Adsorption studies in the field ion microscope with argon imaging

SURFACE

SCIENCE 26 (1971) 197-229 0 North-Holland

ADSORPTION

STUDIES

MICROSCOPE

WITH

Publishi~

IN THE FIELD ARGON

Co.

ION

IMAGING

R. T. LEWIS*+* and R. GOMER James Franck Institute and department of Chemistry, ~~~vers~~~o_fChicago, Chicago, Illinois 60637, U.S.A. Received 20 October 1970 The adsorption of oxygen, CO, CH4 and H2 on tungsten has been investigated by means of Ar ion microscopy, with the aid of an internal channel plate multiplier. The results indicate that CO, H, and probably 0 are not themselves visible in Ar imaging, while CH4 may be under some conditions. CO adsorption at 78% and 300°K does not seem to cause surface reconstruction. However in the presence of Ar, field induced corrosion sets in at F>2.0 V/A and becomes rapid at 3 V/A, where it causes considerable surface disorder. In the case of CH4 corrosion also occurs at < 3 V/A in the presence of Ar. Oxygen at 78°K and small coverages seem to cause little reconstruction if any; rather the visibility of substrate atoms becomes modified. For coverages close to a monolayer the image contrast vanishes almost totally so that it is difficult to draw unequivocal conclusions. There is some evidence that W-O complexes form and stick out above the surface, but this seems to be the exception rather than the rule. Field desorption in the presence of Ar sets in at 2.6 V]A and leads to desorption of W as well as of 0 atoms. In all cases the (110) plane exhibits unusual stability and seems unreconstructed in adsorption and only slightly affected by corrosion; it is not possible to see whether changes occur which leave this surface very densely packed, and hence are unresolved, but gross reconstruction and disorder on (110) can be ruled out by the present experiments. HZ is invisible in Ar imaging and does not affect the surface in any noticeable way.

1. Introduction In recent years much attention has been devoted to the problem of reconstruction in chemisorption, that is to the re-arrangement of the substrate during the adsorption act or on subsequent heating, to form thermodynamically stabler structures with the adsorbate. Much of the original impetus for this work has come from LEED experimentsl). It was at first believed that the appearance of new structures, at least in the case of light adsorbates like H was prima facie evidence for reconstruction. It now appears * American Vacuum Society Predoctoral Fellow 1969-70. t Present address: Parma Technical Center, Union Carbide Corporation, Parma ,Ohio 44129, U.S.A. * In partial fulfXment of the requirements for the Ph. D. degree at the University of Chicago. 197

198

R. T. LEWIS

AND

R. GOMER

however that even H is able to scatter electrons effectively”) because of the importance of multiple scattering3), and that in any case the interpretation of LEED patterns is considerably more complicated and equivocal than at first hoped. To cite only one example, Germer and Mayl) interpreted their LEED results for 0 on the (110) plane of W as reconstruction of the surface to give a mixed oxygen-tungsten surface layer. Tracy and Blakely”) interpreted the same LEED patterns in terms of 0 atoms adsorbed on an essentially undisturbed substrate lattice. Thus, while LEED may reveal reconstruction in some cases, the evidence is often equivocal, and other methods of investigating this problem would clearly be desirable. Since the field ion microscope (FLM)“) is able to reveal substrate structure with essentially atomic resolution, it would appear to be a natural candidate for the job, and in fact considerable effort has gone into attempts to study adsorption and surface reconstruction in this way. Ehrlich6) studied CO and Nz adsorbed on tungsten emitters, using He as imaging gas and concluded that the resulting extra spots corresponded to images of the adsorbates. On the other hand Holscher and Sachtler7) concluded that at the fields required for imaging with He all or most of the adsorbate had been field desorbed and that the extra spots corresponded to displaced W atoms. They also found that a perfect surface could be reattained only by desorbing several atom layers of tungsten, and interpreted their results to mean that the adsorption act itself caused the disorder observed. Miillers) had shown earlier that oxygen was field desorbed in vacua near the W desorption field, 5.7 V/A, but that in the presence of He oxygen could be removed completely at 4.5 V/Ag). From an examination of the disordered patterns after field desorption he concluded that this removed some metal as well as oxygen atoms; this has recently been confirmed in some of his atom probe experiments lo), which show tungsten-oxygen molecular ions among the desorption products. The effect of image gases on oxygen field desorption was also studied by Bassettrr), who conluded that He, Ne and Ar lowered the desorption field by 12, I7 and 32% respectively. Similar results for a number of other adsorbates were also reached by Bell, Swanson and Reedr2), and earlier for H,, CO, N,, and 0, on W by Ehrlichra), who also showed that hydrogen adsorption did not cause rearrangement of tungsten. More recently Brenner and McKinneyr”) investigated CO and N2 adsorption on W with the atom probe, using Ne as imaging gas and concluded that these adsorbates could not be imaged with Ne, the extra spots seen being tungsten atoms. Thus it appears that the high fields required for He or Ne imaging and/or the presence of the image gas in combination with the field profoundly affect adsorption systems and make unequivocal interpretations of the zero field situation difficult if not impossible in many cases. The problem is

ADSORPTIONSTUDIESINFIMWITH

essentially

two-fold.

