.

Properties of Electron Swarm Parameters in Tetrahydrofuran

Reported electron collision cross sections data in the energy range ~ 0 to 300 eV from gaseous biomolecule Tetrahydrofuran (THF) have been used to calculate the electron energy distribution function (EEDF) and swarm parameters for electrically excited of THF, using a two-term solution of the Boltzmann equation. The electron swarm parameters namely (mean energy, drift velocity, diffusion coefficient, electron mobility, characteristic energy, attachment and ionization coefficient), at room temperature and atmospheric pressure are presented over a wide range of applied electric field strength E/N (E is the electric field and N is the gas number density) varying from 0.1 Td to 1000 Td (1Td = 10-17 Vcm2). The EEDF found to be non-Maxwellian. The electron swarm parameters are compared with those calculated using multi term kinetic theory and experimentally using the pulsed Townsend technique. The influence of inelastic cross section on the calculated transport parameters is also explained.

Low Energy Electron Attachment by Some Chlorosilanes.

In this paper, the rate coefficients (k) and activation energies (Ea) for SiCl4, SiHCl3, and Si(CH3)2(CH2Cl)Cl molecules in the gas phase were measured using the pulsed Townsend technique. The experiment was performed in the temperature range of 298–378 K, and carbon dioxide was used as a buffer gas. The obtained k depended on temperature in accordance with the Arrhenius equation. From the fit to the experimental data points with function described by the Arrhenius equation, the activation energies (Ea) were determined. The obtained k values at 298 K are equal to (5.18 ± 0.22) × 10−10 cm3·s−1, (3.98 ± 1.8) × 10−9 cm3·s−1 and (8.46 ± 0.23) × 10−11 cm3·s−1 and Ea values were equal to 0.25 ± 0.01 eV, 0.20 ± 0.01 eV, and 0.27 ± 0.01 eV for SiHCl3, SiCl4, and Si(CH3)2(CH2Cl)Cl, respectively. The linear relation between rate coefficients and activation energies for chlorosilanes was demonstrated. The DFT/B3LYP level coupled with the 6-31G(d) basis sets method was used for calculations of the geometry change associated with negative ion formation for simple chlorosilanes. The relationship between these changes and the polarizability of the attaching center (αcentre) was found. Additionally, the calculated adiabatic electron affinities (AEA) are related to the αcentre.

Low-energy electron interactions with chlorotrimethylsilane (Si(CH3 )3 Cl), dichlorodimethylsilane (Si(CH3 )2 Cl2 ) and chloromethyldimethylsilane (SiH(CH3 )2 (CH2 Cl)).

Silane derivatives are widely used in industrial plasmas for manufacturing lighting devices, solar cells, displays, etc. Models of technological plasmas require quantitative data. The rate coefficients (k) and the activation energies (Ea ) of thermal electron attachment for chlorotrimethylsilane (Si(CH3 )3 Cl), dichlorodimethylsilane (Si(CH3 )2 Cl2 ) and chloromethyldimethylsilane (SiH(CH3 )2 (CH2 Cl)) are reported. This is important for understanding the basic processes occurring in plasmas. The pulsed Townsend technique (known as the electron swarm method) has been applied for the measurements. In this technique, electrons generated by a laser, under a uniform electric field, traverse to an anode and induce a charge on it. In the buffer gas charge grows linearly, but in the presence of a scavenger, electrons are captured, and thus the rate of charge increase slows down with time. From the shape of the pulse, the kinetic parameters are determined. Kinetic parameters from the study of thermal electron attachment by Si(CH3 )3 Cl, Si(CH3 )2 Cl2 and SiH(CH3 )2 (CH2 Cl) were determined for the first time. The corresponding rate coefficients at 298 K are equal to (9.56 ± 0.02) × 10-11 , (6.62 ± 0.02) × 10-11 and (1.24 ± 0.05) × 10-11 cm3 s-1 and Ea values are equal to 0.29 ± 0.01, 0.24 ± 0.01 and 0.31 ± 0.01eV for Si(CH3 )3 Cl, Si(CH3 )2 Cl2 and SiH(CH3 )2 (CH2 Cl), respectively. The experiment was performed in the 298-378K temperature range. The presented results provide important new information about fundamental quantities such as rate coefficients and activation energies for thermal electron capture by chlorinated derivatives of silane. These data can further advance our understanding of thermal electron interactions with chlorosilanes that can be used to control the important species in the plasmas of many modern technologies.

