Interaction of N2 with (100) W

SURFACE

SCIENCE 22 (1970) 365-391 0 North-Holland

INTERACTION

Publishing Co.

OF N, WITH (100) W *

L. R. CLAVENNA**

and L. D. SCHMIDT

Chemical Engineering Department, Minneapolis, Minnesota,

University of Minnesota, 55455, U.S.A.

Received 5 May 1970 The binding states and condensation and desorption kinetics of nitrogen on (100) W are studied using flash desorption mass spectrometry. At moderate exposures there exist three states, a tightly bound 82 state and two weakly bound molecular y states; the saturation densities for each state are 2.5 x 1014molecules cm-2. Very high nitrogen exposure at low temperatures produces in addition to these states a tightly bound (Ed = 49 kcal mole-l) 81 state which desorbs with first order kinetics and at 300°K has a sticking coefficient of less than 10-3. Desorption kinetics for the /32 state at high coverages can be explained quantitatively only by assuming a coverage dependent activation energy or pre-exponential factor; the latter is predicted if desorption is limited by surface diffusion controlled recombination of atoms. The binding states and atomic configurations are shown to be reasonable on the basis of the electronic structures of the adsorbate and the substrate; this predicts the existence of a structure for the 82 state in which alternate sites are occupied and agrees with the measured stoichiometry. The sticking coefficient into the /32 state is measured as a function of coverage and substrate temperature in the interval 195 “K < T< 1035 “K. Condensation appears to proceed via a weakly chemisorbed precursor. Quantitative agreement with the data is obtained using a model in which the sticking coefficient and desorption kinetics of the precursor state are completely independent of the occupation of the 82 state.

1. Introduction The binding states and condensation of H, on (1OO)W have recently been interpreted in a fairly consistent fashion by Tamm and Schmidt ‘) using flash desorption measurements and previously obtained low energy electron diffraction (LEED) results’). It was found that hydrogen exhibits two adsorption states in a saturation ratio of 2: 1 which obey first and second order desorption kinetics, respectively. The more tightly bound atomic state (j3J exists in a structure in which only every other site is occupied, and this state forms as islands on the surface. This behavior was shown to be reasonable on the basis of d-electron structure of tungsten. Condensation of * This work partially supported by ARPA under Grant No. DAHC-15-69-G6. ** NDEA Fellow 365

366

L. R. CLAVENNA

AND

L.D.

SCHhUDT

H, was shown to proceed via a precursor state which was probably weakly chemisorbed in sites independent of the occupation of tightly bound states. In this paper the binding states and condensation of N, on (lOO)W will be investigated using flash desorption mass spectrometry. Since fairly complete LEED data are available3) and only one tightly bound state is observed at moderate exposuressp4), an accurate determination of the energetics and kinetics of the interaction is possible. Comparison of the present results with Hz adsorption on this surface is particularly interesting to test the suggestions advanced previously for that system. It will be seen that there are close similarities between the systems with most of the difference interpretable in terms of electronic structures of the adsorbates. Nitrogen adsorption on polycrystalline W has been studied by many investigators5-ls). Two high temperature states (PI and pz) have been observedg-ll). The PI state obeys first order desorption kinetics with an activation energy of -73 kcal mole-l while the /3z state obeys second order kinetics with an activation energy of N 75 kcal mole-r lO).Two weakly bound groups of states (y and a) have also been observed5,s,s111). These states are molecular since they obey first order desorption kinetics and do not exhibit isotopic exchange; however complete isotopic exchange occurs in both PI and pz stateslOsll). The sticking coefficient on polycrystalline W is initially independent of coverage; this has been interpreted as condensation via a precursor state13,14). Nitrogen adsorption on several individual crystal planes of W including (100) has been examined by Delchar and Ehrlichd) who determined work function changes by contact potential measurement and obtained semiquantitative flash desorption spectra. On (100) W they observed a single high temperature fi state and a split low temperature y state. Work function changes on (1OO)W have also been measured by several other investigators on macroscopic crystals 15916) and by single plane field emission measurements17$ls). Estrup and Anderson331g) examined the LEED structures and measured work function changes for N, on (100) W above 300 “K; they also used flash desportion to determine coverages. In several of these investigations the initial sticking coefficient on (100) W at 300°K has been estimated from the change of work function with exposure to be 0.25 and 0.55 3,4). As on polycrystalline tungsten, the sticking coefficient on (100) W is initially independent of coverage %4g15). We note that most of the flash desorption results we report here have been seen previously. The emphasis in the present work is in determination of the kinetics and stoichiometry with a precision which has not been possible in previous work due to lead effects and use of surfaces which exposed significant amounts of other crystal planes.

INTERACTION

OF

Nz

WITH

(100)

w

361

2. Experimental The apparatus and procedure were quite similar to those described previouslyr). Rates of adsorption and desorption of N, on a (100) oriented surface of W were monitored with a quadrupole mass spectrometer. The most important features of the experiment were the use of tantalum film getters for high pumping speeds (r > 5 msec) when desired and use of single crystal discs heated by electron bombardment to eliminate temperature nonuniformities and other crystal planes associated with lead effects. This permitted precise and reproducible flash desorption traces which could be fitted quantitatively to theoretical curves to determine the stoichiometry and kinetics accurately. Crystals were in the form of oriented and polished discs -$ inch diameter and 0.011 inch thick suspended by a 0.011 inch diameter W wire so that < 10% of the heated surface was not of (100) orientation. Two crystals were used in separate measurements; all results duplicated on both crystals indicated no significant differences. Crystals were cleaned by heating to 2350°K in vacuum and for several hours in 0, at 10s6 torr. A tungsten-rhenium thermocouple welded to the crystal was used to monitor temperatures. Calibrated against an optical pyrometer, temperatures are regarded as accurate to within +2% and were reproducible to within _+1%. Sticking coefficients were determined by pressure-time measurements as described previouslyl). For maximum sensitivity the pumping speed was intentially reduced by not flashing the getters. Flash desorption spectra were used to check for the possibility of contanlination by CO, H, or CO, during adsorption sequences. Constant crystal temperatures below 450 “K were maintained by thermostating the crystal assembly; higher temperatures were provided by means of a focused light beam (to 800°K) and electron bombardment (to 1100°K) using the thermocouple to monitor the temperatures. At intermediate temperatures, measurements using both the focused light beam and electron bombardment gave the same sticking coefficients and saturation amounts, indicating no artifacts from bombardment heating. Before each flash desorption or adsorption measurement, the crystal was flashed to - 2400 “K. The cooling rate was such that within 3 min the crystal was within 10’ of the temperature of the leads. For adsorption measurements pressures were chosen so that the coverage interval of interest was attained at times between 3 and 30 min. Pressures during nitrogen exposure were typically 1 x lop9 to 3 x lo-* torr, although for population of the /I1 state, pressures as high as 10V6 torr were used. Partial pressures of other gases were always less than a few percent of the nitrogen pressure and were considerably less than this at high pressures.