Ar

IMAGING

First there now seems little doubt

199

that most adsorbates

are field-desorbed below He or Ne viewing fields. Second, there is at least the strong suggestion that much of the disorder seen after field desorption of the adsorbate is the result not of adsorption but of the desorption act itself. An obvious way out of the difficulty would be the use of inert image gases requiring lower viewing fields, i.e., having lower ionization potentials, since Z*/F is roughly constants,ls). The principal difficulty here is that the conversion efficiency of ion energy into photons decreases very rapidly with increasing ion mass, most of the energy going into phonons, so that even external image intensifiers are almost useless for Ar imaging, particularly for sharp tips requiring low voltages. The recent release of channel plates on the open market has removed this difficulty since the ion/electron conversion efficiency is not a sensitive function of ion mass. The utilization of channel plates as internal image intensifiers in the FIM is relatively simple and has recently been described in the literature by Southon and Van Oostrom and coworkers16), and by the present authorsl’). Very briefly, channel plates consist of arrays of micro-channeltron electron multipliers. Ions entering a given channel create secondary electrons, which are multiplied and drawn off to a fluorescent screen at the output end of the same channel by an applied voltage. Thus an image point is created on the screen in a location corresponding uniquely to that of the ion impact. The ion image is thus converted to an electron image, with the following advantages : The sensitivity of phosphors is inherently much higher for electrons than ions; electrons do not cause phosphor damage; and finally the gain of the channels is of the order of IO3 or higher. Thus the overall gain in image intensity becomes very great, with no loss in resolution if the tip to channel plate spacing is properly chosen. The present work describes an attempt to exploit Ar imaging for a study of oxygen, CO and CH, adsorption on tungsten. We have recently learned that a somewhat similar study has been carried out by Van Oostromls). 2. Experimental The microscope tube, shown in fig. 1 consisted of a cylindrical Pyrex envelope mounted vertically, closed at the lower end by a flat window and necked down at the upper end to hold the tip assembly. The body of the tube and the window were made conducting with two tin oxide coatings, separated by a gap of - 1 cm to prevent discharges. The window was then coated with willemite. The channel plate, mounted between stainless steel rings was next sealed into position -I mm above the fluorescent screen by cracking open the body of the tube at S in fig. 1 and then resealing it. Three symmetrically spaced stainless steel rods were screwed into the lower

200

R.T.LEWIS

AND

R.GOMER

and one into the upper ring to provide mechanical support and electrical contact. Electrical insulation between the upper ring and the supports leading to the lower was insured by glass spacers. Firm seating of the plate was achieved by means of stainless steel springs on the support rods screwed into the bottom ring, pushing on the top ring via glass spacers, as shown in the inset of fig. 1. A cylindrical grid of fine Pt wire was mounted on the upper support ring to shield the ion beam from the support rods leading to the output end of the channel plate, which were at a different potential. This was found necessary to prevent image distortion at low tip voltages.

J-

B Fig. 1. Schematic diagram of ion microscope tube with channel plate intensifier. (A) Tin oxide conductive coating. (B) Fluorescent screen. (C) Tungsten support rods. (D) Stainless steel fasteners. (E) Stainless steel support rods. (F) Pt foil cold finger shield. (G) Emitter assembly. (H) Electrical connection to shield. (I) Channel plate. (J) Pt wire grid assembly. (K) Detailed drawing showing method of mounting channel plate. (L) Cylindrical glass spacers. (M) Stainless steel springs. (N) Stainless steel collar and set screw. (0) Stainless steel support rings. (S) Envelope cracked open and resealed at this point.

Two channel plates were used, generously provided by the Rauland Division of Zenith Corporation; both were 1.70 in. in diameter and 0.130 in. and 0.10 in. thick respectively. The channel diameters were 0.0075 cm and the channel to channel spacing was 0.0125 cm in both cases. The resistance between the two ends of the plate was 9.5 x 10’ ohm for the first plate, and 4.4 x 10’ ohm for the second. The resistance of the first plate rose irreversibly to > 1O1’ ohm after accidental bake-out at 350°C. The tip assembly shown in fig. 1 was more less or conventional, and included potential leads for temperature measurement. A shield around the

