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Determination of the ionization gauge sensitivity using the relative ionization cross-section
Determination of the ionization gauge sensitivity using the relative ionization cross-section received 23 F Nakao,
May 1975
Central Research Laboratory, Matsushita Electric Industrial Co, Ltd. 1006 Kadoma, Osaka, 571 Japan
The sensitivity of an ionization gauge for many inorganic gases and hydrocarbon gases up to CIO compounds has been determined using the ionization cross-section. Results obtained indicate a linear relationship with a slope of n = 1 between the gauge sensitivity and the ionization cross-section. The ionization cross-section relative to nitrogen for both the inorganic and hydrocarbon gases shows an almost linear increase with the number of electrons per molecule as well as the gauge sensitivity relative to nitrogen. In the absence of better information the gauge sensitivity of a given gas can be determined by the relative ionization cross-sections.
Here S is the absolute sensitivity various gases, and is defined as
1. Introduction A great many papers on the sensitivity of an ionization gauge have been published by many workers.1-20 Most ionization gauges are calibrated with nitrogen as a reference gas, and the sensitivity for various gases is generally represented by the ratio of the absolute sensitivity for various gases to that for the reference gas, i.e., the relative sensitivity. The values of relative sensitivity for common gases appear to be independent to a large extent of the type of gauge used. The values of relative sensitivity for common gases are in reasonably good agreement within an accuracy of f 15 ‘A. For hydrocarbon gases, however, there is little quantitative information in the literature concerning the ionization gauge sensitivity, but the values of relative sensitivity are somewhat doubtful because results obtained by different investigators have sometimes differed significantly.*-” Especially, information on the higher molecular weight hydrocarbons could not be found in the literature. It was of interest to determine the relative ionization cross-sections for many inorganic and organic gases to nitrogen and to establish their adaptability to the ionization gauge sensitivity. We investigated a new method of determining the sensitivity of the ionization gauge by using the ionization cross-section for all of the inorganic gases and for higher mass hydrocarbons up to Cl0 compounds.
2. Sentitivity of the ionivation gauge In the ionization when a stream expressed as
gauge, the current of positive ions, I,,, produced of electrons collides with gas molecules is
I, = QnlZ,,
(1)
where Q is the total ionization cross-section on the absolute basis, n is the density of molecules, I is the total electron path length, and Z, is the current of electrons. Substituting the density of molecules, defined as n = P/kT into (l), we obtain the following significant relation;
Vacuum/Volume
gauge for
S = Ql/kT,
(3)
Table 1. Relative sensitivity of ionization gauge and relative ionization cross-section for inorganic and hydrocarbon gases, referred to nitrogen as a reference gas. The asterisked values were obtained with a cold cathode gauge. (a) Relative sensitivity of ionization gauge and relative ionization cross-section for inorganic gases. Srj
molecule
‘j
He
0.19
-+ 0.04
0.13
i 0.02
Ne
0.33
r
0.10
0.25
-+ 0.05
B
1.37
-+ 0.22
1.23
+ 0.07
Kr
1.91
-+ 0.06
1.84
-+ 0.06
Xe
2.79
t
2.62
+ 0.08
H2
0.44
?r 0.05
0.38
-+ 0.04
D2
0.40
0.18
0.41
NH3
l.ll*+
0.27
1.23
H20
1.25
+ 0.44
1.03
co
1.02
+ 0.08
1.06
1.17*-+
1?: 0.03 1.00
1.00
N2 NO
0.11
1.24
O2
0.87
t
0.09
0.96
Air
0.97
-+ 0.10
0.75
H2S
2.20*+
0.02
2.oj
-+ 0.20
HCl
1.65*+
0.21
1.61
+ 0.02
+ 0.23
1.39
f
0.27
1.30
-+ 0.17
co2
1.36
N20
1.66*&
SF6
2.5
HI%
P = IJSIe.
