Applied Surface Science 227 (2004) 7–16
Correlation of the surface composition of degassed 347 stainless steel with thermally desorbed H2 and CO R.A. Outlawa,*, Xin Zhaoa, Brian C. Hollowaya, Mark R. Davidsonb, Eric Lambersb a
Department of Applied Science, College of William and Mary Williamsburg, P.O. Box 8795, Williamsburg, VA 23187-8795, USA b Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611, USA Received 15 September 2003; accepted 23 September 2003
Abstract Variations in the surface composition of stainless steel after a 24 h, 250 8C bakeout over the temperature range of room temperature to 800 8C have been correlated with desorption of H2 and CO. The surface composition of the 347 stainless steel was monitored by Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) and desorption kinetics were determined from temperature desorption spectroscopy (TDS). Non-linear TDS was used to resolve the surface hydrogen from the bulk hydrogen. H2 and CO were observed to desorb from degassed 347 stainless steel by second-order kinetics, i.e., the gases were generated from atoms at the surface. The oxygen exchange from the surface CrxOy, FexOy to the residing carbon in the surface complex appears to control the CO generation. The onset of H2 desorption occurred slightly ahead of the CO, reached a maximum almost simultaneously (420 8C) and then declined in concert with the AES detected surface C and O. Non-linear TDS applied to large, cylindrical samples of 347 stainless steel showed H2 and CO surface desorption completely resolved from H2 bulk desorption. The steady state hydrogen desorption rate following the bakeout is bulk diffusion limited and was found to be 5:6 1012 Torr l/(s cm2). Some discussion of the surface complex stress on the aforementioned oxide decomposition with temperature is also presented. Similar experiments on 304L stainless steel gave the same results as were observed on 347 stainless steel. # 2004 Elsevier B.V. All rights reserved. PACS: 68.35.M; 82.65.J; 68.10.C; Surface Keywords: Desorption; Outgassing; Composition; Stainless steel
1. Introduction The data in the literature on desorption of hydrogen and carbon monoxide from various stainless steels under different surface preparations, bakeout temperatures and schedules varies significantly [1–9]. * Corresponding author. E-mail address:
[email protected] (R.A. Outlaw).
The origin of the desorbing species is a function of the concentration in the surface complex (defined in this work as the surface metal oxides, sub-oxides and all other species, e.g., carbon and hydrogen, contained on or in) and the concentration in the bulk material. Factors that govern the desorption (outgassing) magnitude include the defect structure of the surface complex, thickness, concentration of the different species in the surface complex and in the bulk and
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2003.09.051
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the degassing procedure applied to the system. In earlier work, it was shown that both CO and H2 desorption from 347 and 304L baked out stainless steel clearly follow second-order kinetics [10]. The supply of C and H located on and in the surface complex (as well as in the bulk) and the oxygen bound in the form of chromium and iron oxides and suboxides combine to form the dominant desorption species, H2 and CO. However, the mechanism by which the desorbed gases are generated has not been definitively shown. The purpose of this paper is to shed some light on the mechanism by showing the correlation of the surface compositional changes in concert with the desorption of CO and H2 and to resolve the resulting surface complex and bulk contributions from room temperature to 800 8C.
2. Experimental The experiments in this study were performed with two different UHV systems: (1) a surface analysis system with Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), heating stage and load lock, a TDS system with conical focusing [11] (samples, S1) and (2) a non-linear TDS furnace system for bulk desorption (samples, S2). Both systems have been previously described in detail [10,12]. The AES was operated at 5 kV and a beam current of 1 mA and the XPS with Mg source. Energy analysis was done using a double pass cylindrical mirror analyzer (CMA) with angle resolve capability. Each system is pumped with turbo-molecular, ion and titanium sublimation pump combinations to achieve background pressures in the low 1 1011 Torr range following a modest bakeout (200 8C). All measurements were made with fully calibrated quadrupole mass spectrometers and ion gauges. Two different sample configurations of 347 stainless steel were prepared in the same way. Samples, S1, disks of 10 mm in diameter and 1 mm thick, were used for linear TDS and for surface analysis. Samples, S2, cylindrical geometry 12.5 mm in diameter and 25 mm in length, were used in the non-linear TDS system for resolving surface from bulk desorption. The much larger volume of S2 contained sufficient bulk hydrogen to permit determination of the hydrogen diffusion coefficient and concentration.
