Ionization and Attachment Coe ﬃ cients in C 4 F 7 N Gas Measured by the Steady-State Townsend Method

: The normalized Townsend ﬁrst ionization coe ﬃ cient α / N and normalized attachment coe ﬃ cient η / N in pure C 4 F 7 N were measured by using the steady-state Townsend (SST) method for a range of reduced electric ﬁelds E / N from 750 to 1150 Td at room temperature (20 ◦ C). Meanwhile, the e ﬀ ective ionization coe ﬃ cients are obtained. All SST experimental results show good agreement with pulsed Townsend (PT) experiment results. Comparisons of the critical electric ﬁelds of C 4 F 7 N with SF 6 and other alternative gases such as c-C 4 F 8 and CF 3 I indicate that C 4 F 7 N has a better insulation performance with a much higher normalized critical electric ﬁeld at 959.19 Td.


Introduction
As is well known, sulfur hexafluoride (SF 6 ), with a good insulation performance and thermal stability, is widely used as an insulation gas and arc quenching medium in many fields such as high-voltage engineering and electrical power applications [1,2]. Unfortunately, as one of the six greenhouse gases, SF 6 has an extremely high global warming potential (GWP 100 ) at 23,500 times that of CO 2 [3]. Thus, in order to slow down global warming, searching for an environment-friendly insulation gas to reduce the use of SF 6 is of great importance.
During the last decades, there has been some research about the discharge characteristics of c-C 4 F 8 [4][5][6] and CF 3 I [7][8][9], which have been thought of as potential alternative gases to SF 6 . Recently, as another newly potential substitutional insulation gas of SF 6 , fluoronitriles (C 4 F 7 N, also known as 3M Novec-4710), which have a GWP value of 2100, have been designed and have attracted great attention [10]. Although C 4 F 7 N gas has a good insulation performance, because of its high boiling temperature, it has to be mixed with other buffer gases such as CO 2 to adapt to the operating conditions under high gas pressure [11]. Nevertheless, it is worthy to obtain the basic electron swarms of C 4 F 7 N, such as the ionization coefficient α and attachment coefficient η, which can be used to evaluate the insulation performance of gases [12].
However, it should be noted that there has been less investigation on the ionization coefficients and attachment coefficients in C 4 F 7 N. It has been reported once that the normalized effective ionization coefficient (α − η)/N within a small range of reduced electric fields (per gas density N) E/N was obtained with the steady-state Townsend (SST) method by Nechmi et al. [13]. The electron rate and transport coefficients in pure C 4 F 7 N were obtained with the pulsed Townsend (PT) method by Chachereau et al. [14]. In the present work, both normalized ionization and normalized attachment coefficients, as well as effective ionization coefficients of C 4 F 7 N, were measured by the SST method, a kind of method which has been widely used to measure these coefficients in different gases like SF 6 [15][16][17], c-C 4 F 8 [4], CF 3 I [8], and so on. It should also be noticed that although the SST method has been well developed during the last decades, and the innovation of the method itself may not be high, the experiments using this method to measure and obtain the discharge parameters and evaluate the insulation abilities of new insulation gases are still significant.

Experiments
The experiments were carried out on an SST apparatus setup in Wuhan University, which the details have been described in previous work [18,19]. The reliability of this SST apparatus has been verified by experiments on known gases such as SF 6 and N 2 , which showed this SST apparatus has great measurement accuracy (<2%) [19]. The theoretical equations used to obtain the experimental results have been introduced as well. Through the update of vacuum-tight gaskets, the background vacuum degree in the ionization chamber can reach~1.0 × 10 −5 Pa at room temperature with a leak rate less than 0.10 Pa/h, which can minimize the effect of the pressure change on experimental results. In the present study, the range of reduced electric fields E/N applied for the SST experiment varied from 750 to 1150 Td (1 Td = 10 −21 Vm 2 ), since the insulation performance of C 4 F 7 N is much better than SF 6 as reported [13,14]. The purity of C 4 F 7 N gas (produced by Beijing Yuji Science and Technology Co., Ltd., China) used in the present study was more than 99.6%, and the impurities were mainly air (~0.3%). The gas pressure was 500 Pa at 20 • C. The initial electron current I 0 of the electron avalanche was about 4 pA, and current I in the nonself-sustained discharge stage was also on the order of picoampere (pA).