368

L. R.CLAVENNA

AND L.D.SCHMIDl

The basic equations for analyzing the pressure-time curves of desorption and adsorption have been described by RedheadzO) and therefore will be presented without proof. Typical pressure-time curves for adsorption are shown in fig. 1. Sticking coefficients were determined from these curves using the relationship

(1) where A is the area of the crystal, z is the pumping time constant, P,, the base pressure when the crystal is saturated, V the volume of the system, f

yFLASH

DESORPTION

ADSORPTION

TIME

--+

Fig. 1. Typical pressure-time curves used to obtain the sticking coefficient of nitrogen as a function of coverage in the 82 state. Curves shown are for crystal temperatures of 298°K and 905°K.

the flux of gas per torr, and G= l/kT, the number of molecules in gas phase per unit volume per torr. The corresponding coverages were determined from the equation

[PO-P]

n = g

dt + “,” [PO - P].

s 0

The second term in both eqs. (1) and (2) is small in most instances. The pumping time constants were determined from plots of log(P-PO) versus time following a rapid flash of the electron bombardment filament. These were always obtained before and after an adsorption sequence and gave a straight line on a semi-log plot over at least a decade variation of P - PO.

INTERACTION

OF

Na

WITH

(loo)

w

369

Theoretical desorption traces were computed and compared to experimental traces in order to examine quantitatively the desorption kinetics and the parameters involved. If one assumes desorption kinetics of order m, a heating rate 6 = dr/dt, and a pumping time T, then P versus T is obtained by solving the first order differential equations

d~_.. CP- Pal = dT

-

and dn dT=-

v$“)n”’ -~ p

exp [ - E,/RT]

with appropriate boundary conditions. Ed and v$,“’may be assumed constant or functions of surface coverage. Numerical solutions to this system of equations were obtained by the Runge-Kutta-Gill method. 3. Results 3.1. FLASHDESORPTION Fig. 2 shows a typical flash desorption sequence obtained for nitrogen

TEMPERATURE

Fig. 2. Flash desorption traces for N2 from (100) W. The solid lines indicate traces obtained by moderate exposure (< 10e4 torr set) with the crystal at 78°K. The insert shows desorption from the saturated y states at a lower heating rate. The trace indicated by the dashed line is that obtained by high exposure to Nz at 78°K with intermittent heating to 305°K. The areas under the saturation curves indicate equal amounts in the yt,y-,and fia states. B = 86O”K/sec except for insert where B = 80”K/sec.

370

adsorbed on posures: two There is also the crystal to

L. R. CLAVENNA

AND

L. D. SCHMIDT

(100) W. Three desorption states are observed for moderate exlow temperatures y states and one high temperature pz state. a high temperature PI state produced upon long exposure of nitrogen at low temperatures.

3.1.1. fiz state The shift of the temperature of maximum desorption rate Tp with initial coverage tIi and the shape of the desorption traces indicate that the /I2 state obeys second order desorption kinetics. For flash desorption with linear heating rate p and a saturation coverage IZ~,it can be shown that so)

ELI

n,v~%.

RT,2=-p

ALLexp[-

E,/RT,],

where it has been assumed that the pumping speed is high and Ed is independent of coverage. Therefore, a plot of ln(e,T,‘) versus l/T, should give a straight line with slope equal to Ed/R.As shown in fig. 3 a straight line is obtained for fI ~0.2 with E,,=73.5kcal mole-’ and n,v~*‘=5.8 x 1013 set-’ . For a saturation coverage no = 2.5 x 1Ol4 molecules cm-*, as discussed later, one obtaines a second order pre-exponential factor of 0.23 cm* molecules-l set-‘. 3.1.2. y state At the low substrate temperatures used to study the y state, nitrogen reversibly adsorbed on the glass walls and made it difficult to control exposure rates or maintain a high and constant pumping speed. Working at liquid 0, temperature (90 OK) rather than that of liquid N, (78 OK) did alleviate the problem somewhat but the flash desorption traces were still not as precise as those obtainable at > 200 “K. The flash desorption trace of the y state, shown in fig. 2, clearly reveals two peaks with maxima at 170 and 190°K. A heating rate of 80 “K set- ’ was used in this measurement to resolve the peaks. Using the nomenclature of Delchar and Ehrlich4) the states are called y+ and y-. No shift in the peak maxima with coverage occurs indicating first order molecular states, and assuming v. = 1Or3 set- ‘, one obtains activation energies of 9.2 and 10.5 kcal mole-l, respectively. This is in good agreement with Delchar and Ehrlich who were unable to resolve the y states by flash desorption but inferred their existence from contact potential measurements (one state increased the work function while the other reduced it). Relative amounts in the two y states were estimated from both integral and differentia120) flash desorption modes. At saturation the amounts of nitrogen adsorbed in the y + and y _ were observed to be equal to within 1Ox,

INTERACTION

I ‘$0.64

I 0.68

OF

I 0.72

I 0.76 +

371

Nz WITH(100) w

I 0.80

I

0.84

C

I8

lO-3 OK-’

Fig. 3. Plot to determine rate parameters for the BZ state according to eq. (5). Points indicate experimental data for coverages from 2.3 x 10’2 molecules cm-a to saturation, 2.5 x 10’4 molecules cm-2. Lines show theoretical fit to data: the solid line for variable Ed as given by eq. (7), the dashed line for variable vof2) as given by eq. (lo), and the dotted line for constant Ed and VO(~).Data were obtained with b= 860”K/sec and r =0.083 sec.

and the total amount in these states was 2.OkO.l times that in the b2 state. From flash desorption traces obtained for various nitrogen exposures at 78”K, the amount of nitrogen desorbing from the y states relative to that from the pz state was determined as shown in fig. 4. It is evident that the pz state is almost completely saturated before the y states begin to fill, although of course the population of states at the adsorption temperature 78 “K is not directly accessible from these measurements.

312

L.R. CLAVENNA

AND

L.D.SCHMIDT

Fig. 4. Plot of the amount of Nz in the 7 states as a function of the amount in the /?z state for adsorption at 78°K. The amounts are expressed relative to the saturation coverage in the j3zstate, npo = 2.5 x 1Ol4molecules cm-z.