of the ionization
3.30
f
0.07
0.08
2.41 + 1.04
2.07
f
0.04
(2) 25/number
9/l 0, 1975. Pergamon Press LtdfPrinted
in Great Britain
431
F Nakao:
Determination
(b) Relative cross-section
sensitivity
of the ionization of ionization
for hydrocarbon
gauge
gauge
sensitivity
and
relative
using the relative ionization
gases.
molecule
Srj
%j
CA4
1.49
rt
0.19
1.63
C2H6
2.53
-+ 0.26
2.74
+ 0.45
C3H8
3.80
t
0.40
3.64
+ 0.37
4.37
It 0.56
4.57
r 0.47
5.60
? 0.76 2 1.44
c4%0 ‘gH12 ‘gH14
6.6*
6.77
C7H16
7.6*
7.72
C8H18
8.18
CgH20
8.86
+ 0.30
ionization
cross-section
absolute ionization cross-section for various gases to that for the reference one, the differences may be regarded as small. In this work we used nitrogen as the reference gas, in a similar way to that for the ionization gauge. This treatment has been partly described in a previous paper.31 From (3) the relative sensitivity for a gas component j to nitrogen is expressed as
QjlQNz.
Sri = Sj/SNz =
(4)
Here we define the right-hand side of (4) as the relative tion cross-section for a gas component j to nitrogen; Xj =
QjlQ,,.
(5)
Then, we have following
significant
relationship;
Srj = xi. C2H2
1.66
? 0.41
2.06
2 0.27
C2H4
2.14
-+ 0.37
2.27
+ 0.28
C3H6
3.16
_+ 0.46
C4H8
3.60
c5Hlo ‘gH12
6.73*-+
0.85
3.25
_+ 0.22
3.82
-+ 0.59
4.81
t
7.22
‘gH18
8.72
clOH20
10.37
c6H6
5.18
_f 0.42
Cyclo-C5H10 Cycle-C6H12
C6H5CH3
* 6.4
5.19 _+0.50
6.01 6.60
+ 1.59
6.81
where k is the Boltzmann constant, T is the absolute temperature of molecules in the ionization region. The absolute sensitivity of the ionization gauge for various gases can be determined from the ionization cross-section if the gauge configuration and the operational conditions are the constant. Redhead’r pointed out that the absolute sensitivity is greatly dependent upon minor changes in the gauge configuration, i.e., grid-to-filament distance, control circuitry, etc. He also found that the scatter of sensitivity for identically designed Bayard-Alpert gauges with identical circuitry and construction techniques may vary as much as 15% in absolute sensitivity. AlpertZ2 noted that the relative sensitivity of the ionization gauge should be independent of these variations. Dushman and Young* found that the absolute sensitivity of the ionization gauge may vary with the type of ionization gauge but the values showed by the ratio of the absolute sensitivities did not exhibit meaningful variations. Riddiford I2 has shown that variations in sensitivity between different gauges of the same type do not exceed + 5 %. On the other hand, the total ionization cross-sections for various molecules involving higher molecular weight hydrocarbons have been measured by many workers.23-30 Although dissimilarities for the values of the absolute total ionization cross-section are found particularly in the higher mass hydrocarbons by the different observers, if we take the ratio of the 432
This equation shows a linear relationship between the relative gauge sensitivity and the relative ionization cross-section. Accordingly, (6) predicts that the values of relative ionization cross-section can apply to express the relative gauge sensitivity. 3. Results and discussion
3.75
Cycle-C3H6
(6)
0.99
6.49
C8H16
ioniza-
A determination of the average values of relative gauge sensitivity for ionization gauges of commercial or laboratory construction could be made from the data available in the literature. All of the values are converted to the relative sensitivity normalized to nitrogen. The data of the ionization cross-section were also taken from the literature, and the average values of relative ionization cross-section were obtained by taking the ratio of the total ionization cross-section for various gases at an electron energy of 75 eV. This electron energy is rather low compared with the grid potential in many ionization gauges but the changing rate of the ionization cross-section may be regarded as small. For example, when the energy of an ionizing electron changes from 75 to 110 eV*, the increasing or
r
H20 He
Ne l_--iA
I
__
2”
4”
Number
of
60
80
100
electrons/molecule
Figure 1. Plot of ionization gauge sensitivity relative to Nz as a function of the number of electrons per molecule for different inorganic gases.
