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Gas desorption from a stainless-steel surface in ultrahigh vacuum devices
ARTICLE IN PRESS
Vacuum 71 (2003) 471–479
Gas desorption from a stainless-steel surface in ultrahigh vacuum devices M. Moraw*, H. Praso" ! Wroc!aw University of Technology, Wybrze’ze Wyspianskiego 27, Wroc!aw, Poland Received 30 August 2002; received in revised form 7 January 2003; accepted 4 February 2003
Abstract Degassing of stainless-steel surface in a vacuum system with high unit pumping speed was investigated. Possibility of efficient surface outgassing at 400 K has been confirmed. An attempt to describe phenomena connected with hydrogen desorption from surface at 300 K is presented. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: UHV; Stainless steel; Gas desorption
1. Introduction Knowledge of binding energy of gas on a surface allows for prediction of temperature increase influence on surface outgassing. In a real system, metal surface–gas, the actual energy values are not known. A phenomenological analysis of material outgassing characteristics [1,2] may be an efficient means of estimation of this energy. Such analysis allows for determination of weighted average binding energy of gas on surface: t E% ¼ Ec þ gRT ln ; tc
ð1Þ
where Ec ; tc (¼ to exp Ec =RT) and g are parameters taken from the shape of characteristics being analysed. Determination of these para*Corresponding author. Tel.: +48-71-320-25-94; fax: +4871-328-35-04. E-mail address: [email protected] (M. Moraw).
meters allows for analytical description of the desorption flux: " ð1gÞ # qo t g 1 t i¼ exp ; ð2Þ ðg 1Þ tc tc tc where qo is the amount of gas adsorbed on the surface in the beginning of the pumping procedure. This formula represents the experimental outgassing curve quite accurately; however, none of the parameters qo ; tc or g; has any real physical meaning. In fact, the binding energy has discrete values and cannot be changed in a continuous way. It may be assumed that in a gas–surface system there is a definite number of binding energies Ej ; a specified amount of gas qoj is attributed to each of these energies. In the pumping process, the outgassing rate related to each of these energy levels is given by ij ¼
qj ; tj
0042-207X/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0042-207X(03)00035-6
ð3Þ
ARTICLE IN PRESS M. Moraw, H. Praso! / Vacuum 71 (2003) 471–479
472
where tj ¼ to exp
2. Desorption measurement Ej RT
ð3aÞ
and t qj ¼ qoj exp : tj Thus, the total desorbed gas flux n n X X qoj t ij ¼ exp : i¼ tj t j¼1 j¼1 j
ð3bÞ
ð4Þ
Such a real process is described by the relationship (2). The obvious question is, how are the some% qo and g; used in this what artificial parameters E; approximation procedure, related to the real parameters Ej and qoj of the system? The answer may be found using experimental data. An experimental example, described below, shows relation between E% and Ej :
An experimental setup is based on a cryopump, whose second stage is working without screening shield (Fig. 1). The Gifford–McMahon supply cooling power is sufficient for obtaining 15 K on the surface 1. For the vacuum vessel temperatures 400 and 450 K, these temperatures were 19 and 23 K, respectively. The measured pumping speed for nitrogen was SN2 ¼ 3:9 m3/s. The active carbon pumping speed of hydrogen was SH2 ¼ 0:81 m3/s. The inner surface of the vacuum vessel was F ¼ 0:2 m2. Thus, the unit pumping speed was SN2 ¼ 19:5 m3/m2s and SH2 ¼ 4 m3/m2s, respectively. Such a high unit pumping speed allowed for readsorption to be neglected. The pressure change in the course of pumping is shown in Fig. 2. After 2 h of pumping there was only hydrogen and water in the vacuum system. Hydrogen was the dominant gas (one
Fig. 1. Vacuum system with cryopump: (1) pumping surface, + 88 86 mm; (2) active coal; (3) screen protecting active coal; (4) vacuum gauge head, IE 514 (Ionivac IM 520); (5) quadrupole mass spectrometer, Quadruvac PGA 100; and (6) vacuum vessel, + 160 300 mm.
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Fig. 2. Changes of pressure p and of gas flux i desorbed from system walls during the pumping process.
should take into account that the pumping speed of water was some six times higher than that hydrogen). Therefore, the gas flux desorbed from the surface was evaluated only for hydrogen pind i ¼ iH2 ¼ sH ; ð5Þ CH2 2 where pind is the gauge reading and CH2 ¼ 0:44 is the relative ionization gauge sensitivity for hydrogen.
