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Atomic oxygen diffusion on and desorption from amorphous silicate surfaces Jiao He, Dapeng Jing† and Gianfranco Vidali* Surface reactions involving atomic oxygen have attracted much attention in astrophysics and astrochemistry, but two of the most fundamental surface processes, desorption and diffusion, are not well understood. We studied diffusion and desorption of atomic oxygen on or from amorphous silicate surfaces under simulated interstellar conditions using a radio-frequency dissociated oxygen beam. Temperature programmed desorption (TPD) experiments were performed to study the formation of ozone from reaction of atomic and molecular oxygen deposited on the surface of a silicate. It is found
Received 13th October 2013, Accepted 2nd January 2014
that atomic oxygen begins to diffuse significantly between 40 K and 50 K. A rate equation model was used to study the surface kinetics involved in ozone formation experiments. The value of atomic oxygen
DOI: 10.1039/c3cp54328e
desorption energy has been determined to be 152 20 meV (1764 232 K). The newly found atomic
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oxygen desorption energy, which is much higher than the well-accepted value, might explain the discrepancy in abundance of molecular oxygen in space between observations and chemical models.
1 Introduction Oxygen is the third most abundant element in space after hydrogen and helium. It has attracted considerable attention among astrophysicists and astrochemists because it is an indicator of metallicity and thus a probe of the evolution of star-forming galaxies.1 It intervenes in many reactions to form other molecules, such as H2O, CO, CO2 and even more complex molecules such as amino acids. Oxygen is found mostly in the gas-phase in diffuse clouds (o10 H atoms per cm3), and in molecular form (H2O, CO, CO2, etc.) in the ices of denser clouds. Furthermore, O is locked in grains, mostly silicates of the type (FexMg1x)2SiO4, 0 o x o 1. It is found that both atomic and molecular oxygen are depleted in the gas-phase, although there is some uncertainty to what extent.2–4 The deficiency of oxygen in the gas-phase, especially in molecular form, is particularly vexing.4–6 Various gas phase models predicted O2 to be the third most abundant molecular species after H2 and CO, at an abundance of above 105 relative to H2 in well-shielded regions (see Goldsmith et al.6 and references therein). At this predicted abundance O2 should play an important role in gas phase cooling. However, the search for O2 using space observatories has found much lower O2 abundances. The survey using the SWAS (Submillimeter Wave Astronomy Satellite)7 sets an upper limit of N(O2)/N(H2) smaller than 2.6 107, which is two Physics Department, Syracuse University, Syracuse, NY 13244-1130, USA. E-mail: [email protected] † Current address: Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14850, USA.
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orders of magnitude lower than model predictions. With the launch of Odin, Larsson et al.8 observed the star forming molecular cloud core r Oph A and found the O2 abundance to be 5 108, averaged over the Odin beam. Recent observation of r Oph A using the Herschel Space Telescope has obtained similar O2 abundance as found with Odin.9 In a recent search for O2 emission in an ionization region towards the Orion bar with Herschel by Melnick et al.,4 O2 was detected, but again, at a much lower abundance than expected. In this region, dust grains are expected to be at higher temperature because of the radiation flux from stars. Oxygen is expected to be ejected from grains, for example by photodesorption, and in the gas-phase it can form O2 via reactions such as O + OH O2 + H. Therefore O2 is expected to be more abundant in the gas-phase by a factor of 10 than it would be in a similar UV quiescent region. Although O2 was detected, its abundance came short of what models of the chemical evolution of that specific space environment predict.10 In trying to reconcile observations with prediction of models, Hollenbach et al.10 and Melnick et al.4 pointed out that if the desorption energy of O is higher than the often assumed value at 800 K11 (by a factor of 1.5 in Hollenbach et al. and a factor of 2 in Melnick et al.), then there would be much less oxygen desorbing from grains and consequently less O available for O2 formation in the gas phase. This value of 800 K for O desorption from dust grains is found in many models of chemical evolution of ISM (interstellar medium) clouds10,12–16 but has no strong theoretical derivation11 and no experimental confirmation. One of the aims of this paper is to address this problem by presenting measurements of laboratory experiments of oxygen chemistry
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on an amorphous silicate surface, an analog of ISM dust grains, under simulated space conditions. Besides atomic oxygen desorption from dust grains, there are other processes involving oxygen that influence the chemical make-up of ISM clouds. Oxygen-related chemical reactions begin when atomic oxygen (O) or molecular oxygen (O2) stick to grain surfaces. According to one estimate, up to 10% of O2 can be in ices.6 Adsorbed O or O2 can react with radicals that are on surfaces of grains to form more complex molecules17 via the Eley–Rideal, hot-atom or Langmuir–Hinshelwood mechanisms. Because of the low temperature of dust grains (10–15 K in dense clouds), kinetics plays a large role in reactions on surfaces. Therefore, it is important to quantify the energetics of adsorption, desorption and diffusion processes so accurate parameters can be entered in codes of the chemical evolution of ISM environments. Oxygen chemistry has been studied on analogs of grain surfaces, both theoretically and experimentally. Xie et al.18 found theoretically that the atom–molecule reaction 3O + HC3N which has a barrier in the gas-phase, can be effectively catalyzed by water ices to be barrierless. Tielens and Hagen11 proposed that water formation is through the hydrogenation of O/O2/O3 on grain surfaces. Lamberts et al.19 used a Monte Carlo code to study the surface reaction of O2 hydrogenation. In all these theoretical studies, the surface kinetics of oxygen was not studied in detail. Experimentally, the formation of ozone from energetic particles has been studied by several groups,20–22 but fewer experiments used atoms or molecules at thermal energy. Extensive work has been done in recent years to study the formation of water. Miyauchi et al.23 investigated water and hydrogen peroxide formation by depositing H on cold O2 ice and obtained the effective reaction rates. Cuppen et al.24 studied O2 hydrogenation by simultaneous H and O2 deposition. Dulieu et al.25 and Jing et al.26 studied water formation via atomic oxygen hydrogenation by depositing O and H via two beam-lines. However, in these and similar experiments, because of the difficulty in obtaining a large dissociation fraction, what is deposited on the surface is not only O, but also O2. O2 and O can react and form O3; therefore, in a typical experiment H is really reacting with a mixture of O, O2, and O3. Further investigation of oxygen surface kinetics is needed to explain the relative ratio among H + O, H + O2 and H + O3 channels. Other than water formation, there has been experimental work done on formation on dust analogs of other oxygen-containing molecules. The formation of CO2 is another reaction that requires grains. Roser et al.,27 and more recently, Raut and Baragiola28 have studied the formation of CO2 on a surface by sending CO molecules together with oxygen atoms via beam-lines, and found low efficiency for the CO + O - CO2 reaction. This might be because O tends to combine with another O to form O2 instead of reacting with CO, or because undissociated O2 diffuses fast on the surface and reacts with O to form O3. All these studies require a better understanding of O/O2 kinetics on surfaces. The fundamental processes of oxygen desorption and diffusion on ISM related surfaces were not investigated until recently. Ward et al.,29 when doing research on the reaction of atomic oxygen
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with CS2 on a HOPG surface, introduced simple rate equations to analyze the data. However, they used the Arrhenius expression for both Langmuir–Hinshelwood and Eley–Rideal mechanisms, which is probably incorrect. In a work by our group, Jing et al.30 studied the formation of molecular oxygen and ozone on an amorphous silicate surface using atomic 16O and 18O beams. (Amorphous silicates and carbonaceous materials are the main components of interstellar dust grains.31) A value of the diffusion energy barrier for atomic oxygen on an amorphous silicate surface was obtained. However, this value is not accurate because an error was found32 in a calculation related to a control experiment to separate contributions of ozone from molecular oxygen in the O2 signal in our detector (ozone is fragile and is known to break up into O2 and O in the ionizer of a quadrupole mass spectrometer). Here we present the results of further experimental investigations on the formation of ozone from reaction with atomic and molecular oxygen on silicates, and introduce a more comprehensive rate equation model to study the kinetics of O and O2 on amorphous silicate surfaces. This has given us what we believe is a more accurate picture of oxygen chemistry and in some respects it differs from some of the results obtained by Jing et al.30 The paper is structured as follows. The next section characterizes the adsorption–desorption of O2 via temperature programmed desorption (TPD) experiments and describes the ozone formation experiments. In Section 3 we present the results of adsorption– desorption experiments and use the direct inversion method to obtain the desorption energy of molecular oxygen. Then the ozone formation experiments are analyzed in detail and a rate equation model is introduced to obtain the desorption energy and diffusion energy barrier of atomic oxygen. Section 4 summarizes the findings and comments on the significance for astrochemistry.
