The adsorption of carbon monoxide on rhenium: Basal (0001) and stepped 14 (0001) × (101̄1) planes

The influence of surface defects on the adsorption of CO by rhenium is investigated using LEED, AES and linear temperature programmed desorption. On both surfaces, thermal desorption reveals two adsorption states, the lower temperature α state being resolved into two substates, and one β state, all desorbing with first order kinetics. The α state is unaffected by the surface texture, its maximum population being the same on both surfaces, around 4 × 10¹⁴ molecules cm^?2, similar to the value found for poly crystalline rhenium. On the other hand, the β state is strongly dependent on surface structure. On Re(0001) a maximum of 4 × 10¹³ molecules cm^?2 was found, and 2 × 10¹⁴ molecules cm^?2 on the stepped surface. The adsorption is activated and can be increased, by heating to 550 K, to 2 × 10¹⁴ molecules cm^?2 on the basal plane and 3.5 × 10¹⁴ molecules cm^?2 on the stepped surface. Ordered structures are now seen in LEED. Comparison of these results with previous results from polycrystalline rhenium indicate that the dissociation of β-CO on the latter surface must occur at defects other than steps.     

Coadsorption of oxygen and carbon monoxide on tungsten: Desorption spectra,electron stimulated desorption and field emission microscopy

CO/W desorption spectra are characterized by an α state and multiple β states; using electron stimulated desorption (ESD) the α state was shown to comprise two sub-states, α₁ and α₂. In this paper the consecutive interactions of O₂ and CO on W are investigated using ESD, flash desorption and field emission microscopy (FEM).Desorption spectra show that the α-CO state is displaced by O₂, in two stages. The ESD probe provides an identification of the first stage with the removal of the α₁-CO state, and energy analysis of ESD ions reveals a large energy shift (～ ? 1.5 eV) during O₂ coadsorption which can be attributed to an incresae in the α₁-CO WC bond length of ～ 0.15 Å. During this O₂-induced displacement, the two β peaks converge into a single peak at the β₁ position; this is ascribed to adatom interactions in the mixed O and C adlayer. Isotope exchange experiments with ²⁸CO and ³⁶O₂ reveal (i) no exchange in the α-CO states, and (ii) complete exchange in the β-CO states, which is consistent with dissociative adsorption in the latter. The amount of coadsorbed O₂ is estimated from these results, and from FEM data: a full monolayer of O adatoms can be coadsorbed on CO-saturated W, but CO pre-adsorption inhibits the formation of W oxides. The β₁-O₂ (ESD active) state also forms on the CO-covered surface: this state is identical in population, ESD cross section and ion energy distribution to β₁-O₂ on clean W, and retains its identity in the mixed layer (it does not undergo isotopic exchange). CO₂ desorption spectra from the mixed layer were also characterised, complete isotopic scrambling being observed.Pre-exposure of tungsten to O₂ inhibits CO adsorption: a monolayer of O₂ is sufficient to prevent CO adsorption, and at low O₂ coverages, every O₂ molecule preadsorbed prevents one CO molecule from adsorbing. Isotopic exchange is again complete in the β states, and a lateral interaction model for desorption kinetics, based on dissociative adsorption in the β-CO state, quantitatively describes the CO desorption spectra.     

Electron beam interactions with CO on W {100} studied by Auger electron spectroscopy

The interaction of 2500 eV electrons with carbon monoxide chemisorbed on tungsten {100} was investigated by rapid-scan Auger electron spectroscopy. When no α state was present the O and C signals from the β state of CO were invariant during electron bombardment, giving an upper limit estimate for the electron stimulated desorption cross section, Q_β of 2 × 10^?21 cm². With the crystal at room temperature and saturated with CO, however, electron-beam induced accumulation of carbon was observed and characterised, the rate of the process being independent of CO pressure at pressures above 2 × 10^?8 Torr. At 450 K the rate was found to be pressure dependent up to at least 6 × 10^?7 Torr. A model is proposed for the accumulation process, which is based on electron beam dissociation of α₂-CO to form adsorbed carbon and gaseous O and the creation of new sites for further α₂-CO adsorption; it is in quantitative agreement with the results and yields a cross section for ESD of α₂-CO (Q_α2 = 1.55×10^?18cm²) in close agreement with direct measurements.     

