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Thermal desorption from adlayer of interacting particles
469
Surface Science 133 (1983) 449-483 North-Holland ~blishing Company
THERMAL DESORPTlON PARTICLES
FROM ADLAYER OF INTERACTING
V.P. ZHDANOV Institute of Catalysis, Novosibirsk
63W90,
USSR
Received 20 January 1983; accepted for publication
31 May 1983
The effect of lateral interaction of adsorbed molecules on the thermal desorption spectra is discussed. In particular, associative desorption of molecules of one kind in the presence of molecules of another kind is considered. This case is of interest from the point of view of NO decomposition on transition metals. Some experimental results concerning associative desorption of nitrogen during NO decomposition have been collected and are discussed briefly. The thermal desorption spectra are calculated for monomolecular desorption in the case of lateral interactions between nearest-neighbour and next-nearest-neighbour pairs of adsorbed molecules. Some general relations between the rates of monomolecular adsorption and desorption are derived.
Complex dependence of surface phenomena on the surface coverages even in the case of uniform perfect surfaces is well known. Lateral interactions of adsorbed molecules form one reason for this dependence. The natural way to describe the effect of lateral interactions of adsorbed molecules on the surface phenomena is by the application of lattice-gas models. Such models have recently been used to describe adsorption and desorption, simple chemical reactions, LEED and surface diffusion (see review [l] and references in ref. [2]). In the present paper we discuss the effect of lateral interactions of adsorbed particles on the programmed thermal desorption. This problem is studied fairly well in the case of lateral interactions between nearest-neighbour pairs of adsorbed molecules. The famous works of Goymour and King [3] and Adams [4] devoted to this case have played an important role in the interpretation of thermal desorption spectra. We consider more complex cases, namely associative desorption of molecules of one kind in the presence of molecules of another kind (section 2), and monomolecular desorption in the case of lateral interactions between nearest-neighbour and next-nearest-neighbour pairs of adsorbed molecules (section 3); in section 4 we discuss some general relations between the rates of monomolecular adsorption and desorption. Experience of the application of lattice-gas models for the cases considered here is limited. 0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
K P. Zhdanoo / Thermal desorption from adlayer
470
For this reason, we perform pure theoretical calculations and do not attempt to interpret in detail any experimental result. However, some experimental thermal desorption spectra which are of interest from the point of view of the calculations have been collected and are presented in this work.
2. Associative
description
Analysis of the thermal desorption spectra of molecules of one kind in the presence of molecules of another kind is of great interest, apparently, from the point of view of NO decomposition on transition metals. It is known [5-141 that NO adsorbs completely or partially dissociatively on Co, Ni, Ru, Rh, Re, Ir and Pt. The activation energy for N, (or NO) desorption is low in comparison with the activation energy for 0, desorption, and, hence, N, (or NO) desorbs in the first place during the thermal desorption process. The thermal desorption spectra for associative desorption from mixed adlayer containing two kinds of particles (N and 0) have been calculated earlier by Bridge and Lambert [5] and by Ducros et al. [6]. They have used the Goymour and Ring method [3] based on the lattice-gas model for adsorbed molecules of one kind. For this reason, they have considered only the cases when all lateral interactions are equal to each other or equal to zero. The more complex cases have been considered by Bridge and Lambert [7] who used a Monte-Carlo procedure. However, their results are limited. In particular, they have analysed the dependence of the N, desorption activation energy on coverages only for three combinations of lateral interactions, and they have not calculated the thermal desorption spectra. Our analysis is more complete. We use here a formalism [2] derived to describe the kinetics of simple chemical processes on uniform surfaces. This formalism gives the possibility of considering all the interactions separately without having to use a Monte-Carlo method. It is possible to note that, using our formalism, we have reproduced [2] the results [7] derived on the basis of a Monte-Carlo procedure. The kinetics of N, desorption is described by the equations [2] d&,/dr K,,
= -Q@,,
= v exp( - E,,/kT) X
eo), P,,
P NN exp( cNN/kT)
+ 0.5P,,
exp( cNo/kT)
+ 0.5P,,
@N
where dN and 0, are the surface coverages, v is the pre-exponential factor (generally taken to be 10’3-10’6 SK’), Ead is the energy difference between the nitrogen molecule in the activated state and the pair of the adsorbed nitrogen atoms located in the neighbouring sites provided that the rest of the sites are that a pair of neighbouring empty, P,,, P,, and P,, are the probabilities
V. P. Zhdanoc / Thermal desorption from adlayer
471
sites are occupied by the particles NN, NO and NZ (Z symbolizes an empty (positive for repulsion), and I is the site), cNN and eNo are lateral interactions number of the neighbouring sites. It is assumed here that an activated complex does not interact with its environment. The following parameters have been used in the calculations: z = 4 (a square lattice), Ead = 35 kcal/mol and v = lOI SC’; the initial nitrogen and oxygen coverages are equal to each other and range from 0.1 to 0.5 with the step A0 = 0.1. The thermal desorption spectra have been calculated (fig. 1) for 27 combinations of lateral interactions. The results of the calculations show that the special features of the thermal desorption spectra (form and location of peaks) strongly depend on the lateral interactions. We do not analyze the thermal desorption spectra in detail. This analysis may be fulfilled by an attentive reader on the basis of simple physical considerations. We consider only the splitting of the thermal desorption peak in the case of the maximum initial coverages 8, = 0, = 0.5. (It should be pointed out that in practice a saturated monolayer of NO, apparently, always contains some undissociated NO as well as N and 0 atoms.) The splitting is absent, low or comparatively strong, respectively, for the lateral interactions (1.5, 1.5, 3) *, (1.5, 1.5, O)or(1.5, 1.5, -3)(seefigs. la, Id and lg). Thiseffect is explained by the special feature of the dependence of the activation energy for N, desorption on coverage 8,. The change of the activation energy due to lateral interactions may be expressed as AE,,(e,,
e,)=
-kTln[K,,/&)~]
-Ead.