All samples were cut from an annealed rod of composition (at.%) Cr ¼ 17:59, Ni ¼ 9:20, Mn ¼ 1:34, Nb ¼ 0:54, Si ¼ 0:33, S ¼ 0:02 and C ¼ 0:04 and Fe ¼ 71. All were prepared for admission into the diagnostic systems by ultrasonic degreasing with Alconox, followed by two rinses with deionized water, a final rinse in ethanol and then dried with purified air. Samples, S2, were then electropolished in ethanol 6% perchloric acid solution at 80 8C followed by two rinses in deionized water, a final rinse in ethanol and then dried with purified air. The electropolished surfaces yielded a high surface reflectivity (Ra 7) and minimized the thickness of the surface complex layer to facilitate bulk desorption. Following the cleaning procedure, all samples were covered until admitted to the diagnostic systems and immediately pumped down (<30 min). S1 samples were studied by fast TDS (linear ramp of 180 8C/min) and S2 samples were studied by slow TDS (non-linear ramp of 60 8C/min initially and then 20 8C/min for the duration of the experiment). Data were taken over the temperature range of room temperature to 800 8C (higher ramp temperatures change the alloy and surface structure, e.g., Cr depletion due to vapor pressure losses). Further details of the procedure have been discussed previously [10–13].
3. Results 3.1. Bakeout of S1 samples Fig. 1a shows AES spectra taken of the S1 samples prepared as described and Fig. 1b shows the AES spectra after a 24 h, 250 8C bakeout. Note in 1a, the predominance of the Fe LMM and O KLL peaks. The C KLL peak is observed and represents the residual carbon in the surface complex following the sample preparation. The magnitude of the carbon peak can vary greatly depending on the preparation method, e.g., the magnitude of the carbon peak can be substantially greater than the oxygen peak if small particle carbide papers are used (imbedded C) or if great care is not taken in cleaning. The Cr 489 eV LMM peak is clearly observed, but the 529 eV peak is unresolved, which suggests that the oxygen is part of a complex Fe (primarily) and Cr oxide and sub-oxide. The nickel signal is very small. No other peaks are significant.
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oxygen from the FexOy and enriched the surface of the sample with CrxOy (nearly stoichiometric Cr2O3). Surface enrichment with Cr has previously been observed by several researchers [14–16]. Fig. 1c shows AES spectra after heating S1 samples to 800 8C. The O and C signals have virtually disappeared and the metal peaks characteristic of the bulk metal have become quite prominent. A significant amount of S has now segregated to the surface. XPS data of the as received surface and after 250 8C bakeout surface is consistent with this analysis. Depth profiling of the surface with Arþ (0.5 nm/min) before and after bakeout is shown in Fig. 2a and b, respectively. Sputtering removed the S and Cl contaminants, immediately. The shape of the C profile indicates that more C has segregated to the surface and is predominantly located in the near surface region. Continuous sputtering through the oxide complex shows Fe and Cr begin to approach bulk levels, consistent with the aforementioned concentration of 71 and 17.6 at.%, respectively. The overall estimate of the thickness of the surface complex is d 3:3 nm, based on the trailing edge half height of oxygen profile [17]. The depth profile of the baked out surface complex in Fig. 2b shows substantial increases in the Cr/Fe ratio, but little change in the oxygen distribution. 3.2. Surface composition as a function of temperature: TDS correlation Fig. 1. (a) AES survey of the 347 stainless steel samples S1 before bakeout. Predominant oxide is Fe2O3. (b) AES survey of S1 after a 24 h, 250 8C bakeout. Note the segregation of C and the Cr peaks. Predominant oxide is now approaching Cr2O3. (c) AES survey of S1 after heating to 800 8C. Oxygen and carbon have disappeared and sulfur has segregated to the surface.
