Diffusion of ammonia on Re(001)

摘要

Faraday Discuss., 1993,96,307-316 Diffusion of Ammonia on Re(001) I. Farbman, Z. Rosenzweig and M. Asscher Department of Physical Chemistry and the Farkas Center for Light-induced Processes, The Hebrew University, Jerusalem 91904, Israel Diffusion of ammonia on Re(001) has been studied utilizing optical second- harmonic diffraction from a surface coverage grating. The diffusion process at initial coverages NH,/Re 0.15 could be simulated only if the coverage- dependent diffusion constant had been considered. The resulting diffusivity D(0) = Do exp[ -E,(O)/RT], is defined by a barrier for diffusion Ern(@= E, -oZ8, with activation energy at zero coverage E, = 3.4 & 0.8 kcal mol-', Do = 2.8 x lo-, cm2 sec-' and the repulsion energy between a pair of nearest neighbour molecules, o = 0.4 0.06 kcal mol-'.The coverage effect on the diffusivity is discussed in terms of the thermodynamic factor, based on equilibrium adsorption measurements. Diffusion is among the more difficult surface processes to study experimentally. Micro- scopic diffusion measurements were performed extensively on field ion microscope (FIM) tips over a limited surface area at low temperatures, studying the diffusion of metal adatoms and small molecules, mostly over refractory metals.'-2 Typically, diffu- sion rates of single particles or dimers were measured, therefore lateral interactions were not considered in most cases. At finite coverages, interactions among neighbour adsorbates and their effect on the diffusion process cannot be neglected.In recent years laser desorption techniques have been developed and applied to the study of macroscopic surface diffusion. The first of those has been the laser-induced thermal desorption (LITD), in which a hole is burnt in a homogeneous adsorbate surface coverage, then the refilling rate as a function of initial coverage and crystal temperature is in~estigated.~~~ The refilling time is entirely due to surface diffusion. Difficulties in the application of this method to systems where the diffusion rate is not totally coverage independent have been pointed out.2*8 More recently, an optical method of laser diffraction from a surface coverage grating was demonstrated to provide information on surface diffusion. Using LITD with a single split laser pulse, an interference pattern is formed which creates a coverage modu- lation in a grating-like f~rm.~-'~ Second-harmonic9-' or linearl3*I4 diffractions from such gratings were then monitored.The decreasing intensity of the first-order diffraction peak is a measure of diffusion of the adsorbate from the filled to the evacuated troughs. Second-harmonic generation (SHG) was also employed in a novel microscopy mode to detect the diffusion of Sn atoms on Ge(lll), over a single coverage step, utilizing Boltzmann-Matano analysis.' Application of the SH diffraction method to follow the surface diffusion of ammonia on Re(OO1) is presented. The NH3/Re(O01) system has previously been investigated, uti- lizing optical SHG for the study of the adsorption mechanismI6 and isothermal and equilibrium desorption kinetics.' 7,1* The extremely strong coverage dependence of the desorption parameters makes this system an ideal case for a study of the role of lateral interactions on diffusion.307 Diflusion of Ammonia on Re(001) Experimental The diffusion experiments were performed in a UHV chamber with a typical base pres- sure of 3 x lo-'' mbar. The chamber is equipped with an ion sputter gun for cleaning the Re(OO1) metal surface, a Kelvin probe for work function change measurements and a quadrupole mass spectrometer (QMS) for temperature-programmed desorption (TPD). The details of the sample preparation and TPD set-up have been given elsewhere.16 The set-up of the optical system includes two p-polarized pulsed Nd : YAG lasers (Quantel YG585) at a fundamental wavelength of 1064 nm, repetition rate of 10 Hz and pulse duration of 10 ns (FWHM).One laser was used for the formation of the coverage modulation (grating). The second laser at much reduced power provided the probe beam. The heating (LITD) laser beam was split into two coherent beams having power density of 0.71, and 0.31, where I, is the total incident power density. Further details on the LITD experiment are given elsewhere.'8*19 The two beams strike the NH,-covered rhenium surface at