The dependence of AE,, on t& for 6, = 0.5 is presented in fig. 2. A strong repulsive interaction between oxygen atoms (eOO = 3 kcal/mol) leads to a weak dependence of the activation energy on ON, a strong attractive interaction leads to a strong dependence of between oxygen atoms (coo = - 3 kcal/mol) the activation energy on 8,. Due to this reason, the splitting is absent in the first case and is comparatively strong in the second case. We have calculated all the N, spectra for fixed parameters Ead, Y and z. It is clear that the effect of these parameters on the special features of the thermal desorption spectra is strong. However, this effect is partly obvious. In particular, the parameters Ead and Y define an average location of spectra (see, e.g., fig. 3 where the N, spectra are compared for Ead = 35 kcal/mol and Ead = 50 kcal/mol). Moreover, the effect of lateral interactions depends slightly on their magnitude relative to the activation energy for desorption. An increase in the desorption activation energy leads to simplification of spectra. An increase of z leads to a stronger dependence of the peak shifts on the initial coverages (provided that lateral interactions are positive). Here it is possible to note that our model, based on the quasi-chemical approximation, is applicable, strictly, * (1.5, 1.5.3) means cNN = 1.5
kcal/mol,cNo= 1.5 kcal/mol andcoo = 3 kcal/mol.
412
V.P. Zhdanov / Thermal desorprion from adlayer
3
400
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I
I
I
0
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n
I
IA
650
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650 T (K)
800
700 T (K)
V. P. Zhdanou / Thermal desorption from adlayer
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413
‘O”
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T
(K)
650 T (K)
I
1
c
/\
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r 0
I-
I
%ri -
-1.5
-1.5
hO\ 0
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-loo
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V.P. Zhdonov / Thermal desorption from ndluyer
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620 T
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600
700
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600
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600
700
600
640 (K)
650
7cm
T
(K)
T
(SC)
Fig. 1. Calculated thermal desorption spectra for associative desorption of nitrogen. Lateral interactions are presented in kcal/mol, the initial nitrogen and oxygen coverages are equal to each other and range from 0.1 to 0.5 with the step A0 = 0.1, the initial temperature is 300 K, and the heating rate is 40 K/s.
V.P. Zhdanov / Thermal &sorption from adIayer
475
-6
-10
0
0.1
0.2
0.3
0.4
0.5 ea
Fig. 2. Dependence of the activation energy for associative desorption of nitrogen on the nitrogen coverage for 0, = 0.5 and T = 500 K. Lateral interactions are presented in kcal/mol.
to z = 2 and z = 4. In the case of a hexagonal surface (z = 6), the dependence of the desorption activation energy on the coverages is more complex than that predicted according to the quasi-chemical approximation (see, e.g., discussion in ref. [S]). However, the quasi-chemic~ approximation is inaccurate only at low temperatures. In particular, the results of our calculations [2] for z = 6 are in good agreement with the results of the Monte-Carlo calculations [‘I] pro-
Fig. 3. The N, spectra calculated for Ead = 35 kcal/mot and E,, = 50 kcal/mol; the initial nitrogen and oxygen coverages are equal to each other and range from 0.1 to 0.5 with the step AB = 0.1, the initial temperature is 300 K, and the heating rate is 40 K/s.
V.P. Zhdanov / Thermal desorption from adlayer
476
vided that the lateral inieractions are not very strong in comparison with k7’. For this reason, we compare below our results calculated for I = 4 with the experimental data from various surfaces (some of these surfaces, e.g. Co(OOOl), Ni(ll1) and Re(OOOl), have z = 6). From a qualitative point of view this comparison is correct. We have also calculated the thermal desorption spectra of oxygen (see fig. 4). Associative desorption of oxygen takes place at high temperatures when nitrogen is absent on the surface. The kinetics of 0, desorption is described by the equations [2]: d@o/dt = -K-&,),
rC,,= v exd - &/kT)
PO0 exp( coo/kr)
PO0 i
+
0.5Poz
80
The symbols used here have the same meaning as those used previously. The following parameters have been used in the calculations: z = 4, ET,, = 65 kcal/mol and v = lOI s-‘. The same lateral interactions coo have been used as in the case of the nitrogen desorption. The thermal desorption spectra calculated in this work are, of course, more diverse than the spectra calculated by Bridge and Lambert [5]. Our results contain some new qualitative features; for example, the above mentioned splitting of the desorption peak in the case of the maximum initial coverages. This effect is absent in the framework of the method used by Bridge and Lambert [5]; meanwhile experimental spectra sometimes contain the splitting of such a kind (see below). Consider now briefly some experimental results concerning associative
900
1100
1300
1000
1200
1100
,200
T (K)
Fig. 4. The calculated thermal desorption spectra for associative desorption of oxygen. Lateral interactions are presented in kcal/mol, the initial oxygen coverage ranges from 0.1 to 0.5 with the step A&, = 0.1, the initial temperature is 300 K, and the heating rate is 250 K/s.
V. P. Zhdanoc / Thermal desorption from adlayer
477
desorption of nitrogen during NO decomposition. NO decomposition on Co(OOO1) has been studied by Bridge and Lambert [7]. They have demonstrated that NO is adsorbed dissociatively at room temperature at all but the highest coverages. If a surface is heated, NO desorbs near 350 K. However, the fraction of nitrogen desorbed as NO is low (B 9%). Associative desorption of nitrogen takes place around 850 K (see fig. 5). Analyzing the N, thermal desorption spectra, Bridge and Lambert have concluded that the lateral interactions eNN and cNO are attractive and coo is repulsive. From a formal point of view it is impossible to exclude other combinations of lateral interactions too (see, e.g., the calculations for the combinations ( - 1.5, 0, 3), ( - 1.5, 1.5, 0), ( - 1.5, 0, 0) and (0, - 1.5, - 3) in figs. lb, Id, le and li). However (according to the referee’s opinion), combinations such as (- 1.5,0,0) and (0, - 1.5, - 3) may be excluded by comparison of the experimental N, desorption spectra in the presence and in the absence of oxygen. This particular effect would not be reproduced by these combinations: in the first case, the adsorbed 0 should have no effect on the N, desorption spectra; in the second case, the N, desorption spectra in the absence of oxygen should show normal second order behaviour. Price et al. [8] have studied NO decomposition on Ni(ll0). They have shown that NO is adsorbed molecularly at room temperature. On heating, NO desorption is practically absent and NO decomposition apparently takes place at 500 K. Associative desorption of nitrogen occurs around 850 K (see fig. 5). The small increase in the desorption temperature with an increase in the initial coverage is interpreted by Price et al. to be due to an attractive interaction between adsorbed molecules. Our calculations support this conclusion (see,
I
I
I
Iii (110)
ES51 ml - 10 K/8 m
600
700
800
900
700
800
900
I
Fig. 5. The experimental thermal desorption spectra for associative NO decomposition on Co(OOO1) [7], Ni( 110) [8] and Ru( 101) [&Ill. units (1 L = 10e6 Torr s) and HR is the heating rate.