Kinetics of low energy electron attachment to some chlorosilanes in the gas phase

The rate coefficients (k’s) and the activation energies (Ea’s) of thermal electron attachment for SiCH3Cl3, SiH(CH3)2Cl, SiHCH3Cl2 and Si(C2H5)3Cl have been measured. The electron attachment processes in the chlorosilane-carbon dioxide mixtures have been investigated using a Pulsed Townsend technique in the temperature range 298 K-378 K. The increase of the rate coefficients with temperature follows the Arrhenius law and the Ea’s have been obtained from the slope of the ln(k) vs. T−1. The rate coefficients at 298 K are equal to 8.72 × 10−11cm3s−1, 6.72 × 10−11cm3s−1, 16.8 × 10−11cm3s−1 and 3.27 × 10−11cm3s−1 and activation energies are: 0.32 eV, 0.24 eV, 0.25 eV and 0.21 eV, respectively for SiCH3Cl3, SiH(CH3)2Cl, SiHCH3Cl2 and Si(C2H5)3Cl.

Assessment of the self-consistency of electron-THF cross sections using electron swarm techniques: Mixtures of THF–Ar and THF–N2

The pulsed Townsend technique has been used to measure transport coefficients in mixtures of tetrahydrofuran (THF) with N2 and argon. These measurements are the first investigations of swarm transport in gas mixtures with THF, with the drift velocity and effective Townsend ionization coefficient reported for a range of reduced electric fields between 0.23 and 800 Td (1 Td = 10−21 V m2). These transport coefficients are compared with those calculated using a multiterm kinetic theory, using the cross section set developed in our previous studies [N. A. Garland et al., Phys. Rev. A 88, 062712 (2013) and M. J. E. Casey et al., J. Chem. Phys. 147, 195103 (2017)]. The swarm technique of iteratively adjusting cross sections to reproduce experimental transport measurements is subsequently utilized in this study to address the deficiencies in the earlier cross section sets, exposed by the gas mixture measurements. Refinement of the low-energy extrapolation of the quasielastic database cross section and the low-energy extrapolation and magnitude of the dissociative electron attachment cross section are detailed, as well as the adjustments to the two previously proposed neutral dissociation cross sections. These refinements were necessary in order to minimize differences between our measured and calculated transport coefficients.

Computation of electron transport and relaxation properties in gases based on improved multi-term approximation of Boltzmann equation

An understanding of electron kinetics is of importance in various applications of low temperature plasmas. We employ a series of model and real gases to investigate electron transport and relaxation properties based on improved multi-term approximation of the Boltzmann equation. First, a comparison of different methods to calculate the interaction integrals has been carried out; the effects of free parameters, such as vmax, lmax, and the arbitrary temperature Tb, on the convergence of electron transport coefficients are analyzed. Then, the modified attachment model of Ness et al. and SF6 are considered to investigate the effect of attachment on the electron transport properties. The deficiency of the pulsed Townsend technique to measure the electron transport and reaction coefficients in electronegative gases is highlighted when the reduced electric field is small. In order to investigate the effect of external magnetic field on the electron transport properties, Ar plasmas in high power impulse sputtering devices are considered. In the end, the electron relaxation properties of the Reid model under the influence of electric and magnetic fields are demonstrated.

Self-consistency of electron-THF cross sections using electron swarm techniques.

