- Email: [email protected]
Simple model for the desorption of hydrogen from Ni surfaces
CHEMICAL PHYSICS LETTERS
Volume 49, number 3
1 August 1977
SIMPLE MODEL FOR THE DESORPTION OF HYDROGEN FROM Ni SURFACES
George COMSA and Rudolf DAVID ~nsh~tur fiir Grenzflichenforschung
D-51 7JZich.
rrrid I’akuurnphysik, Kemforschungsaniage JfiIich,
Germany
Received 19 April 1977
A model is presented which describes features of the “hot”,
non-cosine and non-maxwelLian velocity distriiutions of Hz
molecules desorbing from Ni surfaces. The model, based on detailed balancing, assumes that incident molecules encounter an activation barrier with holes. The model also correlates with results of kinetic measurements: sticking coefficient =0-l,
non-activated adsorption at low temperatures and activated adsorption at high temperatures.
Recent time-of-flight (TOF) measurements of the velocity distribution of HZ, HD and D2 molecuIes associatively desorbing from polycrystalline Ni surfaces [l] have uncovered new experimental features of the desorption process. These concern mainly the angular and surface temperature dependence of the mean energy and speed ratio * of the desorbing molecules (fig1). The data could not be rationalized by means of the existing models [2,3 J . This is so far not surprising because these models were proposed to explain a much more restricted amount of experimental data. It is the purpose of the present paper to propose a simple model which seems to correlate satisfactorily with most of the experimental data on the system hydrogen&ckel. Since the proposed model is related to van Will&en’s “activated-adsorption model” (AA model) [2] a short description of the main features of the latter might be useful. Van Will&en correlares the deviations of the angular distribtltion of the flux of associatively desorbing molecules, A’(S), from the Knudsen cosine law, with the existence of an activation energy for dissociative adsorption. He assumes that this activation barrier, EA, “is constant over the whole surface and the equipotential planes parallel to the surface are flat”. Van Wiliigen obtained the expression of N(0) by * The normalized speed ratio S = (32/9rr - 1)-“*(7
/ja - l)r’* is a measure for the width of the velocity distrrbutions (S = 1 for a maxwellian distribution).
512
calculating the angular distribution of molecules which are able to adsorb dissociatively and by assuming that equilibrium exists between adsorbed H atoms and H2 gas molecules and that detailed balancing applies. He further assumed that the Hz molecules which are energetically able to adsorb on the surface have a sticking probability of 1. In order to compare the predictions of the AA model with the recent experimental results [i] , we calculates using the same procedure and assumptions the expressions of the angular dependence of the mean energy, ,!?(e), and of the speed ratio, S(0). For the free pararneter we chose the value EA = 2.002 kT, * 0.2 eV_ This value corresponds to the experimental mean energy (expressed in Kelvin) E/2k = TE = 19 16 K of D2 molecules desorbing at B = 0” from a surface at T, = 1143 K [l] _ The predictions of the AA model are plotted as dashed lines in fig. 1. it is obvious that the model fails to predict (particularly in the case of figs. la and 1b) the values and even the trends of the experimental data. In addition, the assumed correlation between the deviations from the desorption cosine law and the existence .of an activated adsorption at alI temperatures is in contradiction with the results of kinetic measurements. Indeed, for the H2/Ni system, the experimental IV(S) = COS~-~~,while kinetic measurements at T, < 500 K have shown that the dissociative adsorption of H2 on Ni is non-activated [4]. Goodman’s model [3] is somewhat artificial and ac-
CHEMICAL PHYSICS LETTERS
Volume 49, number 3
1 August 1977
Molecular beam experiments and a detailed balance analysis of the H,/Cu system were reported in two papers by Stickney’s group [5,6] _ The authors demonstrated the efficiency and the correctness of the detailed balance analysis at least for the H,/Cu system [6] . Using nearly monoenergetic H2 beams of differ-
3 8
D2lNi \
Ts=llL3K x
20 LO 60 80 0 desorptlon angle e [degree] F&
1. (a) Mean energy E, (h) speed ratio S and (c) relative flux
versus desorption angle 0. X - mean values of experimental data from ref. [l] _The bars in (a) and (b) represent the errors of the mean from seven TOF-curves. The esperimental errors increase with 8, particularly in (II) [ 11. The plotted curves are the predictions of the models: ---, AA [ 21, AAH (proposed); AAH non-convoluted. _._TnTt [3] and The free parameters of the models were chosen to pive the best i-it in (a) (see text;.
