Recombination of oxygen atoms on the surface of oxidized polycrystalline nickel—temperature and pressure dependences

We adopted the experimental technique proposed by Šorli and Ročak to determine any temperature or pressure dependence of the recombination coefficient. A schematic of the experimental setup is shown in figure 1. The gas was introduced into the system via the mass flow controller, and passed through a narrow quartz tube. The gaseous plasma, which was the source of oxygen atoms, was ignited and sustained in the microwave (MW) cavity inside the narrow quartz tube of inner diameter 4.7 mm by a MW discharge in the surfatron mode. Details about the operation of such a discharge were reported elsewhere [21]. The MW discharge sustained plasma in a rather small volume inside the MW cavity. Oxygen molecules were partially dissociated, ionized, and excited upon plasma conditions. The gas speed through the narrow quartz tube was large, typically more than $100{\text{ m}}{\text{s}}$ at the exhaust of the narrow tube to a wider tube [22]. The large speed was a consequence of a pressure gradient along the glass tube. A typical ratio of pressures on the inlet and outlet side of the tube was 10 or more [23].

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We placed a movable recombinator inside the narrow tube for some of the measurements in order to obtain lower densities of neutral atoms. The recombinator was a titanium rod with a diameter of 2 mm. After the gas passed through the quartz tube, it entered a wider Pyrex tube. The Pyrex tube was pumped with a two-stage rotary pump, which also had an adjustable valve to control the effective pumping speed. The pressure inside the Pyrex tube was measured with a baratron.

Charged particles effectively recombined on the glass surface on the way from the MW cavity to the exhaust from the glass tube. The recombination coefficient for oxygen atoms on quartz glass is of the order of ${10^{ - 4}}$ [24–27], so the loss of atoms was negligible. The gas entering the afterglow chamber (Pyrex tube) thus contained only neutral oxygen atoms in the ground state and oxygen molecules.

The density of oxygen atoms in the ground state in the measuring chamber next to the exhaust of the quartz tube was determined using the Šorli method. A metallic tube made of catalytic material was mounted at the exhaust of the quartz tube, as shown in figure 1(b). Metallic tubes were made from three different materials, i.e. nickel, iron, or cobalt. The inner diameter and the length of the metallic tubes were 6 and 27 mm, respectively. The metallic tube was mounted in such a manner that it fitted tightly on the quartz glass tube, as shown in figure 1(b). Each metallic tube was connected to a thermocouple to enable measuring its temperature. The oxygen atoms arriving from the quartz tube effectively recombined on the surface of the metallic tube by heterogenous surface recombination. The number of atoms entering the metallic tube in a unit of time (${\text{d}}N/{\text{d}}t$) was calculated as follows:

$$\begin{align}\frac{{{\text{d}}N}}{{{\text{d}}t}} = \phi {\text{ }}n,\end{align} \tag{ 2 }$$

where $\phi$ is the effective pumping speed (the volume flow at the exhaust of the narrow glass tube), and $n$ is the number density of oxygen atoms entering the metallic tube. Each atom that recombined on the surface of the metallic tube brought half of the dissociation energy of oxygen molecules, i.e. 2.6 eV. The energy was spent on heating the metallic tube. After igniting the discharge, the temperature of the metallic tube started to rise, and after a prolonged time, it assumed a constant value. When the constant temperature of the metallic tube was reached, the discharge was turned off, and the metallic tube started to cool. Just after turning off the discharge, the cooling rate was equal to the heating when the discharge was on. Knowing the measured time derivative of the metallic tube temperature just after turning off the discharge enabled the estimation of the power dissipated on the surface of the metallic tube. The power is proportional to the number of atoms entering the metallic tube (equation (2)). We can calculate the number density of oxygen atoms at the exhaust of the quartz tube as:

$$\begin{align}n = \frac{{2{\text{ }}{m_{{\text{tube}}}}{c_{{\text{p}}\left( {{\text{tube}}} \right)}}}}{{{W_{\text{D}}}{\text{ }}\phi }}\frac{{{\text{d}}T}}{{{\text{d}}t}}\left( {{\text{tube}}} \right),\end{align} \tag{ 3 }$$

where ${W_{\text{D}}}$ is the dissociation energy of oxygen molecules, and ${m_{{\text{tube}}}}$, ${c_{{\text{p}}\left( {{\text{tube}}} \right)}}$, ${\text{d}}T/{\text{d}}t\left( {{\text{tube}}} \right)$ are the mass, specific heat, and the time derivative of the temperature of the metallic tube, respectively [17]. Equation (3) predicts that all atoms passing the metallic tube from the plasma source into the afterglow chamber (Pyrex tube) recombine to form parent molecules.