Thermal desorption of cyanogen from Pt(100)

Thermal desorption of cyanogen adsorbed on Pt(100) was studied by flash desorption mass spectrometry. By investigating the parent ion and all possible fragmentation products in the mass spectrometer during desorption it was concluded, that desorption takes place exclusively as molecular C₂N₂. Three desorption peaks were observed at 140, 410 and 480°C denoted as α, β₁ and β₂. The respective surface coverages at saturation were determined by quantitative evaluation of the flash desorption curves to be 2.0 ± 0.2 × 10¹⁴ and 5.5 ± 1.0 × 10¹⁴$\text{molecules}\text{cm}{}^2$ for the α and the β states, respectively. First order desorption kinetics was suggested by the coverage dependencé of the desorption spectra for both α and β states with desorption energies of 12 and 38–42 $\text{kcal}\text{mole}$, respectively. A large difference in the sticking probabilities of α and β states was observed with initial values of 0.06 (α) and 0.9 (β). Adsorption experiments at elevated temperatures led to the assumption, that α and β states coexist on the surface with no or very little interactions between them. The results are discussed in terms of different models for the adsorption states.     

Chemisorption of CO on tungsten (100): Combined flash desorption and electron stimulated desorption study. II

The chemisorption of CO on W(100) at ~ 100K has been studied using a combination of flash desorption and electron stimulated desorption (ESD) techniques. This is an extension of a similar study made for CO adsorption on W(100) at temperatures in the range 200–300K. As in the 200–300 K CO layer, both α₁-CO and α₂-CO are formed in addition to more strongly bound CO species upon adsorption at ~ 100K; the α-CO states yield CO⁺ and O⁺ respectively upon ESD. At low CO coverages, the α₁ and α₂-CO states are postulated to convert to β-CO or other strongly bound CO species upon heating. At higher CO coverages, α₁-CO converts to α₂-CO upon thermal desorption or electron stimulated desorption. There is evidence for the presence of other weakly-bound states in the low temperature CO layer having low surface concentration at saturation. The ESD behavior of the CO layer coadsorbed with hydrogen on W(100) is reported, and it is found that H(ads) suppresses either the concentration or the ionic cross section for α₁ and α₂-CO states.     

The displacement of hydrogen by carbon monoxide on the (100) face of tungsten: A photoemission and thermal desorption study

Photoelectron spectra (hv = 21.22 eV) and thermal desorption data were obtained for CO and H coadsorbed on W(100) at 80 K. When the clean surface is exposed to a saturation dose of H₂, subsequent exposure to CO results in the formation of a state whose emission spectrum is similar to that of molecular α-CO. Upon heating to ~280 K, a structural rearrangement occurs in which most of the adsorbed CO is converted to the strongly bound β form as the hydrogen is simultaneously desorbed. These data plus the observation that H₂ cannot be adsorbed to any significant degree on a saturated layer of β-CO suggest that adsorbed β-CO and H occupy the same atomic sites on the W(100) surface. The distinction between long and short range repulsive COH interactions is discussed. For CO adsorbed on clean W(100), the range of activation energies for vigin to β conversion is calculated from the UPS data to be 45–62 kJ/mol.     

Chemisorption of H2 on W(100): Absolute sticking probability,coverage, and electron stimulated desorption

Measurements of both the absolute sticking probability near normal incidence and the coverage of H₂ adsorbed on W(100) at ~ 300K have been made using a precision gas dosing system; a known fraction of the molecules entering the vacuum chamber struck the sample crystal before reaching a mass spectrometer detector. The initial sticking probability S₀ for H₂/W(100) is 0.51 ± 0.03; the hydrogen coverage extrapolated to S = 0 is 2.0 × 10¹⁵ atoms cm^?2. The initial sticking probability S₀ for D₂/W(100) is 0.57 ± 0.03; the isotope effect for sticking probability is smaller than previously reported. Electron stimulated desorption (ESD) studies reveal that the low coverage β₂ hydrogen state on W(100) yields H⁺ ions upon bombardment by 100 eV electrons; the ion desorption cross section is ~ 1.8 × 10^?23 cm². The H⁺ ion cross section at saturation hydrogen coverage when the β₁ state is fully populated is ? 10^?25 cm². An isotope effect in electron stimulated desorption of H⁺ and D⁺ has been found. The H⁺ ion yield is ? 100 × greater than the D⁺ ion yield, in agreement with theory.     