N@)/N(O”)
cordiigly less attractive. It effectively assumes that the desorbed molecules have a maxwellian-type distribution but with different temperatures T, and Tt in the normal and tangential directions_ Goodman himself does not believe his model (T,T, model) to be “correct” [3]. For comparison with the experimental data the values of the parameters were determined so as to obtain the best fit of the experimental points in fig. la: Tn=TE(0=00)=1916KandTt=Ts=1143K.The dotted curves in fig. 1 show that although not “correct” the TnTt model yields much better predictions. It has to be noticed that the assumed maxwellian distribution leads in all cases to S = 1. This is in contrartiction with the experimental data at small 0.
ent energies Ei and different angles of incidence, 8,, they made the very important observation that the sticking probability values, 0, obtained for different Ei and Bi values may be correlated quite well by the parameter EL =Ei COS’0i, i.e. with the energy associated with the normal component of the molecular velocity [S] . This seemed to be a very strong support for van Will&en’s main assumption i.e. for the existence of an activation energy for dissociative adsorption at least in the case of the H?/Cu system. However, Stickney et al. [5] noticed that instead of a step function as predicted by the AA model they obtained an S-shaped curve for o=f(E,). In order to explain this shape they proposed a modification of the AA model “so that it includes a distribution of energy barrier heights rather than a single barrier height”. Unfortunately they did not carry their modified model beyond some qualitative considerations on account of its complexity. Surprisingiy enough the authors did not comment on a very interesting feature at the low energy end of their o = f(E1) curves: the sticking probability 0 does not vanish when EL goes to zero, but levels off at some 15% of omax_ This is in contradiction with any activated adsorption model unless it is admitted that the activation barrier is no longer of constant height but contains “holes” through which a finite fraction of the incident moIecules may dissociatively adsorb rvithorct activation energy. This assumption is in fact the essence of the model we are proposing here. Accordingly a model is proposed in which the features of the desorbing molecules are correlated with the existence of an activated adsorption barrier with holes (AAH model). For calculations a more exact definition of this assumption is necessary: “a fraction 1 - r of the incident molecules encounters an activation barrier of height EA , while the complementary non-vanishing fraction r is adsorbed rvithout (or with negligible) activation energy; the equipotential planes parallel to the surface are flat”. The fundamental characteristic of the AAH model, distinguishing it from the AA model and from the refinement proposed by Stickney’s group [5], 513
Volume 49, number 3 is the fact that it demands a finite
fraction of the incident molecuIes to be adsorbed wvithozctactivation. This
characteristic enables the AAH model to describe fairly well the experimental features of the Hz molecules desorbing from Ni surfaces and a!so the results of kinetic measurements. By assuming onIy one non-zero barrier height and not a “distribution of barrier heights” the AAH model predicts a step function for 0 =f(E,) and not an S-shaped curve as was observed for the H$u system [SJ. We feei, however, that for the present a simple and more transparent two-parameter model has a significant advantage: It can be evaluated straightforwardly and compared quantitatively with experimental data. In addition, a more refined model could fit the data better simply by having more parameters and might therefore kcidentaIIy hide some basic weakness of the model. Starting e.g. from ideas similar to those suggested by Stickney’s group [5] one may imagine that the assumed “potential barrier with holes” might be produced either by the surface structure (favorable and less favorable sites)* or by favorable and less favorable orientations of the incident molecules. FoIIowing van WiIIigen’s procedure with the additional assumption of holes in the activation barrier one obtains the anguiar dependence of the flux of desorbirlg molecules: N(B)a(l
-r)J
u3 exp(-u”/ar2) cos 0 dv VA@)
+I-
J v3exp(-v2/ar2)
cos 8dv.
(1)
0
where CY?= 2kTJm and ?,A@) = (2Ei& CO~%?)~~*. The Iower integral limit, VA(e), is the minimum velocity of a molecule incident with 0, which is able to overcome
the activation
tegrations
barrier
and with _X =
EA.