Fig. 1b shows a dramatic change from Fig. 1a after a 250 8C, 24 h bake in a UHV environment. The C peak has increased by a factor of 2, there are Cl and S contaminants, the Cr peaks are better defined and larger and the Fe peaks have virtually disappeared. The C peak increase is presumed to have come from segregation since no significant gas phase carbon contamination was observed on a sputtered clean control sample over the same period. The Cr 529 eV peak has been resolved and the Fe peaks have diminished significantly, but O has not changed in peak height. This suggests that the Cr has captured the
Auger analysis of the surface of samples S1, as a function of temperature from room temperature up to 800 8C, is shown in Fig. 3a. At approximately 350 8C, the C and O signals begin to slightly increase and reach a maximum at approximately 400 to 425 8C. At this point, there is a significant down turn in the C and O data and a continued steady increase in the Fe and Cr peaks. The low temperature CO desorption peak is complete about 600 8C (as determined by Gaussian peak deconvolution) and is followed by a second CO increase generated from C in the bulk segregating to the surface. The AES spectra also show a rapidly increasing S (T > 400 8C) signal that mirrors the decline in C and O. This decline indicates a decrease in surface concentration and, in turn, an increase in the available surface sites that are populated by S that has segregated to the surface. As the temperature increases, the
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Fig. 2. (a) XPS depth profile of samples S1 before bakeout (data corrected for sensitivity). Note the dominance of Fe/Fe2O3 at the surface and the consistency with Fig. 1a. (b) Depth profile after 24 h, 250 8C bakeout. The Cr now exceeds the Fe in the near surface region and the O distribution is unchanged.
C signal completely disappears at 875 8C (not shown) and the O signal disappears at approximately 1000 8C (not shown) leaving a residual spectra that is free of C and O, but now has a substantial S signal [12]. The primary metal AES peaks (Fe, Cr and Ni) are now quite pronounced as shown in Fig. 1c. This trend
Fig. 3. (a) AES peak to peak data over the temperature range RT to 800 8C of samples S1. The C and O peaks decrease at approximately 400 8C with a mirrored rise of S. Dashed line of Cr profile is averaged data from three runs and smooth curves are data fitted to fifth-order polynomial. (b and c) CO (m/e ¼ 28) and H2 (m/e ¼ 2) TDS spectra, respectively, that peaks and descends in concert with the surface complex breakup.
is very similar and consistent with the AES data versus temperature observed by Achard et al. on 316L þ N stainless steel [15]. They observed the same gradual decline of C and O until 500 8C and then a
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precipitous drop and subsequent disappearance around 900 8C. Fig. 3b and c shows the TDS peaks of CO and H2, respectively, run at 180 8C/min. Small quantities of H2O, CH4 and CO2 were also observed to desorb, but were not significant. No other desorption peaks were observed. The onset of H2 desorption began at 200 8C and grew to a maximum at 410 8C and continued to desorb over the entire temperature range. The low temperature CO peak began to desorb at 300 8C, grew rapidly to a maximum at 420 8C and then declined to a deconvoluted value of near 0 at approximately 600 8C (FWHM of 150 8C). The desorption maximum and decay of these gases corresponds very well with the maximum and decay of C and O AES data in Fig. 3a. The slope change in the
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carbon AES data around 600 8C (consistent with the end of the first or low temperature CO desorption peak) suggests a second-order, bulk diffusion controlled CO generation and desorption. On succeeding third and fourth flashes (not shown), the CO signal declined, dramatically, and reflects the depletion of diffusion controlled C from the bulk. This is consistent with the AES data and the ultimate disappearance of surface carbon. Even after C is fully depleted and the temperature continues to increase, the remaining O disappears, perhaps, desorbing as SO2 (not detected) or incorporating into the bulk. The near simultaneous desorption maximum of H2 with the low temperature CO maximum may be explained by the breakup of the surface complex
Fig. 4. Non-linear TDS of samples S2 with resolved surface and bulk desorption. CO desorption (dashed line) is consistent with Fig. 3b and c and decays smoothly. Both C and H become bulk diffusion controlled.