ADSORPTION

cold finger at channel

STUDIES

IN FIM WITH

plate input potential

Ar

201

IMAGING

served to eliminate

field emission

and to cool the gas supply5). The tip to channel plate distance was adjusted to make each image point cover several channels. In practice this corresponded to 4-5 cm. This point will be discussed further later on. In operation the input end of the channel plate was run at ground, the output end at + 800 to +2000 V; the screen at +3000 to + 5000 V; and the tip at + 3 to + 15 kV. The tube was attached to a bakeable glass vacuum system shown schematically in fig. 2. This consisted of the FIM tube, a small field emission monitor tube, a Ta getter pump and a Bayard-Alpert ion gauge. The system could be isolated from the oil diffusion pump by means of a magnetically operated sliding glass valve. Adsorbates and image gases were admitted through Granville-Phillips variable leaks; for the image gases

To Diffusion *and Roughmg Pumps

w

Fig. 2. Schematic diagram of vacuum line. (FIM) Field ion microscope. (FEMT) Tungsten field emission monitor tube. (GP) Ta film getter pump. (IG) Bayert-Alpert ionization gauge, WL 5966. (VL) Granville-Phillips Variable Leak Valves. (SG) Sliding glass valve. (GPL) Granville-Phillips Type C metal valve. (CGT) Copper foil filled glass trap. (Ar) Argon storage bulb with Ta getter.

an additional Granville-Phillips Type C valve, supplied with an auxiliary bake-out oven was used to obviate replacement of the image gas supply for every bake-out. Ar was purified by storing in bulbs equipped with break-off valves at a pressure of several torr over a Ta getter film prepared in situ just before loading on a greaseless bakeable ultrahigh vacuum line. Oxygen was obtained from the decomposition of copper oxide, prepared by oxidation of outgassed Cu wires in a small electrically heatable Pt crucible, contained in a bulb equipped with a break-off and a seal off. After thorough bake-out on a separate high vacuum line and heating of the metal parts, the source was heated for six hours or longer in 200 torr of 0,. After pumpout to a pressure of < 10m7 torr the source was heated gently, and the bulb sealed off. The source was then heated to fill the bulb with N 1 torr of 0,. Airco Analytical Reagent Grade CO and CH, were transferred without further purification into break-off equipped flasks at pressures of l-3 torr.

202

R.T.LEWlS

AND

R.GOMER

The general procedure was the following. After an initial pump down and leak check, the main system was baked for 8-12 hr at 250°C with heating tapes wrapped around the external tubing, and with the auxiliary oven on the Ar introduction system at 3OO”C, if a fresh flask was used. After cooling to room temperature, the residual pressure was 2-4 x IO-’ Torr, and consisted mostly of carbon monoxide and hydrogen, judged by the field emission patterns and desorption temperatures on the tip in the monitor tube. After extensive outgassing of the 0.015 in. diameter Ta wires in the getter bulb and the ion gauge, the system was baked again at 250°C for 8-12 hr. After cooling to room temperature, the getter filament and ion gauge were outgassed again for several hours. The getter film was then deposited by evaporating Ta with the getter bulb immersed in liquid N,. After deposition the pressure was 2-4 x IO- lo Torr, and the residual gas was mostly H, judged by the desorption temperature (600°K) from the monitor tip. If the sliding glass valve was closed, the ion gauge reading slowly increased with time, but the monitor tip did not show any appreciable increase in contamination rate, indicating that some helium was diffusing through the glass walls. After closing the glass valve, and cooling the getter trap with liquid nitrogen, argon was introduced to the desired pressure (usually i-4 x 1O-4 torr), and the ion gauge turned off. The FIM tip was heated to about 1000°K to remove gross contamination, and then liquid nitrogen was introduced into the cold finger. The tip was field evaporated by alternately raising the voltage to progressively higher values, and then lowering it to examine the ion image. This painstaking process had to be performed with small stepwise increases in evaporation voltage, since the argon image is blurred completely at the W desorption field. Once the voltage necessary to obtain a clean field evaporated surface was determined, subsequent field evaporation was easily performed. For adsorption studies the voltages to the tip and channel plate were then turned off, and the gas under study introduced by opening the inlet valve for a prescribed time. In principle, the pressure of adsorbing gas should be rapidly reduced to negligible values by the high pumping speed of the getter. In practice, there was some adsorption on the cold finger shield, followed by slow re-evaporation. Some of the gases studied apparently also had long retention times on the glass walls which reduced the effective pumping speed of the getter. It was found that operation of the channel plate led to gas release, and thus to some contamination. This could be verified by using the FIM tip as an electron emitter in vacuum, and conforms to the experience of other workers. The gas released has been reported by Van Oostromrg) to have