3.1.3. PI state Additional exposure of the surface at > 195°K to nitrogen (up to 10m4 torr set) showed no additional adsorption states with populations greather than 10% of that in the f12 state. This indicates that the only other states of nitrogen stable above 195 “K must have sticking coefficients less than lo- 3. The same result was obtained at 78°K (or 90°K) if the surface was cooled before adsorption and the desorption heating rate was 50°K set-’ or greater. However, nitrogen exposure to a surface while it was cooling to 78 “K gave, in addition to the y +, y _, and pz states, a small state, fir, desorbing at -900°K. The desorption peak for this state did not shift and was much narrower than that of the second order pz state indicatingJirst order desorption kinetics. Assuming vy’= 1013 se-‘, one obtains Ed=49 kcal mole-‘. The largest population of the PI state was obtained by repeated exposure at 78°K with periodic heating to - 300 “K to evaporate the y states. After this procedure the amount of nitrogen which could be readsorbed into the y states was reduced by approximately twice that in the PI state. The maximum amount which we were able to adsorb in the PI state was -40% of the p2 state or 1.O x lOI molecules cm- 2. This was limited by the time ( < 2000 set)

INTERACTION

and pressure

OF

Nz WITH(100) w

373

(< 1 x lO-‘j torr) to which the crystal could be exposed without

contamination, and no evidence of saturation was obtained. Considerable care was used to ascertain that this state was not a contaminant (such as CO) or a nitrogen state induced by the presence of a gas contaminant. Flash desorption traces at mass 12 and 14 were obtained to determine the relative amounts of C+ and N+ fragments from CO and N,. The trace at mass 14 precisely reproduced that at mass 28; this indicates that the /I1 state is definitely nitrogen. No mass 12 was detected on a scale 100 times more sensitive than that used for mass 14; this indicates a CO coverage of less than 10m2 monolayers. There was also no evidence of H,, H,O, CH4, or CO2 contamination. We therefore conclude that the pi state is one of low sticking coefficient which for moderate nitrogen exposures can be formed by thermal conversion from the low temperature y states. Similar nitrogen states on tungsten with low sticking coefficients have been observed by many investigators. Electron bombardment of nitrogen covered polycrystalline tungsten 2i) and the (100) plane 22) at temperatures where the y states are populated produces a x state which upon heating converts to a state which on polycrystalline tungsten desorbs at 800 to 1100 “K. Ermrichsi) has shown that the state produced by electron impact is strongly electronegative on the (100) plane. On (110) tungsten the only tightly bound /I state is reportedis) to have a sticking coefficient of < 10m3. Work function measurements on the (100) plane at 300°K for macroscopic crystals4116) and field emitters 2s) indicate a drop in q as the /3 state fills and then a very slow rise, indicating population of an additional electronegative state. Hopkins and Usamii6) observed an additional state after nitrogen exposure of 10-l torr set at 300°K which appears identical to the /I1 of fig. 2. The sticking coefficient estimated from these results is N 10-4, in good agreement with the present results, and as in the present case, it was impossible to determine the saturation amount accurately. An additional experimental complication in studying this state is the possibility of activation of nitrogen gas by hot filaments or by electron bombardment. It has been found that Ir and Rh surfaces will not adsorb nitrogen unless an ionization gauge is operating; nitrogen gas is converted to an excited electronic state for which the sticking coefficient on these surfaces is much higher than for nitrogen in its ground state24). In the present measurements only thoriated filaments were used, and no differences in nitrogen adsorption were noted when filaments were on or off. However, activation of nitrogen could significantly affect attempts at comparison of results in different laboratories for the pi state. Adsorption of nitrogen as NH, can also produce an additional state of nitrogen which desorb just below the p2 states+27). This state is produced

314

by repeatedly

L. R. CLAVENNA

saturating

AND

L. D. SCHMIDT

the surface with NH,

and heating

to -600°K

to

evaporate H,, and it can only be produced in significant amounts by this cycling procedure. Unpublished work in this laboratory with NH, on (100) W has shown that by this procedure the low temperature peak of N, from NH, has precisely the characteristics of the j3i peak from N2 alone: first order desorption kinetics with Ed=50 kcal mole-l. It was possible by repeated NH3 dosing to obtain a coverage of Nz in the fil state approximately equal to that in the /I2 state, but no real effort was made to attain saturation of the state. There is some controversyss-27) as to whether or not there is hydrogen on the surface as NH complexes at high temperatures; this prevents unequivocal correlation of the /?i states, but they are observed to be undistinguishable in their desorption kinetics. We conclude therefore that the pi state of nitrogen is one of high binding energy but for which the rate of condensation by direct gas phase impingement is extremely low. It can be formed by thermal conversion from the y states, by conversion from adsorbed NH,, by electron impact of nitrogen in the y state, or by very high nitrogen exposure. 3.2. CONDENSATION The sticking coefficient versus coverage curves are shown in fig. 5 for substrate temperature between 195 and 1035°K. These were obtained from pressure versus time curves similar to those shown in fig. 1 using eqs. (1) and (2). The points shown indicate the coverage intervals used in graphical integration of the pressure-time curves. Data were corrected to eliminate effects due to adsorption on the filament. Crystal cooling corrections were made by obtaining data at several pressures or by allowing the crystal to cool rapidly and then heating with the light beam or by electron bombardment to the desired temperature. For all data points shown in fig. 5 the temperature was within a few degrees of the indicated temperatures. Sticking coefficients which initially increase with coverage have been reported 2*), and this might be expected from island structures if condensation occurs preferentially at the edge of islands. An increase in s with coverage is observed if the crystal is cooling during measurements because of the variation of s with temperature ; however, s decreases monotonically with coverage at all temperature if cooling effects are eliminated. The reproducibility of the data on two crystals is illustrated in fig. 5 by the two sets of data at 300°K. In all runs the reproducibility was within a few percent. The total amounts on the crystal were determined from the areas on the pressure-time curves. A value of n, = (2.0 kO.07) x 1014 molecules cm-’ was obtained at all crystal temperatures between 195 and 905 “K. At 1035 “K the

INTERACTION

OF

Na

WITH

(lo())

w

375

0.5r

Fig. 5. Sticking coefficient for the 82 state as a function of coverage at the indicated crystal temperatures. The open and solid circles compare data obtained on two different (100) W crystals.

coverage was only 1.6 x lOi molecules cm-’ due to evaporation. This saturation coverage was consistent with that calculated assuming a steady state between condensation and evaporation at the temperature and pressure employed. This placed an upper limit on measurements at high substrate temperatures. saturation