400
600
E - 0.2-3 L
800 low T (K)
desorption of nitrogen during E is the exposure in Langmuir
478
V. P. Zhdancw / Thermal desorprion from ndlayer
e.g., the calculations for the lateral interactions ( - 1.5, 0, 0) and (0, - 1.5, 0) in figs. le and If). The interaction of NO with a Ni( 111) surface has been studied by Conrad et al. [9]. It has been shown that NO adsorbs partially dissociatively near 300 K. If a surface is heated, NO desorbs or dissociates; these processes terminate at 500 K. The recombination of adsorbed nitrogen atoms and desorption of N, occurs around 850 K. The N, thermal desorption spectra were not measured in detail and are not reproduced here. Nevertheless, it is possible to note that these spectra also show a small increase in the desorption temperature with an increase in the initial coverage. NO decomposition on Ni(lOO) has been studied by Price and Baker [lo]. The adsorption of NO has been found to occur in both dissociated and molecular forms at room temperature. NO and N, desorption takes place, respectively, at 400 and 750 K. The total intensities of the NO and N, signals are comparable. The thermal desorption spectra were not measured in detail. The interaction of NO with Ru(lO1) has been studied by Lambert and co-workers [5,11]. Apparently, NO is adsorbed molecularly at room temperature. On heating, adsorbed molecules of NO desorb or dissociate, and these processes terminate at 500 K. Associative desorption of nitrogen occurs near 600 K. The total intensity of the NO desorption is low in comparison with the intensity of the N, desorption. Experimental results for N, desorption (see fig. 5) are in good agreement with theoretical calculations for the lateral interactions (1.5, 1.5, 0) (see fig. Id). Baird et al. [ 121 have studied NO decomposition on Rh( 110). It has been found that NO adsorbs dissociatively at room temperature at low coverages followed by non-dissociative chemisorption at higher exposures. On flash desorption, NO desorbs at 400 K. Associative desorption of nitrogen takes place around 500 K (see fig. 6). The total intensity of the NO desorption is low in comparison with the intensity of the N, desorption. The experimental results for the N, desorption are roughly in agreement with our calculations for the lateral interactions (1.5, 1.5, - 3) (see fig. lg). NO decomposition on Re(OOO1) has been studied by Ducros et al. [6]. NO adsorbs dissociatively at low coverages and partially dissociatively at high coverages. On heating, NO desorption is absent. N, desorption occurs near 900 K (see fig. 6). Two states are observed in the spectra. Ducros et al. have supposed that the high temperature state is connected with the associative desorption of nitrogen and the loti temperature state is caused by the reactions 2N0 --, N2gaS+ 20 and NO + N + Nfas + 0. To describe the desorption kinetics of the high temperature state, they have used a model proposed by Goymour and King [3]. From our point of view it is impossible to exclude (see, e.g., the calculations for the lateral interactions (1.5, 1.5, 0) and (1.5, 1.5, - 3) in figs. Id and lg) that NO dissociates completely on heating and that the thermal desorption spectra as a whole are caused only by the associative desorption of nitrogen.
479
V. P. Zhdanov / Thermal desorption from adlayer
I
I
I
I
I
B . 0.2-3.31 HR . 10 K/s
I
I
I
I
Re (0001)
Rh (110)
E - 0.26-3 L
E 6 900 L
I \
I
lK\
300
FIRI 27 K/a
500
700
900
T (XI
Fig. 6. The experimental thermal desorption spectra for associative on Rh(ll0) [12], Re(OOO1) [6] and Ir(ll0) [13]. NO decomposition
desorption
of nitrogen
during
Ibbotson et al. [ 131 have studied NO decomposition on Ir( 110). NO adsorbs molecularly below room temperature. The adsorption becomes competitive with NO dissociation and N, desorption above 400 K. Desorption of NO and N, occurs, respectively, at 350-600 K and 400-650 K; moreover, NO desorption is, at least in part, due to the adatom-adatom recombination. The intensities of NO and N, desorption are comparable. Thus NO desorption affects N, desorption and, strictly speaking, comparison of theory and experiment is impossible. Nevertheless, it is possible to note that the experimental results for N, desorption (see fig. 6) are roughly in agreement with our calculation for the lateral interactions (1.5, 1.5, 3) (fig. la). The most detailed results for NO absorption and decomposition on platinum have been obtained by Gorte et al. [14]. They have shown that NO exhibits large crystallographic anisotropies with the (100) plane having stronger bonding and much higher decomposition activity than the (110) or (111) planes. The major tightly bound state on the (100) plane dissociates to yield - 50% N, and O,, but all other states on all planes desorb without significant decomposition (e.g. the fraction decomposed is less than 2% on the Pt(ll1) surface). N, desorption from Pt(lOO) is sufficiently affected by the desorption of NO. For this reason, the experimental results for Pt(100) are not reproduced here. A comparison of theory and experiment demonstrates that the calculations qualitatively reproduce the various features of the N, thermal desorption spectra. However, the experimental results as a whole are somewhat more complex than the theoretical results. This fact is explained as follows: First, the real lateral interactions and locations of adsorbed molecules are more diverse than those considered in our paper. Second, the mechanism of NO decomposition is in some cases more complex than the one considered (e.g. in the case of
V. P. Zhdanoc / Thermal desorption from adlayer
480
400
500
400
500
400
5oo T (K)
Fig. 7. Effect of the lateral interactions on the thermal desorption spectra. The lateral interactions are presented in kcal/mol, the initial coverage ranges from 0.2 to 1 with the step A0 = 0.2, the initial temperature is 3!IO K, and the heating rate is 40 K/s.
0
0.2
0.4
0.6
0.8 e
1
Fig. 8. The dependence of the desorption activation r=4andT=SOOK.Dottedlinefor~,=2.6and~,= dashed line for c , = 1.4 and l 2 = 0.6 kcal/mole.
energy on the coverage for Ed = 35 kcal/mole, -0.6,solidlinefor~,=2andr,=O,and
Ir(ll0) and Pt(lOO), N, desorption is affected by the desorption of NO). Moreover, in practice a saturated monolayer of NO, apparently, always contains some undissociated NO as well as N and 0 atoms.