2 Experimental 2.1
Apparatus
The apparatus used in this work has been described in detail elsewhere;33 below there is a brief summary, and changes made to it since then are highlighted. The apparatus consists of an ultra-high vacuum main chamber with base pressure lower than 2 1010 Torr at 300 K and of two collimated triply differentially pumped atomic/molecular beam-lines. In this work only one beam-line is used. At the center of the main chamber a sample holder is thermally connected to the cold finger extension of a continuous flow liquid He cryostat. The sample is a 1 mm thick amorphous silicate thin film deposited on a 1/2 inch diameter gold coated copper disk, with temperature controllable from 8 K to 500 K using a Lakeshore 336 temperature controller. Silicate films are obtained by e-beam physical vapor deposition (EB_PVD). Fabrication and characterization methods of the samples are described in Jing et al.33 A triple-pass Hiden quadrupole mass spectrometer (QMS) is mounted on a rotatable platform and is used to detect desorbing substances from the sample and to characterize the products in the beam-lines. A water-cooled radio-frequency (RF) dissociation source is attached
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Fig. 1 Adsorption–desorption of O2 from an amorphous silicate surface kept at 20 K for different coverages. The heating ramp rate during the TPD stage is about 1 K s1. Figure replotted from Jing et al.30
to the beam-line to generate atomic oxygen. The dissociation efficiency is about 25% for molecular oxygen and is constant throughout the experiments. By flooding the chamber with O2 and recording the pressure and QMS counts, a conversion between QMS counts and the number of O2 molecules is obtained. The flux is calculated to be about 7.6 1011 cm2 s1 and 5.0 1011 cm2 s1 for O2 and O respectively (except for experiments as shown in Fig. 1, which is about 20% lower). 2.2
Description of experiments
Direct measurements of atomic oxygen desorption or diffusion are challenging because pure atomic oxygen is unavailable under present experimental conditions. Atomic oxygen is usually mixed with molecular oxygen. When O and undissociated O2 from the beam land on the surface, there are two likely chemical reactions involved: O + O - O2 O + O2 - O3 The surface kinetics of atomic oxygen are studied by quantifying these two reactions, including determining the surface kinetics of O2 and the amount of both reactants and products on the surface. The amounts of O and O2 from the beam-line are characterized by direct beam measurements. The amount of O3 formed can be measured by Fourier transform infrared spectroscopy (FTIR) or TPD. However, the focus of this investigation is on submonolayer coverage when the FTIR signal for O3 is too weak, thus TPD techniques are used instead. When measuring O3 using TPD and the QMS, another difficulty arises because O3 breaks up into O and O2 in the QMS ionizer. Additional efforts are required to determine whether the measured O/O2 are due to O3 breaking up or O/O2 desorption from the surface, which is discussed in detail later. The surface kinetics of O2 can be obtained by performing O2 adsorption–desorption experiments. Information from these experiments enables the quantification of atomic oxygen surface kinetics, including the desorption energy and the diffusion energy barrier.
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Two sets of O2 adsorption–desorption experiments are performed. The first is O2 adsorption–desorption TPD experiments at different exposure temperature to find out the residence time or, equivalently, the steady state coverage for O2. It is found that during exposure at the surface temperature below 20 K, the O2 sticking is unity while at 40 K and 50 K only 0.3 ML and 0.035 ML stick on the surface, respectively. Thus in ozone formation experiments, if the surface temperature rises above 50 K, the amount of O2 on the surface is negligible. The second set of O2 adsorption–desorption experiments is adapted from one of our previous studies.30 Here we summarize it and in the next section we use a direct inversion method to extract the desorption energy distribution. In these experiments the sample is kept at 20 K during the exposure to the molecular oxygen beam. The exposure time is incremented by 1.5 minutes from 1.5 to 15 minutes. The sticking probability of O2 at 20 K is obtained using the King– Wells adsorption–reflection method and is calculated to be close to one. After exposure the sample is warmed up at a rate of about 1 K s1 to a temperature higher than 100 K to thermally desorb O2 molecules. After every 2 to 3 TPD runs the sample is heated up to higher than 230 K to desorb water that could have condensed on the surface. Based on an analysis of TPD peak areas and beam flux it is found that a 10.5 minutes exposure in the set of experiments by Jing (the flux in those experiments is different from the one used in other experiments reported in this paper) is equivalent to 1 ML. Here we focus on experiments at submonolayer coverage, and TPD traces are shown in Fig. 1. An analysis of this set of experiments is in the Results and analysis section. In the ozone formation experiments, we first check the composition of the beam and measure the flux of the various components. When the QMS detector is placed in front of the beam-line, the amount of O3 in the beam is negligible (less than 0.1% of the beam intensity). Ozone formation experiments are carried out next. We keep the amorphous silicate surface at 30 K, 40 K, 50 K and 60 K, and send the dissociated O/O2 beam onto the sample for different durations, then do a TPD. When the exposure temperature is 30 K or 40 K, the sample is warmed up to 50 K and maintained for 2 minutes to desorb O2 before the TPD, so as to make sure the atomic mass 36 TPD peak that appears at about 63 K is not from undissociated O2 in the beam. This simplifies the analysis of ozone cracking in the ionizer. All relevant atomic masses, including mass 18, 36 and 54, are recorded both during the exposure stage and the TPD stage with the QMS facing the sample. In all measurements there is no direct desorption of mass 18 other than background noise. Since O3 can crack into O and O2 in the QMS ionizer, the mass 36 signal is at least partly due to the cracking of O3. The TPD traces are shown in Fig. 3. When the exposure temperature is 60 K, there is no O2 or O3 detected in the TPD (not shown in the figure). This is because O3 starts to desorb at around 60 K, and O3 formed during the exposure at 60 K desorbs quickly.
3 Results and analysis 3.1
Experiments of O2 adsorption–desorption
To extract the desorption energy distribution from adsorption– desorption TPD experiments, the direct inversion method in
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divided by the number of desorption sites on the surface. The order of desorption is taken to be 1 in this paper. Edes is the desorption energy, kB is the Boltzmann constant, and T is the surface temperature. Then, the coverage dependent desorption energy distribution can be calculated for each TPD trace as follows: b dy Edes ðyÞ ¼ kB T ln (2) ny dT A derivative of the distribution gives the Edes distribution f (Edes), which satisfies: Ð (3) f (Edes)dEdes = 1
Fig. 2 Distributions of Edes for O2 on an amorphous silicate surface obtained from direct inversion of TPD data shown Fig. 1.