By performing
the in-
EA/kTs, one gets for the rela-
tive flux:
* In ref. [ 6 ] the simultaneous presence of sites with and with-
out an energy barrier for adsorption, deduced from measurements on flat and stepped Ft(I 11) surfaces, was considered to explain correlations between the shape of the angular dependence of the flux of desorbing molecules and the surface smoothness.
514
1 August 1977
CHEMICAL PHYSICS LETTERS
N(e)
=(I
--r)(l
+x/~os*e)e-~~~~*~
(1 --r)(l
NO”)
+r
+x) eex +r
cos
e-(1’)
For I = 0 (i.e. no holes) eq. (1’) coincides with the fam iar van WiIIigen formuIa [2]. Following a similar procedure one gets the analytica expressions for the anguuiardependence of the mean en ergy of the desorbing molecules q==
T&B) (1 -
r)(x21cos4 e)
(1 --r)(f
+xlc0s2e)
e-x1cos2e e-x~mS2*
+r
1;(2)
as weII as of the speed ratio S(8). The expression for S(0) is too cumbersome to be presented in this letter and will be published elsewhere. As in the case of the other two models the parameters x and r were determined by the best fit to the z(0) points in fig. la. The obtained values are: x = 3 (_“A = 0.3 eV) and r = O-11_ With these values introduced in eq. (2), in the corresponding formula for S(0) and in eq. (1’) the full lines in figs. la, lb and lc are generated_ The values obtained from eq. (2) were subjected to a simple convolution procedure accounting for the finite angular resoIution of the TOF apparatus and for the non-perfect flatness of the polycrystalline surface. (The thin full line in fig. la represents the non-convoluted curve.) The determination of the parameter values is rather precise because the shape and the position of the E(0) curve are extremely sensitive not only to the features of the model but also to the values of the parameters. Indeed the curves corresponding to parameter values outside the ranges2.8Xxc3.2 andO.lO
CHEMICAL PHYSICS LETTERS
Volume 49, number 3
1 August 1977
aging: the model allows S(O”) values smaller than 1 and leads to a correct trend for 8 < 415~.
A final comment should be made concerning the constant value cr = O-l! resulting from eq. (3’) at tem-
The fit in fig. lc is again fairly good. This is, however, not so surprising because the N@)/~(O”) curve is rather insensitive to the features of the model. In addition, the AAH model predicts in accord with the experiments that, in the accessible temperature range, the temperature dependence of the ratio 1?(0”)/ 2kT, and of the shape of the N(B)/N(O”) curve is negligible [1,2] . Finally we wti discuss connections to kinetic experiments. By keeping in mind the assumptions which led to eq. (1) - particularly that the molecules which are energetically able to adsorb dissociatively have a sticking probability of 1 - the integration of eq. (1) over 8 leads to the sticking probability of an isotropic
peratures lower than 500 IS: This value coincides surprisingly well with values of the initial sticking coefficient reported recently: o = 0.1 [7] and CJ= 0.15 + 0.05 [8] for Hz/Ni(lll) and o = 0.1 [lo] and o = 0.1 2 0.02 [8] for HZ/polycrystalline Ni. The coincidence with the value obtained by Lapujoulade and Neil [7] is particularly interesting because, due to the similarity in surface treatment, in both cases the surfaces were probably half-covered with sulfur. In conclusion: the very simpte two-parameter AAH model describes SatisfactoriIy the angularly resolved TOF desorption experiments and correlates rather well with results of kinetic experimentsiFurt.her confrontation with experimental data is necessary for a more elaborate assessment of this model and for final physical interpretations of the assumptions.
gas: o = (1 - r) exp(-EAlkTs)
+r _
(3)
The terms on the right hand side represent the molecules adsorbed with and without activation energy, respectively. With the parameters determined above eq. (3) becomes: o = 0.89 exp(-3429/T,)
(3’)
+ 0.11.