3. Analysis Desorption characteristics (caught by i ¼ f ðtÞ) were analysed in the 2–8 h time interval and the approximation parameters were determined [2]: qo ¼ 0:683 Pa m3 =m2 ;
tc ¼ 8:59 104 s;
g ¼ 0:65: Evaluation of changes of weighted mean binding energy during the pumping process may be done
ARTICLE IN PRESS M. Moraw, H. Praso! / Vacuum 71 (2003) 471–479
474
using tc and g: These energy values are listed in Table 1. It may be assumed that the real binding energy in the surface does not significantly differ from the weighted mean energy evaluated analytically. As an example, for several binding energies Ej arbitrary values for flux of gas desorbed from the surface was calculated. These calculations were made under the assumption that the same amount of gas was attributed to each of the energy values. Results of these calculations are presented in Table 2. These assumed energies have nothing to do with the real situation. The example shows only how the characteristics calculated from formula (4) may fit the experimental one. There is an infinite number of Ej and qoj combinations giving the same result. Among them there are Ejr and qojr values that really appear on the surface. The real values of energy cannot deviate from the value of weighted mean energy taken from the experimental curve. Gas molecules with binding energies lower and higher than the values presented in Table 2 have no influence on the degassing characteristics for the 2–10 h interval. The flux of gas bonded with 90 kJ/mol energy, desorbed from the surface, is 1.1 106 qo after 1 h of pumping and 5.8 1010 qo after 2 h. On the
other hand, the desorption rate of gas molecules bonded with 110 kJ/mol is 6.9 107 qo after 10 h and 5.4 107 qo after 100 h. This means that the gas flux is practically constant over a long time interval.
4. Removal of gas from surface According to (3b) the rate of gas removal from the surface is t q=qo ¼ exp ; ð6Þ t where qo is the amount of adsorbed gas at the beginning of pumping, t is the time of material residence in vacuum, t ¼ to expðE=RTÞ is average time of molecule rest on the surface. It appears from these relations that even a small temperature rise should cause a substantial reduction of gas amount on the surface. Molecules with the binding energy lower than 100 kJ/mol are quite efficiently removed in temperatures as low as 300 K (see Table 2). Table 3 shows the effect of 1-h baking at 400 K on molecules with binding energies higher than 100 kJ/mol. Taking into account surface roughness and some 25 nm thick oxide layer on the stainless steel, it may be assumed that the amount of adsorbed gas is about 1021 molecules/m2, i.e. several Pa m3/m2. The gas flux released from the surface after the 1-h baking process, attributed to particular energy levels, is listed in Table 4. This means that such process should decrease the desorbed gas flux to a very low value and the
Table 1 Weighted average energy of binding Ec ¼ 102:95 kJ/mol t (h)
2
4
6
8
10
50
100
% E(kJ/mol)
98.9
100
100.7
101.2
101.5
104.1
105.3
Table 2 Comparison of calculated and measured desorbed gas flux qoj ¼ 0:1 Pa m3/m2, T ¼ 300 K Ej (kJ/mol) tj (s) t (h) 1 2 4 6 8 10
95 97.5 3.54 103 9.66 103 ij ðPa m3 =m2 sÞ Eq. (3) 105 7.1 106 3.7 106 4.9 106 4.8 107 2.3 106 6.3 108 1.1 106 8.3 109 5.25 107 1.1 109 2.5 107
100 2.63 104 6
3.3 10 2.9 106 2.2 106 1.7 106 1.3 106 9.7 107
105 1.96 105 7
5 10 4.9 107 4.7 107 4.6 107 4.4 107 4.2 107
P
ij ðPa m3 =m2 sÞ 2.1 105 1.2 105 5.45 106 3.3 106 2.27 106 1.64 106
iapr ðPa m3 =m2 sÞ Eq. (2) 2.44 105 1.2 105 5.5 106 3.35 106 2.3 106 1.7 106
iexp ðPa m3 =m2 sÞ 6 105 1.2 105 5.5 106 3.2 106 2.3 106 1.7 106
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Table 3 Degassing rate of surface baked at 400 K for 1 h in vacuum E (kJ/mol) t400 K (s) q=qo
105
110
5.23 —
115
23.5 3 1067
120
106 1.8 1015
125
130
2.15 10 0.19
477 5.3 104
3
134 3
3.21 104 0.89
9.66 10 0.69
Table 4 Gas flux generated from surface after 1-h baking at 400 K, qo ¼ 5 Pa m3 =m2 ; T ¼ 300 K E (kJ/mol) t300 K (s) q ðPa m3 =m2 Þ i ðPa m3 =m2 sÞ
105
110 5
1.96 10 — —
115 6
1.45 10 1.5 1066 1072
120 7
1.08 10 9 1015 8.3 1022
125 7
8.03 10 2.65 103 3.3 1011
130 8
6 10 0.95 1.6 109
134 9
4.43 10 3.45 7.8 1010
2.2 1010 4.45 2 1010
released gas should come from the bulk of the material, under condition that the surface structure remains unchanged.
5. Experimental verification Vacuum system described in Section 2 was baked at 400 K for 1 h. Results of a dozen or so experiments are shown in Fig. 3. Between the consecutive experiments pressure in the system was about 101 Pa. In several experiments the baking temperature was raised to 450 K, but no correlation has been noticed between baking temperature and final pressure after 10 h of pumping. After this time the pressure reached was 8–4 1010 Pa. A short baking in not very high temperature resulted in pressure decrease by two orders of magnitude compared to system not baked. It should be noted that unit pumping speed was high, thus the readsorption process was minimized.