ADSORPTION

STUDIES

IN FIM WITH

Ar IMAGING

203

mass 16. From its behavior in the FIM it is clearly not oxygen, but seems to be CH,. Gas evolution could be decreased by bake-out at 350°C but this led to an irreversible increase in plate resistance. Electron bombardment or prolonged operation at high gain did not seem to decrease gas evolution markedly. Contamination was held within acceptable limits by reducing to an absolute minimum the on-time of the plate and operating it at the lowest gain compatible with successful photography. Images were photographed after reflection from a first surface mirror positioned at 45” to the screen, with a Canon FX camera equipped with a f: 1.2, 50 mm focal length objective. Camera and mirror were mounted in fixed position on a metal base plate which could be accurately positioned relative to the FIM screen after bakeout. Most photographs were taken on Tri-X film at f: 1.2, with exposures of 30 set, to minimize multiplier gain. Development was carried out in Kodak Microdiol for 12-15 min. 3. Results and discussion 3.1. IMAGINGOF

CLEAN

SURF.~CES

The theoretical limit on the resolution of a channel plate is given by the channel-to-channel distance, a,, in our case 0.0125 cm. In order to insure that this limit does not interfere with the inherent resolution of the microscope, 6, it is necessary that the separation on the channel plate between resolvable points exceed 6,, or that 6, < x6//3-,

(1)

where x is the tip to channel plate distance, Y, the tip radius and fl the image compression factori5), usually - 1.5. Preliminary experiments with very large tip-plate separations, x= 8-10 cm, indicated the inherent resolution of Ar imaging at 78 “K to be 6 = 4-5 A for tips with rt E 350 A. Consequently it sufficed to make x=4-5 cm to insure that each image dot encompassed several channels. The resultant overall resolution, was thus not limited by the plate, even for He images of sharp tips at 20°K as shown by fig. 3. Some experimentation showed that Ar imaging was possible only over a very narrow range of temperature near 78 “K. At higher T resolution became poor because of the excessive transverse velocity of Ar ions, while at lower temperatures a thick layer of Ar seemed to form, also leading to almost total loss of resolution. Fig. 4 shows an Ar ion image at 78”K, at a field of 2.0 V/A, based on a He best image field (BIF) of 4.5 V/A. The average radius of curvature of this tip, in the vicinity of the (110) plane, was - 350 A, as determined from Miiller’s formulas) rt = 16n,

(2)

204

R. T. LEWIS

(a)

AND R. GOMER

6)

Fig. 3. Helium images at 78 and 21 “K. (a) 78”K, BIV = 5.4 kV; He pressure * 7 x 10-4 Tri-X exposed for 4 set at f‘: 1.2. (b) 21 “K, BIV = 5.3 kV; He pressure = 6 x 1O-4 Torr; Tri-X exposed for + set at f: I .2.

Torr;

where n is the number of rings between the (I 10) and the (211) planes. The resolution is -4.5 A, since the (111) plane can just be resolved. Thisvalue is in good agreement with Miiller’s semi-empirical estimate”) of 6 for Ar at this temperature. The overall image quality for Ar is somewhat poorer than for He, partly because the lower ionization voltage increases the transverse displacement, partly because the ionization disk is larger, and in part because BlVs seemed to vary more strongly over different regions of the image than with He, particularly for sharp tips, making it hard to get optimal image quality over the entire imate at one voltage. This inhomogeniety may be a consequence of the higher polarizability of Ar, which would tend to draw hopping atoms to the regions of highest local field, i.e. highest local curvature, like (111) or (41 I). The effect would be more pronounced for small emitters than for large ones, since there would be a higher probability in the latter case of ionization before reaching the high field regions. It is interesting that consecutive experiments in He and Ar showed the tungsten evaporation field to be 1.04 times higher in Ar than in He. This would at first seem surprising since Nishikawa and MiillerzU) concluded that at 20°K He and Ne lowered the vacuum evaporation field by 1.3% and IO”/, respectively, while at 78°K He had no effect. However, Van OostromlQ), and Brenner and McKinney21) have recently reported that He does reduce the field even at 78 “K, so that our result can be understood if it postulated that the Ar evaporation field under dc conditions is effectively the vacuum field. This is further confirmed by recent atom probe experiments

ADSORPTION

Fig. 4.

STUDIES

IN FIM WITH

205

Argon image of clean surface after field evaporation at 9.55 kV. Imaged at 3.4 kV in 3-5 x 10m4Torr argon. rt = 30&350 A.

TABLE

Critical desorption

Ar Ne He

L&I IMAGING

15.7 21.5 24.5

1

fields and distances for He, Ne and Ar

2.5 5.0 > 5.4

4.5 3.4 3.7

3.3 2.7 2.5

1.2 0.7 1.2

Z ionization potential; F highest field at which gas is still field adsorbed (from data of ref. 22); xc critical distance calculated from F and eq. (3), assuming 4 =4.5 eV; rw = 1.4 A atomic radius of W; ra Van der Waal’s radius of gas; 3, i = .xc- (u, + rw) is a screening Iength.