Thus the sticking probability is temperature dependent. Therefore the kinetic measurements should be in principle in favor of an activated adsorption process. However, most of the kinetic measurements for the system H2/Ni were performed at temperatures lower than 500 K (see e.g. refs. [4,7,8] ) for which the first term in eq. (3’) is smaller than 10m3 _Thus (T = 0.11 in the whole temperature range T < 500 K, and no evidence of activation could be detected in these kinetic measurements_ On the other hand Palmer et al. [9], using a molecular beam technique, observed an apparent activation energy for adsorption for the same system by raising the beam energy from room temperature to 1800 K. This result is also in accordance with the AAH model because at high temperatures the temperature dependent term in eq. (3’) is no longer negligible *.
It is a pleasure to acknowledge the enlightening discussions with Hans I?. Bonzel, Jan K. Fremerey and Harald Ibach.
References [ 1] G. Comsa, R. David and K.R. Rcndulic, Phys. Rev. Letters 38 (1977) 775. [2] W. van Willigcn, Phys. Letters 28A (1968) 80. [3] F.O. Goodman, Surface Sci. 30 (1972) 525. [4] K. Christmann, 0. Schober, G. Ertl and M. Neumann, J. Chem. Phys. 60 (1974) 4528; G. ErtI, private communication. [S J M. Balooch, M.J. Cardillo, D.R. Miller and RX. Stickney, Surface Sci. 46 (1974) 358. [6] M.J. Cardillo, M. Balooch and R.E. Stickney. Surface Sci. 50 (1975) 263. [7] J. Lapujoulade and KS. Ned, J. Chem. Phys. 57 (1972) 3535. [ 81 H. Rinne, Thesis, TU Hannover (1974). [9] R.L. Palmer, J.N. Smith Jr., H. Saltsburg and D-R. O’Kcefe, J. Chem. Phys. 53 (1970) 1666. -_ Chem. (Leipzig) 253 [IO] M. Procop and J. Vtilter, Z. Pk
(1973) 33.
* When using molecular beams, i.e. a nonisotropic incidence, eq. (3) is no longer applicable. For maxwellian beams inincident with an angle 8 one has to use: u(8) = (l--r)<1
+x/c05%)
exp(-&or%)
+ r_
(3”)
With x = 3, r = 0.11 and a beam temperature of e.g. 1800 K one obtains for 0 = 0” : (r = 0.49 and for 0 = 45”: u = 0.20.
515
Volume 49, number 3
1 August 1977
SIMPLE MODEL FOR THE DESORPTION OF HYDROGEN FROM Ni SURFACES
George COMSA and Rudolf DAVID ~nsh~tur fiir Grenzflichenforschung
D-51 7JZich.
rrrid I’akuurnphysik, Kemforschungsaniage JfiIich,
Germany
Received 19 April 1977
A model is presented which describes features of the “hot”,
non-cosine and non-maxwelLian velocity distriiutions of Hz
molecules desorbing from Ni surfaces. The model, based on detailed balancing, assumes that incident molecules encounter an activation barrier with holes. The model also correlates with results of kinetic measurements: sticking coefficient =0-l,
non-activated adsorption at low temperatures and activated adsorption at high temperatures.
Recent time-of-flight (TOF) measurements of the velocity distribution of HZ, HD and D2 molecuIes associatively desorbing from polycrystalline Ni surfaces [l] have uncovered new experimental features of the desorption process. These concern mainly the angular and surface temperature dependence of the mean energy and speed ratio * of the desorbing molecules (fig1). The data could not be rationalized by means of the existing models [2,3 J . This is so far not surprising because these models were proposed to explain a much more restricted amount of experimental data. It is the purpose of the present paper to propose a simple model which seems to correlate satisfactorily with most of the experimental data on the system hydrogen&ckel. Since the proposed model is related to van Will&en’s “activated-adsorption model” (AA model) [2] a short description of the main features of the latter might be useful. Van Will&en correlares the deviations of the angular distribtltion of the flux of associatively desorbing molecules, A’(S), from the Knudsen cosine law, with the existence of an activation energy for dissociative adsorption. He assumes that this activation barrier, EA, “is constant over the whole surface and the equipotential planes parallel to the surface are flat”. Van Wiliigen obtained the expression of N(0) by * The normalized speed ratio S = (32/9rr - 1)-“*(7
/ja - l)r’* is a measure for the width of the velocity distrrbutions (S = 1 for a maxwellian distribution).