6. Discussion The only gas spectrometer detected by the spectrometer after baking was hydrogen. This allowed the use of relation (5) to calculate the gas flux effused from the surface. After 10 h of pumping in various cycles the desorbed gas flux varied from 7.2 109 to 3.6 109 Pa m3/m2 s.
Fig. 3. Changes of pressure in the vacuum system after 1-h baking at 400 K: (1) after 24 h exposure to air and (2) range of pumping characteristics during successive pumping processes.
For such small amounts of gas its substantial part should come from the bulk of the material. The flux intensity of gas diffusing from the inside to the
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surface may be calculated from the following relationship [3]: ( " #) N 4D X pð2i þ 1Þ 2 i ¼ Co exp ðDtÞ d i¼0 d ¼ Co A;
ð7Þ
where Co is the gas concentration in the material, D (¼ Do expðEo =RTÞ) is the diffusion coefficient, d is the material thickness and t is the time. For calculation of hydrogen diffusion on surface we took stainless steel Do ¼ 1:5 106 m2/s and ED ¼ 50:2 kJ/mol [4]. Thus for 300 K D ¼ 2:7 1015 m2/s. The baked vacuum system reached 300 K after 7 h of work. The values of A calculated for t ¼ 3 h were the following: *
*
for wall thickness d ¼ 2 103 m (vessel sidewall), A ¼ 2:9 1010 m/s; for wall thickness d ¼ 2 102 m (top plate), A ¼ 2:8 1010 m/s.
These calculations gave only approximate values, because the initial condition was not satisfied (uniform gas concentration at t ¼ 0). If the only source of gas after 10 h of pumping was that diffusing from the depth of the material, then gas concentration in the material may be estimated from (7), assuming the flux i value to be 8 109 Pa m3/m2 s: Co ¼ i=AE30 Pa m3 =m3 : This value was incredibly small, if one took into account that the hydrogen content in steel after the metallurgical process could be within the range of 5 102–105 Pa, and baking at 400 K could not drastically decrease the initial level. This meant that the gas flux from the surface was smaller than the flux appearing from classical diffusion calculations. It could be then assumed that the diffusion from the bulk of material was limited by the high hydrogen concentration on the surface. Such hypothesis is supported by the results of Calder and Lewin [5] who measured the effusion rate of hydrogen from stainless steel with low-carbon contents. A plot prepared from their results is shown in Fig. 4. If, in the baking process, hydrogen desorbed from material without any barrier, then after 75 h its concentration should fall
Fig. 4. Hydrogen desorption rate from low-carbon steel baked at 570 K for 75 h (after Calder and Lewin): (1) Calder and Lewin results and (2) theoretical dependence of diffusion flux on temperature.
to some 1011 of the initial value. The gas flux at 575 K should be then 1013 Pa m3/m2 s. In Fig. 4 the relationship between diffusing gas and temperature is plotted with a dashed line. This plot starts, arbitrarily enough, from the point for 573 K. It is visible that the experimental Calder and Lewin curve shows a larger slope than the diffusion-related one. The above results indicate that the surface processes dictate the degassing of material. Additional support for this conclusion comes from another result of Calder and Lewin who baked samples at 1270 K for 3 h and then kept them at 620 K for 25 h. The hydrogen flux from these samples at 300 K was 1.7 1011 Pa m3/m2 s. Probably, this result was not due to an increased diffusion rate at elevated temperature but caused by a reduced hydrogen average residence time on the surface t1270 ¼ 3:3 108 s. Such a value of residence time allows for substantial decrease of
ARTICLE IN PRESS M. Moraw, H. Praso! / Vacuum 71 (2003) 471–479
hydrogen surface concentration and an increase of effective diffusion of gas from the material.