3. Monomolecular
desorption
In this section we discuss the effect of lateral interactions between nearestneighbour and next-nearest-neighbour pairs of adsorbed molecules on the
V.P. Zhdanoo / Thermal desorption from adlayer
481
thermal desorption spectra for monomol~ular desorption. The general equation that describes the effect of lateral interactions of any kind on the desorption rate constant is very simple (see ref. [2] or the next section in the present paper). However, from a mathematical point of view it is rather difficult to calculate accurately the probabilities included in the general equation. We use here the simplest approximations; in particular, the quasi-chemical approximation for nearest-neighbour pairs and the mean field approximation for next-nearest-neighbour pairs of adsorbed molecules. The kinetics of desorption is then described by the equations: dtljdr = - &8,
where Y is the pre-exponential factor, t, and l2 are the lateral interactions between nearest-neighbour and next-nearest-neighbour pairs of adsorbed molecules, Ed is the desorption activation energy at low coverages, and PAA and PAZ are the well known [2] quasi-chemical probabilities (calculated without taking into consideration next-nearest-neighbour pairs). It is assumed here that an activated complex does not interact with its environment. It is interesting to compare the thermal desorption spectra for various combinations of the lateral energies c, and ez provided that the total variation of the desorption activation energy is the same when the coverage varies from zero to unity. The following parameters have been used in the calculations: z = 4, Ed = 35 kcal/mol and Y= lOI s - ‘. The lateral interactions have been chosen as: e, = 1.4 and f2 = 0.6; e, = 2 and =e2= 0; l, = 2.6 and e2 = -0.6 kcal/mol. These values are reasonable from a physical point of view. The thermal desorption spectra are presented in fig. 7. The splitting of the thermal desorption peaks is rather weak in the first case and quite strong in the third case. From a qualitative point of view the effect of lateral interactions between next-nearest-neighbour pairs of adsorbed molecules on the thermal desorption spectra is not very strong. This fact is also demonstrated in fig. 8, where the dependence of the desorption activation energy on the coverage is presented, E,(B)= -kTln(&/v). 4. Relation between the rates of rno~l~~~
adsorption and desorption
The following general equations have been derived earlier [2] for the rates of monomolecular adsorption and desorption of molecules A in the presence of the adsorbed molecules B on the uniform surface dN,/dt
= &@..,
&)N,p - &(&.
@,)N,,
0)
482
V. P. Zhdanoo / Thermal desorption from adlayer
where NA and NAg are respectively the surface and gas phase densities of molecules A, F’, FAg, FA* and FL. are the partition functions of respectively a molecule A and an activated complex A*, PA. i (PO. ;) is the probability that a molecule A (an empty site) has the environment marked by index i; c, (cf) is the lateral interaction of a molecule A (an activated complex A*) and its environment, Ari = ET - ci, and E, and Ed are respectively the adsorption and desorption activation energies at low coverages. The partition functions FAe and FL. are normalized on the elementary site and on the unity of the surface area, respectively and are related as FL* = N,F,.,
(4)
where NO is the density of sites on the surface. In this section we discuss the relationship between the adsorption and desorption rates. We demonstrate in particular that eqs. (l)-(3) give the correct expression for an adsorption isotherm. This fact has been demonstrated earlier [2], but only in the quasi-chemical approximation. An adsorption isotherm is defined by the equality of the adsorption and desorption rates K,N,” = K,N,.
(5)
If we use eqs. (2) and (3) for the adsorption and desorption rates, then it might appear that an adsorption isotherm depends on the characteristics of an activated complex. But in reality the situation is different. Using the definition we have of the probabilities PA, i and PO, i and the grand canonical distribution, p
exp
,=(1-eA-8B)F
A,
I
a
*A
p 0, I)
where E,, = Ed - E, and cc is the chemical potential surface phase. Inserting eq. (6) into eq. (3), we derive: K
d
of molecules
A in the
,z (l -+A-%) h
@A
Using eqs. (2), (4) and (7), we see that expressed as exp(p/kT) = Ni/FA, or p = kT ln( N,P/F,).
an adsorption
isotherm
(5) may be (8)
The right-hand side of this equation is equal to the chemical potential of molecules A in the gas phase. Hence, eq. (8) gives the well known condition of the thermodynamical equilibrium between the adsorbed and the gas phase. Thus, eqs. (l)-(3) give the correct expression for an adsorption isotherm.
V. P. Zhdanoc / Thermal desorption from adlayer
483
Acknowledgement The author
thanks
the referees
for useful comments
on the manuscript.
Supplement Three misprints in our previous papers [2] and [15] should the following way: (1) The correct form of eq. (42) in ref. [2] is i
be corrected
in
-2e,
[i - 2aeA(i -e,)]‘/’ (2) The correct TAA = eA -
form of eq. (5) in ref. [15] is
(1 - [i - heA( i - eA)]“‘}/(Y.
(3) The function sh(e,,/kT) function sh(c,,/ZkT).
in ref. [15] (page L39) must be replaced
by the
References [ 1] [2] (31 [4] [5] [6] [7] [8] [9] [IO] [I 11 [ 121 [13] [l4] (151
D.A. King, Critical Rev. Solid State Mater. Sci. 7 (1978) 167. V.P. Zhdanov, Surface Sci. 111 (1981) 63. C.G. Goymour and D.A. King, J. Chem. Sot. Faraday I, 69 (1973) 749. D.L. Adams, Surface Sci. 42 (1974) 12. M.E. Bridge and R.M. Lambert, Proc. Roy. Sot. (London) A370 (1980) 545. R. Ducros, M. Alnot, J.J. Ehrhardt, M. Housley, G. Piquard and A. Cassuto, Surface (1980) 154. M.E. Bridge and R.M. Lambert, Surface Sci. 94 (1980) 469. G.L. Price, B.A. Sexton and G.B. Baker, Surface Sci. 60 (1976) 506. H. Conrad, G. Ertl, J. Ktippers and E.E. Latta, Surface Sci. 50 (1975) 296. G.L. Price and B.G. Baker, Surface Sci. 91 (1980) 571. P.D. Reed, C.M. Comrie and R.M. Lambert, Surface Sci. 72 (1978) 423. R.J. Baird, R.C. Ku and P. Wynblatt, Surface Sci. 97 (1980) 346. D.E. Ibbotson, T.S. Wittrig and W.H. Weinberg, Surface Sci. 110 (1981) 294. R.J. Gorte, L.D. Schmidt and J.L. Gland, Surface Sci. 109 (1981) 367. V.P. Zhdanov, Surface Sci. 102 (1981) L35.
