- Email: [email protected]

533

ADSORPTION-DESORPTION KINETICS OF CARBON MONOXIDE ON PALLADIUM POLYCRYSTALLINE SURFACES Taro YAMADA, Department I I3, Japan

Takaharu

ONISHI

and Kenzi TAMARU

of Chemistry, Faculty of Science, The University of Tokyo, Hongo, Bunkyo- ky Tokyo

Received 25 March 1983; accepted for publication

23 May 1983

The kinetics of adsorption and desorption of carbon monoxide on palladium polycrystalline surfaces is examined by measuring the “net” adsorption rate and the “net” desorption rate while the adsorption is actually proceeding. The net adsorption rate is proportional to the pressure of CO gas and is almost independent of the surface coverage of CO below 0.5. The initial sticking probability is 0.88, which stays constant in the temperature range between 339 and 466 K. The net desorption rate includes the thermal desorption rate and the adsorption-assisted desorption rate which is an increasing function of the gas-phase pressure of CO. The adsorption-assisted desorption rate increases continuously with the temperature of palladium with an activation energy of 4.9 kcal mot - ‘.

1. Introduction Adsorption of carbon monoxide on palladium was extensively investigated by various techniques from different points of view [ 1- 111. The adsorption rate was measured by the molecular-beam technique on Pd( 111) by Engel [5] and by coverage measurements with temperature programmed desorption (TPD) on Pd( 100) by Behm et al. [ 111. The desorption kinetics was investigated by the conventional method of analysis of thermal desorption peaks [ 12,131, and the activation energy and the frequency factor for desorption were discussed [ 1,111. In those cases thermal desorption procedures were carried out after evacuation of dosed gas, therefore the influence of the gas phase on the desorption kinetics could not be observed. In this paper the rate of adsorption and desorption was measured while the adsorption reaction was actually proceeding by using labelled carbon monoxide. The rate of adsorption of CO CO(g)

2 CO(a)

(1)

o-

is the difference

between

0039-6028/83/0000-0000/$03.00

the rate of net adsorption 0 1983 North-Holland

u,

and that of the net

534

T. Yamada et al. / Adsorption - desorption kineiics of CO on Pd

desorption V=

[email protected]/dt

v _: = v+-

v_,

(2)

where v, and v_ of carbon monoxide on palladium polycrystalline surfaces were estimated during the adsorption at various coverages 0, CO pressures P and palladium temperatures T. An isotope-jump method combined with the flash desorption technique was employed, keeping the reaction condition unchanged.

2. Experimental The experiments were performed in an UHV apparatus whose volume is about 15 1. Fig. 1 shows a schematic view of the apparatus employed. The system was evacuated by a turbomolecular pump with a pumping rate of 61 1 s-’ for CO and the ultimate pressure was less than lo-’ Pa. A single-stage cylindrical mirror analyzer (CMA), an electron gun for AES, a UV photon source for UPS, a quadrupole mass spectrometer (QMS) and a BA gauge were installed around the sample. Three variable leak valves were equipped to introduce gases into the chamber. A home-made temperature programmer was connected to the sample to provide any desired constant temperture above room temperature and linear temperature raising with heating rates up to 150 K s-‘. This circuit consists of Pt-13%Rh/Pt thermocouples, a pre-amplifier, a PID controller, a ramp-function generator and a (5 V, 50 A) DC power amplifier for heating by applying the current directly through the sample. Several pieces of palladium foils (0.05 mm thickness, area about 1.7 cm*, 99.9% purity) obtained from Tanaka Noble Metal Co. Ltd. were employed.

Sample Holder

Fig. 1. Schematic view of apparatus and sample holder.

T. Yamada et al. / Adsorption - desorption kinetics of CO on Pd

535

They were shaped as is shown in fig. 1 and suspended with two 0.3 mm palladium wires to achieve a homogeneous temperature distribution. The surfaces were cleaned by heating at 800 K in 7 X lo-’ Pa of oxygen for several hours followed by flashing at 900 K for a few minutes. No contamination was found by AES after the cleaning. ‘2C’60 was obtained from a commercial cylinder. 90% ‘3C’60 and 99% ‘2C’80 were purchased from Prochem. BOC Ltd. and were used without further purification.