´lek et al.34 and Amiaud et al.35 is adopted. The Polanyi– Dohna Wigner equation is written as:
dyðtÞ ¼ nyðtÞ expðEdes ðyÞ=kB T Þ dt
(1)
where n is the pre-exponential factor of the desorption. In general n depends on the substrate and adsorbate, but in this analysis the standard value n = 1012 s1 is taken. y(t) is the coverage defined as percentage of one monolayer, i.e., the number of particles (atoms or molecules adsorbed on the surface)
Fig. 3
the integration is over the whole desorption energy spectrum. We O2 , from the obtained the desorption energy distribution for O2, Edes silicate surface which is shown in Fig. 2. It can be seen that the distribution is peaked at about 78 meV. The O2 diffusion energy O2 barrier Ediff is difficult to measure directly, especially for nonregular surfaces. Generally it is assumed that Ediff = aEdes, where a is a number adopted to be between 0.3 and 0.8.13 For amorphous surfaces the a value is higher than for regular surfaces. We O2 therefore have an estimate of 23:3 meV o Ediff o 62:4 meV depending on the assumed value of a.
3.2
O3 formation
The TPD results are shown in Fig. 3. There are both mass 36 (m36) and mass 54 (m54) peaks at about 63 K. An integration of
TPD traces of O2 (36 amu) and O3 (54 amu) after O/O2 exposure for the indicated times; the surface temperatures during exposure are 30 K, 40 K and 50 K.
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Paper Integration of TPD traces from Fig. 3. The last row is the TPD yield ratios of mass 36 to mass 54
Texp
30 K
Exposure (min)
10
20
30
5
10
15
30
5
10
15
20
30
13.5 8.2 16.4
30.0 17.2 17.4
46.4 29.5 15.8
7.62 4.29 17.6
15.0 8.41 17.8
20.0 11.9 17.0
39.6 23.5 16.9
5.79 3.23 17.9
11.9 7.51 15.8
14.8 8.63 17.1
19.9 11.2 17.8
24.2 14.1 17.2
4
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N(O2)/10 N(O3)/103 N(O2)/N(O3)
40 K
50 K
TPD areas shown in Fig. 3 is given in Table 1. The ozone yields at Texp = 50 K are about half of the yields when Texp = 30 K. If the desorption energy of O is 800 K (69 meV) as suggested by Tielens and Hagen,11 which is lower than the desorption energy of O2 (78 meV), then because 30 K is close to the desorption peak temperature of O2, an easy calculation can show that the residence times for both O and O2 are orders of magnitude shorter at 50 K than at 30 K. One should see that the ozone yields at 50 K are orders of magnitude lower than that of 30 K. But this disagrees with the experimental results shown in Fig. 3. One then concludes that the desorption energy for O should be higher at 800 K. In Table 1 the integrated TPD area ratio m36/m54 is almost a constant, which is between 15.8 and 17.8 for the experiments plotted in Fig. 3. Besides, mass 36 and mass 54 appear at the same temperature and have a similar shape. Now a question arises: does the TPD peak of mass 36 in Fig. 3 come from the undissociated O2 from the beam, O3 cracking in the ionizer, or O2 (O + O - O2) as a result of O diffusion on the surface during the TPD? The first possibility can be excluded because undissociated O2 desorbs at a temperature below 50 K, and the sample is kept at 50 K for at least 2 minutes before the TPD to make sure there is no undissociated O2 left on the surface. The other two require more analysis. It is necessary to find out which one is true before quantifying the amount of ozone formed. If the mass 36 peak is all coming from O3 cracking in the ionizer then the ozone formed on the surface is not mixed with O; if part of the mass 36 peak is from O2 (O + O - O2) then there is O mixed with O3; in this case the temperature at which O starts to diffuse significantly should be virtually the same as the O3 desorption temperature, since the TPD desorption peak of mass 36 occurs simultaneously with the TPD peak of mass 54. In a previous paper by our group30 we did some analysis of the same TPD peak but with a different experimental setup and a different set of experimental data. Here we summarize that experiment. We used two beam-lines simultaneously, one with dissociated 16O2 and the other with dissociated 18O2. The sample temperature during exposure was 15 K. The TPD peak of O2 that was centered at about 63 K was attributed partly to 16 18 O O as a result of 16O and 18O diffusion during the TPD stage when the surface temperature was higher than about 60 K. The fact that both 16O18O and ozone desorb at the same temperature was explained as a coincidence between atomic oxygen diffusion temperature and ozone desorption temperature. By comparing these data with current work and re-analyzing the previous data, it is found that the contribution of O diffusion to the TPD peak centered at 63 K was overestimated because the
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cross-section data used for O3 break-up in the QMS ionizer might not have been appropriate for our ionizer. Now we analyze the ratio of O2/O3 contributions to the TPD peak centered at 63 K using the data shown in Fig. 3 and try to determine whether the mass 36 peak at 63 K is due to ozone cracking or O diffusion. First let us suppose atomic oxygen starts to diffuse significantly at above 60 K as it was suggested in Jing et al.30 When the exposure temperature Texp is 30 K, the residence time of O2 on the surface is tens of seconds assuming O2 Edes ¼ 78 meV. At this temperature the O2 diffusion rate should be very high. Taking into account that the dissociation rate of O2 is about 25% in our system, the O/O2 ratio in the beam flux is about 2 : 3, and there should be enough O2 to react with all the O. After warming up to 50 K to desorb residual O2, what is left on the surface should be O3 only. Since in the TPD stage the QMS records signals of both mass 36 (O2) and mass 54 (O3), the OQMS /OQMS ratio should be a constant that depends on the 2 3 cracking ratio of O3 in the QMS ionizer; let this constant be C1. In contrast, when Texp is 50 K, the residence time for O2 is very short; it is likely that there is not enough O2 to react with all the O, and it can be expected that there are both O3 and unreacted O left on the surface. As the temperature goes above 60 K in the TPD stage, O starts to diffuse and form O2. Since there is both O3 (from O2 + O) and O2 (from O + O) desorption above 60 K, the OQMS /OQMS ratio from the TPD peak area should be higher than 2 3 C1; let’s call the ratio C2. It can be shown that the percentage of O2 (coming from O + O) that is mixed with O3 in the TPD peak at Texp = 50 K is O2% = (C2 C1)/(C1 + 1), the percentage of O mixed with O3 before TPD is two times that of O2%. As is shown in Table 1, C1 E 16.5 and C2 E 17.2, and the difference between C1 and C2 is well within error bars. The amount of O2 mixed with O3 in the TPD peak is negligible (O2% o 4%). We conclude that the signal of the mass 36 peak in the TPD peaks in Fig. 3 is all due to ozone cracking in the ionizer. One can also obtain a temperature range in which the O starts to diffuse significantly. Because our assumption that O starts to diffuse above 60 K turns out to be not true, T O diff should be lower O than 60 K. Furthermore, if one considers that Tdiff cannot be between 50 K and 60 K, or otherwise there would be a peak of the mass 36 signal between 50 K and 60 K, then the temperature at which O starts to diffuse significantly T O diff should be lower than 50 K.
3.3
Rate equation modeling
Our next step is to quantitatively describe the O2 and O3 formation processes using a rate equation model, and then
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O obtain the diffusion E O diff and desorption E des energy values for O from the data. The rate equations to describe O2 and O3 formation on the sample surface are written as ! E O2 dyðO2 Þ ¼ fluxðO2 Þ nyðO2 Þexp des kB T dt
nyðO2 ÞyðOÞ exp
O2 Ediff
kB T
!