Sci. 94
Surface Science 133 (1983) 449-483 North-Holland ~blishing Company
THERMAL DESORPTlON PARTICLES
FROM ADLAYER OF INTERACTING
V.P. ZHDANOV Institute of Catalysis, Novosibirsk
63W90,
USSR
Received 20 January 1983; accepted for publication
31 May 1983
The effect of lateral interaction of adsorbed molecules on the thermal desorption spectra is discussed. In particular, associative desorption of molecules of one kind in the presence of molecules of another kind is considered. This case is of interest from the point of view of NO decomposition on transition metals. Some experimental results concerning associative desorption of nitrogen during NO decomposition have been collected and are discussed briefly. The thermal desorption spectra are calculated for monomolecular desorption in the case of lateral interactions between nearest-neighbour and next-nearest-neighbour pairs of adsorbed molecules. Some general relations between the rates of monomolecular adsorption and desorption are derived.
Complex dependence of surface phenomena on the surface coverages even in the case of uniform perfect surfaces is well known. Lateral interactions of adsorbed molecules form one reason for this dependence. The natural way to describe the effect of lateral interactions of adsorbed molecules on the surface phenomena is by the application of lattice-gas models. Such models have recently been used to describe adsorption and desorption, simple chemical reactions, LEED and surface diffusion (see review [l] and references in ref. [2]). In the present paper we discuss the effect of lateral interactions of adsorbed particles on the programmed thermal desorption. This problem is studied fairly well in the case of lateral interactions between nearest-neighbour pairs of adsorbed molecules. The famous works of Goymour and King [3] and Adams [4] devoted to this case have played an important role in the interpretation of thermal desorption spectra. We consider more complex cases, namely associative desorption of molecules of one kind in the presence of molecules of another kind (section 2), and monomolecular desorption in the case of lateral interactions between nearest-neighbour and next-nearest-neighbour pairs of adsorbed molecules (section 3); in section 4 we discuss some general relations between the rates of monomolecular adsorption and desorption. Experience of the application of lattice-gas models for the cases considered here is limited. 0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
K P. Zhdanoo / Thermal desorption from adlayer
470
For this reason, we perform pure theoretical calculations and do not attempt to interpret in detail any experimental result. However, some experimental thermal desorption spectra which are of interest from the point of view of the calculations have been collected and are presented in this work.
2. Associative
description
Analysis of the thermal desorption spectra of molecules of one kind in the presence of molecules of another kind is of great interest, apparently, from the point of view of NO decomposition on transition metals. It is known [5-141 that NO adsorbs completely or partially dissociatively on Co, Ni, Ru, Rh, Re, Ir and Pt. The activation energy for N, (or NO) desorption is low in comparison with the activation energy for 0, desorption, and, hence, N, (or NO) desorbs in the first place during the thermal desorption process. The thermal desorption spectra for associative desorption from mixed adlayer containing two kinds of particles (N and 0) have been calculated earlier by Bridge and Lambert [5] and by Ducros et al. [6]. They have used the Goymour and Ring method [3] based on the lattice-gas model for adsorbed molecules of one kind. For this reason, they have considered only the cases when all lateral interactions are equal to each other or equal to zero. The more complex cases have been considered by Bridge and Lambert [7] who used a Monte-Carlo procedure. However, their results are limited. In particular, they have analysed the dependence of the N, desorption activation energy on coverages only for three combinations of lateral interactions, and they have not calculated the thermal desorption spectra. Our analysis is more complete. We use here a formalism [2] derived to describe the kinetics of simple chemical processes on uniform surfaces. This formalism gives the possibility of considering all the interactions separately without having to use a Monte-Carlo method. It is possible to note that, using our formalism, we have reproduced [2] the results [7] derived on the basis of a Monte-Carlo procedure. The kinetics of N, desorption is described by the equations [2] d&,/dr K,,
= -Q@,,
= v exp( - E,,/kT) X
eo), P,,
P NN exp( cNN/kT)
+ 0.5P,,
exp( cNo/kT)
+ 0.5P,,
@N
where dN and 0, are the surface coverages, v is the pre-exponential factor (generally taken to be 10’3-10’6 SK’), Ead is the energy difference between the nitrogen molecule in the activated state and the pair of the adsorbed nitrogen atoms located in the neighbouring sites provided that the rest of the sites are that a pair of neighbouring empty, P,,, P,, and P,, are the probabilities
V. P. Zhdanoc / Thermal desorption from adlayer
471
sites are occupied by the particles NN, NO and NZ (Z symbolizes an empty (positive for repulsion), and I is the site), cNN and eNo are lateral interactions number of the neighbouring sites. It is assumed here that an activated complex does not interact with its environment. The following parameters have been used in the calculations: z = 4 (a square lattice), Ead = 35 kcal/mol and v = lOI SC’; the initial nitrogen and oxygen coverages are equal to each other and range from 0.1 to 0.5 with the step A0 = 0.1. The thermal desorption spectra have been calculated (fig. 1) for 27 combinations of lateral interactions. The results of the calculations show that the special features of the thermal desorption spectra (form and location of peaks) strongly depend on the lateral interactions. We do not analyze the thermal desorption spectra in detail. This analysis may be fulfilled by an attentive reader on the basis of simple physical considerations. We consider only the splitting of the thermal desorption peak in the case of the maximum initial coverages 8, = 0, = 0.5. (It should be pointed out that in practice a saturated monolayer of NO, apparently, always contains some undissociated NO as well as N and 0 atoms.) The splitting is absent, low or comparatively strong, respectively, for the lateral interactions (1.5, 1.5, 3) *, (1.5, 1.5, O)or(1.5, 1.5, -3)(seefigs. la, Id and lg). Thiseffect is explained by the special feature of the dependence of the activation energy for N, desorption on coverage 8,. The change of the activation energy due to lateral interactions may be expressed as AE,,(e,,
e,)=
-kTln[K,,/&)~]
-Ead.
The dependence of AE,, on t& for 6, = 0.5 is presented in fig. 2. A strong repulsive interaction between oxygen atoms (eOO = 3 kcal/mol) leads to a weak dependence of the activation energy on ON, a strong attractive interaction leads to a strong dependence of between oxygen atoms (coo = - 3 kcal/mol) the activation energy on 8,. Due to this reason, the splitting is absent in the first case and is comparatively strong in the second case. We have calculated all the N, spectra for fixed parameters Ead, Y and z. It is clear that the effect of these parameters on the special features of the thermal desorption spectra is strong. However, this effect is partly obvious. In particular, the parameters Ead and Y define an average location of spectra (see, e.g., fig. 3 where the N, spectra are compared for Ead = 35 kcal/mol and Ead = 50 kcal/mol). Moreover, the effect of lateral interactions depends slightly on their magnitude relative to the activation energy for desorption. An increase in the desorption activation energy leads to simplification of spectra. An increase of z leads to a stronger dependence of the peak shifts on the initial coverages (provided that lateral interactions are positive). Here it is possible to note that our model, based on the quasi-chemical approximation, is applicable, strictly, * (1.5, 1.5.3) means cNN = 1.5
kcal/mol,cNo= 1.5 kcal/mol andcoo = 3 kcal/mol.