The drift velocity and first Townsend ionization coefficient of electrons in gaseous tetrahydrofuran are measured over the range of reduced electric fields 4-1000 Td using a pulsed-Townsend technique. The measured drift velocities and Townsend ionization coefficients are subsequently used, in conjunction with a multi-term Boltzmann equation analysis, as a further discriminative assessment on the accuracy and completeness of a recently proposed set of electron-THF vapor cross sections. In addition, the sensitivity of the transport coefficients to uncertainties in the existing cross sections is presented. As a result of that analysis, a refinement of the momentum transfer cross section for electron-THF scattering is presented, along with modifications to the neutral dissociation and dissociative electron attachment cross sections. With these changes to the cross section database, we find relatively good self-consistency between the measured and simulated drift velocities and Townsend coefficients.

Thermal electron attachment to chlorinated alkenes in the gas phase

This paper reports the measurements of the rate coefficients and the activation energies of the electron capture processes with various chlorinated alkenes. The electron attachment processes in the mixtures of chlorinated alkenes with carbon dioxide have been investigated using a Pulsed Townsend technique. This study has been performed in the temperature range (298–378)K. The obtained rate coefficients more or less depended on temperature in accordance to Arrhenius equation. The activation energies (Ea’s) were determined from the fit to the experimental data points with function ln(k)=ln(A)−Ea/kBT. The rate coefficients at 298K were equal to 1.0×10−10cm3s−1, 2.2×10−11cm3s−1, 1.6×10−9cm3s−1, 4.4×10−8cm3s−1, 2.9×10−12cm3s−1 and 7.3×10−12cm3s−1 and activation energies were: 0.27eV, 0.26eV, 0.25eV, 0.21eV, 0.55eV and 0.42eV, for trans-1,2-dichloroethylene, cis-1,2-dichloroethylene, trichloroethylene, tetrachloroethylene, 2-chloropropene, 3-chloropropene respectively.

Pressure-dependent mobility of negative ions in mixtures of H2O with Ar

The mobility of negative ions in H2O–Ar mixtures has been measured with a pulsed Townsend technique. It has been found that for a fixed value of the density-normalized electric field strength, E/N, the mobility of the H2O anions is strongly pressure dependent. We have also found that even for a single, total gas mixture pressure, even though at first sight the mobility of the anions seems to follow Blanc’s relation closely, a closer view indicates that the mobilities tend to shift to higher values as the water vapour concentration decreases. In spite of the lack of mass spectrometry to assess the mass and abundance of the drifting anions under specific conditions of E/N, water vapour concentration and gas pressure, the present measurements are strongly indicative of a complex ion transport and ion-molecule reaction scheme of daughter H2O anions in the H2O–Ar mixture.

Electron drift velocities in He and water mixtures: measurements and an assessment of the water vapour cross-section sets.

The drift velocity of electrons in mixtures of gaseous water and helium is measured over the range of reduced electric fields 0.1-300 Td using a pulsed-Townsend technique. Admixtures of 1% and 2% water to helium are found to produce negative differential conductivity (NDC), despite NDC being absent from the pure gases. The measured drift velocities are used as a further discriminative assessment on the accuracy and completeness of a recently proposed set of electron-water vapour cross-sections [K. F. Ness, R. E. Robson, M. J. Brunger, and R. D. White, J. Chem. Phys. 136, 024318 (2012)]. A refinement of the momentum transfer cross-section for electron-water vapour scattering is presented, which ensures self-consistency with the measured drift velocities in mixtures with helium to within approximately 5% over the range of reduced fields considered.

Kinetics of low energy electron attachment to some fluorinated alcohols in the gas phase

Thermal electron attachment processes in the mixtures of CH3CH2OH, CF3CH2OH, CF3CF2CH2OH, (CF3)2CHOH and CH3CH(OH)CF3 with carbon dioxide have been investigated using an electron Pulsed Townsend technique. Measurements were carried out in the temperature range (298–413)K. The obtained rate coefficients depended on temperature in accordance to Arrhenius equation. From the fit to the experimental data points with function ln(k)=ln(A)−Ea/kBT the activation energies (Ea’s) were determined. The rate coefficients at 298K are equal to 3.2×10−13cm3s−1, 5.1×10−11cm3s−1, 1.1×10−10cm3s−1, 3.0×10−10cm3s−1 and 2.6×10−11cm3s−1 and activation energies are: 0.37eV, 0.25eV, 0.28eV, 0.20eV and 0.23eV, respectively for CH3CH2OH, CF3CH2OH, CF3CF2CH2OH, (CF3)2CHOH and CH3CH(OH)CF3.