* The average potential inside the grid in many I10 V when the grid potential is 150 V.’
about
ionization
gauges is
F Nakao: Determination
of the ionization gauge sensitivity using the relative ionization cross-section
20
40
60
80
Number of electrons/molecule
Figure 3. Plot of ionization cross-section relative to N2 as a functicn of the number of electrons per molecule for different inorganic gases. 0
20
40
60
60
loo
Number of electrons/rrdecule Figure 2. Plot of ionization gauge sensitivity relative to Nz as a function of the number of electrons per molecule for different
hydrocarbon gases and hydrogen.
decreasing rate of the ionization cross-section for argon is less than few per cent, and that for carbon monoxide is only 4.7 %. Molecules having the largest change are helium, oxygen, and nitrogen, and the increase or decrease for these molecules is about 10%. A comparison of the values of relative gauge sensitivity and relative ionization cross-section obtained by this method is shown in Table 1 (a) and (b) together with the standard deviations. Variations in relative gauge sensitivities among different gauges do not show large differences although the values were obtained in various ways by many workers. Deviations in the gauge sensitivity showed about 15 % for both inorganic and hydrocarbon gases, but that in the ionization cross-section was within 10% for inorganic gases, and was about 15% for hydrocarbon gases. Some data of the gauge sensitivity shown in Table 1 were quoted from the data measured with a cold-cathode gauge which used radioactive material as an electron source but the values were quite good for both the active and hydrocarbon gases. The large variations in hydrocarbons are due to the difficulties of measurement, as Young observed an almost linear reported. lo Found and Dushman” relationship between the sensitivity and the number of electrons per molecule for a large number of gases. A plot of the relative gauge sensitivities obtained here for the different inorganic and hydrocarbon gases as a function of the number of electrons per molecule are shown in Figures 1 and 2, respectively. The linearity is quite good, considering the different techniques used by various investigators. All the values for inorganic gases fall on a straight line through nitrogen with a slope of n = 0.87, except for some gases such as He, Ne, SF6 and Hg. The hydrocarbon gases have a higher sensitivity than the inorganic gases listed in Table 1. Also, the higher molecular weight hydrocarbons exhibit the highest sensitivity. Therefore, a plot of the sensitivity for the different hydrocarbons indicate a different straight line having a higher slope through hydrogen with a slope of n = 2.5. In the plot of the hydrocarbon gases
some scatter is recognized, but all types of hydrocarbon gases fall closely on this line. It is of interest to make the same plot for the relative ionization cross-sections. Figure 3 shows the plot of the relative ionization cross-section for inorganic gases to nitrogen as a function of the number of electrons per molecule. Most of inorganic gases fall on a straight line with a slope of n = 0.8. This slope is almost the same as that for the plot of the gauge sensitivity. Some scatter also exists in this plot. For gases such as HCl, H2S, SFs, and Hg, this scatter is thought to be due to the difficulties of measurement. A plot of the relative ionization
0
20
40
60
60
loo
Number of electrons/ molecule
Figure 4. Plot of ionization cross-section relative to Nz as a function of the number of electrons per molecule for different hydrocarbon gases and hydrogen. 433
F Nakao:
Determination
of the ionization
gauge
sensitivity
using the relative