incident angles4 = k5.2" from the normal to the surface. These beams spatially overlapped at the centre of the sample having a spot of 0.5 cm2. The total (both beams) effective laser power density absorbed by the metal per pulse was 4 MW cm-2.A spatial intensity modulation is formed under these conditions owing to interference between the two beams. As a result a periodic NH,-coverage modulation is created in a grating-like form. Having a periodic coverage modulation on the surface, the SH beams generate a diffraction pattern at 532 nm. The diffraction spectrum was obtained by rotating the sample at an angular resolution of 0.25'. The surface diffusion was then measured by following the decay of the first-order SH diffraction peak at various temperatures in the range 100-135 K. At a crystal tem- perature of 80 K, there was no change in the SH intensity at the zero- and first-order diffraction peaks after 3600 s.This indicates that there is no measurable desorption, readsorption, dissociation or diffusion of ammonia at this temperature during the period of 1 h while the probe beam continuously strikes the surface. Each point in the decay curves of the first order SH diffraction is an average of 256 laser pulses, which also defines a temporal resolution in these experiments of 25.6 s. Results and Discussion Coverage-grating Formation Periodic coverage modulation (monolayer grating) on a surface, as a result of LITD, can be simulated accurately only if the surface temperature during the pulsed heating and the precise coverage dependence of the desorption kinetics are known. In addition, the dependence of the second-order susceptibility tensor x$i(O) on surface coverage should be established in an independent experiment.In the NHJRe(OO1) system, this was pre- viously determined by comparing the SHG signal intensity us. ammonia coverage, with coverage determination by TPD. A quadratic dependence of the SHG signal on ammonia coverage, due to linearity of the second-order susceptibility with coverage was found.I6 The time-dependent surface-temperature profile following pulsed laser heating was indirectly determined in this system while monitoring desorption at the ns timescale by employing a pumpprobe experimental scheme." It was concluded that surface cover- age could be calculated 20 ns after the heating laser pulse has initiated, since at this time the pulsed desorption event has been terminated, and no further desorption occurs.A central requirement for the accurate simulation of the desorption rate and thus the remaining surface coverage as a result of LITD, is detailed knowledge of the desorption kinetic parameters. In the NH,/Re(OOl) system very strong coverage-dependent param- I. Farbman, Z. Rosenzweig and M. Asscher 309 eters, determined under equilibrium conditions,' were shown to be valid also during the 5 ns duration of the pulsed desorption e~ent.'~.'~ The first step for enabling surface diffusion measurements is the creation of an adsorbate coverage grating. As a result of interference between the two (split) heating laser beams, laser intensity modulation across the surface is expressed by: I(x) = A: + A: + 2A,A2cos(2nx/s), where A: + A; = I, is the total effective incident power density of the heating laser, s is the grating period (s = i2/2 sin 4).In our experiments i2 = 1.064 pm, the angle of incidence 4 = 5.2", hence s = 5.3 pm. The amplitude of the modulation is determined by the ratio AJA, and the total laser power. Knowing the intensity modulation, heat diffusivity and heat conductivity of the metal, one can derive the spatial modulation in surface temperature during the LITD process.'7 Knowing the temporal and lateral profiles of the surface temperature T[t,I(x)],18we can now integrate the desorption rate equation numerically for any given laser power density along the surface: -d0/dt = Vdes(0)@ eXp{ -Ed(@)/RT[t,I(X)]) (1) n = 1 for first-order desorption, v,,,(8) is the pre-exponential factor and Ed(@ is the activation energy for desorption.The detailed knowledge of the coverage-dependent desorption parameters, enabled us to predict accurately the remaining modulated NH, coverage. A typical calculated initial coverage profile is shown in Fig. 1. The simulated adsorbate grating in Fig. 1 reveals the following: (i) Under the experi- mental conditions mentioned above the coverage modulation changes