The Šorli method will give reliable results providing all the atoms entering metallic tube will actually recombine to form parent molecules. If this is true, the density of atoms in the afterglow chamber (at the position of the nickel disc, see figure 1(a)) when the metallic tube is present is negligible. Since nickel is catalytic for surface recombination of O atoms, the nickel disc mounted close to the exhaust from the quartz tube serves as a catalytic probe. The signal was actually below the detection limit of the probe, which is at the O-atom density of about ${10^{19}}$ m⁻³, so it is possible to conclude that a vast majority of atoms actually recombine on the metallic tube in the configuration of figure 1(b), so equation (2) is a reliable approximation. The probe signal became measurable only at elevated pressures. The correction factor at pressures up to 100 Pa is below a few %, whereas it is up to about 10% at the highest flow probed at our experiments, i.e. 3000 sccm.

The recombination coefficient of nickel was measured after removing the metallic tube from the experimental system, so in the configuration as shown in figure 1(a). Namely, when the metallic tube was absent (figure 1(a)), the flow of atoms into the afterglow chamber was practically the same as the flow into the metallic tube in the configuration as in figure 1(b).

A thin disc of high-purity nickel (99.99%) was placed into the afterglow chamber at the position marked as 'nickel disc' in figure 1. The disc was fixed to thermocouple wires. Before performing systematic measurements at various conditions, the disc was kept at a temperature of about 750 K for half an hour to enable the formation of a stable and thick oxide film. The surface roughness of the oxidized catalytic material was measured by atomic force microscopy and the thickness of the oxide film by ToF-SIMS after cutting the disc.

The recombination coefficient of the nickel disc was measured by calorimetry. Knowing the density of atoms at the position of the catalytic disc enables the calculation of the recombination coefficient:

$$\begin{align}\gamma = \frac{{8{\text{ }}{m_{{\text{disc}}}}{\text{ }}{c_{{\text{p}}\left( {{\text{disc}}} \right)}}}}{{v{\text{ }}{W_{\text{D}}}{\text{ }}\pi {\text{ }}r_{{\text{disc}}}^2{\text{ }}n}}\frac{{{\text{d}}T}}{{{\text{d}}t}}\left( {{\text{disc}}} \right),\end{align} \tag{ 4 }$$

where ${m_{{\text{disc}}}}$, ${c_{{\text{p}}\left( {{\text{disc}}} \right)}}$, ${r_{{\text{disc}}}}$, and ${\text{d}}T/{\text{d}}t\left( {{\text{disc}}} \right)$ are the mass, specific heat, radius, and the time derivative of the temperature of the catalytic disc, respectively [17]. Any temperature or pressure dependence of the recombination coefficient was determined by either keeping the catalytic disc temperature constant at different pressures or keeping the pressure constant but allowing different temperatures of the catalytic discs. The pressure in the system was kept constant at different disc temperatures by variation of the effective pumping speed and the inlet gas flow. By different combinations of these two parameters, it was possible to achieve different atom densities at the position of the catalytic disc at the selected pressure. The atom density was also adjusted by moving the titanium recombinator in the quartz tube, as shown schematically in figure 1.

Atomic force microscopy (AFM) measurements were performed with the A100-AFM microscope produced by A.P.E. Research (Italy) with the NT-MDT silicon tips. Measurements were done in the contact mode with the recording frequency of 0.5 Hz. The resolution of the images was set to 256 × 256 pixels. Images were post-processed with the plane subtraction due to the sample inclination involving a second-order polynomial correction and with the correction of the horizontal scars caused by the rough surface and consequent errors due to the responsiveness of the tip.

The time-of-flight secondary ion emission spectroscopy (ToF-SIMS) analyses were performed on a TOF.SIMS 5 instrument produced by IONTOF (Germany). Micrographs were recorded using Bi⁺ ions with the energy of 30 keV while simultaneously performing sputtering with the second ion gun (dual beam) using Cs⁺ ions with the energy of 1 keV. The current of the Bi⁺ ions was approximately 0.2 pA and the current of the Cs⁺ ions was approximately 564 nA. The analyses with the Bi⁺ primary ions were performed over a 100 × 100 μm scanning area (512 × 512 pixels), located in the center of the 400 × 400 μm etching crater sputtered by the Cs⁺ ion beam. The lateral resolution of the Bi⁺ analysis beam was approximately 200 nm. Hydrogen gas was introduced into the analysis chamber via a capillary to close proximity of the analyzed region to reduce the matrix effect and enable better differentiation between layers of Ni and NiO [28]. The pressure of the H₂ atmosphere in the analysis chamber was 7 × 10^–7 mbar. Secondary ions were analyzed in the m/z range 0–420. Only negative secondary ions were analyzed.