cross-section for the different hydrocarbon gases and hydrogen to nitrogen as a function of the number of electrons per molecule is shown in Figure 4. It should be pointed out that all of the hydrocarbon gases up to Cl0 compounds fall closely on a different straight line having a higher slope than that of the inorganic gases in a similar manner to the relative gauge sensitivity and the higher molecular weight hydrocarbon gases exhibit the largest ionization cross-section. This curve has a slope of n = 2.6. It is not surprising that the slope of this curve is almost equal to the slope in the plot of the relative gauge sensitivity although the molecular weight is larger than that in the data of the gauge sensitivity. From these results it is concluded that, in the absence of better information, the gauge sensitivity or the ionization cross-section of a given inorganic or hydrocarbon gas could be estimated from these curves. For example, Reich 32 had determined that the gauge sensitivities for the hydrocarbon oils such as dibutylphthalate, Narcoil-40, and Octoil-S relative to nitrogen are Sr = 9.2, 13.1, and 13.0, respectively. The values are believed to be quite reasonable from the data shown in Figure 4 if we assume that the molecular weight of the pump fluid vapor in a standard vacuum system is not very large because the pump fluid was subjected to thermal dissociation in the pump boiler. According to equation (6), the relationship between the relative gauge sensitivity and relative ionization cross-section would correspond to a straight line with a slope of n = 1 in a linear plot and all of the values must be fallen closely on this line. The relative ionization cross-section data shown in Figures 3 and 4 were replotted as a function of the relative gauge sensitivity. Figure 5 shows that the relative ionization cross section in the inorganic gases is a fairly good fit to a straight line with a slope of n = 0.96. This linear relation shows that the gauge sensitivity relative to nitrogen can be determined directly from the values of the relative ionization cross-sections. Similarly, in the hydrocarbon gases the relative ionization crosssection plotted against the relative gauge sensitivity is also a quite good fit to a straight line with a slope of n = 1, as shown in Figure 6. This linear relationship also indicates that the gauge sensitivity relative to nitrogen can be estimated directly from the relative ionization cross-sections.
ionization
cross-section
Gauge sensltlvity relatweta nitrogen
Figure 6. Relative ionization cross-section vs relative ionization gauge sensitivity for different hydrocarbon gases.
4. Conclusions The results obtained indicate that the method of determining the gauge sensitivity gives satisfactory results for both the inorganic and hydrocarbon gases. Experiments for determining the relative gauge sensitivity for the higher mass hydrocarbons are very difficult because of the contamination by the carbon or carbonaceous deposit on the ion collector, grid, and walls of the ionization gauge, but by this method the gauge sensitivity for the higher mass hydrocarbon gases and other vapours could easily be estimated. In the absence of better information the ionization cross-section of a given gas or vapour could be estimated from this data. Also, the gauge sensitivity of a given gas or vapour could be determined by this method. The ionization cross-section relative to nitrogen for both the inorganic and hydrocarbon gases shows an almost linear increase with the number of electrons per molecule as well as the gauge sensitivity relative to nitrogen. Acknowledgements
The author would like to express his gratitude to Drs K Nakayama and H Hojo of Electrotechnical Laboratory for their valuable discussions. He is also indebted to Dr S Kisaka and Mr K Iga of the Central Research Laboratory for their continual encouragement and interest for this work. References
Gauge sensltlwtyrelativeto mtrogen
Figure 5. Relative ionization cross-section vs relative ionization gauge sensitivity for different inorganic gases. 434
’ S Dushman and A H Young, Phys Rev, 68, 1945, 278. ’ S Wagener and C B Johnson, J Scient Instrum, 28, 1951, 278. 3 G J Schulz, J AppI Phys, 28, 1957, 1149. 4 H V Anderson, Rev Scient Instrum, 34, 1963, 703. 5 Varian Publication No 87-400-074 (1965). 6 E W Rothe, J Vat Sci Technol. 1, 1964, 66. ’ N G Utterdach and T Griffith, jr,.Reu Scient Instrum, 37, 1966, 866. 6. 1957. 35. ’ H Moesta and R Renn. Vakuum-Technik. 9 N Morgulis, Z Physik, 5, 1934, 407. ” J R Young, J Vat Sci Technol, 10, 1973, 212. ’ ’ K Nakayama and H Hojo, 6th Int Vacuum Congress, 1974, Kyoto, Japan. I2 I Riddiford, J Sci Instrum, 28, 1951, 375. I3 H Schwarz, Z Physik, 122, 1944, 437. I4 G H Metson. Br J Appf Phys, 2, 1951, 46.