from 0 = 0.75 at the 'cold' areas to 0 = 0.15 at the 'hot' areas, for initial coverage 0 = 0.75 (at 1 ML, NH,/Re = 0.25). (ii) Because of the LITD mechanism the adsorbate grating is asym- metric, the depleted areas are narrower than the populated, 'cold' areas where no desorption occurred.This means that the effective diffusion length is only 4 pm, while the theoretical grating period (in our conditions) is 5.3 pm. (iii) The integrated area under the adsorbate grating (the NH,-covered areas) is proportional to the average ammonia coverage after the LITD has been completed. An integrated area of Oeff = 0.7 is calculated for initial coverage of 1 ML, which agrees very well with that obtained by measuring the zero-order SH signal. The zero-order SH intensity decreases by a factor of two compared with the SH signal of 1 ML NH, adsorbed on Re(001), in agreement with the O2 dependence of the SH intensity. I I -1 0 0 10 distance/pm Fig. 1 Simulation of the coverage modulation :monolayer grating. The initial coverage ei = 0.75 ML.Diflusion of Ammonia on Re(001) A diffraction spectrum of the SH intensity obtained by rotating the sample is shown in Fig. 2. The angle y between the different diffraction components is defined by the laser wavelength and the incident angle of the two (split) heating beams. In our case y = 2.1", a value obtained from the diffraction relation for SH: k(20) = 2k(0) -k, , where k, = 2n/s is the wavevector characterizing the grating.' ' The ratio between the first-order SH diffraction beam to the zero-order beam is 1 : 3 and the ratio between the second-order SH diffracted beam to the zero-order beam is 1 : 10. Similar ratios, within 15% accuracy, between the respective squares of the Fourier components, were obtained from Fourier transformation of the simulated surface-coverage modulation discussed above.Diffusion Measurements The diffusion of NH, molecules on the Re surface was monitored by following the decay of the first-order SH diffraction as a function of time at different surface temperatures and for several initial coverages. In Fig. 3 isothermal decay curves of the first-order SH diffraction peak are shown for several crystal temperatures and two initial NH, cover-ages 8/8, = 1 [Fig. 3(a)] and 8/8, = 0.5 [Fig. 3(b)],where 8, is the saturation (1 MI,) ammonia coverage. Diffusion expressions based on Fick's law are typically used to explain surface diffu- sion where mass transport occurs due to gradients in the chemical potential.2 The second Fick's law for one-dimensional diffusion is : aO(x)/at= d/ax {D [O(x)]88(x)/ax) (2) where 8 is the surface concentration and x is the length variable.In the case of weak dependence of the diffusivity on coverage, one may assume, for low enough coverages, the Arrhenius expression for D = Do exp(-Ediff/RT), &iff and Do are the (coverage independent) activation energy for diffusion and the prefactor, respectively. l2 1 A B B~ a "39 41 43 45 47 49 51 angle of incidence/degrees Fig. 2 Diffracted SH signals as a function of sample rotation. The initial coverage is 1 ML. n = A, 0; B, 1 and C, 2. I. Farbman, Z. Rosenzweig and M. Asscher 31 1 1.2 I A 1.o 0.8 0.6 0.4 0.2 v)w.-C 709 v2 -0.2 g 1.0' r v) b 0.87 ? 4-2 0.61 0.4 0.2 0 (c) I I I-0.2 1 I diffusion time/s Fig.3 Decay curves of the first-order SH signals as a function of time. Oi = A, 1 and B, 0.5 ML. Oi = O/O,, where 8, is the ammonia coverage at 1 ML, where NH,/Re x 0.25. Surface temperature is for A: (a)100, (b)110 and (c) 120 K and for B: (a)110, (b) 120 and (c) 130 K. Analysis of the decay curves such as those in Fig. 3, reveals that it is impossible to fit the data obtained from initial coverages higher than NH,/Re = 0.15 by using the simple expression based on a single exponent as assumed for D above. It means that in Fig. 3(b) the single-exponent expression could be used (Oi = 0.5; NH,/Re z 0.12), while for the data in Fig. 3(a),the analysis should include coverage-dependent diffusivity.In this work we assume that the coverage dependence arises from repulsion among neighbour molecules which affect only the barrier for diffusion. As was shown by several recent Monte Carlo simulations,8.20 attractive interactions add to the barrier for diffu- sion at zero coverage, while repulsive ones reduce it. The pre-exponent Do is thus assumed to be coverage independent. The assumption used here, that