The experimental setup shown in figure 1 was first used to evaluate the density of atoms in the measuring chamber at the position where the catalytic discs was mounted (configuration as in figure 1(b)). Equation (3) indicates that the calculated number of atoms entering the afterglow chamber (Pyrex tube) in unit time is independent of the recombination coefficient of the material the metallic tube is made from. We placed three different metallic tubes made from nickel, cobalt, and iron at the exhaust of the quartz tube into the Pyrex tube as shown in figure 1(b). The density of O atoms in the afterglow chamber using these three metallic tubes is plotted in figure 2. There are small deviations from the standard curve, but all measured points are within the limits of the experimental error. The results in figure 2 therefore confirm that the density of atoms, as calculated from equation (3), does not depend on the recombination coefficient of the materials from which the metallic tubes are made. As mentioned earlier, this is because the surface recombination is large enough to transform practically all atoms into molecules when the partially dissociated gas passes through the metallic tube.

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The error bars in figure 2 arise from several repetitions of the measurements (statistical error) as well as the uncertainty of the atom leakage through the metallic tubes. The latter increases with increasing pressure. As mentioned above, the uncertainty of the measured density of oxygen atoms depends on the efficiency of the metallic tubes to recombine atoms, and the efficiency slowly decreases when the pressure increases. Namely, the mean free path of gaseous species decreases with increasing pressure, so there is a certain probability that the atoms will pass the metallic tube without experiencing numerous collisions with the metallic tube surface at elevated pressures, which is necessary for efficient recombination.

Several effects explain the behavior of the O-atom density versus the pressure (figure 2). First, the number of available molecules for dissociation increases linearly with increasing pressure. When this effect prevails, the O atom density also increases linearly with increasing pressure. The linearity persists up to the pressure of about 80 Pa at conditions selected for figure 2. At elevated pressure, the dissociation of oxygen molecules in the plasma is not as efficient as at low pressures because the discharge power is limited. In the case of the results presented in figure 2, we used the discharge power of 180 W. As shown by some other authors, the dissociation of oxygen molecules at elevated power actually increases with increasing discharge power [23]. The measurements were repeated at various gas flows, pressures, and the position of the movable recombinator in order to determine the O-atom density in a broad range of discharge parameters useful for the determination of the recombination coefficients.

The movable recombinator serves for adjustment of the O-atom density in the Pyrex tube irrespective of the discharge power or pressure. Namely, some atoms formed upon dissociation of oxygen molecules in glowing plasma recombine on the surface of the titanium rod. The O-atom density in the Pyrex tube is plotted versus the position of the movable recombinator in figure 3. Position 0 in figure 3 corresponds to the right edge of the MW cavity in figure 1(a). As expected, the O-atom density decreases as the recombinator is moved inside the plasma.

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After measuring the atom density in the afterglow chamber at various conditions, the metallic tubes were removed from the experimental system shown in figure 1(b), and a nickel disc was mounted, as shown in figure 1(a). The disc was connected to very thin thermocouple wires, and the discs temperature was measured versus time at various experimental conditions. A typical example of a disc temperature is shown in figure 4. The discharge was switched on at t = 7 s, and switched off at t = 14 s. One can observe a behavior typical for heating a sample at a constant heating power. Soon after igniting the discharge, the temperature increases linearly with time because the heating power is constant (strictly, it is constant if the recombination coefficient does not depend on the temperature), and any cooling is negligible. As the temperature increases with increasing treatment time, a deviation of linearity is observed, and after about 10 s, the temperature stabilizes. When the temperature is constant, the heating and cooling rates are equal. Cooling depends on various mechanisms, including the grey body radiation, the thermal conductivity of the surrounding gas, cooling by gas drift, and cooling through the thermocouple wires. The latter is negligible because of the very small mass of the wires (0.25 mm diameter). The maximum temperatures of a nickel disc are plotted in figure 5 versus the pressure at the discharge power of 180 W, a fully open butterfly valve, and the recombinator outside the quartz tube.

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The recombination coefficient of the nickel disc is calculated from the time derivative of the disc temperature using equation (4), providing the O atom density in the vicinity of the catalytic disc is known and providing that the disc does not represent such a large sink of atoms so that the O-atom gradient would form around the disc. Numerous measurements were performed at various discharge conditions, which enabled various O-atom densities in the afterglow chamber. Results are shown in figure 6.