7. Recombination of hydrogen atoms on the surface A temperature rise generates a supply of hydrogen atoms to the surface. Hydrogen radicals cause the reduction of oxides. A result of such reaction is water. The most probable reactions on a steel surface are the following: Fe2 O3 þ H-2FeO þ OH; OH þ H-H2 O: The above reactions cause water to appear even in well-processed extremely high vacuum systems [6]. However, the water content is only a few percent of the whole residual gas spectrum. Hydrogen is the dominant gas generated by the surface. Because the binding energy of hydrogen on iron is 134 kJ/mol, approximately, the direct desorption of hydrogen is extremely low (average residence time of an atom on the surface at 300 K is 2.2 1010 s). If the gas generation process is considered as an activated surface process, then its activation energy may be estimated from the flux change with temperature [7]: T1 T2 i2 EER ð8Þ ln ; T2 T1 i1 where i1 is the flux generated at temperature T1 and i2 is the flux in T2 : The flux–temperature relationship for the tested vacuum system was measured several times. The measurements were carried out starting from 109 Pa and when changing the system temperature by 5 K. For the initial temperature 300 K the obtained energies varied from 28.5 kJ/mol to 34 kJ/mol. The fast reaction of the system to the temperature change supported the hypothesis of the surface character of the process. Similar calculations could be made using the results of Calder and Lewin. These results are presented in Table 5. The activation energy values, obtained in both these cases, suggest that the process dynamics depends on the hydrogen atom migration on the
477
Table 5 Activation energy of gas generation from surface for characteristics shown in Fig. 4 T (K) E (kJ/mol)
293 36.4
320 38.5
345 31.4
378 28
418
surface. Hydrogen desorption is caused by recombination, which supplies enough energy for molecules emission from the surface. If the average migration time is known EM tM ¼ to exp ð9Þ RT then, in 1 s the hydrogen atom penetrates qo ¼ 1=tM adsorption centres. In the same time flux from the surface is generated and this may be evaluated using i ¼ qp =tM ; where qp is the number of adsorption centres occupied by hydrogen atoms. The ratio qp =qo may be treated as the rate of surface filling. Results of calculations based on Calder and Lewin data are shown in Table 6. The same calculations done for the system tested by the authors gave the following results: T¼ 300 K; i ¼ 8109 Pa m3/m2 s ¼ 2:15 1012 s1; tM ¼ 1:7 108 s; qo ¼ 5:9 107 ; qp ¼ 3:65 104 ; qp =qo ¼ 6:2 104 : For a total number of adsorption centers qo ¼ 1019 m2 ; the number of occupied centers is qp ¼ 6:2 1015 m2 : These approximate calculations may explain the outgassing efficiency, being at elevated temperature, lower than expected. An additional supply source of hydrogen concentration on the surface is readsorption because, in a real vacuum system, outgassing is carried out in an atmosphere in which hydrogen is dominant. The surface concentration 2.7 1015 m2 (Table 6) corresponds approximately to a spatial concentration 1.4 1023 or 5.2 102 Pa m3/m3. These are data for material baked for 75 h at 570 K; thus, it may be concluded that surface concentration of hydrogen is higher than that corresponding to the concentration of this gas inside the material. This conclusion was supported by another experiment, in which an attempt was made to partially remove the adsorbed layer by short heating the material. Results of this process have
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Table 6 Surface filling rate for hydrogen on steel after baking at 570 K for 75 h, EM ¼ 30 kJ/mol T (K)
293 3
2
i ðPa m =m sÞ i ð1=m2 sÞ tM ðsÞ qo qp qp =qo qp for qo ¼ 1019 /m2
320 9
2 10 5.4 1011 2.2 108 4.5 107 1.2 104 2.7 104 2.7 1015
345 9
7 10 1.9 1012 7.9 109 1.3 108 1.5 104 1.2 104 1.2 1015
378 8
2 10 5.4 1012 3.5 109 2.8 108 1.9 104 6.8 105 6.8 1014
418 8
5.2 10 1.4 1013 1.4 109 7.1 108 2 104 2.8 105 2.8 1014
573 7
1.2 10 3.2 1013 5.6 1010 1.8 109 1.8 104 105 1014
3.3 108 8.8 1012 5.4 1011 1.8 1010 4.7 102 2.6 108 2.6 1011
not require too high a temperature for baking. After 1 h of baking at 400 K, the flux generated by the stainless-steel surface may decrease to 108 Pa m3/m2 s. After such a process hydrogen is the dominant gas. Its source is diffusion from the bulk of the material. This hydrogen does not pass directly to the gas phase but is adsorbed on the surface. Its desorption is possible due to surface migration and subsequent recombination.At any temperature, the surface state tends to reach equilibrium and thus ides ¼ idif þ ir ;
ð10Þ
been shown in Fig. 5. The obtained results are perhaps not very impressive, but a twofold decrease of desorbed flux was obtained (compare Fig. 3).
where ides is the desorbed gas flux, idif is the flux of gas diffusing from the bulk of the material and ir is the readsorbed gas flux. All these fluxes depend on surface concentration which is the equilibrium control factor. During cooling after bake-out the desorption flux decreases and surface concentration increases. It is easy to conclude that the surface concentration increase is also supported by gas coming from the surrounding space. It may then happen that for a very well-degassed material the diffusion direction may be changed and the gas stream will flow from the surface into the material. Thus, the condition for effective outgassing is to keep the system at a very good vacuum during baking and subsequent cooling. This condition requires high unit pumping speed for the pumping assembly.
8. Conclusions
References
Fig. 5. Pressure changes in the vacuum system baked two times.
In vacuum system with a high unit pumping speed, the outgassing of a surface is fast and does
[1] Moraw M. Vacuum 1986;36:523. [2] Moraw M, Praso" H. Vacuum 1996;47:1431.
ARTICLE IN PRESS M. Moraw, H. Praso! / Vacuum 71 (2003) 471–479 [3] Lewin G. Fundamentals of vacuum science and technology. New York: McGraw-Hill, 1967. [4] Sykes C, Burton H, Gegg C. J Iron Steel Inst 1947;156:155. [5] Calder R, Lewin G. Private communication cited by Redhead PA, Hobson JP, Kornelsen EV, The Physical
479
Basis of Ultrahigh Vacuum. New York: American Institute of Physics, 1993. [6] Odaka K, Ueda S. Vacuum 1993;44:713. [7] Moraw M, Praso" H. Vacuum 2002;65:1.