4. Discussion 4.1. SURFACE STRUCTURE

The flash desorption measurements for moderate exposures reveal a single pz state which obeys second order kinetics with an activation energy of 74 kcal mole- I. LEED measurements3) show that a c(2 x 2) structure is formed by this state, and the simplest configuration consistent with these results, proposed by Estrup and Anderson, is shown in fig. 6. Nitrogen atoms in the singly bonded position above protruding substrate atoms or in a bridge position (positions C and A of ref. 1) cannot be eliminated from present experimental evidence, but as discussed previouslyr), considerable hybridization of tungsten d-electrons is required to form such

376

L. R. CLAVENNA

AND

L. D. SCWMIDT

bonds. Furthermore, nitrogen must satisfy its 3 valence electrons, and this seems best achieved in the configuration shown (position B of ref. I). We also postulate that the y states, observed to obey first order desorption kinetics and to have a saturation density twice that of the & state, occupy the B sites excluded to the & state as indicated by the small circles labelled I and 2 in fig, 6. The & state is observed to form from the y states and to reduce the saturation amount in the y states; like the y states it obeys first order desorption kinetics. It is therefore reasonable to assume that the /& and y states occupy the same sites but have different bonding configurations,

Fig. 5, Schematic diagram showinga possible~~~~~rat~o~of e-bonds for the atomic Bz nitrogen state aa (100)W. Large circles indicate W atoms, intermediate circles N atoms, and small numbered circles vacant sites. The o-bond involving the p-orbital of the N atom with the eg orbital of the underlying W atom is not shown.

Thus, we suggest that the & state of nitrogen on (100) W is analogous to the Dz state of hydrogen while the y and PI states of nitrogen correspond to the j3, state of hydrogen. By the arguments advanced previously, occupation of the atomic state excludes the nearest neighbor sites from further similar bonding because a surface atom of tungsten does not have enough electrons of proper energy for the formation of additional adsorption bonds. As for the & state of hydrogen, & nitrogen is predicted to form islands, as seems to be indicated by LEED resultslg), although intensity versus coverage measurements have not yet been carried out at a high enough temperature to decide this definitely. The p2 nitrogen state should be more tightly bound than hydrogen through its three Zp-electrons and should thus

INTERACTION

“tie

up”

tungsten

electrons

OF

more

N2

WITH

(100)

efficiently,

377

w

accounting

for

the

weak

binding of the y states as compared with the PI state of H,. While this picture of N, adsorption is plausible and appealing for its simplicity, the nature of the adsorbate at low temperatures is by no means established. Flash desportion only provides information about the binding at lower temperatures, particularly states at the desorption temperature; when the adsorbate is immobile, intermediate states or a poorly formed BZ state may exist. In fact, there is substantial evidence for this from the work function changes at different temperatures4) and from the fact that the c(2 x 2) pattern is poorly ordered at 300”K, and a well-ordered pattern only forms upon beatings). However, the sticking coefficient shows only a slight variation with substrate temperature, and as will be discussed later, this can be explained quite well assuming a regular layer. We therefore suggest that all adsorbed nitrogen occupies a more or less ordered BZ above -200°K state (if the PI state is not occupied), the size and perfection of the ordered structures depending on temperature. LEED investigations are in progress to examine the intensity and size of the (3, +) spots as functions of substrate temperature and previous annealing conditions above and below room temperature. The order of the nitrogen adsorbate depends on its surface diffusion coefficient. Ehrlich and Huddass) examined the diffusion of nitrogen on a tungsten field emitter and found that at low coverages equilibration over the emitter (a distance of N 1000 A) occurred only after heating to 650 “K for several minutes. Diffusion into the (100) plane across the (100) vicinals occurred under these conditions, but diffusion rates across the (100) plane itself cannot be determined directly from such experiments except to establish that the rate is not lower on the (100) plane than on its vicinals. Tungsten rearrangement may accompany nitrogen adsorption, particularly at high temperatures where tungsten atoms are mobile”s). No evidence of rearrangement was found in these present measurements in that 1) the saturation amount adsorbed is precisely the same at all substrate temperatures from 195 “K to 1035 “K and 2) no extra states are formed by adsorption at high temperatures (> 600 OK) where surface disorder and nitrogen adsorption should be largest. The absence of appreciable rearrangement has also been noted by Estruprs) who examined the temperature dependence of LEED beams from a N, covered (100) W surface and by Ehrlich and Hudda 30) who studied N, adsorption on tungsten field emitters (T<420”K) by field ion microscopy. 4.2. ADSORPTIONBONDS For I-I, adsorption

on (100) W it has been suggested

that the structures

318

L. R. CLAVENNA

AND

L. D. SCHMIDT

and energetics of chemisorption can be correlated in terms of the electronic structures of the substrate and adsorbatei). Similar correlation appears to hold for N, adsorption on this plane also. Further work is in progress to extend these measurements to H, and N, adsorption on other crystal planes of W and to other transition metals in an effort to quantify these considerations, and a more detailed discussion of chemisorption bonds will be given in connection with these results. However, it seems worthwhile to briefly consider some of these implications here. It is evident that the complex binding configurations of N, and H, on single crystal planes of transition metals cannot be explained in terms of continuum models of the surface or in terms of the geometric structures alone, especially for the simple (100) and (110) planes of bee crystals. However, consideration of the directional character of the partially filled d-electron bands of the substrate appears to explain the experimental situation quite well. Arguments involving the crystal field splitting and hybridization of s and d orbitals are not meant to imply that simple atomic d and s wave functions are adequate to explain bonding or that bonds are localized; reference to the e, and t,, subbands and hybridization with the 6s band merely denotes the symmetry of the wave functions around the substrate atom. Thus, it may be useful to talk of sdo, pdc, and pdrr-bonds even though the energies of these bonds cannot be calculated accurately using atomic wave functions as a basis set, just as the tight-binding approximation is useful in discussing the symmetry of particular bands in metals even though these bands may be extremely broad. However it has not been established that chemisorption bonds are nonlocalized. Even though the d bands of transition metals in bulk are several eV wide, near the surface they should be considerably narrower, and the tight binding approximation may be reasonably accurate. Both CJand n-bonds can form between the p-electrons of the N atoms and the d-electrons of the W. A possible configuration of o-bonds of the atomic pZ state is indicated in fig. 6. This involves one ep orbital from the W atom beneath the N atom and four orbitals from the four nearest W atoms in the plane of the surface. The latter would be directed approximately in the [ 1 lo] direction, since the N atoms are almost coplanar with the surface W atoms and would have the symmetry of a d,, orbital. The N atom must maintain its three 2p-electrons in orbitals 90” apart unless there is hybridization with the 2s-electrons. This structure preserves this orientation and maintains the four fold symmetry of the site. An important feature of this configuration is that strong long-range interactions are possible in the plane of the surface. We suggest that the