Ionization and Attachment Coefficients
The normalized ionization coefficient α/N and the attachment coefficient η/N of C 4 F 7 N gas for 750 Td < E/N < 1150 Td were measured respectively. The results were compared to that of SF 6 gas and shown in Figure 1. It was found that with an increasing E/N, the α/N of C 4 F 7 N showed a growing trend, while the η/N showed a clear decreasing trend, which were similar to that of SF 6 [3]. Meanwhile, compared to SF 6 gas, it was apparent that the values of η/N in C 4 F 7 N were much higher than that of SF 6 for the same E/N, which could be explained with the attachment cross-sections in different gases. The higher the attachment cross section is, the stronger the ability of electron attachment is. The total attachment cross-sections of C 4 F 7 N [14], SF 6 [9], and other gases [9,20] have been compared and plotted in Figure 2. As reported [14], the total attachment cross-section in C 4 F 7 N was larger than that of SF 6 above 0.1 eV, while the values of α/N were a little bit smaller than that of SF 6 when E/N < 900 Td. When E/N > 900 Td, the values of α/N in C 4 F 7 N were a little bit higher than that of SF 6 . Therefore, for C 4 F 7 N and SF 6 with similar values of ionization coefficients, C 4 F 7 N had a better insulation performance due to the much higher attachment coefficient than that of SF 6 .  The α/N and η/N measured by the SST method in this work have also been compared to the PT method measured by Chachereau et al. [14], which are plotted in Figure 3. It should be noted that the values of α/N and η/N used for comparisons with the PT method were not given directly in Chachereau's work; they were calculated from parameters such as electron drift velocity (we), ionization rate coefficient (ki), and attachment rate coefficient (ka). It can be found that the trends of varying α/N and η/N in this work showed good agreement with PT experiments. Significantly, the fluctuation of PT was much larger than that of SST, which may be caused by the different experimental principles and conditions, such as a much lower pressure (100 Pa), in the PT experiment.

Effective Ionization Coefficients
The normalized effective ionization coefficient (α − η)/N of C4F7N, in a range of E/N from 750 to 1150 Td, at 20 °C was obtained as well. Figure 4 presents the value (α − η)/N as a function of E/N in C4F7N, and its comparisons with SF6 [3], c-C4F8 [4], CF3I [7], C4F7N [13,14], and C4F7N/N2 mixtures [18] are reported. Notably, the E/N of C4F7N was much greater than other kinds of gases for the same (α − η)/N, which suggests that the insulation ability of C4F7N is much stronger. Once the C4F7N gas mixed with buffer gas N2, the insulation performances of the mixtures were much weaker than pure C4F7N, since N2 is an electrically neutral gas whose attachment coefficients is 0. Meanwhile, the variety of (α  The α/N and η/N measured by the SST method in this work have also been compared to the PT method measured by Chachereau et al. [14], which are plotted in Figure 3. It should be noted that the values of α/N and η/N used for comparisons with the PT method were not given directly in Chachereau's work; they were calculated from parameters such as electron drift velocity (we), ionization rate coefficient (ki), and attachment rate coefficient (ka). It can be found that the trends of varying α/N and η/N in this work showed good agreement with PT experiments. Significantly, the fluctuation of PT was much larger than that of SST, which may be caused by the different experimental principles and conditions, such as a much lower pressure (100 Pa), in the PT experiment.

Effective Ionization Coefficients
The normalized effective ionization coefficient (α − η)/N of C4F7N, in a range of E/N from 750 to 1150 Td, at 20 °C was obtained as well. Figure 4 presents the value (α − η)/N as a function of E/N in C4F7N, and its comparisons with SF6 [3], c-C4F8 [4], CF3I [7], C4F7N [13,14], and C4F7N/N2 mixtures [18] are reported. Notably, the E/N of C4F7N was much greater than other kinds of gases for the same (α − η)/N, which suggests that the insulation ability of C4F7N is much stronger. Once the C4F7N gas mixed with buffer gas N2, the insulation performances of the mixtures were much weaker than pure C4F7N, since N2 is an electrically neutral gas whose attachment coefficients is 0. Meanwhile, the variety of (α The α/N and η/N measured by the SST method in this work have also been compared to the PT method measured by Chachereau et al. [14], which are plotted in Figure 3. It should be noted that the values of α/N and η/N used for comparisons with the PT method were not given directly in Chachereau's work; they were calculated from parameters such as electron drift velocity (w e ), ionization rate coefficient (k i ), and attachment rate coefficient (k a ). It can be found that the trends of varying α/N and η/N in this work showed good agreement with PT experiments. Significantly, the fluctuation of PT was much larger than that of SST, which may be caused by the different experimental principles and conditions, such as a much lower pressure (100 Pa), in the PT experiment.

