Absolute electron impact ionization cross-sections for CF₄: Three dimensional recoil-ion imaging combined with the relative flow technique

Fully or partly halogenated hydrocarbons such as perfluorocarbons (PFCs), chlorofluorocarbons (CFCs), and hydrochlorofluorocarbons (HCFCs) are among the most potent atmosphere-damaging molecules listed under the United Nations Framework Convention on Climate Change (UNFCCC).^1,2 Perfluorocarbons (PFCs) are potent greenhouse gases (GHGs) with exceedingly long atmospheric lifetimes of 10 000 to more than 50 000 years. CF₄ (PFC − 14) is the simplest PFC with the longest-lived greenhouse gas known currently estimated at 50 000 years representing a permanent alteration to the atmosphere.³ They accumulate in the lower layer of the atmosphere, the troposphere, absorb infrared radiation, and trap heat in the atmosphere, which results in continuous global warming and climate change.

Several experimental studies on the ionization by electron impact of PFCs (like CF₄) are reported in the literature, where different methodologies are employed. Christophorou and co-workers (Refs. 4–6) compiled the available information on total and partial electron impact cross-sections (TICS and PICS, respectively). In their first work in 1996,⁴ they presented a compilation of electron impact cross-section measurements, and based on the assessment of that data, they recommended values for various TICS and PICS. Later in 1999,⁵ they updated their previously recommended cross-sections by including data from the TICS of Rao and Srivastava⁷ and Nishimura et al.⁸ In 2004,⁶ they added data on the TICS and PICS of Sieglaff et al. and Torres et al.^9–11 and TICS of Bart et al.¹² 

In this work, we describe a new methodology to determine absolute TICS and PICS by applying three-dimensional ion imaging using a recoil ion momentum spectrometer (RIMS)¹³ and a mixing target gas setup. The mixing setup procedures apply the known relative flow technique (RFT)¹⁴ and were implemented to convert the relative cross-sections measured by the RIMS into absolute values. The validation of the method was applied to CF₄ as a test molecule, which, after ionization, ejects energetic ions. The RIMS makes it possible to analyze the energy distribution of the ions and to judge if ions are not fully collected. In addition, choosing the conditions and the reference gas appropriately in the mixing target procedure avoids inaccuracies in the conversion of relative cross sections into absolute ones.^15,16 The goal after validation of the methodology is to apply it to other molecules, such as halogenated hydrocarbons, chloro- and fluorocarbons, and hydrochloro- and hydrofluorocarbons. For comparison with our results, we will use the cross-sections of Refs. 5 and 6 throughout this work.

It is important to note that large discrepancies are found in published total and partial ionization cross-section data⁶ (see Figs. 1 and 4). The origin of these differences in the cross-sections could be mainly due to two factors: the normalization procedure and the collection efficiency of the ionic energetic species resulting from molecular dissociation. One of the goals of the methodology presented here was to avoid the use of adjusting terms obtained by simulations and corrections related to discrimination effects. The loss of specific fragment ions in the spectrometer due to their excess kinetic energies leads to reduced ion collection efficiency. Another constraint in the measurements is the micro-channel plate (MCP) efficiency, which depends on the molecular mass of the ion, its impacting kinetic energy on the MCP, and the open area ratio (OAR) of the MCP, which must be taken into account.

In Sec. II, we present in detail the experimental set-up and data analysis procedure, based on the electron projectile-recoil ion detection technique that enables the measurement of absolute total and partial molecule ionization cross-sections for an effusive gas mixture jet target set-up. The method is applied to the ionization of CF₄ by electron impact with energies ranging from 30 to 1000 eV. The results of the measurements are presented and compared with available experimental and theoretical data in Sec. III. It is divided into subsections, where the discussions are focused on comparing the experimental methods previously used and the derived data. In Sec. IV, the results are summarized.

The recoil ion momentum spectrometer (RIMS) and the relative flow technique (RFT) setups used in the present study are described in the following.

The recoil ion momentum spectrometer (RIMS) configuration used to measure TICSs and PICSs has been described elsewhere¹⁷ and a description is presented here, including modifications performed on the setup. A schematic drawing of the setup is shown in Fig. 1.