the interaction between nearest-neighbour adsorbates is linear with coverage, means that the effect of the lateral interactions on the way the adsorbates are arranged, is ignored. In the case of 312 Digusion of Ammonia on Re(001) NH, on Re(OO1) this can be expressed as &iff = E, -wZO(x),where E, is the barrier at coverages lower than NH,/Re = 0.15, 2 is the maximum number of nearest neighbours, 2 = 3 at the edge of the grating, and w is the interaction between nearest-neighbour molecules.The diffusivity is then written: D[T, O(x)] = D,exp(coZB/RT) (3) where D,= Doexp(-E,/RT), Do = r(0)A2is the prefactor, r(0) is the microscopic attempt jump frequency and R is the jump length (close in magnitude to the surface unit cell). A more accurate way of accounting for the number of nearest neighbours and the effect of the lateral interactions of the spatial distribution is the application of the quasi- chemical approximation. It is assumed that local equilibrium exists at each point along the grating profile while the (slow) diffusion proceeds.The activation energy for diffusion in this case has the following form: 2 has the same meaning as in eqn. (3), wq is the interaction between a pair of nearest- neighbour adsorbates and B = 1 -exp(coq/RT). The diffusivity in this case is written: D[T, O(X)]= D,exp(-EJRT) Emis the second term in the right-hand side of eqn. (4). We have applied both methods of estimating the coverage effect on the barrier for diffusion, inserted the value of D[T, O(x)] and then numerically integrated the diffusion equation [eqn. (2)]. With each integration interval, a new coverage profile is formed, which is then fast Fourier-transform analysed in order to obtain the new magnitude of the Fourier components. These components are proportional to the Fourier com-ponents resulting from the modulated second-order susceptibility ten~or.~ This pro- cedure follows the smearing out of the grating due to the diffusion event, and thus simulates the change of the first- (or higher)-order Fourier components as a function of time for any given crystal temperature.The fit of the decay with time of the first Fourier component squared to the experimental results (first-order diffracted second-harmonic signal) is demonstrated by the solid lines through the data points in Fig. 3. An important experimental input for this kind of analysis is the magnitude of D,in eqn. (3) and (5). This parameter could be determined by reducing the initial coverage to the level in which a single exponent fits the data well [Fig.3(b)]. As mentioned above, our data show that this is the case for NH,/Re 0.15 (Ole, = 0.6). The results are shown as solid lines through the experimental data points in Fig. 3(b). The temperature depen- dence of the diffusion rate is then analysed using the Arrhenius plot. The resulting values are E, = 3.4 f0.8 kcal mo1-' and Do = 2.8 x lop3cm2 s-'. We should consider E, as the lower limit value for this system since the lowest initial coverage was not zero. Inserting the value of D, into eqn. (3), an average repulsive interaction energy 02 = 1.2 0.2 kcal mol-' is obtained from the slope of a plot of p = wZ/RT us. 1/T for all three initial coverages Oi = 1.0, 0.85, 0.7, as reproduced in Fig. 4. This means that the nearest-neighbours repulsion energy is determined to be co = 0.4 kcal mol-l. Repeating these simulations using the quasi-chemical approximation the results were found to be indistinguishable from the former method.At a crystal temperature of 120 K, the initial diffusion rates are then: 2.7 x 1.3 x 5.9 x and 2.2 x lo-' cm2 s-' for the initial coverages of 1, 0.85, 0.7 and 0.5 ML, respectively. Previous studies have attempted to follow experimentally the evolution of a single- coverage step-like profile e~perimentally.