206

R.T.LEWIS

AND R.GOMER

Fig. Sa

Fig. 5b

ADSORPTION

Fig. 5. Argon images light oxygen coverage field desorption of (b) are present

STUDIES

IN FIM WITH

Ar

IMAGING

207

after light oxygen coverage. (a) Clean tip, BIV =: 3.3 kV. (b) After on (a), BIV = 3.3 kV; arrows point to extra image dots. (c) After at 2.6 V/A, imaged at 3.3 kV; arrows point to image dots which in (a), have disappeared in (b) and re-appeared in (c).

of Miillerss) who found field induced adsorption of inert gases, as shown in table 1. At the W evaporation field Ar is definitely absent while He is present. In a more recent set of experiments Mtiller applied a dc holding field sufficient to adsorb but not to field desorb At-, and then pulsed to cause W desorption. In this way he was able to show that adsorbed Ar lowered the W evaporation field by 20%. This confirms that under the conditions of our experiment the Ar field is effectively the vacuum field. The upper limit of the holding field i.e., that causing field desorption should be roughly given by the well-known critical distance relationss,s) X, r (I - #)/Fe,

(3)

where I and 4 are the ionization potential of the adsorbate and work function of the substrate respectively, and X, the minimum distance of the adsorbate nucleus from the surface of electroneutrality. In the present case, if desorptionis not to occur, xc>ra+rW+A,

(4)

208

R. T. LEWIS

AND R. GOMER

where Y, and rw are the Van der Waals radius of the adsorbate and the radius of tungsten respectively, if it is assumed that the surface of electroneutrality at zero field passes through the centers of the surface tungsten atoms. L is a screening length, which allows for field penetration into the metal. The values of I. required for agreement between the values of X, calculated from eq. (3) Miiller’s F valuesz2), and those based on eq. (4) are listed in table 1. The agreement is good for Ar and He, although A seems high. The value for Ne is somewhat more in line with theoretical estimates24), although these are not very precise. The reason for the discrepancy between the Ne and the He and Ar values could be rationalized in several ways, but this is outside the scope of this paper. The main point, for present purposes, is that there is almost certainly a field-induced layer of Ar on the surface at the Ar viewing field, at least in the absence of adsorbates. 3.2. OXYGEN ADSORPTION The changes produced by adsorption of small amounts of oxygen are shown in figs. 5a and 5b. In this case 0, was admitted with the viewing field on, so that exposure could be monitored easily. (This was difficult with the variable leak alone for small exposures.) Images obtained after zero field adsorption showed no significant differences, except somewhat higher coverages, presumably because of the absence of field ionization of 0, in the gas phase. In fig. 5b, a number of new image points is visible, while some old ones have disappeared, and in addition the intensity of some original dots is increased. These intensity changes are particularly visible on the rings of atoms surrounding the (110) plane. Most of the changes noticeable in fig. 5b occur on regions other than low index planes, although their edges do change. At slightly higher coverages changes can be seen in the interior of the (211) and (11 I) planes; image dots in the (1 IO) plane were seen only once out of -50 adsorption sequences. At low coverages this result could be due to the relatively low sticking coefficient of O2 on (110) 25) and the fact that oxygen can probably skate out of the small (I IO) plane of a tip. There is evidence from field emission work that this occurs at tip temperatures of N lOO”K, even with cold gas26). It will presently be shown that even at high oxygen coverages no image dots appear in (110) before the surface is subjected to some desorption. Fig. 5c shows the image obtained after raising the field for 60 sec. to 2.6 V/A, where Ar promoted field desorption of 0 begins to occur, in agreement with the results of Bassettll). Some image points removed or dimmed by adsorption have now reappeared, while some dots created by adsorption have disappeared. The present results do not allow us to decide whether the extra image

ADSORPTION

STLJLMES IN FIM m

Ar

209

IMAGING

(a)

(b)

Cc)

(4

Fig. 6. Field dependence of image after moderate oxygen coverage. (a) Clean tip, BIV = 2.2 kV. (b) Same tip after oxygen adsorption, imaged at 2.16 kV; hexagonal structures are inherent in the channel plate under uniform ion illumination; they are due to the method of channel plate manufacture. (c) Same tip, imaged at 1.77 kV; arc in image is the result of scattering from the cold finger shield or walls because of the very low image voltage. (d) Same tip, imaged at 1.94 kV.

points caused by 0 adsorption are images of 0 atoms; of O-W complexes; of undisplaced W atoms whose visibility is enhanced by adjacent 0 atoms; or of displaced W atoms. The relatively small number of new dots suggests however that 0 is not visible per se; even if the extra dots were the result of physical rearrangement of the surface, their relatively small number suggests that such reconstruction is the exception rather than the rule, and certainly does not occur on (110) at 77 “K. Since “mild” field desorption restores many