F Nakao: Determination
of the ionization gauge sensitivity using the relative ionization cross-section
I5 G Tominaga, J Vat Sot Jap, 1, 1950, 27. I6 G Tominaga, ibid, 2, 1955, 19. I7 C G Found and S Dushman, Phys. Rev, 23, 1924, 734. ‘a Z Oda and Y Arata, J Vat Sot Jap, 7, 1957, 197. I9 H Ishii and K Nakayama, J Vat Sot Jap, 3, 1960, 77. 2o I Langmuir and H A Jones, Phys Rev, 31, 1928, 357. 21 P A Redhead, J Vat Sci Techtwl, 6, 1969, 848. 22 D Alpert, J Appl Phys, 24, 1953, 7. 23 F W Lampe, J L Franklin and F H Field, J Am Chem Sot, 79, 1957,6129. l4 J W Otvos and D P Stevenson, J Am Chem Sot, 78, 1956, 546.
” H S W Massey and E H S Burhop, EIectronic and Ionic Impact Phemomena, pp 31, 38, and 265. Oxford University Press, London (1952). x J T Tate and P T Smith, Phys Rev, 39, 1932, 270. *’ D Rapp and P Englander-Golden, J Chem Phys, 43, 1965, 1464. 28 P T Smith, Phys Rev, 37, 1931, 808. 2g R K Asundi and M V Kurepa, Electron Control, 15, 1963, 41. 3o F L Mohler, L Williamson and H M Dean, JRes NatZBur Standards, 45,1950, 235. 31 F Nakao, Vacuum, 25, 1975, 201. 32 G Reich, Z Angew Physik, 9, 1957, 23.
435
May 1975
Central Research Laboratory, Matsushita Electric Industrial Co, Ltd. 1006 Kadoma, Osaka, 571 Japan
The sensitivity of an ionization gauge for many inorganic gases and hydrocarbon gases up to CIO compounds has been determined using the ionization cross-section. Results obtained indicate a linear relationship with a slope of n = 1 between the gauge sensitivity and the ionization cross-section. The ionization cross-section relative to nitrogen for both the inorganic and hydrocarbon gases shows an almost linear increase with the number of electrons per molecule as well as the gauge sensitivity relative to nitrogen. In the absence of better information the gauge sensitivity of a given gas can be determined by the relative ionization cross-sections.
Here S is the absolute sensitivity various gases, and is defined as
1. Introduction A great many papers on the sensitivity of an ionization gauge have been published by many workers.1-20 Most ionization gauges are calibrated with nitrogen as a reference gas, and the sensitivity for various gases is generally represented by the ratio of the absolute sensitivity for various gases to that for the reference gas, i.e., the relative sensitivity. The values of relative sensitivity for common gases appear to be independent to a large extent of the type of gauge used. The values of relative sensitivity for common gases are in reasonably good agreement within an accuracy of f 15 ‘A. For hydrocarbon gases, however, there is little quantitative information in the literature concerning the ionization gauge sensitivity, but the values of relative sensitivity are somewhat doubtful because results obtained by different investigators have sometimes differed significantly.*-” Especially, information on the higher molecular weight hydrocarbons could not be found in the literature. It was of interest to determine the relative ionization cross-sections for many inorganic and organic gases to nitrogen and to establish their adaptability to the ionization gauge sensitivity. We investigated a new method of determining the sensitivity of the ionization gauge by using the ionization cross-section for all of the inorganic gases and for higher mass hydrocarbons up to Cl0 compounds.