! EO þ exp diff kB T (4)
O Ediff dyðOÞ 2 ¼ fluxðOÞ 2nyðOÞ exp dt kB T ! ! O2 O Ediff Ediff nyðO2 ÞyðOÞ exp þ exp (5) kB T kB T On the right side of eqn (4) the first term is known from the measurement of the direct beam, the second term describes the desorption of O2, and the third term describes the reaction O2 + O - O3. The O3 formation rate depends on the diffusion rate of O2 both O and O2. However, if Ediff and E O diff are not too close to each other, the one with the lower value dominates the diffusion process, and the other one can be ignored. Since it is already known that O2 starts to diffuse at low temperature (well below O2 desorption peak temperature), we assume O2 O Ediff o Ediff , and the O3 formation term can be approximated O2 =kB T . by nyðO2 ÞyðOÞ exp Ediff
On the right side of eqn (5) the second term is due to the reaction O + O - O2. We assume that the reaction product O2 desorbs immediately after formation so that it doesn’t go into eqn (4). This is a reasonable assumption because the reaction O + O - O2 is strongly exothermic, and thus one expects that O2 leaves the surface upon formation. Direct desorption of O is ignored in eqn (5) since O diffusion should take place before O desorption, O should diffuse and form O2 instead of desorbing directly. This assumption will be verified later after obtaining the desorption energy of O. The equations can be simplified by assuming steady state conditions. When the exposure temperature Texp = 30, 40 or 50 K, reactions should proceed fast and reach a steady state quickly because of O2 high mobility. At steady state, eqn (4) and (5) can be expressed as flux(O2) = O2 desorption rate + O3 formation rate
(6)
flux(O) = O2 formation rate + O3 formation rate
(7)
Eqn (6) and (7) are nothing more than saying that all the O2 coming from the beam either desorb or form ozone, while all the O coming from the beam either form O2 or form ozone. By integrating the TPD peak areas in Fig. 3 (including both mass 36 and mass 54 because both of them are coming from ozone desorption) and comparing with direct beam measurement, eqn (6) and (7) lead to
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at 30 K: O3 formation rate = 0.44 flux(O2) = 0.65 flux(O) at 40 K: O3 formation rate = 0.42 flux(O2) = 0.63 flux(O) at 50 K: O3 formation rate = 0.31 flux(O2) = 0.46 flux(O) Notice that there is a significant drop in the O3 formation rate between 40 K and 50 K. Eqn (7) then suggests that between 40 K and 50 K there is a significantly increasing amount of O that forms O2 instead of O3. One might think that perhaps between 40 K and 50 K O starts to desorb directly; however, it is verified later that O does not desorb significantly. O must start to diffuse significantly between 40 K and 50 K. In Section 3.2 we argued that at 30 K the O should be all consumed by O2, but the QMS measurements show that only 65% of O is consumed. An explanation of this discrepancy might be that in a QMS the detection efficiencies for different gases are different, O3 (including un-cracked O3 and cracked O3) could have lower detection efficiency than O2, the QMS signal height comparison must be corrected for different gases. Thus we let the O3 formation rate = flux(O) at 30 K and correct for the other O3 amounts proportionally. After correction, at 30 K all the O atoms are converted to O3, at 40 K about 97% of O are converted to O3, at 50 K 71% of O is converted to O3 while the remaining 29% diffuse and form O2. Combine eqn (4)–(7) and solve analytically for y(O) and y(O2): ! O2 E O2 Ediff O3 formation rate yðOÞ ¼ exp des fluxðO2 Þ O3 formation rate kB T (8) yðO2 Þ ¼
fluxðO2 Þ O3 formation rate O2 =kB T n exp Edes
(9)
O2 ; in the expression In eqn (8) and (9) the only variable is Ediff O2 O2 ¼ aEdes one lets a = 0.3, 0.4, 0.5, 0.6, 0.7 and 0.8, and Ediff
Table 2 Calculation of O coverages y(O) and O2 coverages y(O2) at 30 K, 40 K, and 50 K, and of the O desorption energy E O des, assuming different a values. The units for coverages and desorption/diffusion energies are ML and meV, respectively
EO diff
EO des
2.9 106 9.1 108
45
150
2.3 106 5.7 106
1.8 105 9.1 108
61
152
5.9 107 1.0 102
2.2 105 5.7 106
1.1 104 9.1 108
76
153
y(O) y(O2)
1.2 105 1.0 102
2.1 104 5.7 106
6.6 104 9.1 108
92
153
0.7
y(O) y(O2)
2.4 104 1.0 102
2.1 103 5.7 106
4.0 103 9.1 108
108
154
0.8
y(O) y(O2)
5.0 102 1.0 102
2.0 102 5.7 106
2.4 102 9.1 108
123
154
a
T
30 K
40 K
50 K
0.3
y(O) y(O2)
1.4 109 1.0 102
2.4 107 5.7 106
0.4
y(O) y(O2)
2.9 108 1.0 102
0.5
y(O) y(O2)
0.6
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calculate y(O) and y(O2) values for different values of T and a. The calculated values of y(O) and y(O2) are shown in Table 2. To estimate the O diffusion energy barrier E O diff, we consider that at Texp = 50 K 29% of O diffuse and form O2 instead of O3, and plug in the values of y(O) corresponding to different a values, and T = 50 K, into the following equation: O E 2nyðOÞ2 exp diff 0:29 fluxðOÞ kB T and then calculate for E O diff. The desorption energy of O can be O calculated using E O = E des diff/a. Here we assume that the a values are the same for both atomic and molecular oxygen. The calculated results are shown in Table 2. It can be seen that even if a varies between 0.3 and 0.8, the calculated atomic oxygen desorption energy E O des is almost the same. The value is EO = 152 2 meV. The uncertainty in the E O des des value comes mostly from the uncertainty in the determination of the O3 formation efficiency. By allowing a large 50% uncertainty in the determination of the O3 amount, the change in the E O des value is 20 meV at most. Then it can be concluded that the desorption energy for atomic oxygen is E O des = 152 20 meV (1764 232 K). In the above discussion no O direct desorption is assumed. This assumption can be verified now. The ratio between the amount of O due to O desorption and the O + O - O2 amount can be calculated as: O nyðOÞ exp Edes =kB T O =kB T 2nyðOÞ2 exp Ediff The value is between 4.2 106 for a = 0.3 and 1.6 102 for a = 0.8, which is much less than 1. Thus the assumption is correct and it is fine to ignore the atomic oxygen desorption term in eqn (5).
4 Conclusions The diffusion energy barrier and desorption energy for atomic oxygen on interstellar dust grain surfaces at low temperature are essential for simulation codes of the chemical evolution of interstellar environments. By performing TPD experiments of ozone formation and using a rate equation model, we have obtained a new value for atomic oxygen desorption energy on an amorphous silicate surface, even though there have been known technical difficulties found in the past.30,33 The value of atomic oxygen desorption energy is found to be 152 20 meV (1764 232 K) which is about double the prior estimated value that has been used widely in the literature. Models of the chemical evolution of ISM environments using the old estimate gave predictions of oxygen abundance in severe disagreement with observations. Our value is in good agreement with an estimate that Melnick et al.4 gave to reconcile their own most recent observations of O2 with modeling predicted abundances. In this work we also found that (1) the desorption energy of O2 from amorphous silicate surfaces is peaked at 78 meV (905 K); (2) the ranges of diffusion energy barriers for atomic and molecular oxygen are 45–123 meV and 23.3–62.4 meV,
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respectively, for assumed a values from 0.3 to 0.8. Katz et al.36 and Perets et al.37,38 used rate equations to fit H2 formation data on polycrystalline olivine, amorphous carbon, amorphous silicates and amorphous water ice, finding that a is in the 0.7–0.8 range (these values could be lower because the analyses gave only a lower limit to the desorption energy of H). These values are higher than the ones typically found for physisorbed atoms on ordered surfaces, where the rule of thumb is that a is around 0.3.39 Analyses of TPD data of HD, D2 and O2 on amorphous ice and amorphous silicates show a wide distribution of adsorption energy sites.33,40,41 There should be a corresponding distribution of diffusion energy barriers. Which diffusion energy barrier is the one controlling the reactions depends on many factors, including whether deep adsorption sites are saturated.42 These results should also be valuable to interpret experiments of molecule formation in ices where the mobility of oxygen might be important.
Acknowledgements This work is supported by the NSF, Astronomy & Astrophysics Division (Grants No. 0908108 and 1311958), and NASA (Grant No. NNX12AF38G). We thank Dr J. Brucato of the Astrophysical Observatory of Arcetri for providing the samples used in these experiments.