210

R.T.LEWIS

AND

R.GOMER

Fig. 7a

Fig. lb

Fig. 7c Fig. 7. Argon images after field desorption of a heavy oxygen dose. (a) C&m tip, BIV ==3.32 kV. (bf After adsorption of a heavy dose and %efd desorption at 2.7 VjA for 1 min, imaged at 3.2 kV. fc) After further field desorption at 3.3 V/A for 1 min, imaged at 3.3 kV.

of the original dots it appears that at least in certain lattice positions 0 atoms deenhance the visibility of W atoms, but can be desorbed without removal of these adjacent W atoms. Images obtained after adsorption of larger doses at 78°K and zero field are shown in fig. 6. These doses corresponded to 4 changes on the monitor tip of 0.6-1.2 eV, i.e. to 0.3-0.6 monolayers of oxygen. At the Ar BIV for the clean surface the image is almost completeIy blurred, as shown in fig. Sb, The degree of blurring increases with coverage, i.e., the higher B, the smaller the number of individual image dots. As the field is reduced, a rather small number of quite Iarge image dots appears as shown in figs. 6c and 6d. No dots were ever observed in the (I 10) plane. For F<2 V/.4 the field did not affect the stability of the image points. The image points seen in figs. 6b and 6c are almost certainly due to protruding, or otherwise abnormal W-O complexes representing uncharacteristic, rather than characteristic configurations. Thus, even for 8=0.3 to 0.6 there may not be a great deal of reconstruction at 77°K anywhere and none on the (110) plane.

212

R.T.

LEWIS

AND R. GOMER

The progress of field desorption from a surface covered with a large 0 dose at 78 “K and zero field is shown in fig. 7. The image immediately after adsorption is similar to that of fig. 6b and is not shown. Field desorption at 2.7 V/A restores contrast and makes it possible to image at the original BIV. The surface now is considerably disordered, and contains many out of place atoms. Further desorption at 3.9 Vjl$ removes only some of these. According to Bassett’s 11) results Ar promoted desorption at 3.5 V/A removes virtually all 0 so that the image of fig. 7c represents that of a disordered W surface. This could be confirmed by further field desorption, which required the removal of several atoms layers at 5.7 V/A before a perfect W surface was restored. It is noteworthy that the central (110) plane in fig. 7c is smaller than in fig. 7a, but otherwise unchanged, indicating the removal of W atoms from its edge, but not its center. Occasionally one or two image points could be seen in the central (110) plane after desorption, indicating either that some disorder occurred there during desorption, or that something had diffused into it. Some evidence for the latter hypothesis was found in CO adsorption, and will be discussed later. Figs. 7b and 7c indicate that the other low index planes are completely disordered after field desorption. Because of the loss of contrast after adsorption and before field desorption, the present experiments cannot determine conclusively whether the disorder seen after field desorption resulted from adsorption alone, from desorption alone, or from a combination of both. It has already been pointed out that the small number of image points seen at low F before field desorption suggests that adsorption per se causes relatively little disorder. This does not exclude highly ordered reconstruction in which all image contrast is somehow lost. In any case the results of field desorption show that a disordered W surface does image with normal contrast at normal BIV, so that the loss of contrast is due to 0 adsorption rather than to disorder per se. At high oxygen coverages some of the large, very bright image dots were affected by the field even below 2 V/A. As F was increased, movement and disappearance of some image points was seen, usually below 1.5 V/A. Figs. 8a and 8b show the irreversible change of a quadruplet to a doublet at 1.7 V/A. Similar results could be seen repeatedly after heavy oxygen exposure. At high coverages reversible field effects also occurred. A large elliptical dot is shown at 1.6 V/A in fig. 9a, split into a doublet at 1.75 V/A. (fig. 9b). If the field was reduced to 1.6 V/A the dot returned to a singlet after 3-10 sec. The process was reversible over at least 50 cycles, and still occurred when the field was reduced to zero and then raised again. These phenomena probably correspond to changes in the configuration of W-O complexes, whose stability depends on the field. Some heating sequences were also performed. To prevent contamination

ADSORPTION

STUDIES

W FIM WITH

Ar

IMAGING

213

(b) Fig .8. Field-induced irreversible changes in image dots after heavy oxygen dose. (a) Tip as in fig. 6 after cleaning by field evaporation of a few layers of W, follow ed by hea vy oxygen dose. Large entity at the top of photograph is barely resolvable into3 four brig:ht dots; imaged at 1.7 V/J%. (b) Entity shown in (a) has spontaneously and icreve :rsibly changed to doublet ; imaged at 1.7 V/k.

214

R.T.LEWIS

AND

R.GOMER

Fig. 9. Field-induced reversible changes at high coverage. (a) Large elliptical dot in top of photograph; imaged at 1.6 V/A. (b) Same entity, split into doublet after raisir lg field to I .7 V/A (photographed at 1.6 VIA, just before spontaneous reversion to s inglet).