2. Sentitivity of the ionivation gauge In the ionization when a stream expressed as
gauge, the current of positive ions, I,,, produced of electrons collides with gas molecules is
I, = QnlZ,,
(1)
where Q is the total ionization cross-section on the absolute basis, n is the density of molecules, I is the total electron path length, and Z, is the current of electrons. Substituting the density of molecules, defined as n = P/kT into (l), we obtain the following significant relation;
Vacuum/Volume
gauge for
S = Ql/kT,
(3)
Table 1. Relative sensitivity of ionization gauge and relative ionization cross-section for inorganic and hydrocarbon gases, referred to nitrogen as a reference gas. The asterisked values were obtained with a cold cathode gauge. (a) Relative sensitivity of ionization gauge and relative ionization cross-section for inorganic gases. Srj
molecule
‘j
He
0.19
-+ 0.04
0.13
i 0.02
Ne
0.33
r
0.10
0.25
-+ 0.05
B
1.37
-+ 0.22
1.23
+ 0.07
Kr
1.91
-+ 0.06
1.84
-+ 0.06
Xe
2.79
t
2.62
+ 0.08
H2
0.44
?r 0.05
0.38
-+ 0.04
D2
0.40
0.18
0.41
NH3
l.ll*+
0.27
1.23
H20
1.25
+ 0.44
1.03
co
1.02
+ 0.08
1.06
1.17*-+
1?: 0.03 1.00
1.00
N2 NO
0.11
1.24
O2
0.87
t
0.09
0.96
Air
0.97
-+ 0.10
0.75
H2S
2.20*+
0.02
2.oj
-+ 0.20
HCl
1.65*+
0.21
1.61
+ 0.02
+ 0.23
1.39
f
0.27
1.30
-+ 0.17
co2
1.36
N20
1.66*&
SF6
2.5
HI%
P = IJSIe.
of the ionization
3.30
f
0.07
0.08
2.41 + 1.04
2.07
f
0.04
(2) 25/number
9/l 0, 1975. Pergamon Press LtdfPrinted
in Great Britain
431
F Nakao:
Determination
(b) Relative cross-section
sensitivity
of the ionization of ionization
for hydrocarbon
gauge
gauge
sensitivity
and
relative
using the relative ionization
gases.
molecule
Srj
%j
CA4
1.49
rt
0.19
1.63
C2H6
2.53
-+ 0.26
2.74
+ 0.45
C3H8
3.80
t
0.40
3.64
+ 0.37
4.37
It 0.56
4.57
r 0.47
5.60
? 0.76 2 1.44
c4%0 ‘gH12 ‘gH14
6.6*
6.77
C7H16
7.6*
7.72
C8H18
8.18
CgH20
8.86
+ 0.30
ionization
cross-section
absolute ionization cross-section for various gases to that for the reference one, the differences may be regarded as small. In this work we used nitrogen as the reference gas, in a similar way to that for the ionization gauge. This treatment has been partly described in a previous paper.31 From (3) the relative sensitivity for a gas component j to nitrogen is expressed as
QjlQNz.
Sri = Sj/SNz =
(4)
Here we define the right-hand side of (4) as the relative tion cross-section for a gas component j to nitrogen; Xj =
QjlQ,,.
(5)
Then, we have following
significant
relationship;
Srj = xi. C2H2
1.66
? 0.41
2.06
2 0.27
C2H4
2.14
-+ 0.37
2.27
+ 0.28
C3H6
3.16
_+ 0.46
C4H8
3.60
c5Hlo ‘gH12
6.73*-+
0.85
3.25
_+ 0.22
3.82
-+ 0.59
4.81
t
7.22
‘gH18
8.72
clOH20
10.37
c6H6
5.18
_f 0.42
Cyclo-C5H10 Cycle-C6H12
C6H5CH3
* 6.4
5.19 _+0.50
6.01 6.60
+ 1.59
6.81
where k is the Boltzmann constant, T is the absolute temperature of molecules in the ionization region. The absolute sensitivity of the ionization gauge for various gases can be determined from the ionization cross-section if the gauge configuration and the operational conditions are the constant. Redhead’r pointed out that the absolute sensitivity is greatly dependent upon minor changes in the gauge configuration, i.e., grid-to-filament distance, control circuitry, etc. He also found that the scatter of sensitivity for identically designed Bayard-Alpert gauges with identical circuitry and construction techniques may vary as much as 15% in absolute sensitivity. AlpertZ2 noted that the relative sensitivity of the ionization gauge should be independent of these variations. Dushman and Young* found that the absolute sensitivity of the ionization gauge may vary with the type of ionization gauge but the values showed by the ratio of the absolute sensitivities did not exhibit meaningful variations. Riddiford I2 has shown that variations in sensitivity between different gauges of the same type do not exceed + 5 %. On the other hand, the total ionization cross-sections for various molecules involving higher molecular weight hydrocarbons have been measured by many workers.23-30 Although dissimilarities for the values of the absolute total ionization cross-section are found particularly in the higher mass hydrocarbons by the different observers, if we take the ratio of the 432
This equation shows a linear relationship between the relative gauge sensitivity and the relative ionization cross-section. Accordingly, (6) predicts that the values of relative ionization cross-section can apply to express the relative gauge sensitivity. 3. Results and discussion