512
calculating the angular distribution of molecules which are able to adsorb dissociatively and by assuming that equilibrium exists between adsorbed H atoms and H2 gas molecules and that detailed balancing applies. He further assumed that the Hz molecules which are energetically able to adsorb on the surface have a sticking probability of 1. In order to compare the predictions of the AA model with the recent experimental results [i] , we calculates using the same procedure and assumptions the expressions of the angular dependence of the mean energy, ,!?(e), and of the speed ratio, S(0). For the free pararneter we chose the value EA = 2.002 kT, * 0.2 eV_ This value corresponds to the experimental mean energy (expressed in Kelvin) E/2k = TE = 19 16 K of D2 molecules desorbing at B = 0” from a surface at T, = 1143 K [l] _ The predictions of the AA model are plotted as dashed lines in fig. 1. it is obvious that the model fails to predict (particularly in the case of figs. la and 1b) the values and even the trends of the experimental data. In addition, the assumed correlation between the deviations from the desorption cosine law and the existence .of an activated adsorption at alI temperatures is in contradiction with the results of kinetic measurements. Indeed, for the H2/Ni system, the experimental IV(S) = COS~-~~,while kinetic measurements at T, < 500 K have shown that the dissociative adsorption of H2 on Ni is non-activated [4]. Goodman’s model [3] is somewhat artificial and ac-
CHEMICAL PHYSICS LETTERS
Volume 49, number 3
1 August 1977
Molecular beam experiments and a detailed balance analysis of the H,/Cu system were reported in two papers by Stickney’s group [5,6] _ The authors demonstrated the efficiency and the correctness of the detailed balance analysis at least for the H,/Cu system [6] . Using nearly monoenergetic H2 beams of differ-
3 8
D2lNi \
Ts=llL3K x
20 LO 60 80 0 desorptlon angle e [degree] F&
1. (a) Mean energy E, (h) speed ratio S and (c) relative flux
versus desorption angle 0. X - mean values of experimental data from ref. [l] _The bars in (a) and (b) represent the errors of the mean from seven TOF-curves. The esperimental errors increase with 8, particularly in (II) [ 11. The plotted curves are the predictions of the models: ---, AA [ 21, AAH (proposed); AAH non-convoluted. _._TnTt [3] and The free parameters of the models were chosen to pive the best i-it in (a) (see text;.
N@)/N(O”)
cordiigly less attractive. It effectively assumes that the desorbed molecules have a maxwellian-type distribution but with different temperatures T, and Tt in the normal and tangential directions_ Goodman himself does not believe his model (T,T, model) to be “correct” [3]. For comparison with the experimental data the values of the parameters were determined so as to obtain the best fit of the experimental points in fig. la: Tn=TE(0=00)=1916KandTt=Ts=1143K.The dotted curves in fig. 1 show that although not “correct” the TnTt model yields much better predictions. It has to be noticed that the assumed maxwellian distribution leads in all cases to S = 1. This is in contrartiction with the experimental data at small 0.