INTERACTION

OF

Nz WITH(loo) w

319

structure formed may be visualized as a two-dimensional tungsten nitride with the stoichiometry W,N. Bulk transition metal nitrides derive their stability largely from the strengthening of metal-metal bonds due to the presence of interstitial N atoms, precisely the configuration envisioned in fig. 6. We shall consider these interactions in detail in a later paper. It should be noted that hydrogen adsorption on (100) W fits into this picture, forming a two-dimensional W,H upon saturation of the /IZ state and WH,., upon saturation of both states. We strongly emphasize that three-dimensional hydrides and nitrides are not proposed - only that W-adsorbate interactions in the plane of the surface form a two-dimensionally coherent structure. Island formation for the /I2 states of both adsorbates is, of course, readily visualized in this picture. The nature of the bonds formed for the y and /I1 states is quite unknown. The bond energies in the y states are a small fraction of the dissociation energy of N,, and one should be able to regard these states as chemisorbed N, molecules. However, the pi state is very strongly adsorbed and, even though it obeys first order kinetics, its electronic structure must be quite different than that of the gas molecule. One possibility is that N, in the /I1 state is bonded to the four nearest atoms in the plane of the surface while y states are bonded only to the atom below the site. It is also possible to devise an explanation for the existence of two types of y states due to interactions parallel to the surface. Orbitals for cr bonding and their symmetries for the /I2 state are sketched in fig. 6. This is the orbital configuration for minimum energy which occurs at k= (3, 3, 0) n/ain the tungsten lattice. Of course, only two electrons can occupy a given state, and all states with energies below the Fermi energy will be filled; however, this should be the configuration for maximum bonding. Examination of the sites for the y states reveals that one has four-fold symmetry (type 1) and one only two-fold symmetry (type 2). The major bonding interactions are postulated to occur perpendicular to the surface for these states, but there should be slightly different electronic environments for the two sites which could produce the 1.3 kcal mole-’ difference in binding energy and the difference in dipole moments of the y+ and y_ states. 4.3. DIPOLEMOMENTANDADSORBATECHARGE The charge on the adsorbate is an important quantity in determining the nature of the adsorption bond and is crucial to binding energy calculations. While work function changes for chemisorption on transition metals are typically < 1 eV, much less than the 3 eV observed for the ionic alkali metal adsorbates, nonmetal adsorbates have much smaller diameters, and therefore a large charge transfer should produce a smaller work function change.

380

L. R. CLAVENNA

AND L. D. SCHMIDT

The dipole moment Helmholtz equation

,u is related

to the work

function

change

Acj = 2ne’pn.

by the

(6)

The dipole moment due to a charged adsorbed atom is assumed to result from the charge and its image in the metal, and since only the real part of this dipole affects 4, the factor 2n is used in eq. (6) rather than the 4rc appropriate for an adsorbate with an intrinsic dipole moment. We shall in this section determine the dipole moment and estimate the charge on N and H atoms in the p2 states on (100) W with the configuration proposed. At saturation of this state by N, and H, (5.0 x lOI atoms cmm2), Estrup and Andersona,s) determined work function changes of -0.65 eV for N, and +0.30 eV for H,. Delchar and Ehrlich4) obtained a somewhat smaller A+ for N,, but we shall use that of Estrup and Anderson as the same method was used in obtaining the value for H,. In both cases 4 was linear in n indicating no depolarization. Eq. (6) gives a dipole moment of - 0.68 Debye per N atom and + 0.32 D per H atom. These values give the net charge redistribution perpendicular to surface associated with the surface complex, and they depend only on the atom density assumed at saturation. Estimation of the actual charge on the adsorbate, however, requires assumptions regarding the position of the adsorbate atoms perpendicular to the surface and the placing of the image plane; i.e., the charge and its image fq are assumed to be at distances f 1 from a hypothetical plane behind which the metal electrons distribute themselves to screen out external electric fields. Fig. 7 indicates schematically the configuration assumed. The figure is drawn approximately to scale assuming a radius of -0.6 A for the adsorbate, the single bond radius of the nitrogen atom. The major uncertainty is in the position assumed for the image plane. This is certainly not a precise quantity because the electron distribution is not uniform parallel to the surface and a screening length of 0.5 to 1.O A

IMAGE

PLANE

Fig. 7. Configuration used to calculate the charge redistribution perpendicular to the surface due to the adsorption of atomic nitrogen or hydrogen on (100) W. The diagram shows a cross section of the (100) W surface along the [l lo] direction with atoms adsorbed in type B sites’). The image plane is drawn to pass through the center of the outermost layer of the W atoms.

INTERACTION

must be included.

OF

Nz

WITH

(100)

In fig. 7 we have arbitrarily

381

w

indicated

the image plane to

pass through the center of the outermost of W atoms. Using these assumptions one obtains a positive charge 0.15 to 0.22 electrons for nitrogen depending on the radius chosen and a negative charge of 0.37 for hydrogen using its covalent radius. There are too many uncertainties in these quantities to give much reliance to the values of the adsorbate charges or in fact, even their signs. If the image plane were farther back than assumed due to screening, the charges would be somewhat smaller. Also the radius of the adsorbate should be larger if it is negatively charged and smaller if positively charged. If the image plane were above the centers of the outermost W atoms, the charge could, in fact, reverse sign in which case the image approximation breaks down entirely. This could be true especially for hydrogen which, because of its size, could be beneath the surface with a positive charge and still produce the observed work function increase. The important feature which we wish to emphasize from these estimations is that the adsorbates are not necessarily neutral, and therefore, the ionic contributions to bonding may be significant. 4.4. RATEPARAMETERSFORSECONDORDERDESORPTION Jt has been noted above that the flash desorption data of the p2 state for 8 ~0.2 conforms to the second order plot of fig. 3 with v$“=O.23 cm* molecules- ’ set -r and Ed0 = 73.5 kcal mole-’ ; however, for larger coverages the data of fig. 3 deviate from the straight line predicted by eq. (5). The values of vy’ and E,, obtained at low coverage were used with eqs. (3) and (4) to generate theoretical flash desorption traces which are compared to the experimental traces in fig. 8 for 0=0.18 and 1.O. Although the agreement obtained at low coverage is within the precision of the data, the experimental trace at saturation is considerably wider than that predicted theoretically. Thus, while desorption from the p2 state obeys precise second order kinetics with these parameters for low coverages, it deviates from this at higher coverages. Among the possible causes for this deviation are: 1) additional binding states, 2) a coverage dependent activation energy, and 3) a coverage dependent pre-exponential. Additional binding, while impossible to unequivocally eliminate, is highly unlikely in that the shape of the experimental curves can not be fitted by any simple combination of first and second order states. If the activation energy varied with coverage as E, = E,, - cc0 with tl a constant,

the experimental

curves can be fitted moderately

(7) well.