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Atomic oxygen diffusion on and desorption from amorphous silicate surfaces Jiao He, Dapeng Jing† and Gianfranco Vidali* Surface reactions involving atomic oxygen have attracted much attention in astrophysics and astrochemistry, but two of the most fundamental surface processes, desorption and diffusion, are not well understood. We studied diffusion and desorption of atomic oxygen on or from amorphous silicate surfaces under simulated interstellar conditions using a radio-frequency dissociated oxygen beam. Temperature programmed desorption (TPD) experiments were performed to study the formation of ozone from reaction of atomic and molecular oxygen deposited on the surface of a silicate. It is found
Received 13th October 2013, Accepted 2nd January 2014
that atomic oxygen begins to diffuse significantly between 40 K and 50 K. A rate equation model was used to study the surface kinetics involved in ozone formation experiments. The value of atomic oxygen
DOI: 10.1039/c3cp54328e
desorption energy has been determined to be 152 20 meV (1764 232 K). The newly found atomic
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oxygen desorption energy, which is much higher than the well-accepted value, might explain the discrepancy in abundance of molecular oxygen in space between observations and chemical models.
1 Introduction Oxygen is the third most abundant element in space after hydrogen and helium. It has attracted considerable attention among astrophysicists and astrochemists because it is an indicator of metallicity and thus a probe of the evolution of star-forming galaxies.1 It intervenes in many reactions to form other molecules, such as H2O, CO, CO2 and even more complex molecules such as amino acids. Oxygen is found mostly in the gas-phase in diffuse clouds (o10 H atoms per cm3), and in molecular form (H2O, CO, CO2, etc.) in the ices of denser clouds. Furthermore, O is locked in grains, mostly silicates of the type (FexMg1x)2SiO4, 0 o x o 1. It is found that both atomic and molecular oxygen are depleted in the gas-phase, although there is some uncertainty to what extent.2–4 The deficiency of oxygen in the gas-phase, especially in molecular form, is particularly vexing.4–6 Various gas phase models predicted O2 to be the third most abundant molecular species after H2 and CO, at an abundance of above 105 relative to H2 in well-shielded regions (see Goldsmith et al.6 and references therein). At this predicted abundance O2 should play an important role in gas phase cooling. However, the search for O2 using space observatories has found much lower O2 abundances. The survey using the SWAS (Submillimeter Wave Astronomy Satellite)7 sets an upper limit of N(O2)/N(H2) smaller than 2.6 107, which is two Physics Department, Syracuse University, Syracuse, NY 13244-1130, USA. E-mail: [email protected] † Current address: Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14850, USA.
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orders of magnitude lower than model predictions. With the launch of Odin, Larsson et al.8 observed the star forming molecular cloud core r Oph A and found the O2 abundance to be 5 108, averaged over the Odin beam. Recent observation of r Oph A using the Herschel Space Telescope has obtained similar O2 abundance as found with Odin.9 In a recent search for O2 emission in an ionization region towards the Orion bar with Herschel by Melnick et al.,4 O2 was detected, but again, at a much lower abundance than expected. In this region, dust grains are expected to be at higher temperature because of the radiation flux from stars. Oxygen is expected to be ejected from grains, for example by photodesorption, and in the gas-phase it can form O2 via reactions such as O + OH O2 + H. Therefore O2 is expected to be more abundant in the gas-phase by a factor of 10 than it would be in a similar UV quiescent region. Although O2 was detected, its abundance came short of what models of the chemical evolution of that specific space environment predict.10 In trying to reconcile observations with prediction of models, Hollenbach et al.10 and Melnick et al.4 pointed out that if the desorption energy of O is higher than the often assumed value at 800 K11 (by a factor of 1.5 in Hollenbach et al. and a factor of 2 in Melnick et al.), then there would be much less oxygen desorbing from grains and consequently less O available for O2 formation in the gas phase. This value of 800 K for O desorption from dust grains is found in many models of chemical evolution of ISM (interstellar medium) clouds10,12–16 but has no strong theoretical derivation11 and no experimental confirmation. One of the aims of this paper is to address this problem by presenting measurements of laboratory experiments of oxygen chemistry
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on an amorphous silicate surface, an analog of ISM dust grains, under simulated space conditions. Besides atomic oxygen desorption from dust grains, there are other processes involving oxygen that influence the chemical make-up of ISM clouds. Oxygen-related chemical reactions begin when atomic oxygen (O) or molecular oxygen (O2) stick to grain surfaces. According to one estimate, up to 10% of O2 can be in ices.6 Adsorbed O or O2 can react with radicals that are on surfaces of grains to form more complex molecules17 via the Eley–Rideal, hot-atom or Langmuir–Hinshelwood mechanisms. Because of the low temperature of dust grains (10–15 K in dense clouds), kinetics plays a large role in reactions on surfaces. Therefore, it is important to quantify the energetics of adsorption, desorption and diffusion processes so accurate parameters can be entered in codes of the chemical evolution of ISM environments. Oxygen chemistry has been studied on analogs of grain surfaces, both theoretically and experimentally. Xie et al.18 found theoretically that the atom–molecule reaction 3O + HC3N which has a barrier in the gas-phase, can be effectively catalyzed by water ices to be barrierless. Tielens and Hagen11 proposed that water formation is through the hydrogenation of O/O2/O3 on grain surfaces. Lamberts et al.19 used a Monte Carlo code to study the surface reaction of O2 hydrogenation. In all these theoretical studies, the surface kinetics of oxygen was not studied in detail. Experimentally, the formation of ozone from energetic particles has been studied by several groups,20–22 but fewer experiments used atoms or molecules at thermal energy. Extensive work has been done in recent years to study the formation of water. Miyauchi et al.23 investigated water and hydrogen peroxide formation by depositing H on cold O2 ice and obtained the effective reaction rates. Cuppen et al.24 studied O2 hydrogenation by simultaneous H and O2 deposition. Dulieu et al.25 and Jing et al.26 studied water formation via atomic oxygen hydrogenation by depositing O and H via two beam-lines. However, in these and similar experiments, because of the difficulty in obtaining a large dissociation fraction, what is deposited on the surface is not only O, but also O2. O2 and O can react and form O3; therefore, in a typical experiment H is really reacting with a mixture of O, O2, and O3. Further investigation of oxygen surface kinetics is needed to explain the relative ratio among H + O, H + O2 and H + O3 channels. Other than water formation, there has been experimental work done on formation on dust analogs of other oxygen-containing molecules. The formation of CO2 is another reaction that requires grains. Roser et al.,27 and more recently, Raut and Baragiola28 have studied the formation of CO2 on a surface by sending CO molecules together with oxygen atoms via beam-lines, and found low efficiency for the CO + O - CO2 reaction. This might be because O tends to combine with another O to form O2 instead of reacting with CO, or because undissociated O2 diffuses fast on the surface and reacts with O to form O3. All these studies require a better understanding of O/O2 kinetics on surfaces. The fundamental processes of oxygen desorption and diffusion on ISM related surfaces were not investigated until recently. Ward et al.,29 when doing research on the reaction of atomic oxygen
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with CS2 on a HOPG surface, introduced simple rate equations to analyze the data. However, they used the Arrhenius expression for both Langmuir–Hinshelwood and Eley–Rideal mechanisms, which is probably incorrect. In a work by our group, Jing et al.30 studied the formation of molecular oxygen and ozone on an amorphous silicate surface using atomic 16O and 18O beams. (Amorphous silicates and carbonaceous materials are the main components of interstellar dust grains.31) A value of the diffusion energy barrier for atomic oxygen on an amorphous silicate surface was obtained. However, this value is not accurate because an error was found32 in a calculation related to a control experiment to separate contributions of ozone from molecular oxygen in the O2 signal in our detector (ozone is fragile and is known to break up into O2 and O in the ionizer of a quadrupole mass spectrometer). Here we present the results of further experimental investigations on the formation of ozone from reaction with atomic and molecular oxygen on silicates, and introduce a more comprehensive rate equation model to study the kinetics of O and O2 on amorphous silicate surfaces. This has given us what we believe is a more accurate picture of oxygen chemistry and in some respects it differs from some of the results obtained by Jing et al.30 The paper is structured as follows. The next section characterizes the adsorption–desorption of O2 via temperature programmed desorption (TPD) experiments and describes the ozone formation experiments. In Section 3 we present the results of adsorption– desorption experiments and use the direct inversion method to obtain the desorption energy of molecular oxygen. Then the ozone formation experiments are analyzed in detail and a rate equation model is introduced to obtain the desorption energy and diffusion energy barrier of atomic oxygen. Section 4 summarizes the findings and comments on the significance for astrochemistry.