ent energies Ei and different angles of incidence, 8,, they made the very important observation that the sticking probability values, 0, obtained for different Ei and Bi values may be correlated quite well by the parameter EL =Ei COS’0i, i.e. with the energy associated with the normal component of the molecular velocity [S] . This seemed to be a very strong support for van Will&en’s main assumption i.e. for the existence of an activation energy for dissociative adsorption at least in the case of the H?/Cu system. However, Stickney et al. [5] noticed that instead of a step function as predicted by the AA model they obtained an S-shaped curve for o=f(E,). In order to explain this shape they proposed a modification of the AA model “so that it includes a distribution of energy barrier heights rather than a single barrier height”. Unfortunately they did not carry their modified model beyond some qualitative considerations on account of its complexity. Surprisingiy enough the authors did not comment on a very interesting feature at the low energy end of their o = f(E1) curves: the sticking probability 0 does not vanish when EL goes to zero, but levels off at some 15% of omax_ This is in contradiction with any activated adsorption model unless it is admitted that the activation barrier is no longer of constant height but contains “holes” through which a finite fraction of the incident moIecules may dissociatively adsorb rvithorct activation energy. This assumption is in fact the essence of the model we are proposing here. Accordingly a model is proposed in which the features of the desorbing molecules are correlated with the existence of an activated adsorption barrier with holes (AAH model). For calculations a more exact definition of this assumption is necessary: “a fraction 1 - r of the incident molecules encounters an activation barrier of height EA , while the complementary non-vanishing fraction r is adsorbed rvithout (or with negligible) activation energy; the equipotential planes parallel to the surface are flat”. The fundamental characteristic of the AAH model, distinguishing it from the AA model and from the refinement proposed by Stickney’s group [5], 513
Volume 49, number 3 is the fact that it demands a finite
fraction of the incident molecuIes to be adsorbed wvithozctactivation. This
characteristic enables the AAH model to describe fairly well the experimental features of the Hz molecules desorbing from Ni surfaces and a!so the results of kinetic measurements. By assuming onIy one non-zero barrier height and not a “distribution of barrier heights” the AAH model predicts a step function for 0 =f(E,) and not an S-shaped curve as was observed for the H$u system [SJ. We feei, however, that for the present a simple and more transparent two-parameter model has a significant advantage: It can be evaluated straightforwardly and compared quantitatively with experimental data. In addition, a more refined model could fit the data better simply by having more parameters and might therefore kcidentaIIy hide some basic weakness of the model. Starting e.g. from ideas similar to those suggested by Stickney’s group [5] one may imagine that the assumed “potential barrier with holes” might be produced either by the surface structure (favorable and less favorable sites)* or by favorable and less favorable orientations of the incident molecules. FoIIowing van WiIIigen’s procedure with the additional assumption of holes in the activation barrier one obtains the anguiar dependence of the flux of desorbirlg molecules: N(B)a(l
-r)J
u3 exp(-u”/ar2) cos 0 dv VA@)
+I-
J v3exp(-v2/ar2)
cos 8dv.
(1)
0
where CY?= 2kTJm and ?,A@) = (2Ei& CO~%?)~~*. The Iower integral limit, VA(e), is the minimum velocity of a molecule incident with 0, which is able to overcome
the activation
tegrations
barrier
and with _X =
EA.
By performing
the in-
EA/kTs, one gets for the rela-
tive flux:
* In ref. [ 6 ] the simultaneous presence of sites with and with-
out an energy barrier for adsorption, deduced from measurements on flat and stepped Ft(I 11) surfaces, was considered to explain correlations between the shape of the angular dependence of the flux of desorbing molecules and the surface smoothness.
514
1 August 1977
CHEMICAL PHYSICS LETTERS
N(e)
=(I
--r)(l
+x/~os*e)e-~~~~*~
(1 --r)(l
NO”)
+r
+x) eex +r
cos
e-(1’)
For I = 0 (i.e. no holes) eq. (1’) coincides with the fam iar van WiIIigen formuIa [2]. Following a similar procedure one gets the analytica expressions for the anguuiardependence of the mean en ergy of the desorbing molecules q==
T&B) (1 -
r)(x21cos4 e)
(1 --r)(f
+xlc0s2e)
e-x1cos2e e-x~mS2*
+r
1;(2)
as weII as of the speed ratio S(8). The expression for S(0) is too cumbersome to be presented in this letter and will be published elsewhere. As in the case of the other two models the parameters x and r were determined by the best fit to the z(0) points in fig. la. The obtained values are: x = 3 (_“A = 0.3 eV) and r = O-11_ With these values introduced in eq. (2), in the corresponding formula for S(0) and in eq. (1’) the full lines in figs. la, lb and lc are generated_ The values obtained from eq. (2) were subjected to a simple convolution procedure accounting for the finite angular resoIution of the TOF apparatus and for the non-perfect flatness of the polycrystalline surface. (The thin full line in fig. la represents the non-convoluted curve.) The determination of the parameter values is rather precise because the shape and the position of the E(0) curve are extremely sensitive not only to the features of the model but also to the values of the parameters. Indeed the curves corresponding to parameter values outside the ranges2.8Xxc3.2 andO.lO
CHEMICAL PHYSICS LETTERS
Volume 49, number 3
1 August 1977
aging: the model allows S(O”) values smaller than 1 and leads to a correct trend for 8 < 415~.