Vacuum 71 (2003) 471–479
Gas desorption from a stainless-steel surface in ultrahigh vacuum devices M. Moraw*, H. Praso" ! Wroc!aw University of Technology, Wybrze’ze Wyspianskiego 27, Wroc!aw, Poland Received 30 August 2002; received in revised form 7 January 2003; accepted 4 February 2003
Abstract Degassing of stainless-steel surface in a vacuum system with high unit pumping speed was investigated. Possibility of efficient surface outgassing at 400 K has been confirmed. An attempt to describe phenomena connected with hydrogen desorption from surface at 300 K is presented. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: UHV; Stainless steel; Gas desorption
1. Introduction Knowledge of binding energy of gas on a surface allows for prediction of temperature increase influence on surface outgassing. In a real system, metal surface–gas, the actual energy values are not known. A phenomenological analysis of material outgassing characteristics [1,2] may be an efficient means of estimation of this energy. Such analysis allows for determination of weighted average binding energy of gas on surface: t E% ¼ Ec þ gRT ln ; tc
ð1Þ
where Ec ; tc (¼ to exp Ec =RT) and g are parameters taken from the shape of characteristics being analysed. Determination of these para*Corresponding author. Tel.: +48-71-320-25-94; fax: +4871-328-35-04. E-mail address: [email protected] (M. Moraw).
meters allows for analytical description of the desorption flux: " ð1gÞ # qo t g 1 t i¼ exp ; ð2Þ ðg 1Þ tc tc tc where qo is the amount of gas adsorbed on the surface in the beginning of the pumping procedure. This formula represents the experimental outgassing curve quite accurately; however, none of the parameters qo ; tc or g; has any real physical meaning. In fact, the binding energy has discrete values and cannot be changed in a continuous way. It may be assumed that in a gas–surface system there is a definite number of binding energies Ej ; a specified amount of gas qoj is attributed to each of these energies. In the pumping process, the outgassing rate related to each of these energy levels is given by ij ¼
qj ; tj
0042-207X/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0042-207X(03)00035-6
ð3Þ
ARTICLE IN PRESS M. Moraw, H. Praso! / Vacuum 71 (2003) 471–479
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where tj ¼ to exp
2. Desorption measurement Ej RT
ð3aÞ
and t qj ¼ qoj exp : tj Thus, the total desorbed gas flux n n X X qoj t ij ¼ exp : i¼ tj t j¼1 j¼1 j
ð3bÞ
ð4Þ
Such a real process is described by the relationship (2). The obvious question is, how are the some% qo and g; used in this what artificial parameters E; approximation procedure, related to the real parameters Ej and qoj of the system? The answer may be found using experimental data. An experimental example, described below, shows relation between E% and Ej :
An experimental setup is based on a cryopump, whose second stage is working without screening shield (Fig. 1). The Gifford–McMahon supply cooling power is sufficient for obtaining 15 K on the surface 1. For the vacuum vessel temperatures 400 and 450 K, these temperatures were 19 and 23 K, respectively. The measured pumping speed for nitrogen was SN2 ¼ 3:9 m3/s. The active carbon pumping speed of hydrogen was SH2 ¼ 0:81 m3/s. The inner surface of the vacuum vessel was F ¼ 0:2 m2. Thus, the unit pumping speed was SN2 ¼ 19:5 m3/m2s and SH2 ¼ 4 m3/m2s, respectively. Such a high unit pumping speed allowed for readsorption to be neglected. The pressure change in the course of pumping is shown in Fig. 2. After 2 h of pumping there was only hydrogen and water in the vacuum system. Hydrogen was the dominant gas (one
Fig. 1. Vacuum system with cryopump: (1) pumping surface, + 88 86 mm; (2) active coal; (3) screen protecting active coal; (4) vacuum gauge head, IE 514 (Ionivac IM 520); (5) quadrupole mass spectrometer, Quadruvac PGA 100; and (6) vacuum vessel, + 160 300 mm.
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Fig. 2. Changes of pressure p and of gas flux i desorbed from system walls during the pumping process.
should take into account that the pumping speed of water was some six times higher than that hydrogen). Therefore, the gas flux desorbed from the surface was evaluated only for hydrogen pind i ¼ iH2 ¼ sH ; ð5Þ CH2 2 where pind is the gauge reading and CH2 ¼ 0:44 is the relative ionization gauge sensitivity for hydrogen.