3. Results 3.1. ~eu~~rements oj~~j~ce conce~tr~tio~~ oj’2C’60 and 12C’a0 as junctions of adsorption time Prior to the rate measurements, the isotope exchange reaction 13pQ-J

+ iZ~l80

~

13po

+ 12~160

and disproportionation 2 ‘2C’80 + 12C’*Oz + “C(a) were examined by the method described by Shindo, Egawa, Onishi and Tamaru [ 141 at temperatures between 339 and 850 K and at pressures between 1.3 x 10e6 and 1.3 x 1O-4 Pa. No significant evolution of r3C’80 or ‘2C’802 was observed and no carbon deposit was detected by AES. The amounts of adsorbed ‘2C’60 and ‘2C’80 were measured by the following procedures: (1) Flash the sample foil to clear the surface. (2) Keep the sample at the desired temperature 2’. (3) At time t = 0, start introducing ‘2C*80, keeping the pressure at the desired value P. (4) At time t = t, when the surface concentration cf “C”O reaches the desired value, N(t,), switch the gas quickly from ‘2C’80 to ‘2C’60 at the same pressure P. (5) At time t = t, + t, flash the sample up to 850 K in 4 s and record the flash desorption pressure traces of ‘2C’60 (28 AMU) or 12C’80 (30 AMU) by the mass spectrometer. Those procedures make o, and u_ distinguishable during the process of adsorption. Fig. 2 shows an example of traces of substrate temperature and pressures of ‘2C’60 and ‘2C’g0 during those procedures. The surface concentration of “CL60 at time t = t, + t,, n(t, + t2), was calculated by integrating the ‘2C’60 flash desorption pressure trace after subtracting the background, i.e., the pressure of ‘2C’60 introduced. In the case of ‘2C’s0 the background is

T. Yamada et al. / Adsorption - desorption kinetics of CO on Pd

+ 0

t,-1-t*----+

I

10

20

30

t1.3 Fig. 2. An example of temperature and pressure traces during measurement for t, = 10 s and t, = 10 s. (A) Palladium temperature T. Until t = t, + t2, T was kept at 380 K and then quickly raised at a heating rate of about 120 K s-’ to measure amounts of ‘2C’60 and ‘2C’s0 adsorbed. (B), (C) Pressures of 12C160 and ‘2C’80 in the chamber. From t = 0 to t = t,, ‘2C’80 was leaked at P=8.1~10-~ Pa. At t=tl, ‘2C’80 was stopped and switched into ‘*C”‘O at the same pressure. The peak areas during flashing i(tl + t2) and i*(t, + f2) gave the adsorbed amounts n(t, + t2) and n*(t, + t2) by eq. (3).

practically negligible and its amount of adsorption, n*(t, + t2), was obtained by simply integrating the flash desorption pressure trace. Conversion of the integrated values of pressure traces i and i* [Pa s] into surface concentrations n and n* [molecules cm- *] can be done by the equation n(n*)

= (s/AkT,)i(i*),

(3)

where A denotes the surface area of the sample [cm*], s the pumping rate [m3 s- ‘1 and T, the gas-phase temperature, i.e., room temperature [K]. Those procedures gave relatively precise values of N(t), n(t), and n*(t) in the range of T < 500 K and P < 2 X 10m5 Pa. At temperatures and pressures out of this range, the measurements became difficult because too large a background reduces the precision of n(t) and the adsorption reaches its equilibrium too rapidly to measure. 3.2. Adsorption

isotherms and the full coverage

The surface concentration at adsorption equilibrium can be obtained by measuring only n(t, + tz) with t, = 0 and long enough t,. Fig. 3 shows the results of adsorption isotherms. These results are similar to those of work function measurements on Pd(210) obtained by Conrad et al. [4]. The maximum surface concentration obtained was the value for T = 339 K and P = 1.3

T. Yamada et al. f Adsorption - desorption kinetics of CO on Pd

,

4

8

537

12

P I IdSPa

Fig. 3. Adsorption isotherms given in surface concentration N(w) as a function of gas-phase pressure of CO (P) and palladium temperature T which is shown in the figure. The gas-phase temperature T, was 298 K.

X lo-’ Pa at lower temperatures and lOI molecules cme2 as the saturated reasonable agreement compared with With this value of A$,, the coverage of by

higher pressures, which was N, = 6.4 x surface concentration. This value is in the results reported previously [4,15,16]. ‘2Ci60 and that of ‘2Ci80 were defined

e*(t) = n*(t)/&,

O(r) = ND&

(4)

and the total coverage by @(t)[email protected](t)+8*(t)=

[~(r)+n*(z)]/N()=N(t)/N,.