382

L. R. CLAVENNA

AND

L. D. SCHMIDT

The theoretical traces obtained for CI= 11 .O kcal monolayer-’ are shown in fig. 8. It is also found that the theoretical second order plot compares well with the experimental plot indicated by the solid line in fig. 3.

c .: 3

VARIABLE

0.6

0.2

E,,

,/CONSTANT

Ed avo(*)

-

Oh.-

I

600

1000

1200

1400

1600

1600 OK

TEMPERATURE

Fig. 8. Theoretical fit to flash desportion traces for the 8~ state. Points indicate experimental data for 0 = 1.0 and 0.18. Lines indicate theoretical fits: solid line for variable Ed f2) as given by eq. (IO), and dotted line for as given by eq. (7), dashed line for variable YO constant Ed and v@. All models give essentially the same fit at low coverages. Data were obtained with B = 860”K/sec and 7 = 0.083 sec.

A third cause for the deviation of the flash desorption traces from those prediced by eqs. (3) and (4) is a variation of vb’) with coverage. It was shown previously’) that the rate of molecular desorption of dissociated species, if recombination occurs by surface diffusion, could be written as the frequency of collisions of atoms times the probability of desorption of the pair thus formed. The collision frequency l/z can be estimated assuming a random walk diffusion process using the Einstein relation 7=12/D where 1 is the mean distance an atom must move in recombination, and D is the surface diffusion coefficient. It was then assumed in ref. 1 that Z=n-*, the nearest neighbor distance, to give second order kinetics with vi” = a2vo,

(8)

where a is the jump length, roughly the interatomic spacing, and v,, is the vibrational frequency of the adsorbed atom. Eq. (8) predicts values of vb” which are higher than those predicted by the two-dimensional gas model and in better agreement with experimental values. The mean diffusion distance between collisions should be in-* for low

INTERACTION

OF Nz

WITH

(100)

w

383

coverages. However, as the coverage approaches saturation, rz-* approaches a, and the approximation obviously breaks down. A better approximation is E=n-f-aa,,

(9)

where a, is the minimum separation of an atom pair during collision. This gives a second order pre-exponential factor of 2 (2) v”

= [

1 - ;.;1,

@]” ’

(101

where n has been replaced by the fractional coverage using the relation na2 =B. At low coverages the kinetics should thus be second order with

v$~)=$v,,. However, at high coverages the rate of desorption is no longer proportional to e2 but is increased by the factor [l -(uJu) @I-‘. This is a probable cause of the “variable order” of desorption kinetics for nitrogen on polyc~stalline tungsten discussed by Madey and Yatesis). Fig. 8 shows the theoretical fits to the experimental curve assuming second order desorption with E,,=73.5 kcal mole-’ and the frequency factor given by eq. (10). The value of a2vo=0.2 cm2 moleculesV1 see-’ was obtained from the low coverage pre-exponential in fig. 3, and a,/a was used as an adjustable parameter. It is seen in fig. 8 (and fig. 3) that good agreement is obtained for a,/a=0.99. The flash desorption curve is extremely sensitive to the choice of a,/a at high coverage because vi” approaches infinity as a,/a approaches unity. This suggests that a, is approximately equal to the distance between adsorption sites. If a,/a is chosen as 0.9, the curve is narrowed by only - IO%, the main difference being that the initial rise in the curve begins at a slightly higher temperature. We conclude that either a variable activation energy of desorption or a variable pre-exponential factor will quantitatively explain the desorption kinetics of the B2 state at all coverages. While a variable Ed is a possibiIity we find similar behavior for all atomic states of N, and H, on the single crystal planes of W and MO which have been studied so far while all first order states can always be fit quantitatively using constant values of v0 and It appears likely that Ed is almost constant for all of these states. Electrostatic repulsion of the charged atoms should cause the binding energy to fall with coverage by a fraction of the work function change produced. This will generally be rather small. The attractive interaction between adsorbate atoms which results in the c(2 x 2) structure and probably island formation must be strong enough to overcome the electrostatic repulsion and produce ordered structures stable to - 1200 and -400°K for Bz nitrogen and hydrogen, respectively. That these structures are destroyed

384

L. R. CLAVENNA

AND L. D. SCHMIDT

at these temperatures is shown from LEED intensities and from the fact that desorption occurs with second order kinetics rather than the lower order kinetics which might be expected for direct desorption from ordered structures. This can be regarded as a two-dimensional phase transition between a lattice gas and the ordered structure. The heat of the transition should be an appreciable fraction of the desorption energies, since the above temperatures can be regarded as the critical temperatures for the process. 4.5. CONDENSATION The data of fig. 5 represent sticking coefficients of N, at 300 “K impinging on a (100) W surface at temperatures of 195 “K to 1035 “K. As temperature is increased over this range s,,, the sticking coefficient at zero coverage, decreases in two approximately linear segments with a break at 700°K as shown in fig. 9. The experimentally determined saturation amounts are constant at (2.OkO.07) x 1014 molecules cm-‘, in good agreement with the 2.5 x 1014 molecules cm-’ predicted from the model of fig. 6. The general shape of the curves in fig. 5 is very similar to that for the pz state of hydrogen, and since the states are postulated to occupy the same sites, most of the arguments advanced regarding condensation of hydrogen should apply to nitrogen also. As for hydrogen the constancy of s to high coverages indicates the existence of a precursor state, for which the sticking

TEMPERATURE

Fig. 9.

The initial sticking coefficient SOand the condensation parameter shown as function of crystal temperature for the 82 state.

k of eq. (16)

INTERACTION

OF

Nz

WITH

(loo)

w

385

coefficient is completely independent of the coverage in the fi2 state. This also seems to argue in favor of a chemisorbedprecursor since condensation limited by momentum transfer into a physical adsorbed state should depend sensitively on the mass of the surface species. Jn the present case considerably more precision is possible than was possible with H, because a much wider range of temperatures is accessible and there is only a single final state under conditions where the /?r state is negligible. In the following sections we shall examine models of condensation and compare them with the experimental results in an effort to further elucidate the mechanism. 4.5.1.