3. Analysis Desorption characteristics (caught by i ¼ f ðtÞ) were analysed in the 2–8 h time interval and the approximation parameters were determined [2]: qo ¼ 0:683 Pa m3 =m2 ;
tc ¼ 8:59 104 s;
g ¼ 0:65: Evaluation of changes of weighted mean binding energy during the pumping process may be done
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using tc and g: These energy values are listed in Table 1. It may be assumed that the real binding energy in the surface does not significantly differ from the weighted mean energy evaluated analytically. As an example, for several binding energies Ej arbitrary values for flux of gas desorbed from the surface was calculated. These calculations were made under the assumption that the same amount of gas was attributed to each of the energy values. Results of these calculations are presented in Table 2. These assumed energies have nothing to do with the real situation. The example shows only how the characteristics calculated from formula (4) may fit the experimental one. There is an infinite number of Ej and qoj combinations giving the same result. Among them there are Ejr and qojr values that really appear on the surface. The real values of energy cannot deviate from the value of weighted mean energy taken from the experimental curve. Gas molecules with binding energies lower and higher than the values presented in Table 2 have no influence on the degassing characteristics for the 2–10 h interval. The flux of gas bonded with 90 kJ/mol energy, desorbed from the surface, is 1.1 106 qo after 1 h of pumping and 5.8 1010 qo after 2 h. On the
other hand, the desorption rate of gas molecules bonded with 110 kJ/mol is 6.9 107 qo after 10 h and 5.4 107 qo after 100 h. This means that the gas flux is practically constant over a long time interval.
4. Removal of gas from surface According to (3b) the rate of gas removal from the surface is t q=qo ¼ exp ; ð6Þ t where qo is the amount of adsorbed gas at the beginning of pumping, t is the time of material residence in vacuum, t ¼ to expðE=RTÞ is average time of molecule rest on the surface. It appears from these relations that even a small temperature rise should cause a substantial reduction of gas amount on the surface. Molecules with the binding energy lower than 100 kJ/mol are quite efficiently removed in temperatures as low as 300 K (see Table 2). Table 3 shows the effect of 1-h baking at 400 K on molecules with binding energies higher than 100 kJ/mol. Taking into account surface roughness and some 25 nm thick oxide layer on the stainless steel, it may be assumed that the amount of adsorbed gas is about 1021 molecules/m2, i.e. several Pa m3/m2. The gas flux released from the surface after the 1-h baking process, attributed to particular energy levels, is listed in Table 4. This means that such process should decrease the desorbed gas flux to a very low value and the
Table 1 Weighted average energy of binding Ec ¼ 102:95 kJ/mol t (h)
2
4
6
8
10
50
100
% E(kJ/mol)
98.9
100
100.7
101.2
101.5
104.1
105.3
Table 2 Comparison of calculated and measured desorbed gas flux qoj ¼ 0:1 Pa m3/m2, T ¼ 300 K Ej (kJ/mol) tj (s) t (h) 1 2 4 6 8 10
95 97.5 3.54 103 9.66 103 ij ðPa m3 =m2 sÞ Eq. (3) 105 7.1 106 3.7 106 4.9 106 4.8 107 2.3 106 6.3 108 1.1 106 8.3 109 5.25 107 1.1 109 2.5 107
100 2.63 104 6
3.3 10 2.9 106 2.2 106 1.7 106 1.3 106 9.7 107
105 1.96 105 7
5 10 4.9 107 4.7 107 4.6 107 4.4 107 4.2 107
P
ij ðPa m3 =m2 sÞ 2.1 105 1.2 105 5.45 106 3.3 106 2.27 106 1.64 106
iapr ðPa m3 =m2 sÞ Eq. (2) 2.44 105 1.2 105 5.5 106 3.35 106 2.3 106 1.7 106
iexp ðPa m3 =m2 sÞ 6 105 1.2 105 5.5 106 3.2 106 2.3 106 1.7 106
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Table 3 Degassing rate of surface baked at 400 K for 1 h in vacuum E (kJ/mol) t400 K (s) q=qo
105
110
5.23 —
115
23.5 3 1067
120
106 1.8 1015
125
130
2.15 10 0.19
477 5.3 104
3
134 3
3.21 104 0.89
9.66 10 0.69
Table 4 Gas flux generated from surface after 1-h baking at 400 K, qo ¼ 5 Pa m3 =m2 ; T ¼ 300 K E (kJ/mol) t300 K (s) q ðPa m3 =m2 Þ i ðPa m3 =m2 sÞ
105
110 5
1.96 10 — —
115 6
1.45 10 1.5 1066 1072
120 7
1.08 10 9 1015 8.3 1022
125 7
8.03 10 2.65 103 3.3 1011
130 8
6 10 0.95 1.6 109
134 9
4.43 10 3.45 7.8 1010
2.2 1010 4.45 2 1010
released gas should come from the bulk of the material, under condition that the surface structure remains unchanged.
5. Experimental verification Vacuum system described in Section 2 was baked at 400 K for 1 h. Results of a dozen or so experiments are shown in Fig. 3. Between the consecutive experiments pressure in the system was about 101 Pa. In several experiments the baking temperature was raised to 450 K, but no correlation has been noticed between baking temperature and final pressure after 10 h of pumping. After this time the pressure reached was 8–4 1010 Pa. A short baking in not very high temperature resulted in pressure decrease by two orders of magnitude compared to system not baked. It should be noted that unit pumping speed was high, thus the readsorption process was minimized.