2 Experimental 2.1
Apparatus
The apparatus used in this work has been described in detail elsewhere;33 below there is a brief summary, and changes made to it since then are highlighted. The apparatus consists of an ultra-high vacuum main chamber with base pressure lower than 2 1010 Torr at 300 K and of two collimated triply differentially pumped atomic/molecular beam-lines. In this work only one beam-line is used. At the center of the main chamber a sample holder is thermally connected to the cold finger extension of a continuous flow liquid He cryostat. The sample is a 1 mm thick amorphous silicate thin film deposited on a 1/2 inch diameter gold coated copper disk, with temperature controllable from 8 K to 500 K using a Lakeshore 336 temperature controller. Silicate films are obtained by e-beam physical vapor deposition (EB_PVD). Fabrication and characterization methods of the samples are described in Jing et al.33 A triple-pass Hiden quadrupole mass spectrometer (QMS) is mounted on a rotatable platform and is used to detect desorbing substances from the sample and to characterize the products in the beam-lines. A water-cooled radio-frequency (RF) dissociation source is attached
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Fig. 1 Adsorption–desorption of O2 from an amorphous silicate surface kept at 20 K for different coverages. The heating ramp rate during the TPD stage is about 1 K s1. Figure replotted from Jing et al.30
to the beam-line to generate atomic oxygen. The dissociation efficiency is about 25% for molecular oxygen and is constant throughout the experiments. By flooding the chamber with O2 and recording the pressure and QMS counts, a conversion between QMS counts and the number of O2 molecules is obtained. The flux is calculated to be about 7.6 1011 cm2 s1 and 5.0 1011 cm2 s1 for O2 and O respectively (except for experiments as shown in Fig. 1, which is about 20% lower). 2.2
Description of experiments
Direct measurements of atomic oxygen desorption or diffusion are challenging because pure atomic oxygen is unavailable under present experimental conditions. Atomic oxygen is usually mixed with molecular oxygen. When O and undissociated O2 from the beam land on the surface, there are two likely chemical reactions involved: O + O - O2 O + O2 - O3 The surface kinetics of atomic oxygen are studied by quantifying these two reactions, including determining the surface kinetics of O2 and the amount of both reactants and products on the surface. The amounts of O and O2 from the beam-line are characterized by direct beam measurements. The amount of O3 formed can be measured by Fourier transform infrared spectroscopy (FTIR) or TPD. However, the focus of this investigation is on submonolayer coverage when the FTIR signal for O3 is too weak, thus TPD techniques are used instead. When measuring O3 using TPD and the QMS, another difficulty arises because O3 breaks up into O and O2 in the QMS ionizer. Additional efforts are required to determine whether the measured O/O2 are due to O3 breaking up or O/O2 desorption from the surface, which is discussed in detail later. The surface kinetics of O2 can be obtained by performing O2 adsorption–desorption experiments. Information from these experiments enables the quantification of atomic oxygen surface kinetics, including the desorption energy and the diffusion energy barrier.
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Two sets of O2 adsorption–desorption experiments are performed. The first is O2 adsorption–desorption TPD experiments at different exposure temperature to find out the residence time or, equivalently, the steady state coverage for O2. It is found that during exposure at the surface temperature below 20 K, the O2 sticking is unity while at 40 K and 50 K only 0.3 ML and 0.035 ML stick on the surface, respectively. Thus in ozone formation experiments, if the surface temperature rises above 50 K, the amount of O2 on the surface is negligible. The second set of O2 adsorption–desorption experiments is adapted from one of our previous studies.30 Here we summarize it and in the next section we use a direct inversion method to extract the desorption energy distribution. In these experiments the sample is kept at 20 K during the exposure to the molecular oxygen beam. The exposure time is incremented by 1.5 minutes from 1.5 to 15 minutes. The sticking probability of O2 at 20 K is obtained using the King– Wells adsorption–reflection method and is calculated to be close to one. After exposure the sample is warmed up at a rate of about 1 K s1 to a temperature higher than 100 K to thermally desorb O2 molecules. After every 2 to 3 TPD runs the sample is heated up to higher than 230 K to desorb water that could have condensed on the surface. Based on an analysis of TPD peak areas and beam flux it is found that a 10.5 minutes exposure in the set of experiments by Jing (the flux in those experiments is different from the one used in other experiments reported in this paper) is equivalent to 1 ML. Here we focus on experiments at submonolayer coverage, and TPD traces are shown in Fig. 1. An analysis of this set of experiments is in the Results and analysis section. In the ozone formation experiments, we first check the composition of the beam and measure the flux of the various components. When the QMS detector is placed in front of the beam-line, the amount of O3 in the beam is negligible (less than 0.1% of the beam intensity). Ozone formation experiments are carried out next. We keep the amorphous silicate surface at 30 K, 40 K, 50 K and 60 K, and send the dissociated O/O2 beam onto the sample for different durations, then do a TPD. When the exposure temperature is 30 K or 40 K, the sample is warmed up to 50 K and maintained for 2 minutes to desorb O2 before the TPD, so as to make sure the atomic mass 36 TPD peak that appears at about 63 K is not from undissociated O2 in the beam. This simplifies the analysis of ozone cracking in the ionizer. All relevant atomic masses, including mass 18, 36 and 54, are recorded both during the exposure stage and the TPD stage with the QMS facing the sample. In all measurements there is no direct desorption of mass 18 other than background noise. Since O3 can crack into O and O2 in the QMS ionizer, the mass 36 signal is at least partly due to the cracking of O3. The TPD traces are shown in Fig. 3. When the exposure temperature is 60 K, there is no O2 or O3 detected in the TPD (not shown in the figure). This is because O3 starts to desorb at around 60 K, and O3 formed during the exposure at 60 K desorbs quickly.
3 Results and analysis 3.1
Experiments of O2 adsorption–desorption
To extract the desorption energy distribution from adsorption– desorption TPD experiments, the direct inversion method in
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divided by the number of desorption sites on the surface. The order of desorption is taken to be 1 in this paper. Edes is the desorption energy, kB is the Boltzmann constant, and T is the surface temperature. Then, the coverage dependent desorption energy distribution can be calculated for each TPD trace as follows: b dy Edes ðyÞ ¼ kB T ln (2) ny dT A derivative of the distribution gives the Edes distribution f (Edes), which satisfies: Ð (3) f (Edes)dEdes = 1
Fig. 2 Distributions of Edes for O2 on an amorphous silicate surface obtained from direct inversion of TPD data shown Fig. 1.
´lek et al.34 and Amiaud et al.35 is adopted. The Polanyi– Dohna Wigner equation is written as:
dyðtÞ ¼ nyðtÞ expðEdes ðyÞ=kB T Þ dt
(1)
where n is the pre-exponential factor of the desorption. In general n depends on the substrate and adsorbate, but in this analysis the standard value n = 1012 s1 is taken. y(t) is the coverage defined as percentage of one monolayer, i.e., the number of particles (atoms or molecules adsorbed on the surface)
Fig. 3
the integration is over the whole desorption energy spectrum. We O2 , from the obtained the desorption energy distribution for O2, Edes silicate surface which is shown in Fig. 2. It can be seen that the distribution is peaked at about 78 meV. The O2 diffusion energy O2 barrier Ediff is difficult to measure directly, especially for nonregular surfaces. Generally it is assumed that Ediff = aEdes, where a is a number adopted to be between 0.3 and 0.8.13 For amorphous surfaces the a value is higher than for regular surfaces. We O2 therefore have an estimate of 23:3 meV o Ediff o 62:4 meV depending on the assumed value of a.