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According to figure 6, the recombination coefficient increases steeply with the pressure in the range of 10–30 Pa. The coefficient is about 0.20 at 10 Pa and 0.25 at 30 Pa. Thereafter, the recombination coefficient starts decreasing with further pressure increase. At first glance, one may conclude that the recombination coefficient increases with increasing pressure up to about 30 Pa and decreases at elevated pressures. The observations arising from the behavior of the measured curve in figure 6, however, should be taken with precautions because not only is the pressure changing, but the temperature of the catalytic disc when turning off the discharge also depends on the pressure (figure 5). Figure 6 only indicates some dependencies, but it is unclear whether the dependence is directly due to pressure-related or temperature-related effects. Interestingly, very similar results were reported by Cvelbar et al for a cobalt catalyst [19].

Similar results as in figure 6 can be presented versus the maximum temperature of the catalytic disc. Results for nickel are shown in figure 7. In addition, we also provide the results of the calculated recombination coefficient at several discharge powers. We were changing the gas pressure in the same manner as for results shown in figure 5 at a constant pumping speed, but we calculated the recombination coefficient versus maximum temperature at various discharge powers. We see that all four curves in figure 7 exhibit a rather unexpected behavior. The recombination coefficient increases with increasing temperature up to about 800 K, but starts decreasing thereafter and assumes a rather low value when the temperature is decreased. The highly surprising results are explained by the fact that probe temperature does not only depend on atom density in the vicinity of the probe but also on the gas pressure. The turn in the curve in figure 7 indicates decreasing $\gamma$ with increasing pressure. Taking into account the pressure, which was measured simultaneously, one may deduce that a rather high recombination coefficient is measured at low pressure, the highest measured at moderate pressure, whereas at large pressures, the recombination coefficient decreases again. The turning point in figure 7 is observed for all four discharge powers, but the absolute values are different. The differences are due to the increasing O-atom density with increasing discharge power. The larger O-atom density at a fixed pressure will cause a higher catalyst temperature because of the larger flux of oxygen atoms onto the catalyst surface, whereas the cooling through the gas at a fixed pressure remains the same, irrespective of the discharge power.

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Considering figures 5 and 6, one can conclude either about pressure or temperature dependence of the recombination coefficient or both. In order to clarify, we performed measurements at fixed temperatures of the nickel sample and at several pressures. This was possible by changing the input power of the MW generator and the position of the movable recombinator (figure 1).

Figure 8 represents the recombination coefficients for a nickel disc kept at nine different temperatures, ranging from 370 K to 750 K, and at various pressures between 41 and 214 Pa. Such broad conditions were achieved by changing the flow of gas through the system and varying the discharge power. Furthermore, we were moving the titanium recombinator in the quartz tube (figure 1) to achieve lower densities of neutral atoms at large discharge powers, which allowed for measurements at temperatures of the nickel disc below the value that would be reached without the recombinator. One can observe a monotonous decrease in the recombination coefficient with increasing pressure in figure 8. These measurements clearly indicate that the gas pressure influences the recombination coefficient. The difference between the lowest and the highest pressure, however, is not dramatic—less than a factor of 2.

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The lowest measurable point for 750, 700, and 650 K in figure 8 is at the pressure of about 79 Pa. Namely, the probe does not heat up to 650 K at lower pressures simply because O atom density is too low (see figure 5). Lower temperatures are achievable in our experimental system also at slightly lower pressures. The recombination coefficient decreases with increasing pressure and the differences are not large at elevated pressures. It was not possible to measure the curve at higher pressure because it was not possible to heat the catalyst to such a high temperature at elevated pressures.

The pressure dependence of recombination coefficients has already been mentioned by several authors [29–31]. A feasible explanation is the screening of the oxygen atom adsorption sites by oxygen molecules. This effect is, of course, more pronounced at elevated pressures simply because the flux of molecules on the surface increases linearly with increasing pressure. Still, the rather small slope of the curve at around 200 Pa indicates a significant number of recombination sites even at elevated pressures. Figure 8, therefore, indicates that recombination at various elevated temperatures remains relatively large even at high pressures (does not approach zero).

As mentioned earlier and according to figure 8, the recombination coefficient should also depend on the temperature because the mobility of surface adatoms increases with increasing temperature. The measured temperature dependence of the recombination coefficient for the nickel disc at the pressures of 41, 79, 117, 156, and 214 Pa is plotted in figure 9. The measured dots are somewhat scattered, but the general trend is obvious: the recombination coefficient increases with increasing surface temperature.