412
V.P. Zhdanov / Thermal desorprion from adlayer
3
400
500
600
400
500
600
700
500
I
I
I
0
500
600
600
700
700
800
550
600
600
700
n
I
IA
650
800
550
600
600
-1.5 0
650 T (K)
800
700 T (K)
V. P. Zhdanou / Thermal desorption from adlayer
400
500
500
600
600
500
600
550
600
500
413
‘O”
600
550
T
(K)
650 T (K)
I
1
c
/\
I
I
r 0
I-
I
%ri -
-1.5
-1.5
hO\ 0
600
700
800
600
-loo
800
600
700
800 T (K)
V.P. Zhdonov / Thermal desorption from ndluyer
474
500
400
600
500
600
560
600
580
620 T
400
600
500
500
600
700
700
600
600
500
600
700
600
640 (K)
650
7cm
T
(K)
T
(SC)
Fig. 1. Calculated thermal desorption spectra for associative desorption of nitrogen. Lateral interactions are presented in kcal/mol, the initial nitrogen and oxygen coverages are equal to each other and range from 0.1 to 0.5 with the step A0 = 0.1, the initial temperature is 300 K, and the heating rate is 40 K/s.
V.P. Zhdanov / Thermal &sorption from adIayer
475
-6
-10
0
0.1
0.2
0.3
0.4
0.5 ea
Fig. 2. Dependence of the activation energy for associative desorption of nitrogen on the nitrogen coverage for 0, = 0.5 and T = 500 K. Lateral interactions are presented in kcal/mol.
to z = 2 and z = 4. In the case of a hexagonal surface (z = 6), the dependence of the desorption activation energy on the coverages is more complex than that predicted according to the quasi-chemical approximation (see, e.g., discussion in ref. [S]). However, the quasi-chemic~ approximation is inaccurate only at low temperatures. In particular, the results of our calculations [2] for z = 6 are in good agreement with the results of the Monte-Carlo calculations [‘I] pro-
Fig. 3. The N, spectra calculated for Ead = 35 kcal/mot and E,, = 50 kcal/mol; the initial nitrogen and oxygen coverages are equal to each other and range from 0.1 to 0.5 with the step AB = 0.1, the initial temperature is 300 K, and the heating rate is 40 K/s.
V.P. Zhdanov / Thermal desorption from adlayer
476
vided that the lateral inieractions are not very strong in comparison with k7’. For this reason, we compare below our results calculated for I = 4 with the experimental data from various surfaces (some of these surfaces, e.g. Co(OOOl), Ni(ll1) and Re(OOOl), have z = 6). From a qualitative point of view this comparison is correct. We have also calculated the thermal desorption spectra of oxygen (see fig. 4). Associative desorption of oxygen takes place at high temperatures when nitrogen is absent on the surface. The kinetics of 0, desorption is described by the equations [2]: d@o/dt = -K-&,),
rC,,= v exd - &/kT)
PO0 exp( coo/kr)
PO0 i
+
0.5Poz
80
The symbols used here have the same meaning as those used previously. The following parameters have been used in the calculations: z = 4, ET,, = 65 kcal/mol and v = lOI s-‘. The same lateral interactions coo have been used as in the case of the nitrogen desorption. The thermal desorption spectra calculated in this work are, of course, more diverse than the spectra calculated by Bridge and Lambert [5]. Our results contain some new qualitative features; for example, the above mentioned splitting of the desorption peak in the case of the maximum initial coverages. This effect is absent in the framework of the method used by Bridge and Lambert [5]; meanwhile experimental spectra sometimes contain the splitting of such a kind (see below). Consider now briefly some experimental results concerning associative
900
1100
1300
1000
1200
1100
,200
T (K)
Fig. 4. The calculated thermal desorption spectra for associative desorption of oxygen. Lateral interactions are presented in kcal/mol, the initial oxygen coverage ranges from 0.1 to 0.5 with the step A&, = 0.1, the initial temperature is 300 K, and the heating rate is 250 K/s.
V. P. Zhdanoc / Thermal desorption from adlayer
477
desorption of nitrogen during NO decomposition. NO decomposition on Co(OOO1) has been studied by Bridge and Lambert [7]. They have demonstrated that NO is adsorbed dissociatively at room temperature at all but the highest coverages. If a surface is heated, NO desorbs near 350 K. However, the fraction of nitrogen desorbed as NO is low (B 9%). Associative desorption of nitrogen takes place around 850 K (see fig. 5). Analyzing the N, thermal desorption spectra, Bridge and Lambert have concluded that the lateral interactions eNN and cNO are attractive and coo is repulsive. From a formal point of view it is impossible to exclude other combinations of lateral interactions too (see, e.g., the calculations for the combinations ( - 1.5, 0, 3), ( - 1.5, 1.5, 0), ( - 1.5, 0, 0) and (0, - 1.5, - 3) in figs. lb, Id, le and li). However (according to the referee’s opinion), combinations such as (- 1.5,0,0) and (0, - 1.5, - 3) may be excluded by comparison of the experimental N, desorption spectra in the presence and in the absence of oxygen. This particular effect would not be reproduced by these combinations: in the first case, the adsorbed 0 should have no effect on the N, desorption spectra; in the second case, the N, desorption spectra in the absence of oxygen should show normal second order behaviour. Price et al. [8] have studied NO decomposition on Ni(ll0). They have shown that NO is adsorbed molecularly at room temperature. On heating, NO desorption is practically absent and NO decomposition apparently takes place at 500 K. Associative desorption of nitrogen occurs around 850 K (see fig. 5). The small increase in the desorption temperature with an increase in the initial coverage is interpreted by Price et al. to be due to an attractive interaction between adsorbed molecules. Our calculations support this conclusion (see,
I
I
I
Iii (110)
ES51 ml - 10 K/8 m
600
700
800
900
700
800
900
I
Fig. 5. The experimental thermal desorption spectra for associative NO decomposition on Co(OOO1) [7], Ni( 110) [8] and Ru( 101) [&Ill. units (1 L = 10e6 Torr s) and HR is the heating rate.