The adsorption of acetylene on W(100) at room temperature: An electron spectroscopic study

The adsorption of acetylene on W(100) at room temperature has been studied by AES, ELS, thermal desorption, mass spectrometry, work function and LEED in one vacuum chamber. AES line profile analysis shows that there are at least two adsorption processes occurring at room temperature. Further, it is possible to explain all the AES results by assuming non-sequential adsorption into just two states, denoted by α and β. This picture was substantiated and embellished by comparison with other standard surface techniques. The α-state comprises either a C₂H₂ unit with an activation energy for desorption of $\text{2.3}\text{eV}\text{molecule}\text{(53}\text{kcal mole}{}^{\mathrm{?1}}\text{)}$ or CH units bounded through the carbon of the β-state. Saturation coverage for the α-state is 3 × 10¹⁴ molecules cm^?2. The β-state is dissociative at low acetylene exposures and comparison between a carbon covered surface and the β-state suggest the latter to be dissociative up to saturation. There also appears to be ca. 10¹⁴ hydrogen atoms cm^?2 on W(100) on room temperature acetylene saturation, the carbon content of the β-state being 9 × 10¹⁴ atoms cm^?2. The residual C?C bond from the molecule in the β-state remains unknown. No sign of ordering in the adsorbed species was detected, save the possibility of (1 × 1) in the β-state. Acetylene adsorption at 580 K showed hydrogen from the β-state to block acetylene adsorption by 15% at saturation. A two-site adsorption model for the β-state is proposed to explain the results. The α-state is bonded through the carbon of the β-state and it is speculated that the former adsorbs onto “β” domains where there is a critical minimum size for the latter.     

Adsorption of nitrogen on platinum

The adsorption and desorption of nitrogen on a platinum filament have been studied by thermal desorption techniques. Nitrogen adsorption becomes significant only after any carbon contamination is removed from the surface by heating the platinum filament in oxygen, and after the CO content in the background gas is reduced substantially. At room temperature nitrogen populates an atomic tightly bound β-state, E^≠ = 19 kcal mole^?1. The saturation coverage of the (3-state is 4.5 × 10¹⁴ atoms cm^?2. Formation of the (β-state is a zero order process in the pressure range studied. At 90 K two additional α₁- and α₂-desorption peaks are observed. The activation energy for desorption for the α₂-state is 7.4 kcal mole^?1 at low coverage decreasing to 3 kcal mole^?1 at saturation of this state, 6 × 10 molecules cm^?2. The maximum total coverage in the α-states was 1.2 × 10¹⁵ molecules cm^?2. A replacement process between the β- and α-states has been observed where each atom in the (β-state excludes two molecules from the α-state.     

CO chemisorption on PtCu surfaces I. CO on (1 × 3) Pt0.98Cu0.02(110)

Thermal desorption and photoemission spectroscopy (PES) have been used to investigate the chemisorption of CO on an annealed Pt_0.98Cu_0.02(110) surface. The clean surface shows 9.1 ± 2.6% Cu within the top 4 Å, and is (1 × 3) reconstructed. Thermal desorption of CO has revealed the existence of various adsorption states with these respective heats of adsorption: (α) 35.2 to 37.8 kcal/mol and (β) 24.5 to 26.3 kcal/mol on Pt sites, (γ) 16.0 to 17.2 kcal/mol on PtCu “mixed” sited, and (δ) 12.9 to 13.9 kcal/mol on Cu sites. PES observation of Cu 3d-derived states (using hv = 150 eV) and the $\text{Cu 2p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ core levels (using Mg Kα radiation) shows that the electronic structure of the Cu constituent is changed only when CO adsorbs on the Pt-Cu “mixed” sites or the Cu sites. Furthermore, the CO states associated with Pt sites reflect the structural difference between the (1 × 3) alloy surface and the (1 × 2) pure Pt(110) surface: α-CO on the alloy surface desorbs at a temperature 17 to 21 K. higher than the maximum desorption temperature of CO from pure Pt(110), and the ratio of β-CO to α-CO desorption from the alloy surface is larger than the ratio of low temperature to high temperature peaks in the desorption of CO from pure Pt(110).     