3.75
Cycle-C3H6
(6)
0.99
6.49
C8H16
ioniza-
A determination of the average values of relative gauge sensitivity for ionization gauges of commercial or laboratory construction could be made from the data available in the literature. All of the values are converted to the relative sensitivity normalized to nitrogen. The data of the ionization cross-section were also taken from the literature, and the average values of relative ionization cross-section were obtained by taking the ratio of the total ionization cross-section for various gases at an electron energy of 75 eV. This electron energy is rather low compared with the grid potential in many ionization gauges but the changing rate of the ionization cross-section may be regarded as small. For example, when the energy of an ionizing electron changes from 75 to 110 eV*, the increasing or
r
H20 He
Ne l_--iA
I
__
2”
4”
Number
of
60
80
100
electrons/molecule
Figure 1. Plot of ionization gauge sensitivity relative to Nz as a function of the number of electrons per molecule for different inorganic gases.
* The average potential inside the grid in many I10 V when the grid potential is 150 V.’
about
ionization
gauges is
F Nakao: Determination
of the ionization gauge sensitivity using the relative ionization cross-section
20
40
60
80
Number of electrons/molecule
Figure 3. Plot of ionization cross-section relative to N2 as a functicn of the number of electrons per molecule for different inorganic gases. 0
20
40
60
60
loo
Number of electrons/rrdecule Figure 2. Plot of ionization gauge sensitivity relative to Nz as a function of the number of electrons per molecule for different
hydrocarbon gases and hydrogen.
decreasing rate of the ionization cross-section for argon is less than few per cent, and that for carbon monoxide is only 4.7 %. Molecules having the largest change are helium, oxygen, and nitrogen, and the increase or decrease for these molecules is about 10%. A comparison of the values of relative gauge sensitivity and relative ionization cross-section obtained by this method is shown in Table 1 (a) and (b) together with the standard deviations. Variations in relative gauge sensitivities among different gauges do not show large differences although the values were obtained in various ways by many workers. Deviations in the gauge sensitivity showed about 15 % for both inorganic and hydrocarbon gases, but that in the ionization cross-section was within 10% for inorganic gases, and was about 15% for hydrocarbon gases. Some data of the gauge sensitivity shown in Table 1 were quoted from the data measured with a cold-cathode gauge which used radioactive material as an electron source but the values were quite good for both the active and hydrocarbon gases. The large variations in hydrocarbons are due to the difficulties of measurement, as Young observed an almost linear reported. lo Found and Dushman” relationship between the sensitivity and the number of electrons per molecule for a large number of gases. A plot of the relative gauge sensitivities obtained here for the different inorganic and hydrocarbon gases as a function of the number of electrons per molecule are shown in Figures 1 and 2, respectively. The linearity is quite good, considering the different techniques used by various investigators. All the values for inorganic gases fall on a straight line through nitrogen with a slope of n = 0.87, except for some gases such as He, Ne, SF6 and Hg. The hydrocarbon gases have a higher sensitivity than the inorganic gases listed in Table 1. Also, the higher molecular weight hydrocarbons exhibit the highest sensitivity. Therefore, a plot of the sensitivity for the different hydrocarbons indicate a different straight line having a higher slope through hydrogen with a slope of n = 2.5. In the plot of the hydrocarbon gases
some scatter is recognized, but all types of hydrocarbon gases fall closely on this line. It is of interest to make the same plot for the relative ionization cross-sections. Figure 3 shows the plot of the relative ionization cross-section for inorganic gases to nitrogen as a function of the number of electrons per molecule. Most of inorganic gases fall on a straight line with a slope of n = 0.8. This slope is almost the same as that for the plot of the gauge sensitivity. Some scatter also exists in this plot. For gases such as HCl, H2S, SFs, and Hg, this scatter is thought to be due to the difficulties of measurement. A plot of the relative ionization