(5)

3.3. Overall rate of adsorption, and net rate of desorption and that of adsorption Fig. 4 shows typical examples of the functions 8(t), e*(r), and Q(t) obtained by repeating the procedures described in section 3.1 with a constant t, and different t,. The overall adsorption rate as a function of coverage is obtained by eq. (2). Usually e(t) was obtained by measuring n(tz) or N(t,) with time taking t, = 0. The overall rate of adsorption, V(e), was numerically calculated from these points by v(a)=

[Q(tz’*)-g(r:)]/(1:+‘-fl)

and the average coverage 0 = [s(z:)

+ s(t:+‘>]/2,

(6)

where ti and t;’ ’ are two succeeding t2’s when the n( Q’s were measured. The net rate of desorption, u_, and that of adsorption, u,, were estimated as the gradients of respectively the t--8* curve and the t-8 curve at t = t, + 0,

538

T. Yamada et al. / Adsorption - desorption kinetics of CO on Pd

0

60

0

t,

120

180

tls

Fig. 4. An example of a series of coverage measurements for t, = 60 s, T = 380 K and P = 2.0 x 10m6 Pa. (0) ‘2C’s0 coverage 8*; the dashed line is an exponential curve given by eq. (9) fitted to those data. (0) ‘2C’60 coverage 0. (0) Total coverage of CO8 = 0 + 0;; The gradient of line a gives - o _, and that of the line b gives o+.

i.e., v_(@(t,))

= -de*@,

~+(@(t,))

= d%,

+ O)/dt,

(7) (8)

+ O)/dt,

because just after t = I, only adsorption of ‘2C’60 and desorption of 12C180 occur. As is seen in fig. 4, a t-0* curve is well expressed by an exponential function e*(t)

= e*(t,)

exp( -ht

(9)

- t,)),

Fig. 5. The overall adsorption rate V as a function of coverage 8 and palladium P = 2.0X 10V6 Pa. (0) T = 380 K, (0) 419 K, (m) 443 K, (0) 466 K.

temperature

T.

T. Yamadaet al. / Adsarprion- desarptiankineticsof CO on Pd

539

from which the value of p for 8*, and, consequently, that of t)_ is obtained by u_= @*(f,);

(10)

u+ may be estimated not only by differentiating following equation:

the t-8 curves but also by the

u+= v+ 2)_.

(11)

The measurements were carried out in the temperature range of 380 Q T f 466 K and the pressure range of 1.3 X 10m6 G P d 1.3 X 10e5 Pa. The results are given in fig. 5, where it is shown that V is a non-linear function of 0 and that the 8-V curve depends on the substrate temperature T. The plots of Y are identical to those of effective sticking probabi~ty S, since S is proportional to V devided by the collision frequency onto the surface, i.e., S= V/F,

F=~/N,=&-‘x

10-4P//w,

(12)

where m denotes the mass of a molecule [kg], F the collision frequency onto the surface [molecules cmm2 s- ‘1 and F the collision frequency expressed in monolayers s-‘. Fig. 5 is quite similar to the 0-S curve given by Engel [S] on Pd( 111). It is demonstrated in fig. 6 that u_. is practically proportional to (E3at constant pressure, which is given by the equation: u_= /[email protected];

(13)

o, was then calculated by o,=

[email protected]

Fig. 6. The net rate of desorption o_. and that of adsorption V+ palladium temperature T. P = 2.0X 10V6 Pa. u_ is plotted with marks. (a), (0) 7’1380 K; (W), (0) 419 K; (A), (A) 443 K; (v), (v) are indicated with arrows. The dashed line was given by fitting the eq. (14).

(14)

as functions of coverage 8 and filled marks and u+ with open 466 K. The rates at equilibrium calculation of all the u, plots to

540

T. Yamada et al. / Aabrption

- desorption kinetics of CO on Pd

P / ,WPa Fig. 7. The initial adsorption rate V(0) as a function of gas-phase pressure P and palladium temperature T. (m) T= 339 K, (0) 380 K, (m) 419 K, (0) 443 K. (A) 466 K.