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Several authors have reported a similar trend when it comes to the temperature dependence of the recombination coefficient [9, 16, 32–42]. Many agree that the dependence can be described with an Arrhenius plot in the form of:

$$\begin{align}\gamma \left( T \right) = A{\text{ }}{{\text{e}}^{ - B/T}},\end{align} \tag{ 5 }$$

where $A$ and $B$ are parameters usually gleaned from empirical results. Equation (5) was taken as a basis for our own empirical equation, but we also considered the pressure dependence. Several formulas were considered, with a few viable candidates. In the end, the best agreement for both pressure and temperature dependence of $\gamma$ in the range of the probed pressures and temperatures was found to be in the form of:

$$\begin{align}\gamma \left( {p,T} \right) = \frac{A}{{\sqrt p }}{{\text{e}}^{ - B/T}},\end{align} \tag{ 6 }$$

where $A = 17{\text{ P}}{{\text{a}}^{1/2}}$ and $B = 1400{\text{ K}}$. While we could not find any data on the pressure dependence of $\gamma$ for nickel, the exponential factor $B$ is in agreement with Dickens and Sutcliffe when using the Arrhenius plot [9]. This exponential factor corresponds to an energy of $0.121{\text{ eV}}$, which is significantly lower than the dissociation energy of an oxygen molecule.

The flexibility of the experimental system adopted for this research enabled variation of the nickel disc temperature irrespectively from the pressure in the afterglow chamber or the atom density near the catalyst. This is particularly important because the simultaneous variation of both the pressure and the catalyst temperature may lead to misinterpretation of the recombination coefficient dependence, as demonstrated in figures 5 and 6. The results presented in figures 7 and 8 are reliable, but not very accurate because a rather large scattering of measured points is observed. The scattering comes from the inaccuracy of measuring the density of oxygen atoms in the afterglow chamber (a few examples are shown in figure 2) as well as somehow arbitrary determination of the maximal catalyst temperature (figure 4). The latter is probably the effect of increasing gas temperature with increasing plasma duration.

The empirical formula obtained from measured points in figures 7 and 8 does not fit perfectly the measured values. It should be taken only as a recommended approximation for the range of probed pressures and temperatures of the oxidized nickel samples at turning off the discharge generator. Although similar temperature behavior was reported by numerous authors ([9, 16, 32–42]), the scientifically spotless explanation remains to be invented. Qualitatively, one can explain the temperature behavior by increasing mobility of surface adatoms with increasing temperature. As mentioned above, the Langmuir–Hinshelwood model predicts the association of two adatoms accommodated on the surface to a molecule, which is, contradictory to atoms, not trapped by rather strong chemical bonds, so it desorbs and leaves the surface. The association of neighboring adatoms will require close proximity because the average distance between oxygen atoms in the O₂ molecule is only about 0.12 nm [43], while the average distance between atoms on the surface of solid material is roughly $0.2 - 0.3$ nm [44]. Such proximity is more likely to occur at an increased amplitude of bonded O-atoms oscillation, and the amplitude increases with increasing temperature. Any discussion on the exact mechanisms at the atomic scale is beyond the scope of this article.

The formula (6) indicates the recombination inversely proportional to the square root of pressure. Obviously, the formula is void at low pressures, because the coefficient would approach infinity when the pressure will approach 0. The formula is valid only in the range of pressures used in this work. We selected the range of pressures between 40 and 200 Pa because the measurements were feasible in this range. In fact, many reactors employing weakly ionized oxygen plasma for tailoring surface properties of solid materials exhibit the maximum O-atom density within this range [45].

As already mentioned, metals form oxide films upon exposure to oxygen at elevated temperatures. The film thickness will increase with increasing temperature (and, to less extent, also the oxidation time). Even if the catalytic disc is polished, the oxide film will be rather rough. The recombination coefficient should depend on the roughness because the roughness increases the effective surface when compared to the geometrical surface area. All measurements of the recombination coefficient were performed after thorough oxidation of the nickel disc as explained above. AFM images of a nickel surface oxidized at different temperatures are shown in figure 10, progressing from a clean nickel surface (a), oxidation at 400 K (b), oxidation at 600 K (c), oxidation at 800 K (d), oxidation at 1000 K (e), and oxidation at 1200 K (f). The RMS surface roughness (${S_q}$) increased with increasing oxidation temperature from $10{\text{ nm}}$ to $70{\text{ nm}}$. The catalytic nickel disc, which was used in experiments after forming a stable oxide film at around 1000 K, is shown in figure 10(e). The roughness was estimated at ${S_q} = 60{\text{ nm}}$. The thickness of the oxide film after thorough oxidation of the nickel disc was determined by ToF-SIMS. As shown in figure 11, the thickness was about 10 µm.

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