400
600
E - 0.2-3 L
800 low T (K)
desorption of nitrogen during E is the exposure in Langmuir
478
V. P. Zhdancw / Thermal desorprion from ndlayer
e.g., the calculations for the lateral interactions ( - 1.5, 0, 0) and (0, - 1.5, 0) in figs. le and If). The interaction of NO with a Ni( 111) surface has been studied by Conrad et al. [9]. It has been shown that NO adsorbs partially dissociatively near 300 K. If a surface is heated, NO desorbs or dissociates; these processes terminate at 500 K. The recombination of adsorbed nitrogen atoms and desorption of N, occurs around 850 K. The N, thermal desorption spectra were not measured in detail and are not reproduced here. Nevertheless, it is possible to note that these spectra also show a small increase in the desorption temperature with an increase in the initial coverage. NO decomposition on Ni(lOO) has been studied by Price and Baker [lo]. The adsorption of NO has been found to occur in both dissociated and molecular forms at room temperature. NO and N, desorption takes place, respectively, at 400 and 750 K. The total intensities of the NO and N, signals are comparable. The thermal desorption spectra were not measured in detail. The interaction of NO with Ru(lO1) has been studied by Lambert and co-workers [5,11]. Apparently, NO is adsorbed molecularly at room temperature. On heating, adsorbed molecules of NO desorb or dissociate, and these processes terminate at 500 K. Associative desorption of nitrogen occurs near 600 K. The total intensity of the NO desorption is low in comparison with the intensity of the N, desorption. Experimental results for N, desorption (see fig. 5) are in good agreement with theoretical calculations for the lateral interactions (1.5, 1.5, 0) (see fig. Id). Baird et al. [ 121 have studied NO decomposition on Rh( 110). It has been found that NO adsorbs dissociatively at room temperature at low coverages followed by non-dissociative chemisorption at higher exposures. On flash desorption, NO desorbs at 400 K. Associative desorption of nitrogen takes place around 500 K (see fig. 6). The total intensity of the NO desorption is low in comparison with the intensity of the N, desorption. The experimental results for the N, desorption are roughly in agreement with our calculations for the lateral interactions (1.5, 1.5, - 3) (see fig. lg). NO decomposition on Re(OOO1) has been studied by Ducros et al. [6]. NO adsorbs dissociatively at low coverages and partially dissociatively at high coverages. On heating, NO desorption is absent. N, desorption occurs near 900 K (see fig. 6). Two states are observed in the spectra. Ducros et al. have supposed that the high temperature state is connected with the associative desorption of nitrogen and the loti temperature state is caused by the reactions 2N0 --, N2gaS+ 20 and NO + N + Nfas + 0. To describe the desorption kinetics of the high temperature state, they have used a model proposed by Goymour and King [3]. From our point of view it is impossible to exclude (see, e.g., the calculations for the lateral interactions (1.5, 1.5, 0) and (1.5, 1.5, - 3) in figs. Id and lg) that NO dissociates completely on heating and that the thermal desorption spectra as a whole are caused only by the associative desorption of nitrogen.
479
V. P. Zhdanov / Thermal desorption from adlayer
I
I
I
I
I
B . 0.2-3.31 HR . 10 K/s
I
I
I
I
Re (0001)
Rh (110)
E - 0.26-3 L
E 6 900 L
I \
I
lK\
300
FIRI 27 K/a
500
700
900
T (XI
Fig. 6. The experimental thermal desorption spectra for associative on Rh(ll0) [12], Re(OOO1) [6] and Ir(ll0) [13]. NO decomposition
desorption
of nitrogen
during
Ibbotson et al. [ 131 have studied NO decomposition on Ir( 110). NO adsorbs molecularly below room temperature. The adsorption becomes competitive with NO dissociation and N, desorption above 400 K. Desorption of NO and N, occurs, respectively, at 350-600 K and 400-650 K; moreover, NO desorption is, at least in part, due to the adatom-adatom recombination. The intensities of NO and N, desorption are comparable. Thus NO desorption affects N, desorption and, strictly speaking, comparison of theory and experiment is impossible. Nevertheless, it is possible to note that the experimental results for N, desorption (see fig. 6) are roughly in agreement with our calculation for the lateral interactions (1.5, 1.5, 3) (fig. la). The most detailed results for NO absorption and decomposition on platinum have been obtained by Gorte et al. [14]. They have shown that NO exhibits large crystallographic anisotropies with the (100) plane having stronger bonding and much higher decomposition activity than the (110) or (111) planes. The major tightly bound state on the (100) plane dissociates to yield - 50% N, and O,, but all other states on all planes desorb without significant decomposition (e.g. the fraction decomposed is less than 2% on the Pt(ll1) surface). N, desorption from Pt(lOO) is sufficiently affected by the desorption of NO. For this reason, the experimental results for Pt(100) are not reproduced here. A comparison of theory and experiment demonstrates that the calculations qualitatively reproduce the various features of the N, thermal desorption spectra. However, the experimental results as a whole are somewhat more complex than the theoretical results. This fact is explained as follows: First, the real lateral interactions and locations of adsorbed molecules are more diverse than those considered in our paper. Second, the mechanism of NO decomposition is in some cases more complex than the one considered (e.g. in the case of
V. P. Zhdanoc / Thermal desorption from adlayer
480
400
500
400
500
400
5oo T (K)
Fig. 7. Effect of the lateral interactions on the thermal desorption spectra. The lateral interactions are presented in kcal/mol, the initial coverage ranges from 0.2 to 1 with the step A0 = 0.2, the initial temperature is 3!IO K, and the heating rate is 40 K/s.
0
0.2
0.4
0.6
0.8 e
1
Fig. 8. The dependence of the desorption activation r=4andT=SOOK.Dottedlinefor~,=2.6and~,= dashed line for c , = 1.4 and l 2 = 0.6 kcal/mole.
energy on the coverage for Ed = 35 kcal/mole, -0.6,solidlinefor~,=2andr,=O,and
Ir(ll0) and Pt(lOO), N, desorption is affected by the desorption of NO). Moreover, in practice a saturated monolayer of NO, apparently, always contains some undissociated NO as well as N and 0 atoms.