The pulsed-electron-beam time-of-flight mass spectrometer apparatus was modified by the addition of a needle required for studies where the use of a supersonic gas jet is not feasible. One of the main reasons why supersonic jets cannot be used is due to the limited availability of gas samples, as in the case of perfluorocarbons (PFCs), chlorofluorocarbons (CFCs), and hydrochlorofluorocarbons (HCFCs) molecules, which will be consumed very quickly if used with the supersonic jets. The ions produced from the electron–molecule collisions were measured using RIMS with a crossed geometry of electron and molecular beams. The electron beam is pulsed at a repetition rate of 15.75 kHz by applying a voltage pulse with a length of 200 ns. It is focused close to the exit of a needle by three lenses and magnetically guided by Helmholtz coils placed outside the vacuum chamber. This needle with an inner diameter of 1.0 mm is pointing out parallel to the pusher plate and perpendicular to the time-of-flight spectrometer axis, therefore expanding the gas into the interaction region. The effusive gas flow is controlled by a precision leak valve and the pressure in the chamber is kept around 1.5 × 10⁻⁷ mbar during operation of the gas beam. The target density in the effusive beam is at least two orders of magnitude higher than in the supersonic gas jet and the gas is at room temperature.

The ionized species created in a collision are collected by a short two-stage spectrometer with a total length of 11 cm and nine electrode rings of 9 cm inner diameter, each set at 10 mm apart, divided into three sections. The drift length is twice the acceleration length satisfying the Wiley–McLaren geometry¹⁸ for the time-focusing condition. This is needed to prevent the spread of flight times of the ions with different starting positions due to the size of the interaction region of 2 mm along the spectrometer axis. The first two electrodes (electrodes 1 and 2), as shown in Fig. 1, define the pusher region, where the needle is positioned at half the distance between them. While the projectile pulse traverses the spectrometer, the interaction region is kept field-free to avoid any deflection of the electron beam. With a delay of 100 ns, voltage pulses of +100 V and +40 V are applied to the pusher electrode 1 and the needle, respectively. Thus, the ions are extracted from the interaction region and pushed into the acceleration section. This region is defined by the set of electrodes from 2 to 5, which are connected in series by 100 kΩ resistors, where electrode 2 is at ground and electrode 5 at −184 V. The voltage gradient of 224 V/35 mm accelerates and drives the ions into a field free region of 70 mm defined by electrodes 5–9 and two subsequent grids kept at −184 V. A homogeneous and strong electric field is applied between the final grid and front of the MCPs set at −184 and −2600 V, respectively, accelerating the ions to higher energies before hitting the front MCP.

The pulse settings on the spectrometer, pusher, and needle are triggered by the same signal applied to the electron beam, and pusher plate and needle voltages are set by distinct pulse generators with filters defining quite sharp rise and fall signals. Different voltage settings on the pusher and needle were probed with commitment to optimize the time-focusing condition as well as the detection of the momenta distributions of the ions.

Time difference between the electron pulse signal and the MCP signal provides the time of flight information. The electron cloud produced by the MCPs hits on a position-sensitive delay-line anode (DLD configuration), which records the X and Y-hit position distribution of the ions on the detector.¹⁹ The time and hit position signals are fed to a multi-hit time-to-digital converter, and the raw data events are recorded in list file mode by the Cobold data acquisition and analysis software.²⁰ The X–Y coordinates of the setup are defined as follows: the X-axis (horizontal) is along the electron beam and the Y-axis (vertical) is perpendicular to the electron beam and the extraction direction (Fig. 1).

The majority of the dissociating ions of CF₄ can have high kinetic energies that can reach up to 15 eV in dissociative double ionization channels.^21–23 To collect those ions that are emitted in the transversal plane, a detector with large MCPs of 80 mm in diameter in a chevron configuration is used. Figure 2(a) shows a two dimensional map (2D-map) of the Y position and time-of-flight distribution of the ions for events coming from single hits with 200 eV collision energy.

The projection onto the Y-axis of the 2D map shown in Fig. 2(b) reveals that essentially all ions with low to high momenta/kinetic energies are collected. There are no significant losses due to the kinetic energy of the ions. The sharp drop in intensity shown at Y = 39 mm in Fig. 2(b) indicates that a small fraction of the F⁺ distribution is not measured. It was determined to be below 1% and can be considered negligible [see the intensity log scale in Fig. 2(b)]. The projection onto the X-axis of the 2D-map corresponds to the time of flight spectrum of single ions of CF₃ and Kr (T₁ spectrum). The TOF peaks of $CF3+$⁠, $CF2+$⁠, CF⁺, F⁺, $CF32+$⁠, and $CF22+$ as well as of the mixing gas krypton, Kr⁺, Kr²⁺, and Kr³⁺, clearly discriminated in gray filled pattern, can be observed in Fig. 2(c). The time resolution of the setup allowed the discrimination of krypton isotopes, which occur in nature as a mixture of six different, stable isotopes with masses of 78 (0.4%), 80 (2.3%), 82 (11.6%), 83 (11.5%), 84 (57.0%), and 86 (17.3%). The parent ion $CF4+$ is not expected to be detected because its ionic states are not stable but dissociate within femtoseconds.¹¹ The production of $CF3+$ dominates over other dissociation channels, which are almost an order of magnitude smaller.