Models

Ehrlich 13) developed a model of condensation in which the sticking coefficient is limited by the competition between chemisorption and evaporation from the precursor state. Tamm and Schmidtl) generalized this model in order to compare experimental results for H, adsorption. By their model, condensation of a gas molecule A, via a precursor state is assumed to proceed through the following steps kg(e) s*f A s+A*--A,, k*d

(11)

where k, and k,* are the rate constants for conversion into the tightly bound state A, and desorption from the precursor state A* respectively, and s* is the sticking coefficient in the precursor state A*. The factor g(0) is the probability of finding suitable vacant sites for strong chemisorption : [ 1 - O] for single site adsorption, [ 1 - 01’ for random two site adsorption, etc. This model gives a sticking coefficient which varies with coverage as’)

so[1 + Kl

s=i +-ii/g (e)’

(12)

where so =s*/[ 1 + K] is the sticking coefficient at zero coverage and K= k,*/k,. Kisliuk14) considered a more complex situation in which the precursor migrates from site to site over the surface. Conversion into the strongly bound state for a precursor on a given site is determined by the probabilities (or normalized rate constants) of chemisorption into the nearest vacant site P,, diffusion to another precursor site P,, or desorption P,, if the nearest chemisorption site is empty and Pi if filled. Kisliuk obtained the expressions s*p, [l - 0-j s = Pa + Pb - 8 [Pa + Pb - PJ

(13)

386

L. R. CLAVENNA

for single site chemisorption,

AND

L. D. SCHMIDT

and s*p, [l - tI12

s = Pa + Pb - lq2P,

+ Pb - P;] + e2p,

(14)

for random two-site chemisorption. We include in the above expressions s* which Risliuk assumed to be unity. Kisliuk then wrote these expressions in terms of two constants and attempted to fit the available data for nitrogen on polycrystalline W to them. He concluded that the second expression gave fair agreement but only ifs* was much less than unity. A more readily interpreted form of these expressions is

s=

1+

s* (Pb[l -

e] + q,e>/P&e>

;

this is correct for any g (0) and contains the four parameters explicitly. Two limiting cases of eq. (15) are of interest. If desorption from the precursor is completely independent of the occupation of adjacent chemisorbed sites, then Pb = Pb)and eq. (15) becomes

soCl + kl

’ = 1+ k/g(O)

(16)

where k =PJP, and so = s*/[l + k]. This expression is identical to that obtained by Tamm and Schmidt, eq. (12) with K= k. On the other hand if desorption of the precursor is much more rapid when the adjacen ttightly bound sites are occupied, then Pi $=Pb and eq. (15) becomes SO s =

1 + k’e/g (e)

(17)

where k’ = Pd/P, and so = s*. We note first that for g(0) = [ 1 -S] the models of Tamm and Schmidt and Kisliuk give the same form for s(0). Eqs. (12) and (16) are identical as written, and letting k’ = k/[ 1 + k], it is easy to show that eqs. (14) and (17) are the same. This says that for nondissociative adsorption the successive site and simple competing rates approximations is not so for other forms of g (0). 4.5.2.

give precisely the same s(e). This

Comparison with experimental results

As the coverage approaches saturation, g(S) goes to zero, and the second term in the denominator of the above expressions predominates to give curves in fig. 5 cannot be simply s m g (0). The “tails” on the experimental reconciled with g (0) = [ I- e] since s would approach zero linearly with 8. Therefore, single uncorrelated sites cannot determine chemisorption rates at

INTERACTION

OF

N 2 WITH

(100)

387

w

least at high coverage. However, choosing g(8)= [l -@I” one obtains theoretical curves which agree much better with the observed behavior. Fig. 10 shows the best fits of the experimental data to the two models discussed above, eqs. (16) and (17), taking g (8) = [ 1- t?]’ with s,, k, and k’ used as adjustable parameters. It is seen that while both models give reasonable qualitative agreement, eq. (16) fits the data better in all cases. The successive site model with PL S Pb, predicts values of s which are too high at low coverage and too low at high coverage while the Tamm and Schmidt model agrees almost quantitatively at all coverages and temperatures.

e v,

0.6

Fig. 10. Theoretical fit to the normalized sticking coefficient versus coverage curves for the 8~ state. Points indicate experimental data obtained at the indicated crystal temperatures. Lines indicate theoretical fits. The solid lines correspond to eq. (16) with k chosen to fit the curve at a given temperature, and the dashed lines correspond to eq. (17) with k’ as the adjustable parameter.

Fig. 9 shows a plot of k and se versus temperature. It is evident that, while k increases monotonically with temperature, a definite break occurs at T=700”K. Since k is defined as Pb/Pa, the ratio of the rate constants of desorption and conversion from the precursor state, it should be of the form k

N

exp [ - (E& - E&)/RT]

.

(18)

Fig. 11 shows plots of log k, log sO, and log s* versus l/T. It is seen that two more or less straight line segments are obtained with activation energies of f0.83 kcal mole-l for Tc6OO”K and +3.1 kcal mole-’ for T>6OO”K, and as expected E& > E&.

388

L. R. CLAVENNA

AND

L. D. SCHMIDT

As discussed previously nitrogen in the /!I2 state becomes mobile at - 650”K, and it is reasonable to associate the break in s0 and k at this temperature with a change in the mechanism of condensation when the p state is mobile. The break in s* (and so) is not simply explained in these terms since it is difficult to see how mobility of the pz state should influence the properties of the precursor significantly. This perhaps indicates additional complexities in the condensation process which are not accounted for by the models.

1000 r

I,

400

600 I

300 1

200°K

I

*ca lo-’-

x,o

IO-

-

1

0

1

I

I

I

2

f,,0-33

OK“

I

I

4

5

Fig. 11. Plots of log so, log k, and log s* versus l/T. The quantities k and s* correspond to the model of condensation given by eq. (16) with P ‘b = PD. For the log k versus l/T curve the linear segments give activation energies of + 0.83 kcal mole-l for T< 600°K and + 3.1 kcal mole-l for T> 600°K.

INTERACTION

OF

Nz

WITH

(100)

w

389

It is possible that the y state is the precursor for the /I2 state. Since I!?,,_ for up to the desorption this state is N 10 kcal mole-’ and it is immobile2s) temperature (implying a large value of Edin), the measured activation energy predicted by eq. (18) should be small as observed. However, it is tempting to associate the precursor state on (100) W with the type C sites directly above the outermost W atoms since both the sticking coefficient and desorption rate from this state are observed to be completely independent of the occupation of the pz state as discussed previously. This would not be expected for the y state if it occupies the type B sites.