from the values of p and V obtained in fig. 5. The S-u, curve at the substrate temperature crosses with the O-U_ line of the corresponding temperature T to give its equilibrium coverage (indicated by arrows in fig. 6). o_ increases with increasing temperature T, but all the u, plots, except those corresponding to coverages near equilibrium, seem to be located on one curve shown in fig. 6. Pressure dependences of V, Q_, and a+ were also examined. In the pressure range studied, the curves of G-V and 8-v+ were obtained from the curves similar to those in figs. 5 and 6 under different pressures. The initial rates of adsorption, V(0) = u+(O), were calculated by extrapolating the curves to 8 = 0 and were plotted as a function of T and P in fig. 7. V(O) is proportional to the CO pressure and stays unchanged at different temperatures. The initial sticking probability S,, may be calculated from the gradient of the line, which gives 5’, = 0.88 in the whole range of measurements. The results are similar to those of Engel’s molecular beam experiments [S] on Pd(100) and Campbell et al.‘s on Pt( 111) [ 171. The pressure dependence of v_, which is undoubtedly an increasing function of P is shown in fig. 8. 3.4. The dependence of the net rate of desorption upon temperature

and pressure

As is shown in figs. 6 and 8, the net rate of desorption, o_, is practically proportional to 8, as given in eq. (13), and the rate constant p was measured in

T. Yamada et al. / Adsorption - desorption kinetics of CO on Pd

0 0

5

lb

P I lO+Pa

Fig. 8. The net desorption rate u_ as a function of coverage 8 and gas-phase pressure P. T = 380 K.(O)P=l.3X10~6Pa,(O)2.0X10~6Pa,(~)4.0X10~6Pa,(~)8.1~10~6Pa,(A)l.3XlO~5 Pa. The equilibrium points are indicated with arrows. Fig. 9. The rate constants of net desorption a as a function of gas-phase pressure P and palladium temperature T. (0) T = 339 K, (0) 380 K, (m) 419 K, (0) 443 K, (A) 466 K.

the range of 339 Q Tg 466 K and 1.3 x 10e6(p < 1.3 X 10e5 Pa. The results are shown in fig. 9. u_ is approximately a first-order function of the CO pressure, which leads to the following equation: p=

/Jo+ pp,

(15)

where p” is the rate constant proportinal to the pressure. equation: u_=

d!(8) +tf(c&

P).

when P = 0, whereas $’ is a part of ~1which is is identical to the following This expression

(16)

Here v’!! represents thermal desorption, which occurs independently of the ambient CO pressure, whereas UC denotes the rate of desorption assisted by adsorption. p” and pp are corresponding rate constants if eq. (13) stands individually for I$!. and u!. u!! is ordinarily given by the Polanyi-Wigner equation [18] and measured by the TPD technique. u?! was estimated by the procedures described in section 3.1 with P = 1.3 x 10e5 Pa for t, = 60 s leaking

T. Yamada et al. / Adsorption - desorption kinetics of CO on Pd

542

0.4

‘m : e 0.2 .

0

Fig. 10. The thermal desorption rate o! as a function of coverage 8 and palladium temperature T.

(e) T = 339 K, (0) 380 K, (m) 419 K, (0) 443 K, (A) 446 K.

20

7 Nm ‘0 =

10

P =\

P I1 O+Pa Fig. 11. The pressure-dependent part of the net desorption rate constant, cp, as a function of gas-phase pressure P and palladium temperature T. (e) T = 339 K, (0) 380 K, (B) 419 K, (0) 443 K, (A) 466 K. The dashed line shows F [s-l] given by eq. (12).

T. Yam& et al. / Adsorprion - desorption kinetics of CO on Pd

543

no CO for t,, which corresponds to the conditions with a CO coverage under was measured and o! was estimated in the same manner as V with eq. (6). The results are shown in fig. 10. Since u!! is very small, it was difficult to obtain precise values, especially at low temperatures, but it is suggested that u!?_is quite a non-linear function of 8. In the whole range the thermal desorption rate u? is much slower than the adso~tion-assisted desorption rate such that the 8-v_ curves seem to be linear. The rate constants for u!!_,i.e. p”, with respect to 8 were roughly estimated by fitting straight lines to the data in fig. 10 and pp was obtained as a function of T and P. The plots for pp are shown in fig. 11. In this range of measurements pp is proportional to P, therefore, pp can be written as

P co = 0. n*(t, + t2)

or

pP=kpP

pp= k,F.

07)

An additional experiment was carried out to establish the exact form of UC as a function of P at pressures higher than those in fig. 11 at T = 339 K. The desorption took place too fast to measure by ordinary procedures at temperatures higher than 339 K. $’ is not exactly proportinal to P, but to Po.79, as given in fig. 12, and eq. (17) is only an approximate form which is valid in the range of 339 G T G 466 K and 1.3 x 10m6 Q P d 1.3 X low5 Pa. The temperature dependence of the rate constant of assisted desorption pp was estimated by the approximate form of eq. (17). The temperature dependence of k, or k, can be expressed by k, =

2.5 X IO6 exp( -4.9 kcal mol-‘/RF)

Pa-’ s-‘,

88 47 fn N ‘0

2 .

c 0

1 1

I 2

4

6

810

20

40

80

P fl O-‘Pa Fig. 12. The pressure-dependent part of the net desorption rate constant, ~4 as a function of gas-phase pressure P (logarithm-logarithm plots). T= 339 K. pp is fitted by cp [S-I] = 1.6 x 102(P[Pa])0~79.