Electron stimulated desorption of carbon monoxide from a (111) niobium surface

Electron stimulated desorption of CO from the (111) face of a Nb single crystal produced both CO⁺ and O⁺ ions after adsorption at 150°K on a clean surface. When the surface was heated to above 250 °K only O⁺ ions were observed, and this current disappeared as the temperature was increased to 700 °K. Readsorption (at 150 °K) was inhibited following the 700 °K heating. These data indicate the formation on heating of a tightly bound surface phase with very low ionic desorption cross section. Threshold energies for CO⁺ and O⁺ ion production were 10.0 ± 0.5 eV and 19.0 ± 0.5 eV, respectively. The cross section for electron stimulated depopulation of the O⁺ producing phase was (4 ± 1) × 10^?18 cm² for 100 eV electrons.     

The adsorption and desorption of oxygen on the Pt(110) surface; A thermal desorption and LEED/AES study

The interaction of oxygen with a Pt(110) crystal surface has been investigated by thermal desorption mass spectroscopy, LEED and AES. Adsorption at room temperature produces a β-state which desorbs at ~800 K. Complete isotopic mixing occurs in desorption from this state and it populates with a sticking probability which varies as (1 ? θ)², both observations consistent with dissociative adsorption. The desorption is second order at low coverage but becomes first order at high coverage. The saturationcoverage is 3.5 × 10¹⁴ mol cm^?2. The spectra have been computer analysed to determine the fraction desorbing by first (β₁) and second (β₂) order kinetics as a function of total fractional coverage θ using this fraction as the only adjustable parameter. The β₁ desorption commences at θ ～ 0.25 and β₁ and β₂ contribute equally to the desorption at saturation. The kinetic parameters for β₁ desorption were calculated from the variation of peak temperature with heating rate as ν₁ = 1.7 × 10⁹ s^?1 and E^≠₁ = 32 kcal mole^?1 whereas two different methods of analysis gave consistent parameters ν₂ = 6.5 × 10^?7 cm² mol^?1 s^?1 and E^≠₂ = 29 and 30 kcal mole^?1 for β₂ desorption. The kinetics of desorptior are discussed in terms of the statistics for occupation of near neighbour sites. While many fea tures of the results are consistent with this picture, it is concluded that simple models considering either completely mobile or immobile adlayers with either strong or zero adatom repulsion are not completely satisfactory. The thermal desorption surface coverage has been correlated with the AES measurements and it has been possible to use the AES data for PtO as an internal standard for calibration of the AES oxygen coverage determination. At low temperature (170 K) oxygen populates an additional molecular α-state. Adsorption into the α- and β-states is competitive for the same sites and pre-saturation of the β-state at 300 K excludes the α-state. This, together with the AES observation that the adsorption is enhanced and faster at 450 than 325 K suggests a low activation energy for adsorption into the β-state.     

An electron spectroscopic investigation of the adsorption of NO on Ni(111)

The adsorption, decomposition, and desorption of NO on the close packed Ni(111) surface have been investigated by XPS, XPS satellites, XAES, UPS, and LEED between 125 and 1000 K. At adsorption temperatures below 300 K a single molecular species (v) is formed with about unit sticking coefficient, which is interpreted as bridge-bonded; its saturation coverage is about 85% of that of CO, i.e. 0.5 relative to surface Ni atoms. Adsorption at 300 to 400 K yields dissociative adsorption (β) followed by molecular adsorption; above 400 K only dissociated species are formed. Upon heating, a full molecular layer dissociates only after some NO desorption (at 380–400 K), while dilute layers (below half coverage) dissociate already above 300 K without NO desorption. Together with quantitative findings this shows that for dissociation of one v-NO, the space of two is required. N₂ desorption from the β-layer occurs above 740 K; the oxygen staying behind diffuses into the crystal above 800 K. Readsorption of NO onto a β-layer or onto an oxygen precoverage at 125 K leads, besides to an α₁-state similar to v-NO, to another molecular state (α₂) which is interpreted as linearly bound. The resulting total coverage is considerably higher than in a virgin layer. This shows that the blocking of dissociation in a full v-layer is probably not due to β requiring the same sites, but to kinetic hindrance; an influence of β-induced surface reconstruction cannot be excluded, however. The LEED results agree with a previous report and are well compatible with the other results.     