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structure eliminating surface and solid state defect sites. The small shoulder on the hydrogen signal at approximately 675 8C represents desorption from the bulk. This is a small signal because of the small size and disk geometry (1 mm thick) of the samples that is conducive to efficient depletion of dissolved hydrogen in the bulk during the 250 8C bakeout. This was confirmed by the absence of any significant desorption on the second flash. The FWHM of the surface desorption peak after deconvolution from the bulk desorption peak is 200 8C. Twenty samples of 347 (and 304L) were prepared in the same way and all yielded almost identical spectra to that shown in Fig. 3. 3.3. Bulk hydrogen desorption To resolve hydrogen desorption from the bulk, larger samples (S2) were prepared and run in the UHV desorption system. These samples were electropolished (to minimize the oxide thickness), as described above. Since the electropolishing was carried out at 80 8C, insignificant hydrogen was added to the samples and this was verified by a control sample that was not electropolished. The samples were admitted to the system through a load lock. Fig. 4 shows a typical desorption run with an initially rapid temperature increase (60 8C/min) to T 600 8C and then a slower increase (20 8C/ min) to the final temperature of 800 8C. The data show surface desorption peaks of H2 at 380 8C and CO at 410 8C. This data compares very well to the TDS data in Fig. 3b and c. The only difference is the absence of the second bulk diffusion controlled CO peak shown in Fig. 3b. After desorption of the surface CO peak, the CO signal decays smoothly to a very low level as the hydrogen diffusion from the bulk becomes dominant. All other species are insignificant when the hydrogen reaches a maximum at 700 8C. The decay of the hydrogen signal and depletion of bulk hydrogen at a steady temperature of 800 8C required over 2 h. 3.4. Primary CO source Outgassing in all-metal seal stainless steel vacuum systems that have been thoroughly baked out is well known to be predominantly H2 although mass spectra often indicate the next most abundant specie to be CO (CO2 and CH4 are also observed). Fig. 5 shows a
Fig. 5. Typical UHV residual gas spectra following a 4-day bakeout at 380 8C. QMS emission current is 2.5 mA.
typical UHV spectra for a very clean, baked out stainless steel system at room temperature where the CO is still a significant partial pressure. The TDS data presented above show that although CO is a clear and unambiguous desorption component at elevated temperatures, it is not a significant component desorbing from the system walls at room temperature because of the stability of the oxides. The source of CO in the gas phase at room temperature may be emission from hot cathodes and materials in the vicinity of hot cathodes. Electron stimulated desorption (ESD) from the grid is another possibility. On the other hand, the source of the H2 is from the bulk and extensive surface area of the system walls and components. When the mass spectrometer emission current and, therefore, the filament temperature is incrementally reduced from 1 mA emission down to <0.3 mA, Fig. 6 shows the concomitant reduction in the CO, CH4 and CO2 to H2 ratio. Since the sensitivity ratio of the carbon bearing gases to H2 remains approximately the same, the observed decrease in
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Fig. 6. CO/H2, CH4/H2 and CO2/H2 ratios as a function of time after mass spectrometer emission current (and therefore the filament temperature) is incrementally reduced. This data indicates the decreasing carbon bearing gas generation from the hot filament ion sources compared to the constant H2 outgassing from chamber and component walls.
the ratio strongly suggests that the carbon bearing gases are almost entirely coming from the ion source of the diagnostic instruments either from hot filament reactions or ESD from the grid. Thus, a good system bakeout lowers the outgassing rate because it lowers the supply of surface water and H in the bulk. Hydrogen outgassing can also be affected by the thickness of the oxide. If the surface oxide is minimized, then there is minimal surface limitation to the egress of hydrogen into the vacuum system so the magnitude of the outgassing is essentially controlled by a bulk supply function. A thick oxide formed over the bulk introduces a diffusion barrier to the H in solid solution and limits the outgassing rate [5,8,9].