ADSORPTION

STUDlEs

IN FIM WITH

Ar

215

IMAGIXG

(a)

(cl

(4

Fig. 10. Images after moderate oxygen exposure and heating to various temperatures. (a) Image of clean tungsten tip, BIV = 3.1 kV. (b) After adsorption of a moderate dose on (a) at 78°K; imaged at 2.82 kV. (c) After heating (b) to 200°K for 1 min; imaged at 2.77 kV. (d) After heating (c) to 300°K for 1 min; imaged at 2.83 kV.

from the shank, emitters were heated to 1000°K before field desorption. Blanks were then made by heating the clean field desorbed emitters to 300°K; the experiment was carried on only if the image after heating differed negligibly from the original. Adsorption was allowed to occur only at zero field, to prevent higher coverages on the shank, where the field is lower, since this might have led to subsequent diffusion into the visible region. It was therefore somewhat difficult to control dose size accurately; experiments were confined to moderate or high coverages. The results of

216

R. T. LEWIS

AND R. COMER

Fig. Ila

Fig. ilb

heati Chat cons least aton

ing after adsorption to moderate coverage at 78°K are shown in fig. 10. lges began to occur at 200°K and, were extensive at 300°K; t:hey isted mostly of the removal of large image dots and reemergence ‘, at in part, of the W lattice structure. This can be seen fairly clearly for the 1 rings around the (1 to) plane in fig. 11. Adsorption at 78 “K destr -0p

ADSORPTION STUDIES INFIMWITH

Ar

IMAGING

217

Fig. llc Fig. 11, Oxygen behavior around the (110) plane. (a) Image of the (110) plane, clean tip, 3.45 kV. (b) After adsorption of a heavy dose on (a) at 78”K, 3.31 kV. (c) After heating (b) to 300°K for 1 min, 3.31 kV.

almost all contrast, while heating to 200°K restores enough of the original image dots seen on the clean surface to define these atom rings. It is interesting to note again that no changes are visible in the (110) plane proper, either during adsorption or heating. The changes observed at 200-300°K on the plane edges around (110) can most easily be understood as removal of some 0 atoms by diffusion to more tightly binding sites. Engel and Gomer 2s) observed diffusion into the (110) plane of a thermally annealed tip only at T2 400 “K. It is known however that thermally annealed emitters have considerably higher step heights around the (110) plane, so that diffusion into (110) on such a tip might require more activation energy and hence higher T than diffusion down the monatomic steps of a field evaporated tip. The changes observed in the atomically rougher regions must correspond to local rearrangement of 0 and possibly W atoms, i.e. incipient reconstruction. Some experiments were also performed on thermally annealed emitters (fig. 1:2). Adsorption of large doses of oxygen at 78 “K led to far less blurring than with field evaporated emitters (fig. 12b) probably because already protruding atoms are predominantly imaged. However, considerable displacement of image dots occurs. In addition the (111) region now contains a much larger number of image points. It is most likely that these correspond to enhanced visibility of W atoms, rather than to 0 images, since a change

218

R.T.LEWIS

AND

R.GOMER

Fig. 12a

Fig. 12b

ADSORPTION

STUDIES

IN FIM WITH

Fig. 12~

Fig. 12d

Ar

IMAGING

219

220

R.T.LEWB

AND R.GOMER

Fig. 12e

Fig. 12f

ADSORPTION

STUDIES

IN FIM WITH

Ar

IMAGING

221

in viewing field on the clean surface produces a similar increase. It is quite possible however that the new dots in (111) are the result of reconstruction. Heating to 300°K (fig. 12d) produced relatively few changes; this is consistent with the discussion of the preceding paragraph. Heating to 1000 “K produced some buildup in (11 l), requiring a reduction in BIV (fig. 12e). It is interesting that increasing the voltage to the original BIV led to almost complete blurring in this region (fig. 12f). 3.3. CARBON

MONOXIDE ADSORPTION

The adsorption of CO on W has been extensively studied by many techniques 27, 28). Three adsorption states seem to occur on all crystal planes investigated: a virgin state, formed at 20-100°K; one or more beta states formed by thermal conversion from the virgin state at -300°K; there is some evidence for complexity and possible reconstruction at 500-900°K of the beta layer 27). Readsorption on beta layers creates electropositive alpha-states. The present experiments at 78°K therefore refer to a virgin layer, while experiments at 300°K involved low temperature beta layers. Since the field desorbed W surface reverts to a thermally disordered one at 700”K, it was not possible to investigate phenomena in the beta layer at high temperatures on field evaporated tips. Unlike oxygen, CO was not rapidly pumped by the getter, presumably because of partial retention by the cold surfaces and glass walls in the system. This could be shown by field evaporating tips after introduction of CO and then noting image changes. Thus coverage increased slowly with time during experiments; it will be seen that this did not affect the conclusions significantly. In heating sequences the same precautions as in the oxygen experiments were taken. Visual observation of the pattern after adsorption at 78°K at zero field to a coverage of 8=0.3-0.6 (determined from work function changes of 0.3-0.5 eV on the monitor under comparable exposures), indicated virtually no changes from the clean image. Soon after the viewing field was applied extra spots appeared, moved on the surface, oscillated in intensity, sometimes disappeared, and in some cases became stable with time. Fig. 13b, a 30 set time exposure, is an averaged representation of these phenomena. Even so it shows relatively little changes from the clean image, fig. 13a. It