~'-', Utilizing the Boltzmann-Matano' analysis, it is possible to obtain the coverage dependence of the diffusion rate. This way the coverage dependence of both the activation energy for diffusion and the prefactor I. Farbman, Z.Rosenzweig and M. Asscher 3.0 2.5 2.0 B 1.5 1.o 0.5 7.5 8.5 9.5 10.5 11.5 103 KIT Fig. 4 B = Zw/RT us. 1/T. The resulting interaction parameter w = 0.2 0.06 kcal mol-(2= 6) is obtained for three different initial coverages: Bi = 0, 0.7 ML.1;A, 0.85 and ., could be determined. In the coverage grating-SH diffraction experiments, the coverage at each point along the grating can be simulated quite accurately. This, in principle, should enable the determination of coverage-dependent diffusion rate constants, however, it is impossible to distinguish the effect of coverage on the activation energy from its effect on the prefactor. Note that, in our analysis, we have assumed that increas- ing the coverage decreases the barrier for diffusion, while the prefactor is independent of coverage.Using the Boltzmann-Matano analysis, it was shown in ref. 23, that for Sn on Ge(11 l), the opposite occurs, namely the only effect of coverage is on the prefactor, while the activation energy is insensitive to changes in coverage. The analysis used in this work does not enable us to rule out coverage effect on the prefactor also. The relatively weak repulsive interaction between nearest neighbours determined from the diffusion measurements is in sharp contrast to the strong repulsion and thus the remarkable change in the activation energy for desorption with coverage, deter- mined from equilibrium measurements.' While the overall trend is similar in both cases, namely a decreasing barrier as the coverage increases, the details differ signifi- cantly in magnitude as well as in the overall 0 dependence.The difference may arise from the lateral arrangement of adsorbates at high coverages. In these cases, neighbour molecules may be distributed around an adsorbate in such a way that in spite of the decreased diffusion barrier, the net diffusion rate will be kept slow. This then is analysed as if the effective interaction is weak. Compensation effects on Edif,and Do, if they exist, may lead to the same results. Similar geometrical constraints should not influence the desorption, therefore one observes the full magnitude of the repulsion in desorption measurements. In an attempt to address the coverage effect on the activation energy for diffusion, we have employed the thermodynamic approach suggested in ref.24. The diffusivity as a function of coverage should be written in terms of the chemical potential p as follows:24 The microscopic jump frequency r(8)is expected to be a complicated function of surface coverage. Nevertheless, if the thermodynamic factor a = a(p/kT)/d In 8 is measur-able experimentally, the diffusivity can still be expressed in the usual way D(0) = Do exp[ -&iff/RT]. However, now the activation energy for diffusion, Ediff, and the pre- factor, Do, should be written as functions of Provided that the diffusion occurs in a 314 Digusion of Ammonia on Re(001) surface-temperature range where equilibrium exists between the adsorbed layer and the gas phase, the chemical potential in the two phases should be the same.At low enough pressures the following equality holds : a = [d(p/kT)/d In t?]T = [a In P/a In t?]T (7) This means that a may be evaluated from adsorption isotherms. Adsorption- desorption equilibria measurements for the NHJRe(001) system were performed and the corresponding desorption kinetic parameters as a function of coverage were determined, utilizing SHG as the surface-coverage monitoring te~hnique.'~ It is potentially possible, therefore, to extract a from these experiments. The lowest surface temperature at which a could be determined from isothermal adsorption-desorption data was 160 K. The highest temperature at which diffusion measurements could be taken was 135 K.The temperature gap between these two experiments prevents direct application of eqn. (7) to estimate the effects of coverage on the diffusivity. Nevertheless, evaluation of a at decreasing surface temperatures provides a useful tool to examine the validity of the assumption made above on the origin of the repulsion among nearest neighbours, namely the linear decrease of the barrier for diffusion with increasing coverage. Once a is known and the isosteric heat of adsorption curve as a function of coverage has been determined, the activation energy for diffusion is given by : Ediff= E, + (a In 8/a In P),(aq/a In 8) (8) The values for Edifrcomputed from eqn. (8) based on the data in ref. 17 for the isosteric heat of adsorption q and the equilibrium measurements, are reproduced in Fig.5 at three surface temperatures 240, 190 and 160 K. These are plotted as a function of 8 and 3 2 1 r I--Eo lu Y -2;-1 kl -2 -3 -4 Fig. 5 Ediffplotted as a function of coverage. The solid line is the linear model for repulsion [eqn. (3) in the text]. (-), (--) and (. . . . a) were computed accounting for the thermodynamic factor a [see eqn. (8) in the text] at 240, 190 and 160 K, respectively. The data for the evaluation of Ed,, from eqn. (8) was taken from ref. 17. In the insert, l/a is plotted against surface temperature. I. Farbman, Z. Rosenzweig and M. Asscher 315 compared to Ediffobtained from the linear model used in this work, see eqn. (3). It is shown clearly that although at 240 K the two ways to evaluate Ediff[eqn.