The axial symmetric construction of the recoil ion spectrometer (Fig. 1) images the longitudinal (p_z) and transversal momentum components of ions $(px2+py2)$⁠. The longitudinal Z component p_z relies on the time-of-flight of the ion, and the transversal X and Y components depend on the hit (X, Y) position of the ion on the detector and its TOF. The momenta are derived by applying Newton’s equations of motion. Figure 3 shows the image for the hit X–Y position of the $CF3+$ ion on the detector for impact of 200 eV electrons, selecting the events correlated with the time-of-flight of the $CF3+$ ion.

The ion–ion pair production was also measured as shown in Fig. 4(a). The figure presents the 2D-map of coincident ion–ion detection, where the horizontal and vertical axes denote the TOF of the first and second ions to reach the detector, respectively. The fragmentation channel $CF42+→CF3+$ + F⁺ is a pure Coulomb-explosion channel, while all others are incomplete Coulomb-explosion channels, where three or more species are generated involving the ejection of neutral fragments: $CF2+$ + F⁺ + F, CF⁺ + F⁺ + 2F, C⁺ + F⁺ + 3F and F⁺ + F⁺ + CF₂. As outlined, in the five dominating channels, the major ion–ion pair formation corresponds to the ejection of one fluorine atomic ion. To the extent that this assumption is valid, Fig. 4(b) depicts the projection onto the vertical axis (Y-axis) of the 2D-map for two T₁ time windows, as indicated by the red and blue boxes in Fig. 4(a). This produces two coincidence spectra (T₂-coinc spectra) where the first ion detected was C⁺ (red) and F⁺, respectively. Figure 4(c) presents the TOF spectrum of single events showing the intensities of the dissociative single ionization channels [Fig. 2(c)]. Here, Fig. 4(c) is included for a better comparison of the contribution of the low intensity fragmentation channels for single ionization with the intensities of the same fragments originating from double ionization. For all measured electron impact energies, the event counts from dissociative double ionization are lower than those from dissociative single ionization as shown in Figs. 4(b) and 4(c). Triple ionization was considered negligible as already verified in Ref. 23. The detector counting rate was maintained at around 1000 counts/s compared to a projectile pulse rate of 15.75 kHz to avoid a high random coincidence rate.

For comparison, electron impact measurements on CF₄ were done using a high resolution time-of-flight mass reflectron spectrometer. A detailed description of the setup is reported in Ref. 28. For 200 eV electrons, Fig. 5 shows the time-of-flight spectrum acquired by the reflectron, which is indicated by a red solid line superimposed with the present measurements described by a blue solid line. It demonstrates clearly the disadvantage of measuring absolute cross-sections with such a spectrometer. The comparison between the T₁ spectrum measured with the RIMS setup and the reflectron one shows that the latter was adequate for high mass resolution measurement of all ions produced in the electron–molecule collision, but on the other hand, the ions emitted with high momenta/kinetic energies were not fully collected [Figs. 5(a)–5(c)]. The line structure with two maxima for an individual ionic fragment stems from losses of ions, which are emitted transversally to the spectrometer axis. These ions have small longitudinal momenta and would show up in the line center. On the other hand, the spectrometer has higher acceptance for ions emitted forward and backward along the spectrometer axis with small transversal momentum, which result in the two observed peaks. Only simulations with previous knowledge of the kinetic energy distribution of each fragment ion species can correct these data. The peak intensities of all spectra shown were normalized to the peak maxima of the $CF3+$⁠.