T. Yamada et al. / Adsorption - desorption kinetics of CO on Pd

544

or k,=

5.2 x IO2 exp( -4.9

kcal mol-‘/RT),

(18)

which is obtained by Arrhenius plots of the gradients of lines in fig. 11. The activation energy for I.?!, when first-order desorption is assumed, could not be calculated accurately from the results in fig. 10 because the temperature range was narrow. The values previously obtained by TPD [ 11,151, around 30 kcal mol- ‘, may be considered to be appropriate in this case. It is to be noted here that k, may be more than unity at higher temperatures which suggests the possibility to have more than one molecule desorbed by collision with one molecule from the gas phase. 3.5. Desorption

of CO assisted by argon

In the procedures described in section 3.1 Ar was used instead of ‘2C’60 in order to look into what kind of effect causes the assisted desorption. At pressures between 1.3 X 10F6 and 1.3 X IO- 5 Pa of Ar at 380 K. u_ did not change appreciably from u!. given in fig. 10. Thus, the presence of Ar in the gas phase did not influence the rate of desorption of adsorbed CO. Since Ar is not chemisorbed at this temperature, the result indicates that the assisted desorption must proceed through a chemical process.

4. Discussion 4.1. Net rate of adsorption As is seen in fig. 6, the net rate of adsorption v, is not proportional to the fraction of open sites 1 - 0 and is almost independent of the palladium temperature except near the equilibrium coverage. u+ may be considered to be constant for 0 < 0 < 0.5 and may be treated by eq. (12) in a manner similar to that of the sticking probability S. Weakly-bonded precursor-state models were employed to explain the non-linear relation of the O-S curves; first by Kisliuk [ 191 and Ehrlich [20,21], and later generalized by Kohlt and Gomer [22]. Tamm and Schmidt [23,24], and King and Wells [26]. According to this model, the sticking probability is given by 0, -=s=s, F

(

[email protected]

0

-’

K 1

(19)

for the non-dissociative adsorption on a single site [22]. The data given in fig. 6 may be approximately fitted to eq. (19) to obtain a roughly-averaged u, at all the substrate temperatures. The behaviour of v+ is qualitatively demonstrated by the changes along a temperature-independent

T. Yamada et al. / Adsorpiion - desorption kinetics of CO on Pd

545

curve with respect to coverage and slightly diminishes just before reaching the equilibruim point of the corresponding temperature. The initial sticking probability for other gases explained by precursor models, such as H,/W(lOO) and H,/W(lll) [23,24], N,/W(llO) [25,26] or O,/W( 110) [22], are obviously dependent upon substrate temperature, whereas in this case the initial sticking probability is independent of temperature. 4.2. Net desorption rate It is clearly shown that the desorption of CO from Pd surfaces is strongly enhanced by the presence of CO molecules in the gas phase. This kind of phenomenon was qualitatively observed by Yates and Goodman on Ni(lOO) where a “C”O adlayer was exposed to a ‘2C’60 fluxed beam [27], and also by Matsushima over Pd and Rh foils [28]. Tamm and Schmidt observed an acceleration of desorption in the presence of gas phase molecules in the H,/W( 111) system [24]. Tamm and Schmidt assumed that the molecules in a weakly-bonded state, which is adsorbed to a saturation coverage, and those in the chemisorbed state exchange mutually, and they explained the dependence of the rate of desorption upon temperature and pressure measured by using H, and D,. The fractional order of desorption with respect to P in a wide range can be inferred from the adsorption isotherms, which is equivalent to the equation u, = u_. According to the adsorption isotherms of Conrad et al. on several single crystal surfaces [4] under very high pressures the adsorption approaches full coverage at all the substrate temperatures studied, which requires u_ should increase more slowly than proportional to P when we suppose u, is proportional to P. Those adsorption isotherms can be explained better by u_ which includes P than by u_ without P. It is demonstrated in eq. (13) that the assisted desorption takes place uniformly over the entire surfaces, its rate being proportional to the coverage. The mechanism of assisted desorption is irrespective of the energy states of surface CO usually resolved as.TDS peaks. This kind of pressure dependence of the desorption rate suggests the possibility that reactant molecules can enhance desorption of tightly-bonded product molecules in some catalytic processes.