4.6. COMPARISONWITHPOLYCRYSTALLINETUNGSTEN There are interesting similarities and differences between the behavior of nitrogen on polycrystalline and (100) tungsten. The p2 state on (100) is within the broad group of states identified as the “/I2 state” on polycrystalline tungsten, as is the j3 state or states on (111) W observed by Delchar and Ehrlich4). The initial sticking coefficient for the /Jz state on (100) at room temperature is within the range of measured sticking coefficients on polycrystalline samples, 0.1 to 0.5 5l sl g, 31). The /I1 state on (100) W, however, does not correspond to the state designated as /31 on polycrystalline tungsten. While both states appear to obey first order kinetics, the PI state on (100) W has an activation energy of 49 kcal mole-’ and a sticking coefficient of ~10~~ at 300°K compared to the polycrystalline values of Ed = 73 kcal mole-l found by RigbylO) and s> 10m2 found by Ogurig). Much of the interpretation of the structure for the p2 states on (100) W has also been suggested before in the interpretation of measurements on polycrystalline samples. Thus, an atomic state which at saturation occupies less than the number of surface sites available has been postulated from the kinetics and amount adsorbed. Studies in which nitrogen and hydrogen were coadsorbed indicate that these gases compete for adsorption sitesss~aa~ss); CO, on the other hand, does not appear to occupy the same sites as H2 orN, since the presence of one gas does not exclude adsorption of the other in a simple fashion sap 34). The present measurements permit a much more detailed interpretation than for measurements on polycrystalline surfaces because the kinetics and stoichiometry demonstrate that for moderate exposures above 195 “K only a single B2 state exists. On polycrystalline samples there are many crystal planes in different proportions resulting in a lack of reproducibility; the complexity of these states makes quantitative interpretation of the structure and kinetics impossible.

390

L. R. CLAVENNA

AND

L.D.SCHMlDT

5. Summary From the fairly complete data available on the structure, desorption kinetics, and stoichiometry of nitrogen on (100) tungsten, a model for the adsorbate has been postulated which seems to agree with the experimental results and with what one expects from the electronic structures of the substrate and adsorbate. A more detailed interpretation of the electronic configurations and the nature of the bonding interactions must await measurements of the charges and types of bonding, possibly by electron spectroscopy. Further information on the structures should be obtainable from mixed adsorption studies and more quantitative LEED measurements. Two results of this work which could have important implications in engineering situations are the existence of tightly bound states with sticking coefficients so low that they can only be populated at extremely high exposures or under special conditions and the variation of the second order preexponential factor with coverage. The latter can lead to desorption for high coverages at temperatures several hundred degrees below those expected from the low coverage rate parameters. Condensation into the f12 state can be fit remarkably well over the entire range of coverage and temperature by a model in which the desorption and diffusion rates of a precursor state are independent of the population in the pz state. The parameter k which is the ratio of these rates contains an activation energy which changes at N 600 “K. This seems to indicate that there is a single mechanism operative below and above this temperature and that the break may be associated with the mobility of the adsorbate. The sticking coefficient of the precursor state s* exhibits a slight break at -600°K presumably also connected with the onset of mobility of the p2 state.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15)

P. W. Tamm and L. D. Schmidt, J. Chem. Phys. 51(1969) 5352; 52 (1970) 1150. P. J. Estrup and J. Anderson, J. Chem. Phys. 45 (1966) 2254. P. J. Estrup and J. Anderson, J. Chem. Phys. 46 (1967) 567. T. A. Delchar and G. Ehrlich, J. Chem. Phys. 42 (1965) 2686. G. Ehrlich, J. Phys. Chem. 60 (1956) 1388. T. W. Hickmott and G. Ehrlich, J. Phys. Chem. Solids 5 (1958) 47. P. Kisliuk J. Chem. Phys. 30 (1959) 174. G. Ehrlich, J. Chem. Phys. 34 (1961) 29. T. Oguri, J. Phys. Sot. Japan 18 (1963) 1280; 19 (1964) 83. L. J. Rigby, Can. J. Phys. 43 (1965) 532. J. T. Yates, Jr. and T. E. Madey, J. Chem. Phys. 43 (1965) 1055. T. E. Madey and J. T. Yates, Jr., J. Chem. Phys. 44 (1966) 1675. G. Ehrlich, J. Phys. Chem. 59 (1955) 473. P. Kisliuk, J. Phys. Chem. Solids 5 (1958) 78; 3 (1957) 95. T. E. Madey and J. T. Yates, Jr., Nuovo Cimento Suppl. [I] 5 (1967) 483.

INTERACTION

OF

Nz WITH(100) W

391

16) B. J. Hopkins and S. Usami, in: Pruc. Berkeley Intern. Muter. Conf, 4th, University of California, Berkeley, June 1968 (1969) p. 67-l ; B. J. Hopkins, S. Usami and B. Williams, Vide 139 (1969) 26. 17) A. G. J. van Oostrom, Doctoral Thesis, University of Amsterdam, June 1965. IS) A. A. Holscher, J. Chem. Phys. 41(1964) 579. 19) P. J. Estrup in: Proc. Berkeley Intern. Muter. C’onf, 4th, University of California, Berkeley, June 1968 (1969) p. 19-l. 20) P. A. Redhead, Vacuum 12 (1962) 203; Trans. Faraday Sot. 57 (1961) 641. 21) W. Ermrich, Philips Res. Rept. Suppl. No. 3 (1967); Nuovo Cimento Suppl. [I] 5 (1967) 582. 22) J. T. Yates, Jr. and T. E. Madey, in: Proc. Berkeley Intern. Mater. ConJ, 4th, University of California, Berkeley, June 1968 (1969) p. 19-l. 23) G. Ehrlich and T. G. Hudda, J. Chem. Phys. 35 (1961) 1421. 24) V. J. Mimeault and R. S. Hansen, J. Phys. Chem. 70 (1966) 3001. 25) P. J. Estrup and J. Anderson, J. Chem. Phys. 49 (1968) 523. 26) K. Matsushita and R. S. Hansen, J. Chem. Phys. 51(1969) 472. 27) J. W. May, R. J. Szostak and L. H. Germer, Surface Sci. 15 (1969) 37. 28) J. H. Singleton, J. Vacuum Sci. Technol. 5 (1968) 109. 29) D. W. Bassett, Proc. Roy. Sot. (London) A 286 (1965) 191. 30) G. Ehrlich and F. G. Hudda, J. Chem. Phys. 36 (1962) 3233. 31) J. A. Becker and C. D. Hartman, J. Phys. Chem. 57 (1953) 157. 32) J. T. Yates, Jr. and T. E. Madey, private communication. 33) L. J. Rigby, Can. J. Phys. 43 (1965) 1020. 34) L. J. Rigby, Can. J. Phys. 42 (1964) 1256.