3. Monomolecular
desorption
In this section we discuss the effect of lateral interactions between nearestneighbour and next-nearest-neighbour pairs of adsorbed molecules on the
V.P. Zhdanoo / Thermal desorption from adlayer
481
thermal desorption spectra for monomol~ular desorption. The general equation that describes the effect of lateral interactions of any kind on the desorption rate constant is very simple (see ref. [2] or the next section in the present paper). However, from a mathematical point of view it is rather difficult to calculate accurately the probabilities included in the general equation. We use here the simplest approximations; in particular, the quasi-chemical approximation for nearest-neighbour pairs and the mean field approximation for next-nearest-neighbour pairs of adsorbed molecules. The kinetics of desorption is then described by the equations: dtljdr = - &8,
where Y is the pre-exponential factor, t, and l2 are the lateral interactions between nearest-neighbour and next-nearest-neighbour pairs of adsorbed molecules, Ed is the desorption activation energy at low coverages, and PAA and PAZ are the well known [2] quasi-chemical probabilities (calculated without taking into consideration next-nearest-neighbour pairs). It is assumed here that an activated complex does not interact with its environment. It is interesting to compare the thermal desorption spectra for various combinations of the lateral energies c, and ez provided that the total variation of the desorption activation energy is the same when the coverage varies from zero to unity. The following parameters have been used in the calculations: z = 4, Ed = 35 kcal/mol and Y= lOI s - ‘. The lateral interactions have been chosen as: e, = 1.4 and f2 = 0.6; e, = 2 and =e2= 0; l, = 2.6 and e2 = -0.6 kcal/mol. These values are reasonable from a physical point of view. The thermal desorption spectra are presented in fig. 7. The splitting of the thermal desorption peaks is rather weak in the first case and quite strong in the third case. From a qualitative point of view the effect of lateral interactions between next-nearest-neighbour pairs of adsorbed molecules on the thermal desorption spectra is not very strong. This fact is also demonstrated in fig. 8, where the dependence of the desorption activation energy on the coverage is presented, E,(B)= -kTln(&/v). 4. Relation between the rates of rno~l~~~
adsorption and desorption
The following general equations have been derived earlier [2] for the rates of monomolecular adsorption and desorption of molecules A in the presence of the adsorbed molecules B on the uniform surface dN,/dt
= &@..,
&)N,p - &(&.
@,)N,,
0)
482
V. P. Zhdanoo / Thermal desorption from adlayer
where NA and NAg are respectively the surface and gas phase densities of molecules A, F’, FAg, FA* and FL. are the partition functions of respectively a molecule A and an activated complex A*, PA. i (PO. ;) is the probability that a molecule A (an empty site) has the environment marked by index i; c, (cf) is the lateral interaction of a molecule A (an activated complex A*) and its environment, Ari = ET - ci, and E, and Ed are respectively the adsorption and desorption activation energies at low coverages. The partition functions FAe and FL. are normalized on the elementary site and on the unity of the surface area, respectively and are related as FL* = N,F,.,
(4)
where NO is the density of sites on the surface. In this section we discuss the relationship between the adsorption and desorption rates. We demonstrate in particular that eqs. (l)-(3) give the correct expression for an adsorption isotherm. This fact has been demonstrated earlier [2], but only in the quasi-chemical approximation. An adsorption isotherm is defined by the equality of the adsorption and desorption rates K,N,” = K,N,.
(5)
If we use eqs. (2) and (3) for the adsorption and desorption rates, then it might appear that an adsorption isotherm depends on the characteristics of an activated complex. But in reality the situation is different. Using the definition we have of the probabilities PA, i and PO, i and the grand canonical distribution, p
exp
,=(1-eA-8B)F
A,
I
a
*A
p 0, I)
where E,, = Ed - E, and cc is the chemical potential surface phase. Inserting eq. (6) into eq. (3), we derive: K
d
of molecules
A in the
,z (l -+A-%) h
@A
Using eqs. (2), (4) and (7), we see that expressed as exp(p/kT) = Ni/FA, or p = kT ln( N,P/F,).
an adsorption
isotherm
(5) may be (8)
The right-hand side of this equation is equal to the chemical potential of molecules A in the gas phase. Hence, eq. (8) gives the well known condition of the thermodynamical equilibrium between the adsorbed and the gas phase. Thus, eqs. (l)-(3) give the correct expression for an adsorption isotherm.
V. P. Zhdanoc / Thermal desorption from adlayer
483
Acknowledgement The author
thanks
the referees
for useful comments
on the manuscript.
Supplement Three misprints in our previous papers [2] and [15] should the following way: (1) The correct form of eq. (42) in ref. [2] is i
be corrected
in
-2e,
[i - 2aeA(i -e,)]‘/’ (2) The correct TAA = eA -
form of eq. (5) in ref. [15] is
(1 - [i - heA( i - eA)]“‘}/(Y.
(3) The function sh(e,,/kT) function sh(c,,/ZkT).
in ref. [15] (page L39) must be replaced
by the
References [ 1] [2] (31 [4] [5] [6] [7] [8] [9] [IO] [I 11 [ 121 [13] [l4] (151
D.A. King, Critical Rev. Solid State Mater. Sci. 7 (1978) 167. V.P. Zhdanov, Surface Sci. 111 (1981) 63. C.G. Goymour and D.A. King, J. Chem. Sot. Faraday I, 69 (1973) 749. D.L. Adams, Surface Sci. 42 (1974) 12. M.E. Bridge and R.M. Lambert, Proc. Roy. Sot. (London) A370 (1980) 545. R. Ducros, M. Alnot, J.J. Ehrhardt, M. Housley, G. Piquard and A. Cassuto, Surface (1980) 154. M.E. Bridge and R.M. Lambert, Surface Sci. 94 (1980) 469. G.L. Price, B.A. Sexton and G.B. Baker, Surface Sci. 60 (1976) 506. H. Conrad, G. Ertl, J. Ktippers and E.E. Latta, Surface Sci. 50 (1975) 296. G.L. Price and B.G. Baker, Surface Sci. 91 (1980) 571. P.D. Reed, C.M. Comrie and R.M. Lambert, Surface Sci. 72 (1978) 423. R.J. Baird, R.C. Ku and P. Wynblatt, Surface Sci. 97 (1980) 346. D.E. Ibbotson, T.S. Wittrig and W.H. Weinberg, Surface Sci. 110 (1981) 294. R.J. Gorte, L.D. Schmidt and J.L. Gland, Surface Sci. 109 (1981) 367. V.P. Zhdanov, Surface Sci. 102 (1981) L35.
Sci. 94