5. Conclusion (1) The net rate of adsorption and that of desorption of carbon monoxide on palladium polycrystalline surfaces were measured by the isotope-jump method combined with coverage measuremen by flash desorption. (2) The net rate of adsorption u, is almost independent of the palladium

546

T. Yamada et al. / Adsorption - desorption kinetics of CO on Pd

temperature T except near the adsorption equilibrium. u, is quite a non-linear function of 1 - 0, especially u, is almost constant in the range of 0 Q 0 < 0.5. The initial sticking probability for 339 Q T < 466 K and 1.3 X 1O-6 < P < 1.3 X 10d5 Pa is 0.88. (3) The net desorption rate u_ is written as the sum of the thermal desorption rate u’? and the adsorption-assisted desorption rate up. u” is a non-linear function of coverage 0. u! is proportional to Po.79 in a wide range ofP,butintherangeof339~T~466Kand1.3X10-6~P~1.3x10-5Pa, u’_ is approximately given by U-‘=

2.5 x lo6 exp( -4.9

kcal mol-‘/RT)P[Pa]O

= 5.2 x lo* exp( -4.9

kcal mol-‘/RT)F[s-‘10.

References 25a (1970) 1906. [II G. Ertl and J. Koch, Z. Naturforsch. 121R.R. Ford, Advan. Catalysis 2 1 (1970) 5 1. 131 J. Ktippers, H. Conrad, G. Ertl and E.E. Latta, Japan J. Appl. Phys., Suppl. 2, Part 2 (1974) 225. 141 H. Conrad, G. Ertl, J. Koch and E.E. Latta, Surface Sci. 43 (1974) 462. [51 T. Engel, J. Chem. Phys. 69 (1978) 373. [61 H. Conrad, G. Ertl and J. Kiippers, Surface Sci. 76 (1978) 323. [71 T. Engel and G. Ertl, J. Chem. Phys. 69 (1978) 1267. Surface Sci. 72 (1978) 5 13. PI A.M. Bradshaw and F.M. Hoffmann, [91 S.D. Bader, J.M. Blakeley, M.B. Brodsky, R.J. Friddle and R.L. Panosh, Surface Sci. 74 (1978) 405. [lOI J.C. Bertolini and B. Imelik, Surface Sci. 80 (1979) 586. G. Ertl and M.A. Van Hove, J. Chem. Phys. 73 (1980) 2984. [Ill R.J. Behm, K. Christmann, 1121 P.A. Redhead, Trans. Faraday Sot. 57 (196 1) 641. [I31 P.A. Redhead, Vacuum 12 (1962) 203. A34 (1979) 96. [I41 H. Shindo, C. Egawa, T. Onishi and K. Tamaru, Z. Naturforsch. 1151 C.M. Comrie and W.H. Weinberg, J. Chem. Phys. 64 (1976) 250. [I61 W. Erley and H. Wagner, J. Chem. Phys. 72 (1980) 2207. 1171 C.T. Campbell, G. Ertl, H. Kuipers and J. Segner, Surface Sci. 107 (1981) 207. [I81 L.A. Petermann, in: Progress in Surface Science, Vol. 3, Part 1, Ed. S.G. Davison (Pergamon, New York, 1973) p. 1. [I91 P. Kisliuk, J. Phys. Chem. Solids 3 (1957) 95; 5 (1958) 78. PO1 G. Ehrlich, J. Phys. Chem. 59 (1955) 473. PII G. Ehrlich, J. Phys. Chem. Solids 5 (1958) 47. WI C. Kohrt and R. Gomer, J. Chem. Phys. 52 (1970) 3283. ~231 P.W. Tamm and L.D. Schmidt, J. Chem. Phys. 51 (1969) 5352. v41 P.W. Tamm and L.D. Schmidt, J. Chem. Phys. 52 (1970) 1150. v51 L.R. Clavenna and L.D. Schmidt, Surface Sci. 22 (1970) 365. [26] D.A. King and M.G. Wells, Proc. Roy. Sot. (London) A339 (1974) 245. [27] J.T. Yates, Jr. and D.W. Goodman, J. Chem. Phys. 73 (1980) 5571. [28] T. Matsushima, J. Catalysis 64 (1980) 38.

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