The influence of the temperature on electron attachment to some Br-substituted alkanes

Thermal electron attachment rate coefficients and activation energies for CH3CH2Br, CH3CH2CH2Br, CH3CHBrCH3, CF3CHBrCH3, CH3(CH2)2CH2Br and CH2F(CH2)2CH2Br have been measured using the Pulsed Townsend technique over the temperature range (298–378)K. The corresponding rate coefficients (k’s) at 298K were equal to 9.3±2.10×10−13, 2.9±0.20×10−12, 2.7±0.07×10−12, 1.1±0.06×10−9, 6.6±1.10×10−12 and 2.3±0.3×10−10cm3s−1, respectively. Activation energies (Ea’s) were determined from the fit of the Arrhenius function to the experimental points and were found to be equal to 0.35±0.002, 0.35±0.004, 0.31±0.004, 0.19±0.002, 0.33±0.006 and 0.22±0.002eV, respectively for CH3CH2Br, CH3CH2CH2Br, CH3CHBrCH3, CF3CHBrCH3, CH3(CH2)2CH2Br and CH2F(CH2)2CH2Br molecules.

Measurement of Electron Swarm Parameters in Nitrous Oxide

This study has measured the density-normalized effective ionization coefficients (α−η)/N, the electron drift velocity Ve and the diffusion coefficient DL in nitrous oxide (N2O) using a pulsed Townsend technique. The range of the overall density-normalized electric field strength E/N is from 100 Td to 400 Td (1 Td=10−17 V·cm2). From the above plots of (α−η)/N, we have derived the limiting field strength, (E/N)lim ≈ 150 Td, which is the value of E/N at which (α−η)/N = 0.

Determination of Electron Swarm Parameters in Pure CHF3 and CF4 by a Time-Resolved Method

The density-normalized effective ionization coefficient (α − η)/N (α and η are the ionization and attachment coefficients respectively), the electron drift velocity Ve and density-normalized longitudinal diffusion coefficient NDL in trifluoromethane (CHF3) and carbon tetrafluoride (CF4) were measured using a pulsed Townsend technique over a wide E/N range. From the plots of (α − η)/N, we have derived the limiting field strength, (E/N)lim, which is valid for the analysis of insulation characteristics and applications to power equipment. Comparisons of the electron swarms parameters between CHF3 and CF4 have been performed, and the global warming potential (GWP) is also taken into account.

Drift and clustering of daughter negative ions of H2O in parent gas

The mobility of daughter negative ions of H2O in parent gas has been measured with a pulsed Townsend technique over the density-reduced field strength, E/N, range 9–100 Td and a pressure range 2–16 Torr. It has been found that the mobility of the anions is dependent on the gas pressure. Using a transport theory considering the influence of the permanent dipole field of H2O, we have found that the pressure-dependent mobilities can be associated with a series of cluster ions of the type OH−(H2O)n (n = 1–3), with the mass of the cluster species increasing with the total gas pressure. Also, the mobility of H− and OH− could be estimated. Using a Townsend avalanche simulator we have been able to explain the measured ionic currents in terms of an ion–molecule reaction scheme with a single set of swarm and reaction coefficients for each value of the density-reduced field strength, E/N, at several pressures. Regarding the positive ions, the only drifting ion is H3O+, the mobility of which could be estimated. The rate constants relative to the formation of the OH−(H2O)n (n = 1–3) species were also derived from this study.