4. Discussion Fig. 1b shows the change in surface composition due to the 24 h, 250 8C bakeout that is enriched in Cr
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and C from segregation. The depth profiles shown in Fig. 2a and b shows a significant increase of Cr from the bakeout. Since there is a weak indication of Fe peak in Fig. 1b and the oxygen peak has stayed approximately the same, the segregated Cr apparently has robbed the FexOy of some oxygen and become the dominant species (approaching Cr2O3) at the surface. One also notes that the distribution of the oxygen with depth after bakeout is relatively unchanged. A slight Cr depletion region can also be observed at approximately 4nm depth. It is interesting that these changes in the surface composition are thermally induced by a 24 h, 250 8C bakeout. Mischler et al. observed similar behavior with AES depth profiles on the electrochemically treated surface of Fe–Cr alloy (24 wt.%) at room temperature. After correction for inelastic mean free path, the Cr concentration bulge at the surface was quite dominant [18]. The second-order desorption of H2 and CO from the surface in concert with the disappearance of C and O from the surface strongly suggests the source and mechanism of the thermal reaction. Once the C and O were gone, no further emission of the CO with heating occurred. The source of the oxygen is the oxide and sub-oxides of Cr and Fe. The sources of the C and H are the interstices and defects in these oxides as well as in the bulk metal. The disappearance of the surface oxide complex also destroyed the residence and available sites for bound surface hydrogen so that one could reasonably expect a near simultaneous desorption of H2. The smaller desorption energy for H2 (Ea ¼ 59 8 kJ/mol) compared to CO (Ea ¼ 117 8 kJ/mol) explains the earlier onset of desorption of H2 at 200 8C compared to the onset of desorption of CO at 300 8C [10]. Desorption of H2 from the bulk of samples S1 and S2 is reasonably consistent. Deconvolution of the data in Fig. 3c shows a small, but distinct peak at 675 8C which is H2 desorption from the bulk of samples S1 and matches the more obvious and well resolved bulk desorption peak in samples S2 at 700 8C (see Fig. 4). The 25 8C difference in the peaks of the two sets of data could easily be explained by the differences in the system and in the surface complex. Clearly, the S2 bulk hydrogen desorption was diffusion limited. The linear decay (on a semilog plot) permitted the H diffusion coefficient in the stainless steel to be determined. The value of the pre-exponential factor and the
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activation energy were determined to be, respectively, D0 ¼ 7:01 107 m2/s and DH ¼ 48:0 kJ/mol [12]. The hydrogen concentration measured by integrating the area under the bulk diffusion curve of Fig. 4 gave a value of 2:1 1018 atoms/cm3. This indicates a large reservoir of hydrogen for outgassing at room temperature in the absence of sufficient bakeout or vacuum firing procedures to deplete that concentration. With this data, the steady state hydrogen desorption rate from the samples following the bakeout of 250 8C for 24 h was determined. A value of 5:6 1012 Torr l/ (s cm2) was calculated for the outgassing rate and is in excellent agreement with the experimental work of Calder and Lewin [2]. They obtained a value of 4 1012 Torr l/(s cm2) conducted after a bakeout of 300 8C for 24 h. The H2 TDS measurements of Hirohata et al. appear to be consistent with those in this paper [7]. Although, the TDS data on 316L does not resolve the surface and bulk hydrogen, the shoulder on their desorption curves of all the surface finishes (machined to electropolished) appears to peak at 400 8C. The data of Ishikawa and Odaka on CO and H2 desorption from 316L stainless steel is very similar to what is presented here, but with a very different surface pretreatment [8]. They did repeated surface exposures of 450 8C in air and then bakeout in vacuum at 150 8C for 5 h. Their TDS data shows both CO and H2 peaks around 400 8C which is consistent with the surface desorption interpretation presented here as well as the second diffusion controlled peaks from the bulk (700 8C). The absence of the second CO peak in Fig. 4 may be expected in light of the much slower TDS. In Fig. 3b, the second desorption peak appears to be diffusion controlled C coming to the surface and reacting with the available O and desorbing. Subsequent flashes require higher and higher temperatures. This indicates that the C is diffusing from deeper in the surface region or bulk. Ultimately, the C was almost completely depleted (C diffusion length becomes too long for the 4 min duration of the experiment). In the slow non-linear TDS, the duration of the experiment is much longer and the C diffusing from the near surface region may have been unresolved and desorbed in a single peak in the 10 min run. Secondly, the electropolishing substantially reduced the surface complex thickness to <1.5 nm which, in turn, minimized the C in the surface complex and also allowed the