6. Discussion The only gas spectrometer detected by the spectrometer after baking was hydrogen. This allowed the use of relation (5) to calculate the gas flux effused from the surface. After 10 h of pumping in various cycles the desorbed gas flux varied from 7.2 109 to 3.6 109 Pa m3/m2 s.
Fig. 3. Changes of pressure in the vacuum system after 1-h baking at 400 K: (1) after 24 h exposure to air and (2) range of pumping characteristics during successive pumping processes.
For such small amounts of gas its substantial part should come from the bulk of the material. The flux intensity of gas diffusing from the inside to the
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surface may be calculated from the following relationship [3]: ( " #) N 4D X pð2i þ 1Þ 2 i ¼ Co exp ðDtÞ d i¼0 d ¼ Co A;
ð7Þ
where Co is the gas concentration in the material, D (¼ Do expðEo =RTÞ) is the diffusion coefficient, d is the material thickness and t is the time. For calculation of hydrogen diffusion on surface we took stainless steel Do ¼ 1:5 106 m2/s and ED ¼ 50:2 kJ/mol [4]. Thus for 300 K D ¼ 2:7 1015 m2/s. The baked vacuum system reached 300 K after 7 h of work. The values of A calculated for t ¼ 3 h were the following: *
*
for wall thickness d ¼ 2 103 m (vessel sidewall), A ¼ 2:9 1010 m/s; for wall thickness d ¼ 2 102 m (top plate), A ¼ 2:8 1010 m/s.
These calculations gave only approximate values, because the initial condition was not satisfied (uniform gas concentration at t ¼ 0). If the only source of gas after 10 h of pumping was that diffusing from the depth of the material, then gas concentration in the material may be estimated from (7), assuming the flux i value to be 8 109 Pa m3/m2 s: Co ¼ i=AE30 Pa m3 =m3 : This value was incredibly small, if one took into account that the hydrogen content in steel after the metallurgical process could be within the range of 5 102–105 Pa, and baking at 400 K could not drastically decrease the initial level. This meant that the gas flux from the surface was smaller than the flux appearing from classical diffusion calculations. It could be then assumed that the diffusion from the bulk of material was limited by the high hydrogen concentration on the surface. Such hypothesis is supported by the results of Calder and Lewin [5] who measured the effusion rate of hydrogen from stainless steel with low-carbon contents. A plot prepared from their results is shown in Fig. 4. If, in the baking process, hydrogen desorbed from material without any barrier, then after 75 h its concentration should fall
Fig. 4. Hydrogen desorption rate from low-carbon steel baked at 570 K for 75 h (after Calder and Lewin): (1) Calder and Lewin results and (2) theoretical dependence of diffusion flux on temperature.
to some 1011 of the initial value. The gas flux at 575 K should be then 1013 Pa m3/m2 s. In Fig. 4 the relationship between diffusing gas and temperature is plotted with a dashed line. This plot starts, arbitrarily enough, from the point for 573 K. It is visible that the experimental Calder and Lewin curve shows a larger slope than the diffusion-related one. The above results indicate that the surface processes dictate the degassing of material. Additional support for this conclusion comes from another result of Calder and Lewin who baked samples at 1270 K for 3 h and then kept them at 620 K for 25 h. The hydrogen flux from these samples at 300 K was 1.7 1011 Pa m3/m2 s. Probably, this result was not due to an increased diffusion rate at elevated temperature but caused by a reduced hydrogen average residence time on the surface t1270 ¼ 3:3 108 s. Such a value of residence time allows for substantial decrease of
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hydrogen surface concentration and an increase of effective diffusion of gas from the material.