Measurements and analysis of electron transport coefficients obtained by a pulsed Townsend technique

A review of a wide range of electron swarm studies in several pure gases and gas mixtures is given. These studies include the determination of the cross section set for electrons in C2H2F2 (R134a) based on recent measurements of transport data, the re-analysis of the cross sections for electrons in N2O and its mixtures with N2 and SF6 and, finally, the analysis of electron transport in N2–Ar and Xe–He mixtures. It was found that in the case of R134a further studies of the characteristic energy are needed for its mixtures with argon in pure gases in order to obtain a reliable set of cross sections. For N2O, a set has been developed that fits a wide range of data. However, some verification of significant changes in the shape of the attachment cross section should still be done. In two different sets of data for the mixtures of Xe and He and of Ar and N2, the existing cross sections do a very good job throughout most of the energy range, although some small adjustments may be sought at the higher end of the relevant energy range for xenon. In this paper we summarize the work already described in separate papers for each of the He–Xe and Ar–N2 mixtures, and we present here a number of transport coefficients and analyses that were not included in the original papers.

Transport coefficients and cross sections for electrons in N2O and N2O/N2 mixtures

A standard swarm analysis of electron scattering cross sections in nitrous oxide (N2O) is presented. The experimental results for drift velocities and effective ionization coefficients (differences between the ionization and attachment coefficients), obtained over an extended range of E/N (electric field normalized to the gas number density) by the pulsed-Townsend technique, are compared with the numerical solution of the Boltzmann equation. Our analysis shows that commonly used sets of cross sections have to be modified in order to fit the new experimental data, in particular the dissociative cross sections for attachment and electronic excitation (with a threshold energy of around 4.0 eV). Using a single set of cross sections it was possible to fit both the data for pure N2O and those for the N2O/N2 mixtures with 20%, 40%, 60% and 80% N2O.

The influence of the temperature on electron attachment to some halocontaining molecules

Thermal electron attachment rate coefficients for CH 2ClCHClCH 2Cl, CH 2ClCH 2Br, CH 2ClCH 2CH 2Br and CF 2ClCFCl 2 have been measured using the Pulsed Townsend technique over the temperature range T = 298–358 K. The corresponding rate coefficients at 298 K are equal to 1.7(4) × 10 −10, 7.9(15) × 10 −10, 3.4(5) × 10 −10 and 3.1(1) × 10 −8 cm 3 molec. −1 s −1, respectively. With rising temperature we have observed an increase of the rate coefficients k( T), which shows an Arrhenius-type behaviour. Activation energies E a of 0.16(1) eV (CH 2ClCHClCH 2Cl), 0.12(1) eV (CH 2ClCH 2Br), 0.20(1) eV (CH 2ClCH 2CH 2Br) and 0.08(1) eV (CF 2ClCFCl 2) were determined from the fit to the experimental data points with a function ln( k) = ln( A) − E a / k B T.

The Mobility of Negative Ions in $\hbox{CF}_{3} \hbox{I}$, $\hbox{CF}_{3}\hbox{I}{-}\hbox{N}_{2}$ , $\hbox{CF}_{3}\hbox{I}{-}\hbox{Ar}$, $\hbox{CF}_{3}\hbox{I}{-}\hbox{Xe}$, $\hbox{C}_{2}\hbox{F}_{6}$, and $\hbox{CHF}_{3}$, and of Positive Ions in $\hbox{C}_{2} \hbox{F}_{4}$ and $\hbox{c-C}_{4}\hbox{F}_{8}$

Using a pulsed Townsend technique, the drift velocity and the mobility of positive ions in C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> and C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> and those of negative ions in C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> , CHF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , and CF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> I and its mixtures with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , Ar, and Xe are reported. The overall range of the density-normalized electric field is 4-600 times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-17</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sup> ldrcm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Ion identification is provided by means of previous studies on partial ionization and electron attachment. Thus, it is suggested that the predominant drifting ion in the discharge is C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> for C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> and c-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> , F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> for C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> and CHF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , and I <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> for CF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> I. The use of more comprehensive theories of ion motion considering the influence of a permanent dipole moment (CHF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> and CF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> I) has provided reasonable agreement between low-field measured and calculated mobilities. The mobility of negative ions in CF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> I-N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , CF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> I-Ar, and CF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> I-Xe mixtures agrees reasonably well with the predicted values by Blanc's law.