Effective Ionization Coefficients
The normalized effective ionization coefficient (α − η)/N of C 4 F 7 N, in a range of E/N from 750 to 1150 Td, at 20 • C was obtained as well. Figure 4 presents the value (α − η)/N as a function of E/N in C 4 F 7 N, and its comparisons with SF 6 [3], c-C 4 F 8 [4], CF 3 I [7], C 4 F 7 N [13,14], and C 4 F 7 N/N 2 mixtures [18] are reported. Notably, the E/N of C 4 F 7 N was much greater than other kinds of gases for the same (α − η)/N, which suggests that the insulation ability of C 4 F 7 N is much stronger. Once the C 4 F 7 N gas mixed with buffer gas N 2 , the insulation performances of the mixtures were much weaker than pure C 4 F 7 N, since N 2 is an electrically neutral gas whose attachment coefficients is 0. Meanwhile, the variety of (α − η)/N with E/N showed a linear trend for all these gases nearby the normalized critical electric field (E/N) lim (for αη = 0). Moreover, compared to the data reported, our results of normalized effective coefficients in C 4 F 7 N were in good agreement with that of Nechmi et al. [13] as well as Chachereau [14]. Meanwhile, more values in the E/N that varied from 750 to 1150 Td were obtained in the present work. − η)/N with E/N showed a linear trend for all these gases nearby the normalized critical electric field (E/N)lim (for α -η = 0). Moreover, compared to the data reported, our results of normalized effective coefficients in C4F7N were in good agreement with that of Nechmi et al. [13] as well as Chachereau [14]. Meanwhile, more values in the E/N that varied from 750 to 1150 Td were obtained in the present work. According to the bond length values of the C4F7N molecule [21], the structure of the C4F7N molecule could be drawn as in Figure 5. A recent study [22] shows that the bonds of C-1 to C-2 and C-1 to C-3 have the smallest bond energy, which is 3.812 eV/atom. The second smallest bond energy is 4.556 eV/atom, which belongs from C-1 to F-1. The bond energy of S-F in SF6 is 3.432 eV/atom, which is smaller than the smallest bond energy in C4F7N. It is well known that the smaller the bond energy is, the weaker the interaction between atoms will be. Since the C4F7N and SF6 molecules have a strong ability to attach electrons, they can easily adsorb electrons and, hence, become negatively charged molecules. Then, these charged molecules could accelerate under an electric field, applied between two plate electrodes, and collide with other molecules. Thus, the collision may lead to the breaking of weak bonds and forming new particles such as F in SF6 and CF3 in C4F7N. For the same electric field, the bonds of SF6 are easier to be broken than bonds C-1 to C-2 (or C-3) of C4F7N. Consequently, the new particles formed in the SF6 gas, such as F, would further take part in the discharging process. However, the CF3 formed in C4F7N more easily adorbs electrons than the F formed in SF6, since there is more F in CF3, and fluorine has strong electronegativity. Then, SF6 is more likely to exhibit ionization characteristics, which could lead to the higher effective ionization coefficients of SF6 than that of C4F7N for the same E/N. According to the bond length values of the C 4 F 7 N molecule [21], the structure of the C 4 F 7 N molecule could be drawn as in Figure 5. A recent study [22] shows that the bonds of C-1 to C-2 and C-1 to C-3 have the smallest bond energy, which is 3.812 eV/atom. The second smallest bond energy is 4.556 eV/atom, which belongs from C-1 to F-1. The bond energy of S-F in SF 6 is 3.432 eV/atom, which is smaller than the smallest bond energy in C 4 F 7 N. It is well known that the smaller the bond energy is, the weaker the interaction between atoms will be. Since the C 4 F 7 N and SF 6 molecules have a strong ability to attach electrons, they can easily adsorb electrons and, hence, become negatively charged molecules. Then, these charged molecules could accelerate under an electric field, applied between two plate electrodes, and collide with other molecules. Thus, the collision may lead to the breaking of weak bonds and forming new particles such as F in SF 6 and CF 3 in C 4 F 7 N. For the same electric field, the bonds of SF 6 are easier to be broken than bonds C-1 to C-2 (or C-3) of C 4 F 7 N. Consequently, the new particles formed in the SF 6 gas, such as F, would further take part in the discharging process. However, the CF 3 formed in C 4 F 7 N more easily adorbs electrons than the F formed in SF 6 , since there is more F in CF 3 , and fluorine has strong electronegativity. Then, SF 6 is more likely to exhibit ionization characteristics, which could lead to the higher effective ionization coefficients of SF 6 than that of C 4 F 7 N for the same E/N.