egress of C in the near surface region to be much faster. Therefore, it is possible that since the experiment in Fig. 4 goes much slower, the CO was unresolved and all contained in the one peak. The impact of increasing temperature on this surface layer is dramatic. The onset of CO desorption begins at 300 8C, reaches a peak at 400 8C and continues until there is free Cr and Fe. The reaction of surface carbon with Fe2O3 and Cr2O3, for example, is given by Fe2 O3 þ 3C ! 3CO þ 2Fe Cr2 O3 þ 3C ! 3CO þ 2Cr The free energy change, DG, for the Cr2O3 reaction in the region of 300–400 8C where CO begins to desorb is more than þ100 kcal/mol, so energy must be added to force the reaction to proceed. One possibility is the thermal energy plus the existing film stress are sufficient to favor an exchange mechanism between the metal oxide and/or suboxide with the carbon located in defects and interstitial sites. This is somewhat analogous to the recrystallization temperature of heavily cold worked solids where the dislocation network creates very high stress and determines the temperature at which atoms begin to move for stress relief (recovery, recrystallization and grain growth); the higher the stress, the lower the recrystallization temperature [19]. Little data in the literature addresses the stress in oxide films. Abel and Hoffman [20] found substantial tensile stress in oxidized Fe films on stainless steel substrates (Fe3O4) and that it varied linearly with oxide thickness in the temperature range of 250– 310 8C. They found that the average tensile stress for the magnetite to be 100 MPa for a 200 nm film so a linear approximation would be 1.5 MPa in an oxide film of 3 nm. Large tensile stress has been reported by Howes and Richardson for the initial stages of iron-chromium alloy oxidation at high temperature [21]. Poole and Shreir have reported measuring a compressive stress of 2:7 103 kg/cm2 for Fe2O3 in layers of less than 50 nm thickness [22]. Whether tensile or compressive (controlled by defects), this stress level is large and certainly could affect the reaction driving force. Above 400 8C, the decomposition of the surface complex is rapid and in concert with desorption of CO.
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Fig. 5 is an RGA survey that shows the predominance of hydrogen in the system following a good bakeout (>250 8C). The higher the temperature and the longer the duration of the bakeout the more dominant the m/e ¼ 2 peak. Bacher et al. [23] recently measured the reduction in bulk hydrogen content in 316L ESR as a function of a 12 h bakeout at temperatures up to 500 8C. This data suggests a hydrogen reduction in stainless steel bulk concentration of about 50% with a 24 h, 250 8C bakeout. The residual CO is usually the next most prevalent residual gas (sometimes CH4) and does not significantly change following a bakeout. Fig. 6 shows the substantial reduction in the CO, CH4 and CO2 to H2 ratio as a function of reduced emission current. This suggests that the source of hydrogen is primarily from the stainless steel bulk/surface area of the system walls and components and the source of carbon bearing gases is primarily from the ion sources. Thus, one can reduce the CO background in the system by minimizing the filament temperature. This was also concluded in the work of Watanabe et al. [24].
5. Conclusions Bakeout of the sample at 250 8C for 24 h results in Cr segregating to the surface and becoming the dominant metal in the oxide complex. Carbon segregation also occurs and doubles the surface concentration. These results are supported by XPS depth profiles. Linear TDS experiments have shown that CO and H2 desorption from degassed 347 and 304 stainless steel have second-order kinetics and that the gases are generated from the atomic C and H residing on and in defects of the surface complex. At 200 8C, the H atoms begin to combine and desorb as H2 and at 300 8C, the C begins to react with the oxygen from the oxides and sub-oxides (CrxOy, FexOy) and desorb as CO. AES and XPS data correlates well with the TDS data and show an initial slight decrease in the surface C and O with temperature until 420 8C when there is a slight up turn to a maximum. This appears to be a point of maximum surface complex decomposition and corresponds with a maximum in CO and H2 desorption. With further increase in temperature, the surface C and O decrease in concert with the desorbing CO. Molecular hydrogen desorption also peaks at
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410 8C, most likely because of the breakup of the surface complex and the complete disappearance of surface and solid state sites. Large cylindrical samples of stainless steel (run using slower and non-linear TDS) provided consistent results with the aforementioned data and resulted in better separation of the surface H and CO desorption from the bulk H desorption. The H desorption data permitted determination of the hydrogen diffusion coefficient and the hydrogen concentration from which the outgassing rate at 20 8C was found to be 5:6 1012 Torr l/(s cm2). Room temperature RGA spectra of stainless steel systems after bakeout >250 8C, clearly shows H2 as the dominant residual gas emanating from the chamber walls. The smaller CO signal usually observed was shown to be mostly from the hot filament ion sources in the gauges, mass spectrometers and other diagnostic instruments.
Acknowledgements The authors would like to thank Professor Dennis Manos of this Department (College of William and Mary) for many helpful discussions and Professor Robert Orwoll of this Department (College of William and Mary) for his discussions of the energetics of the oxide layer.
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