3.2
O3 formation
The TPD results are shown in Fig. 3. There are both mass 36 (m36) and mass 54 (m54) peaks at about 63 K. An integration of
TPD traces of O2 (36 amu) and O3 (54 amu) after O/O2 exposure for the indicated times; the surface temperatures during exposure are 30 K, 40 K and 50 K.
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Paper Integration of TPD traces from Fig. 3. The last row is the TPD yield ratios of mass 36 to mass 54
Texp
30 K
Exposure (min)
10
20
30
5
10
15
30
5
10
15
20
30
13.5 8.2 16.4
30.0 17.2 17.4
46.4 29.5 15.8
7.62 4.29 17.6
15.0 8.41 17.8
20.0 11.9 17.0
39.6 23.5 16.9
5.79 3.23 17.9
11.9 7.51 15.8
14.8 8.63 17.1
19.9 11.2 17.8
24.2 14.1 17.2
4
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N(O2)/10 N(O3)/103 N(O2)/N(O3)
40 K
50 K
TPD areas shown in Fig. 3 is given in Table 1. The ozone yields at Texp = 50 K are about half of the yields when Texp = 30 K. If the desorption energy of O is 800 K (69 meV) as suggested by Tielens and Hagen,11 which is lower than the desorption energy of O2 (78 meV), then because 30 K is close to the desorption peak temperature of O2, an easy calculation can show that the residence times for both O and O2 are orders of magnitude shorter at 50 K than at 30 K. One should see that the ozone yields at 50 K are orders of magnitude lower than that of 30 K. But this disagrees with the experimental results shown in Fig. 3. One then concludes that the desorption energy for O should be higher at 800 K. In Table 1 the integrated TPD area ratio m36/m54 is almost a constant, which is between 15.8 and 17.8 for the experiments plotted in Fig. 3. Besides, mass 36 and mass 54 appear at the same temperature and have a similar shape. Now a question arises: does the TPD peak of mass 36 in Fig. 3 come from the undissociated O2 from the beam, O3 cracking in the ionizer, or O2 (O + O - O2) as a result of O diffusion on the surface during the TPD? The first possibility can be excluded because undissociated O2 desorbs at a temperature below 50 K, and the sample is kept at 50 K for at least 2 minutes before the TPD to make sure there is no undissociated O2 left on the surface. The other two require more analysis. It is necessary to find out which one is true before quantifying the amount of ozone formed. If the mass 36 peak is all coming from O3 cracking in the ionizer then the ozone formed on the surface is not mixed with O; if part of the mass 36 peak is from O2 (O + O - O2) then there is O mixed with O3; in this case the temperature at which O starts to diffuse significantly should be virtually the same as the O3 desorption temperature, since the TPD desorption peak of mass 36 occurs simultaneously with the TPD peak of mass 54. In a previous paper by our group30 we did some analysis of the same TPD peak but with a different experimental setup and a different set of experimental data. Here we summarize that experiment. We used two beam-lines simultaneously, one with dissociated 16O2 and the other with dissociated 18O2. The sample temperature during exposure was 15 K. The TPD peak of O2 that was centered at about 63 K was attributed partly to 16 18 O O as a result of 16O and 18O diffusion during the TPD stage when the surface temperature was higher than about 60 K. The fact that both 16O18O and ozone desorb at the same temperature was explained as a coincidence between atomic oxygen diffusion temperature and ozone desorption temperature. By comparing these data with current work and re-analyzing the previous data, it is found that the contribution of O diffusion to the TPD peak centered at 63 K was overestimated because the
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cross-section data used for O3 break-up in the QMS ionizer might not have been appropriate for our ionizer. Now we analyze the ratio of O2/O3 contributions to the TPD peak centered at 63 K using the data shown in Fig. 3 and try to determine whether the mass 36 peak at 63 K is due to ozone cracking or O diffusion. First let us suppose atomic oxygen starts to diffuse significantly at above 60 K as it was suggested in Jing et al.30 When the exposure temperature Texp is 30 K, the residence time of O2 on the surface is tens of seconds assuming O2 Edes ¼ 78 meV. At this temperature the O2 diffusion rate should be very high. Taking into account that the dissociation rate of O2 is about 25% in our system, the O/O2 ratio in the beam flux is about 2 : 3, and there should be enough O2 to react with all the O. After warming up to 50 K to desorb residual O2, what is left on the surface should be O3 only. Since in the TPD stage the QMS records signals of both mass 36 (O2) and mass 54 (O3), the OQMS /OQMS ratio should be a constant that depends on the 2 3 cracking ratio of O3 in the QMS ionizer; let this constant be C1. In contrast, when Texp is 50 K, the residence time for O2 is very short; it is likely that there is not enough O2 to react with all the O, and it can be expected that there are both O3 and unreacted O left on the surface. As the temperature goes above 60 K in the TPD stage, O starts to diffuse and form O2. Since there is both O3 (from O2 + O) and O2 (from O + O) desorption above 60 K, the OQMS /OQMS ratio from the TPD peak area should be higher than 2 3 C1; let’s call the ratio C2. It can be shown that the percentage of O2 (coming from O + O) that is mixed with O3 in the TPD peak at Texp = 50 K is O2% = (C2 C1)/(C1 + 1), the percentage of O mixed with O3 before TPD is two times that of O2%. As is shown in Table 1, C1 E 16.5 and C2 E 17.2, and the difference between C1 and C2 is well within error bars. The amount of O2 mixed with O3 in the TPD peak is negligible (O2% o 4%). We conclude that the signal of the mass 36 peak in the TPD peaks in Fig. 3 is all due to ozone cracking in the ionizer. One can also obtain a temperature range in which the O starts to diffuse significantly. Because our assumption that O starts to diffuse above 60 K turns out to be not true, T O diff should be lower O than 60 K. Furthermore, if one considers that Tdiff cannot be between 50 K and 60 K, or otherwise there would be a peak of the mass 36 signal between 50 K and 60 K, then the temperature at which O starts to diffuse significantly T O diff should be lower than 50 K.
3.3
Rate equation modeling
Our next step is to quantitatively describe the O2 and O3 formation processes using a rate equation model, and then
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O obtain the diffusion E O diff and desorption E des energy values for O from the data. The rate equations to describe O2 and O3 formation on the sample surface are written as ! E O2 dyðO2 Þ ¼ fluxðO2 Þ nyðO2 Þexp des kB T dt
nyðO2 ÞyðOÞ exp
O2 Ediff
kB T
!