(3) and (8)] give significantly different results, as temperature decreases they become closer to each other. It seems as if the two expressions converge to a similar behaviour if both could be calculated in the temperature range where the diffusion measurements were taken. In order to check further the convergence at lower temperatures, the inverse of the ther- modynamic factor (l/a = i7 In O/i7 In P), was evaluated as a function of temperature from the equilibrium data.17 The results are shown in the insert of Fig. 5. It is seen that, in the temperature range 180-220 K, l/a changes significantly, while slow but steady decrease with temperature is observed below 170 K. The continuous descent of l/a towards tem- peratures where the diffusion measurements were performed, further supports the con- clusion, stated above, that the linear and the thermodynamic models converge to similar values at low temperatures.Summary SHG diffraction from LITD-generated surface-coverage grating was employed for the study of ammonia diffusion on Re(OO1). The decay of the first-order SH diffraction signal was monitored as a function of time at several crystal temperatures as an indication of the diffusion process at the surface. It was found that the diffusion rate is sensitive to the initial surface coverage for Ole, 0.5. The experimental results were simulated by assuming that nearest-neighbour molecules affect the diffusion rate by changing only the barrier for diffusion.Solving the second Fick's diffusion law in combination with a fast Fourier-transform analysis of the evolving coverage profile with time as a function of crystal temperature, the following diffusion rate parameters were obtained : at sufficiently low coverage (O/O, 0.5 in this case) D,= Do exp(-E,/RT), Do= 2.8 x cm2 s-l, E, = 3.4 & 0.8 kcal mol, while at higher coverages, where the barrier for diffusion is Ediff= Eo -ZwO, we have determined the effective repulsion energy cc) = 0.4 & 0.06 kcal mol-'. The validity of this linear model was checked against an approach based on the evaluation of the thermodynamic factor a = [d(p/kT)/d In elTfrom equilibrium isother- mal adsorption-desorption data obtained previously for the NH3/Re(O01) system.Exact comparison between the two approaches could not be made owing to the difference in the temperature range over which the diffusion and the isothermal adsorption measure- ments were performed. However, examination of the data suggests that the two expres- sions converge to provide very similar values in the temperature range where the diffusion measurements were made. Finally, the repulsive term between nearest neighbours and its effect on the diffusion rate is far smaller than expected from comparison with the effect of repulsion, due to increased coverage, on the activation energy for desorption. This may arise from lateral organizations of adsorbates which compensate the real repulsion between nearest-neighbour pairs.Stimulating discussions with A. Ben-Shaul and R. Kosloff are gratefully acknowledged. The Farkas Center is supported by the Bundesministerium fur Forschung und Technol- ogie and the Minerva Gesellschaft fur die Forschung mbh. References 1 G. Ehrlich and K. Stolt, Annu. Rev. Phys. Chem., 1980,31,603. 2 R.Gomer, Rep. Prog. Phys., 1990,53,917. 3 R.Viswanathan, D.R. Burgess, P. C. Stair and E. Weitz, J. Vac.Sci. Technol., 1982,20,605. 4 S. M.George, A. M. DeSantolo and R. B. Hall, Surf: Sci., 1985,159, L425. 5 C.H.Mak, J. L. Brand, A. A. Deckert and S. M. George, J. Chem. Phys., 1986,85, 1676. 6 E.G.Seebauer and L. D. Schmidt, Chem. Phys. Lett., 1985,123,129. Diusion of Ammonia on Re(001) 7 B. Roop, S. A. Costello, D.R. Mullins and J. M. White, J. Chem. Phys., 1987,86, 3003. 8 M. C. Tringides and R. Gomer, Surf. Sci., 1992,265,283. 9 X-Dong Xiao, X. D. Zhu, W. 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