0
20
40
60
60
loo
Number of electrons/ molecule
Figure 4. Plot of ionization cross-section relative to Nz as a function of the number of electrons per molecule for different hydrocarbon gases and hydrogen. 433
F Nakao:
Determination
of the ionization
gauge
sensitivity
using the relative
cross-section for the different hydrocarbon gases and hydrogen to nitrogen as a function of the number of electrons per molecule is shown in Figure 4. It should be pointed out that all of the hydrocarbon gases up to Cl0 compounds fall closely on a different straight line having a higher slope than that of the inorganic gases in a similar manner to the relative gauge sensitivity and the higher molecular weight hydrocarbon gases exhibit the largest ionization cross-section. This curve has a slope of n = 2.6. It is not surprising that the slope of this curve is almost equal to the slope in the plot of the relative gauge sensitivity although the molecular weight is larger than that in the data of the gauge sensitivity. From these results it is concluded that, in the absence of better information, the gauge sensitivity or the ionization cross-section of a given inorganic or hydrocarbon gas could be estimated from these curves. For example, Reich 32 had determined that the gauge sensitivities for the hydrocarbon oils such as dibutylphthalate, Narcoil-40, and Octoil-S relative to nitrogen are Sr = 9.2, 13.1, and 13.0, respectively. The values are believed to be quite reasonable from the data shown in Figure 4 if we assume that the molecular weight of the pump fluid vapor in a standard vacuum system is not very large because the pump fluid was subjected to thermal dissociation in the pump boiler. According to equation (6), the relationship between the relative gauge sensitivity and relative ionization cross-section would correspond to a straight line with a slope of n = 1 in a linear plot and all of the values must be fallen closely on this line. The relative ionization cross-section data shown in Figures 3 and 4 were replotted as a function of the relative gauge sensitivity. Figure 5 shows that the relative ionization cross section in the inorganic gases is a fairly good fit to a straight line with a slope of n = 0.96. This linear relation shows that the gauge sensitivity relative to nitrogen can be determined directly from the values of the relative ionization cross-sections. Similarly, in the hydrocarbon gases the relative ionization crosssection plotted against the relative gauge sensitivity is also a quite good fit to a straight line with a slope of n = 1, as shown in Figure 6. This linear relationship also indicates that the gauge sensitivity relative to nitrogen can be estimated directly from the relative ionization cross-sections.
ionization
cross-section
Gauge sensltlvity relatweta nitrogen
Figure 6. Relative ionization cross-section vs relative ionization gauge sensitivity for different hydrocarbon gases.
4. Conclusions The results obtained indicate that the method of determining the gauge sensitivity gives satisfactory results for both the inorganic and hydrocarbon gases. Experiments for determining the relative gauge sensitivity for the higher mass hydrocarbons are very difficult because of the contamination by the carbon or carbonaceous deposit on the ion collector, grid, and walls of the ionization gauge, but by this method the gauge sensitivity for the higher mass hydrocarbon gases and other vapours could easily be estimated. In the absence of better information the ionization cross-section of a given gas or vapour could be estimated from this data. Also, the gauge sensitivity of a given gas or vapour could be determined by this method. The ionization cross-section relative to nitrogen for both the inorganic and hydrocarbon gases shows an almost linear increase with the number of electrons per molecule as well as the gauge sensitivity relative to nitrogen. Acknowledgements
The author would like to express his gratitude to Drs K Nakayama and H Hojo of Electrotechnical Laboratory for their valuable discussions. He is also indebted to Dr S Kisaka and Mr K Iga of the Central Research Laboratory for their continual encouragement and interest for this work. References
Gauge sensltlwtyrelativeto mtrogen
Figure 5. Relative ionization cross-section vs relative ionization gauge sensitivity for different inorganic gases. 434
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