! EO þ exp diff kB T (4)
O Ediff dyðOÞ 2 ¼ fluxðOÞ 2nyðOÞ exp dt kB T ! ! O2 O Ediff Ediff nyðO2 ÞyðOÞ exp þ exp (5) kB T kB T On the right side of eqn (4) the first term is known from the measurement of the direct beam, the second term describes the desorption of O2, and the third term describes the reaction O2 + O - O3. The O3 formation rate depends on the diffusion rate of O2 both O and O2. However, if Ediff and E O diff are not too close to each other, the one with the lower value dominates the diffusion process, and the other one can be ignored. Since it is already known that O2 starts to diffuse at low temperature (well below O2 desorption peak temperature), we assume O2 O Ediff o Ediff , and the O3 formation term can be approximated O2 =kB T . by nyðO2 ÞyðOÞ exp Ediff
On the right side of eqn (5) the second term is due to the reaction O + O - O2. We assume that the reaction product O2 desorbs immediately after formation so that it doesn’t go into eqn (4). This is a reasonable assumption because the reaction O + O - O2 is strongly exothermic, and thus one expects that O2 leaves the surface upon formation. Direct desorption of O is ignored in eqn (5) since O diffusion should take place before O desorption, O should diffuse and form O2 instead of desorbing directly. This assumption will be verified later after obtaining the desorption energy of O. The equations can be simplified by assuming steady state conditions. When the exposure temperature Texp = 30, 40 or 50 K, reactions should proceed fast and reach a steady state quickly because of O2 high mobility. At steady state, eqn (4) and (5) can be expressed as flux(O2) = O2 desorption rate + O3 formation rate
(6)
flux(O) = O2 formation rate + O3 formation rate
(7)
Eqn (6) and (7) are nothing more than saying that all the O2 coming from the beam either desorb or form ozone, while all the O coming from the beam either form O2 or form ozone. By integrating the TPD peak areas in Fig. 3 (including both mass 36 and mass 54 because both of them are coming from ozone desorption) and comparing with direct beam measurement, eqn (6) and (7) lead to
3498 | Phys. Chem. Chem. Phys., 2014, 16, 3493--3500
at 30 K: O3 formation rate = 0.44 flux(O2) = 0.65 flux(O) at 40 K: O3 formation rate = 0.42 flux(O2) = 0.63 flux(O) at 50 K: O3 formation rate = 0.31 flux(O2) = 0.46 flux(O) Notice that there is a significant drop in the O3 formation rate between 40 K and 50 K. Eqn (7) then suggests that between 40 K and 50 K there is a significantly increasing amount of O that forms O2 instead of O3. One might think that perhaps between 40 K and 50 K O starts to desorb directly; however, it is verified later that O does not desorb significantly. O must start to diffuse significantly between 40 K and 50 K. In Section 3.2 we argued that at 30 K the O should be all consumed by O2, but the QMS measurements show that only 65% of O is consumed. An explanation of this discrepancy might be that in a QMS the detection efficiencies for different gases are different, O3 (including un-cracked O3 and cracked O3) could have lower detection efficiency than O2, the QMS signal height comparison must be corrected for different gases. Thus we let the O3 formation rate = flux(O) at 30 K and correct for the other O3 amounts proportionally. After correction, at 30 K all the O atoms are converted to O3, at 40 K about 97% of O are converted to O3, at 50 K 71% of O is converted to O3 while the remaining 29% diffuse and form O2. Combine eqn (4)–(7) and solve analytically for y(O) and y(O2): ! O2 E O2 Ediff O3 formation rate yðOÞ ¼ exp des fluxðO2 Þ O3 formation rate kB T (8) yðO2 Þ ¼
fluxðO2 Þ O3 formation rate O2 =kB T n exp Edes
(9)
O2 ; in the expression In eqn (8) and (9) the only variable is Ediff O2 O2 ¼ aEdes one lets a = 0.3, 0.4, 0.5, 0.6, 0.7 and 0.8, and Ediff
Table 2 Calculation of O coverages y(O) and O2 coverages y(O2) at 30 K, 40 K, and 50 K, and of the O desorption energy E O des, assuming different a values. The units for coverages and desorption/diffusion energies are ML and meV, respectively
EO diff
EO des
2.9 106 9.1 108
45
150
2.3 106 5.7 106
1.8 105 9.1 108
61
152
5.9 107 1.0 102
2.2 105 5.7 106
1.1 104 9.1 108
76
153
y(O) y(O2)
1.2 105 1.0 102
2.1 104 5.7 106
6.6 104 9.1 108
92
153
0.7
y(O) y(O2)
2.4 104 1.0 102
2.1 103 5.7 106
4.0 103 9.1 108
108
154
0.8
y(O) y(O2)
5.0 102 1.0 102
2.0 102 5.7 106
2.4 102 9.1 108
123
154
a
T
30 K
40 K
50 K
0.3
y(O) y(O2)
1.4 109 1.0 102
2.4 107 5.7 106
0.4
y(O) y(O2)
2.9 108 1.0 102
0.5
y(O) y(O2)
0.6
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calculate y(O) and y(O2) values for different values of T and a. The calculated values of y(O) and y(O2) are shown in Table 2. To estimate the O diffusion energy barrier E O diff, we consider that at Texp = 50 K 29% of O diffuse and form O2 instead of O3, and plug in the values of y(O) corresponding to different a values, and T = 50 K, into the following equation: O E 2nyðOÞ2 exp diff 0:29 fluxðOÞ kB T and then calculate for E O diff. The desorption energy of O can be O calculated using E O = E des diff/a. Here we assume that the a values are the same for both atomic and molecular oxygen. The calculated results are shown in Table 2. It can be seen that even if a varies between 0.3 and 0.8, the calculated atomic oxygen desorption energy E O des is almost the same. The value is EO = 152 2 meV. The uncertainty in the E O des des value comes mostly from the uncertainty in the determination of the O3 formation efficiency. By allowing a large 50% uncertainty in the determination of the O3 amount, the change in the E O des value is 20 meV at most. Then it can be concluded that the desorption energy for atomic oxygen is E O des = 152 20 meV (1764 232 K). In the above discussion no O direct desorption is assumed. This assumption can be verified now. The ratio between the amount of O due to O desorption and the O + O - O2 amount can be calculated as: O nyðOÞ exp Edes =kB T O =kB T 2nyðOÞ2 exp Ediff The value is between 4.2 106 for a = 0.3 and 1.6 102 for a = 0.8, which is much less than 1. Thus the assumption is correct and it is fine to ignore the atomic oxygen desorption term in eqn (5).
4 Conclusions The diffusion energy barrier and desorption energy for atomic oxygen on interstellar dust grain surfaces at low temperature are essential for simulation codes of the chemical evolution of interstellar environments. By performing TPD experiments of ozone formation and using a rate equation model, we have obtained a new value for atomic oxygen desorption energy on an amorphous silicate surface, even though there have been known technical difficulties found in the past.30,33 The value of atomic oxygen desorption energy is found to be 152 20 meV (1764 232 K) which is about double the prior estimated value that has been used widely in the literature. Models of the chemical evolution of ISM environments using the old estimate gave predictions of oxygen abundance in severe disagreement with observations. Our value is in good agreement with an estimate that Melnick et al.4 gave to reconcile their own most recent observations of O2 with modeling predicted abundances. In this work we also found that (1) the desorption energy of O2 from amorphous silicate surfaces is peaked at 78 meV (905 K); (2) the ranges of diffusion energy barriers for atomic and molecular oxygen are 45–123 meV and 23.3–62.4 meV,
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respectively, for assumed a values from 0.3 to 0.8. Katz et al.36 and Perets et al.37,38 used rate equations to fit H2 formation data on polycrystalline olivine, amorphous carbon, amorphous silicates and amorphous water ice, finding that a is in the 0.7–0.8 range (these values could be lower because the analyses gave only a lower limit to the desorption energy of H). These values are higher than the ones typically found for physisorbed atoms on ordered surfaces, where the rule of thumb is that a is around 0.3.39 Analyses of TPD data of HD, D2 and O2 on amorphous ice and amorphous silicates show a wide distribution of adsorption energy sites.33,40,41 There should be a corresponding distribution of diffusion energy barriers. Which diffusion energy barrier is the one controlling the reactions depends on many factors, including whether deep adsorption sites are saturated.42 These results should also be valuable to interpret experiments of molecule formation in ices where the mobility of oxygen might be important.
Acknowledgements This work is supported by the NSF, Astronomy & Astrophysics Division (Grants No. 0908108 and 1311958), and NASA (Grant No. NNX12AF38G). We thank Dr J. Brucato of the Astrophysical Observatory of Arcetri for providing the samples used in these experiments.
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