The recorded intensities of the ions measured by the RIMS were converted into absolute ionization cross-sections using the RFT.^14,29–31 Here, the CF₄ gas is mixed with an equal amount of the reference gas krypton, for which accurate absolute cross section data are available. To prepare the mixed gas sample, CF₄ gas and the Kr reference gas were filled first into a small reservoir in equal amounts (50 mbar each), which were measured with a capacitance manometer (Fig. 1). Then the mixed gas was allowed into a second reservoir with a four times larger volume than the small one. Diffusion leads to the mixing of the two gases until the distribution is uniform throughout the volume. Since the diffusion time required to achieve equilibrium distribution is proportional to gas pressure and, therefore, inversely proportional to the volume,³² the larger reservoir is advantageous for faster mixing. Then, a second gate valve is opened, and the mixture is injected into the system through an ultra-fine leak valve and a capillary needle. The flow was monitored by measuring the increase in chamber pressure before starting the measurements and after stopping the experiments, and the pressure in the injection line was monitored constantly. It was verified that the volume of gas loaded in the large reservoir and the flow controlled by the leak valve were set in the best condition and that changes in pressure were negligible.

The ion detection efficiencies of the MCP depend on different factors such as its open area, the MCP operating voltage, the ion mass/charge ratio, and the impact energy of the ions on the MCP. The MCPs used in the experiment were standard ones with an open area of 52%. The operating voltage was maximized, and the threshold adjustment of the constant fraction discriminator for the MCP signal was minimized. The ions were pre-accelerated by −2600 V before hitting the MCP. For the analysis of the relative cross sections for different ions, it must be considered that ions with a high mass/charge ratio are usually detected with less efficiency than those with lower ones. There are several procedures described in the literature for determining the detection efficiencies of MCPs.^33,41–49 In the present work, the detector efficiency approach recommended by Krems et al. was followed.³³ They provide an analytic formula to express the efficiencies for ions that scale to a single curve as a function of the impact energy divided by the square root of the ion mass.^33,41 To reduce the influence of this correction on the absolute cross section calibration procedure, it is desirable to have similar efficiencies for the ions from the reference gas and the ions from CF₄.

The ratios of the efficiency for Kr⁺ and efficiencies for CF₄ fragment ions $(εKr(Kr+)/εCF4(a))$ adopted in the analysis are shown in Fig. 7. They range from 0.95 for $CF3+$ down to 0.69 for the lighter C⁺.

To test our absolute cross section calibration method and in particular the detector efficiencies entering, we produced absolute cross-sections of Kr²⁺ and compared with literature data. Therefore, as described in Eqs. (1) and (8), the true intensities of the krypton ions Kr⁺ and Kr²⁺ were obtained from the measured line intensities and the detection efficiencies. Finally, using these true intensities and published absolute cross-sections for Kr⁺, the σ_Kr(E_i, Kr²⁺) was calculated. A comparison of σ_Kr(E_i, Kr²⁺) between the present derived values and literature values of σ_Kr(E_i, Kr²⁺) (Fig. 8) shows good agreement, providing confidence that the present measurements and the evaluation of the ion detection efficiencies are reliable.^{39,40,50–54}

The linearity in the ion production with the density of the samples in the gas mixture was examined for different pressure ratios (R_gas) of the CF₄ and Kr. Primarily, equal pressures of 50 mbar for both gases were selected. Then the production of $CF3+$ and Kr⁺ for the mixing ratios 3:1, 2:1, 1:1, 1:2, and 1:3 of CF₄ and Kr gases were measured. In a second step, the ratio of $Nt(CF3+)$ to N^t(Kr⁺) (R_counts) was divided by the respective gas mixing ratios (R_gas), and an average constant value was obtained (Fig. 9). This result shows that both gases are mixed homogeneously and the flow rates are in accordance with their mixing ratios.

From the theoretical side, several calculations of total ionization cross-sections as a function of electron energy are available in the literature based on different models in an effort to improve the agreement between models and accessible experimental data at the time of the calculations. The most widely accepted models are the binary-encounter-Bethe BEB and dipole BED method,^55–57 the Deutsch and Märk DM formalism,⁵⁸ and the modified additivity rule MAR.⁵⁹ In the case of molecules containing heavy atoms, like fluorine, electron correlations and empirical corrections have been introduced to improve the calculations. For example, Deutsch and Märk modified the Lotz formulas for molecules containing fluorine to describe the cross-section anomaly of fluorine molecules.⁶⁰ In Fig. 10, the present data are compared to several calculations and to Christophorou et al.^4–6 recommended values, and an average of the results of some datasets.