Characterization of the adsorption and decomposition of methanol on Ni(110)

The chemisorption, condensation, desorption, and decomposition of methanol, both CH₃OH and CH₃OD, on a clean Ni(110) surface have been characterized using high resolution electron energy loss spectroscopy, temperature programmed reaction spectroscopy, and low energy electron diffraction. The vibrational spectrum of the saturated chemisorbed layer, 7.4 × 10¹⁴ molecules cm^?2, is almost identical to the infrared spectrum of liquid or solid methanol. Condensation of multilayers of methanol is facile at 80 K. The only quasi-stable intermediate isolated during the decomposition is a methoxy species, CH₃O, which decomposes thermally to CO and H. The evolution of both CO and H₂ occurs in desorption limited processes.     

Electron stimulated desorption of CO from

The electron impact behavior of CO adsorbed on was investigated. The desorption products observed were neutral CO, CO⁺, and O⁺. After massive electron impact residual carbon, C/W = 0.15, but not oxygen was also found, suggesting that energetic neutral O, not detected in a mass analyzer must also have been formed. Formation of β-CO, i.e., dissociated CO with C and O on the surface was not seen. The total disappearance cross section varies only slightly with coverage, ranging from 9 × 10 ⁻¹⁸ cm² at low to 5 × 10⁻¹⁸ cm² at saturation (CO/W = 0.75). The cross section for CO⁺ formation varies from 4 × 10⁻²² cm² at satura to 2 × 10⁻²¹ cm² at low coverage. That for O⁺ formation is 1.4 × 10⁻²² cm² at saturation and 2 × 10⁻²¹ cm² Threshold energies are similar to those found previously [J.C. Lin and R. Gomer, Surf. Sci. 218 (1989) 406] for and CO/Cu₁/W(110) which suggests similar mechanisms for product formation, with the exception of β-CO on clean W(110). It is argued that the absence or presence of β-CO in ESD hinges on its formation or absence in thermal desorption, since electron impact is likely to present the surface with vibrationally and rotationally activated CO in all cases; β-CO formation only occurs on surfaces which can dissociate such CO. It was also found that ESD of CO led to a work function increase of the remaining Pd₁/W(110) surface of 500 meV, which could be annealed out only at 900 K. This is attributed to surface roughness, caused by recoil momentum of energetic desorbing entities.     

Adsorption of CO on the (110) plane of tungsten electron impact,thermal desorption,and work function measurements

The adsorption of CO on the (110) plane of tungsten has been studied using electron impact desorption, thermal desorption, and work function measurements in a single apparatus combining these various techniques. It is concluded that a single molecular adsorption state exists at 20–250 K (virgin-CO). At 300–400 K, 60% of the low temperature layer desorbs, the remainder converting principally to a beta-1 state, which has very small electron impact cross section; in addition to beta-1 an O⁺ yielding state, which we call beta-precursor is formed. The beta-1 state is stable to 900 K, where some desorption and conversion of the remaineder to a beta-2 state occurs. The O⁺ yielding state decays with increasing T and is gone at 800 K. Readsorption on beta-1 leads to two types of adsorption states called alpha and gamma, which seem to be site specific. Electron impact desorption yields mostly CO⁺ and CO for virgin, O⁺ for beta-precursor, and CO⁺ and CO for the readsorption states. There is no isotopic mixing in virgin or in readsorbed CO, nor does readsorbed CO exchange with beta-1 or beta precursor. There is complete isotopic mixing in beta desorption. In addition, massive EID creates another state, characterized by a large dipole moment, also yielding O⁺ in EID. This state can be converted to beta-1 by heating to 400 K. The total disappearance cross sections for the various states are virgin-CO5 × 10^?17cm²; γ-CO 1.6 × 10^?16cm²; α-CO 5 × 10^?17cm²; β-precursor 6 × 10^?18cm²and 1.2 × 10^?19cm²; EID induced state 8 × 10^?18cm². In addition, cross sections for ion production are determined and found to be several orders of magnitude less than total disappearance cross sections. These results, and Leed and coverage data obtained in parallel investigations are used to formulate models of the various adsorption states. It is concluded that virgin and readsorbed CO are molecular and beta-precursor and beta dissociated, although strong interactions between C and O remain. The electron impact desorption of physisorbed CO was investigated and found to yield C⁺, O⁺, and neutral CO, but very little CO⁺. These results suggest primary dissociation of CO by electron impact, and desorption of neutral physisorbed CO by the energetic fragments. Physisorbed CO⁺, although undoubtedly created, lies on the attractive part of its potential curve relative to the surface, and thus does not desorb as CO⁺.     