Critical Electric Fields
In order to more clearly compare and evaluate the insulation performance quantitatively, the (E/N)lim of these four gases have been sorted out in Table 1. It is apparent that C4F7N has a superior performance of gas insulation, as it had a high (E/N)lim value (959.19 Td). The relative deviation of (E/N)lim of C4F7N measured in this work was about 2.41% of that measured by Nechmi et al. [13] and was about 1.73% of that measured by Chachereau et al. [14], which could testify that the experiments in the present study were of high credibility at the same time. Furthermore, it could be found that the value of (E/N)lim of C4F7N was about 2.68 times that of pure SF6 gas. However, the dielectric strength of C4F7N at atmospheric pressure was about 2 times that of SF6 as reported [10], slightly less than 2.68 times, which could be caused by different behaviors of ion kinetics under different gas pressures [14]. The higher the gas pressure, the greater the effect of ion kinetics.

Critical Electric Fields
In order to more clearly compare and evaluate the insulation performance quantitatively, the (E/N)lim of these four gases have been sorted out in Table 1. It is apparent that C4F7N has a superior performance of gas insulation, as it had a high (E/N)lim value (959.19 Td). The relative deviation of (E/N)lim of C4F7N measured in this work was about 2.41% of that measured by Nechmi et al. [13] and was about 1.73% of that measured by Chachereau et al. [14], which could testify that the experiments in the present study were of high credibility at the same time. Furthermore, it could be found that the value of (E/N)lim of C4F7N was about 2.68 times that of pure SF6 gas. However, the dielectric strength of C4F7N at atmospheric pressure was about 2 times that of SF6 as reported [10], slightly less than 2.68 times, which could be caused by different behaviors of ion kinetics under different gas pressures [14]. The higher the gas pressure, the greater the effect of ion kinetics.

Critical Electric Fields
In order to more clearly compare and evaluate the insulation performance quantitatively, the (E/N) lim of these four gases have been sorted out in Table 1. It is apparent that C 4 F 7 N has a superior performance of gas insulation, as it had a high (E/N) lim value (959.19 Td). The relative deviation of (E/N) lim of C 4 F 7 N measured in this work was about 2.41% of that measured by Nechmi et al. [13] and was about 1.73% of that measured by Chachereau et al. [14], which could testify that the experiments in the present study were of high credibility at the same time. Furthermore, it could be found that the value of (E/N) lim of C 4 F 7 N was about 2.68 times that of pure SF 6 gas. However, the dielectric strength of C 4 F 7 N at atmospheric pressure was about 2 times that of SF 6 as reported [10], slightly less than 2.68 times, which could be caused by different behaviors of ion kinetics under different gas pressures [14]. The higher the gas pressure, the greater the effect of ion kinetics. 355.27 [13] 358.66 [14] 351.80 [16]

Conclusions
In the present work, both the α/N and η/N in C 4 F 7 N have been measured by using the SST method for E/N from 750 to 1150 Td at 20°C, and they were compared to that of pure SF 6 gas. Moreover, the value of (α − η)/N was obtained for 750 Td < E/N < 1150 Td. All results measured by the SST method showed good agreement with PT experiments. The critical electric field (E/N) lim of C 4 F 7 N was about 959.19 Td. The comparison indicated that the insulation performance of C 4 F 7 N is superior to that of SF 6 , and C 4 F 7 N could be considered as a candidate insulation gas to replace SF 6 in the high-voltage engineering field.