A final comment should be made concerning the constant value cr = O-l! resulting from eq. (3’) at tem-
The fit in fig. lc is again fairly good. This is, however, not so surprising because the N@)/~(O”) curve is rather insensitive to the features of the model. In addition, the AAH model predicts in accord with the experiments that, in the accessible temperature range, the temperature dependence of the ratio 1?(0”)/ 2kT, and of the shape of the N(B)/N(O”) curve is negligible [1,2] . Finally we wti discuss connections to kinetic experiments. By keeping in mind the assumptions which led to eq. (1) - particularly that the molecules which are energetically able to adsorb dissociatively have a sticking probability of 1 - the integration of eq. (1) over 8 leads to the sticking probability of an isotropic
peratures lower than 500 IS: This value coincides surprisingly well with values of the initial sticking coefficient reported recently: o = 0.1 [7] and CJ= 0.15 + 0.05 [8] for Hz/Ni(lll) and o = 0.1 [lo] and o = 0.1 2 0.02 [8] for HZ/polycrystalline Ni. The coincidence with the value obtained by Lapujoulade and Neil [7] is particularly interesting because, due to the similarity in surface treatment, in both cases the surfaces were probably half-covered with sulfur. In conclusion: the very simpte two-parameter AAH model describes SatisfactoriIy the angularly resolved TOF desorption experiments and correlates rather well with results of kinetic experimentsiFurt.her confrontation with experimental data is necessary for a more elaborate assessment of this model and for final physical interpretations of the assumptions.
gas: o = (1 - r) exp(-EAlkTs)
+r _
(3)
The terms on the right hand side represent the molecules adsorbed with and without activation energy, respectively. With the parameters determined above eq. (3) becomes: o = 0.89 exp(-3429/T,)
(3’)
+ 0.11.
Thus the sticking probability is temperature dependent. Therefore the kinetic measurements should be in principle in favor of an activated adsorption process. However, most of the kinetic measurements for the system H2/Ni were performed at temperatures lower than 500 K (see e.g. refs. [4,7,8] ) for which the first term in eq. (3’) is smaller than 10m3 _Thus (T = 0.11 in the whole temperature range T < 500 K, and no evidence of activation could be detected in these kinetic measurements_ On the other hand Palmer et al. [9], using a molecular beam technique, observed an apparent activation energy for adsorption for the same system by raising the beam energy from room temperature to 1800 K. This result is also in accordance with the AAH model because at high temperatures the temperature dependent term in eq. (3’) is no longer negligible *.
It is a pleasure to acknowledge the enlightening discussions with Hans I?. Bonzel, Jan K. Fremerey and Harald Ibach.
References [ 1] G. Comsa, R. David and K.R. Rcndulic, Phys. Rev. Letters 38 (1977) 775. [2] W. van Willigcn, Phys. Letters 28A (1968) 80. [3] F.O. Goodman, Surface Sci. 30 (1972) 525. [4] K. Christmann, 0. Schober, G. Ertl and M. Neumann, J. Chem. Phys. 60 (1974) 4528; G. ErtI, private communication. [S J M. Balooch, M.J. Cardillo, D.R. Miller and RX. Stickney, Surface Sci. 46 (1974) 358. [6] M.J. Cardillo, M. Balooch and R.E. Stickney. Surface Sci. 50 (1975) 263. [7] J. Lapujoulade and KS. Ned, J. Chem. Phys. 57 (1972) 3535. [ 81 H. Rinne, Thesis, TU Hannover (1974). [9] R.L. Palmer, J.N. Smith Jr., H. Saltsburg and D-R. O’Kcefe, J. Chem. Phys. 53 (1970) 1666. -_ Chem. (Leipzig) 253 [IO] M. Procop and J. Vtilter, Z. Pk
(1973) 33.
* When using molecular beams, i.e. a nonisotropic incidence, eq. (3) is no longer applicable. For maxwellian beams inincident with an angle 8 one has to use: u(8) = (l--r)<1
+x/c05%)
exp(-&or%)
+ r_
(3”)
With x = 3, r = 0.11 and a beam temperature of e.g. 1800 K one obtains for 0 = 0” : (r = 0.49 and for 0 = 45”: u = 0.20.
515