Adsorption of oxygen on the (110) plane of tungsten at low temperatures

Isotope labelling experiments have established that the adsorption of O₂ on the W(110) plane at 20 K leads first to the formation of a dissociated atomic layer. A weakly bound molecular species, α-O₂, forms only when the atomic layer is essentially complete (O/W = 0.6). The desorption of α-O₂ was found to be first order with an activation energy of $\text{E = 1.9}\text{kcal}\text{mole}$ and a frequency factor γ = 3 × 10⁹ s^?1. The activation energy is shown to be less than the enthalpy of desorption and the meaning of this result is discussed.     

Untersuchungen der Oxidbildung und Adsorption von Erdalkalien an einer sauerstoffvorbelegten Wolframoberfläche mit Hilfe der Oberflächenionisation

The surface ionization of alkaline-earth elements on tungsten has been studied in dependence on the temperature T and the surrounding oxygen partial pressure po₂; the values of the ionization efficiency β together with those of the change of the work function ΔΦ of the surface have been applied to get information about chemical reactions of the incident alkaline-earth atoms with adsorbed oxygen and about the adsorption of alkaline-earth elements on tungsten.Whereas in the high temperature range the tungsten surface is clean, towards lower temperatures (i.e. below ≈ 2500 K at po₂ = 1 × 10^?6 Torr or below ≈ 2000 K at po₂ = = 1 × 10^?9 Torr), an adsorption of oxygen increases the work function Φ and, consequently, the ionization efficiency β of incident metal atoms. A characteristic feature of the surface ionization of the alkaline-earth elements, however, is a rapid re-decrease of β with further decreasing temperature, which occurs at T ≈ 1400 K for Mg/W, T ≈ 1600 K for Ca/W, T ≈ 1800 K for Sr/W, and at T ≈ 2000 K for Ba/W. It is shown that this behaviour of β is caused by two different reasons: Whereas in the case of Mg/W a substantial Mg adsorption leading to a reduction of the work function is responsible for the decrease of β solely, the β values of Ca and Sr are additionally influenced by chemical reactions of the incident metal atoms with adsorbed oxygen resulting in an alkaline-earth oxide desorption. In the system $\text{Ba}\text{W}$ the decrease of the ionization efficiency β can be referred to BaO formation exclusively.Assuming a thermodynamic equilibrium between the different adparticles and using experimental values of the dissociation energy of the alkaline-earth oxides (in the gas phase), the results are in good agreement with theoretical calculations.     

Adsorption of oxygen on W(110): II. The high coverage range

The structure and composition of the interaction layer between oxygen and a W(110) surface for oxygen coverages θ above 0.5 monolayers is studied with LEED, AES, thermal desorption and work function change measurements. Oxygen is adsorbed by depositing WO₂ followed by annealing. The results are interpreted in terms of a topmost layer consisting only of oxygen atoms followed by the formation of isolated three-dimensional WO₃ crystals after saturation of the two-dimensional oxidation layer at 15 × 10¹⁴ O atoms cm^?2. All available experimental evidence is compatible with this interpretation.     

Desorption kinetics and directional dependence of the surface diffusion of potassium on stepped W(100) surfaces

Using a surface ionisation ion microscope the desorption parameters and the diffusion constant of potassium were measured on stepped W(100) surfaces. The activation energy of ionic desorption as well as the corresponding prefactor do not depend on the step density; the mean adsorption lifetime τ can be expressed as τ=1.6×10^?14s exp(2.44 eV/kT).Whereas the surface diffusion of potassium on “flat” W(100) and on W(S)-[9(100)×(110)] was found to be isotropic, on W(S)- [5(100)×(110)] and W(S)-[3(100)×(110)] it occurs preferentially parallel to the step direction. The diffusion constant D_∥ for this direction has roughly the same value for all investigated surfaces: D_∥=7.8×10^?2 cm²s^?1 exp(?0.42 eV/kT). For the direction perpendicular to the steps D⊥ depends on the step density, whereby the activation energy as well as the prefactor increase with increasing step density.