7. Recombination of hydrogen atoms on the surface A temperature rise generates a supply of hydrogen atoms to the surface. Hydrogen radicals cause the reduction of oxides. A result of such reaction is water. The most probable reactions on a steel surface are the following: Fe2 O3 þ H-2FeO þ OH; OH þ H-H2 O: The above reactions cause water to appear even in well-processed extremely high vacuum systems [6]. However, the water content is only a few percent of the whole residual gas spectrum. Hydrogen is the dominant gas generated by the surface. Because the binding energy of hydrogen on iron is 134 kJ/mol, approximately, the direct desorption of hydrogen is extremely low (average residence time of an atom on the surface at 300 K is 2.2 1010 s). If the gas generation process is considered as an activated surface process, then its activation energy may be estimated from the flux change with temperature [7]: T1 T2 i2 EER ð8Þ ln ; T2 T1 i1 where i1 is the flux generated at temperature T1 and i2 is the flux in T2 : The flux–temperature relationship for the tested vacuum system was measured several times. The measurements were carried out starting from 109 Pa and when changing the system temperature by 5 K. For the initial temperature 300 K the obtained energies varied from 28.5 kJ/mol to 34 kJ/mol. The fast reaction of the system to the temperature change supported the hypothesis of the surface character of the process. Similar calculations could be made using the results of Calder and Lewin. These results are presented in Table 5. The activation energy values, obtained in both these cases, suggest that the process dynamics depends on the hydrogen atom migration on the
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Table 5 Activation energy of gas generation from surface for characteristics shown in Fig. 4 T (K) E (kJ/mol)
293 36.4
320 38.5
345 31.4
378 28
418
surface. Hydrogen desorption is caused by recombination, which supplies enough energy for molecules emission from the surface. If the average migration time is known EM tM ¼ to exp ð9Þ RT then, in 1 s the hydrogen atom penetrates qo ¼ 1=tM adsorption centres. In the same time flux from the surface is generated and this may be evaluated using i ¼ qp =tM ; where qp is the number of adsorption centres occupied by hydrogen atoms. The ratio qp =qo may be treated as the rate of surface filling. Results of calculations based on Calder and Lewin data are shown in Table 6. The same calculations done for the system tested by the authors gave the following results: T¼ 300 K; i ¼ 8109 Pa m3/m2 s ¼ 2:15 1012 s1; tM ¼ 1:7 108 s; qo ¼ 5:9 107 ; qp ¼ 3:65 104 ; qp =qo ¼ 6:2 104 : For a total number of adsorption centers qo ¼ 1019 m2 ; the number of occupied centers is qp ¼ 6:2 1015 m2 : These approximate calculations may explain the outgassing efficiency, being at elevated temperature, lower than expected. An additional supply source of hydrogen concentration on the surface is readsorption because, in a real vacuum system, outgassing is carried out in an atmosphere in which hydrogen is dominant. The surface concentration 2.7 1015 m2 (Table 6) corresponds approximately to a spatial concentration 1.4 1023 or 5.2 102 Pa m3/m3. These are data for material baked for 75 h at 570 K; thus, it may be concluded that surface concentration of hydrogen is higher than that corresponding to the concentration of this gas inside the material. This conclusion was supported by another experiment, in which an attempt was made to partially remove the adsorbed layer by short heating the material. Results of this process have
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Table 6 Surface filling rate for hydrogen on steel after baking at 570 K for 75 h, EM ¼ 30 kJ/mol T (K)
293 3
2
i ðPa m =m sÞ i ð1=m2 sÞ tM ðsÞ qo qp qp =qo qp for qo ¼ 1019 /m2
320 9
2 10 5.4 1011 2.2 108 4.5 107 1.2 104 2.7 104 2.7 1015
345 9
7 10 1.9 1012 7.9 109 1.3 108 1.5 104 1.2 104 1.2 1015
378 8
2 10 5.4 1012 3.5 109 2.8 108 1.9 104 6.8 105 6.8 1014
418 8
5.2 10 1.4 1013 1.4 109 7.1 108 2 104 2.8 105 2.8 1014
573 7
1.2 10 3.2 1013 5.6 1010 1.8 109 1.8 104 105 1014
3.3 108 8.8 1012 5.4 1011 1.8 1010 4.7 102 2.6 108 2.6 1011
not require too high a temperature for baking. After 1 h of baking at 400 K, the flux generated by the stainless-steel surface may decrease to 108 Pa m3/m2 s. After such a process hydrogen is the dominant gas. Its source is diffusion from the bulk of the material. This hydrogen does not pass directly to the gas phase but is adsorbed on the surface. Its desorption is possible due to surface migration and subsequent recombination.At any temperature, the surface state tends to reach equilibrium and thus ides ¼ idif þ ir ;
ð10Þ
been shown in Fig. 5. The obtained results are perhaps not very impressive, but a twofold decrease of desorbed flux was obtained (compare Fig. 3).
where ides is the desorbed gas flux, idif is the flux of gas diffusing from the bulk of the material and ir is the readsorbed gas flux. All these fluxes depend on surface concentration which is the equilibrium control factor. During cooling after bake-out the desorption flux decreases and surface concentration increases. It is easy to conclude that the surface concentration increase is also supported by gas coming from the surrounding space. It may then happen that for a very well-degassed material the diffusion direction may be changed and the gas stream will flow from the surface into the material. Thus, the condition for effective outgassing is to keep the system at a very good vacuum during baking and subsequent cooling. This condition requires high unit pumping speed for the pumping assembly.
8. Conclusions
References
Fig. 5. Pressure changes in the vacuum system baked two times.
In vacuum system with a high unit pumping speed, the outgassing of a surface is fast and does
[1] Moraw M. Vacuum 1986;36:523. [2] Moraw M, Praso" H. Vacuum 1996;47:1431.
ARTICLE IN PRESS M. Moraw, H. Praso! / Vacuum 71 (2003) 471–479 [3] Lewin G. Fundamentals of vacuum science and technology. New York: McGraw-Hill, 1967. [4] Sykes C, Burton H, Gegg C. J Iron Steel Inst 1947;156:155. [5] Calder R, Lewin G. Private communication cited by Redhead PA, Hobson JP, Kornelsen EV, The Physical
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Basis of Ultrahigh Vacuum. New York: American Institute of Physics, 1993. [6] Odaka K, Ueda S. Vacuum 1993;44:713. [7] Moraw M, Praso" H. Vacuum 2002;65:1.