Binary-Encounter-dipole Bethe (BEB) and Binary-Encounter-dipole Born (BED) models known as classical-BEB,^61,62 Kim–BEB,^12,55,63 RHF–BEB (restricted Hartree Fock wave functions-BEB),^8, CAS–BEB (complete-active-space SCF wave functions-BEB),^8, AE–BEB (all electrons BEB),^64, siBEB^8, ECP–BEB (effective core potentials-BEB),^64, α-BEB (target polarizability BEB),⁶⁴ Additivity rule-BEB,^62, siBED (simplified iBED⁶⁵ with shielding long-range dipole potential),⁶³ semiempirical Harland and Vallance (HV)^10,66 DM methods,^10,12 and Modified Additivity Rule (MAR) formalism¹⁰ were proposed to best describe the CF₄ experimental cross-sections in shape, energy of the maxima, and the maximum of the total ionization cross-section. Molecular ab initio information required by the BEB, BED, and DM models were included in the calculations at several quantum chemistry levels and a series of basis sets, with and without electron correlation, Jahn–Teller splitting, and interaction potentials.

The peak maxima of the theoretical cross-sections range from 4 × 10⁻²⁰ m^2 64 in better agreement with the present value to 10 × 10⁻²⁰ m².⁶² The positions of the maxima vary from 75⁶² to 140 eV.^12,63 The present data do not allow the precise determination of the energy position of the maximum, and for that purpose, additional measurements are needed around electron energies of 100 eV.

The CF₄ molecule is one of the most experimentally studied fluoromethanes. Figure 11 shows the present data and collects the sets of reported single ionization cross-section Refs. 8–10, 12, and 67–73. The doubly ionized meta-stable ions $CF22+$ and $CF32+$ were not included in the single ionization cross-section evaluation.

The uncertainties of the present data are the combined uncertainties present in the two techniques, yielding in total and statistical uncertainties of around 10%. The accuracy limit of extracting the ion’s intensities was estimated to be significantly smaller, as all ions were well distinguished from each other by their time-of-flight and full momentum. The density proportion of the gas mixture (1:1) was well fixed by selecting a total gas pressure (100 mbar) in the small container. The uncertainties in previous absolute cross-section measurements are partially due to the various corrections applied.

In all the datasets, except the data in Ref. 73, the cross-section maxima are higher than in the present data. The displacement of the energy positions of the maxima is less pronounced in the experimental datasets than in the theoretical predictions. Earlier experimental works were further revised or revisited as discussed extensively in Refs. 4–6. The corrections applied to those experimental works due to undetected energetic fragments that are lost in the collection and detection steps and due to the inclusion of false events in the single ionization spectrum when for ion pair production one of the ions is not detected might have steadily overestimated the total and partial single ionization cross-sections.

In summary, this work reports a new experimental methodology to extract absolute PICS and TICS using a recoil ion imaging technique (RIMS) and the relative flow technique (RFT). The method was validated through several test procedures and data comparisons with theoretical and experimental results available in the literature. Revisiting the theoretical results, these indicated that the cross-sections based on BEB and DM models are closely dependent on the electron-collision description and that the electron correlation always increases the BEB cross-sections.

The present experimental data are obtained with 4π solid angle acceptance for all ions, even with significant kinetic energies. Therefore, no corrections due to reduced transmission of the spectrometer are required, which is essential for the determination of precise absolute cross sections. The loss of energetic ions implies the requirement of ion trajectory simulations as a resource to correct the experimental deficiencies. For this purpose, previous knowledge of the kinetic energy distribution of the ions is needed, and this information is not always available. In the literature, cases are found where corrections of previous total and partial cross-section values were reported after the review of the signal processing and the addition of ion trajectory simulations and efficiency factors. These corrections have substantially affected the published experimental data. Therefore, the methodology presented here ensures the precise determination of absolute cross sections and minimizes the inclusion of correction factors, which would enhance inaccuracies.

Finally, the single ionization cross-sections provided in the present work are corrected for false events coming from ion-ion pair channels, that is, from dissociative double ionization. Therefore, the methodology presented here ensures the precise determination of absolute cross sections and minimizes the inclusion of correction factors, which enhances inaccuracies.

The project 21GRD02 BIOSPHERE has received funding from the European Partnership on Metrology, co-financed by the European Union’s Horizon Europe Research and Innovation Program and the Participating States. Funder ID: 10.13039/100019599. Grant No. 21GRD02 BIOSPHERE.

The authors have no conflicts to disclose.

W. Wolff: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). M. Dogan: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). H. Luna: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). L. H. Coutinho: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). D. Mootheril: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Woonyong Baek: Project administration (supporting); Resources (supporting); Writing – review & editing (equal). T. Pfeifer: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). A. Dorn: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

Data supporting this study are openly available. The research is declared as open access under license CCBY4.0.