Fig. 12. Heating sequence for oxygen adsorption on thermally annealed tip. (a) Clean tip, after flashing to - 2000°K; 11.9 kV. (b) After exposure to heavy 02 dose at 78°K; note image points in (111); 11.9 kV. (c) After heating to 300°K for 30 set, 11.9 kV. (d) Tip of (c) imaged at 10.5 kV; note decrease in image points in (Ill). (e) After heating to 1000°K for 30 set; 9.28 kV. (f) Emitter of(e) imaged at 11.9 kV.

222

R.T.LEWlS

AND R.GOMER

(a)

(b)

(cl

(4

Fig. 13. Images after carbon monoxide adsorption and heating. (a) Clean emitter, 2.62 kV. (b) After carbon monoxide adsorption on (a) at 78°K; 2.62 kV. (c) Image after carbon monoxide adsorption on (a) and field desorption at 2.8 V/A for 1 min; imaged at 2.0 V/A. (d) After heating (b) to 300°K for 30 set; 2.62 kV.

must therefore be concluded that such changes as occur at 78°K are due to field-corrosion. It could be shown that the rate of corrosion increased with increasing coverage, and at constant 8 with time, provided the field was on. In the absence of applied field no changes occurred, until the field was turned on. This indicates that the effects are not simply due to slow increases in coverage with time. Corrosion rates seemed roughly uniform over the surface except for the (110) plane, which was changed somewhat less rapidly. Fig. 13~ shows an image of the emitter used in fig. 13a after adsorption

ADSOR~IONST~DIES~NFI~

at

78 “K followed

WITH Ar IMAGING

223

by raising the field to 2.8 V/A. Here the surface is corroded

and image dots are visible on the (110) plane. In general exposure to fields of 2.8-3.0 V/A led to complete disorder and loss of the original symmetry of the image. The fact that increases in field have these effects proves incidentally that CO was present on the surface but caused only minor changes at 2 V/A. Heating of a 78°K layer to 300°K produced very few changes as shown in fig. 13d. The (110) plane is undisturbed, except at the edges, and no image dots appear on it. Similar results were obtained for adsorption directly at 300°K. It must be concluded from these results (a) that CO is not visible in Ar ion imaging; (b) that adsorption at 78°K or 300°K causes no reconstruction per se; and (c) that field desorption does lead to corrosion and some restructuring of the surface. In addition it appears that there are field induced changes even below onset of desorption, namely displacement of W atoms. It is probable that the mechanism suggested by Brenner and McKinneyi”), who observed the same phenomenon in Ne ion microscopy applies here: Under the influence of the field and Ar, some W-CO complexes become mobile, move to new sites and eventually decompose, thus leaving displaced W atoms as the extra image points. It is not certain whether all of the extra image points seen in the (110) plane arise from this mechanism or whether corrosion occurs there directly at high field. 3.4.

METHANE

ADSORPTION

Methane was investigated because the results of Bell et a1.i2) suggest that it would not be desorbed at Ar BIF, and also to compare its behavior with that of the principal impurity released by the channel plate, which has been reported’s) to have mass 16, but which clearly is not oxygen. The image obtained after exposure to a large dose is shown in fig. 14b. Visual observation showed the surface to be intensely active. Many image dots appeared spontaneously, moved a short distance and then vanished. The number of moving dots which eventually became stabilized was much smaller than for CO. No stable dots on the (110) plane were seen initially. Original W image points oscillated rapidly in intensity, and in some regions, for instance around (21 I), in position. The image shown in fig. 14b is a 30 set time exposure and hence a composite of these effects, which accounts for the lack of contrast. Similar behavior was seen also below 2 V/A. The movement is not all due to arrival of CH, from the gas phase. If the tip was field desorbed, the rate of movement, now due to residual CH, in the gas phase, was decreased very markedly. Thus the main effect must be the movement of adsorbed entities.

R.T.LEWIS

224

AND R.GOMER

(b)

GO

(cl Fig. 14. Methane. adsorption. (a) Clean tip, 3.25 kV. (b) After methane adsorption on (a) at 78°K: 3.1 I kV (see text}. (c) After methane adsorption, and field desorption at 2.9 V/A; imaged at 2.0 VIA.

The behavior of CH, is qualitatively similar to that of CO, but differs in its details. The number of transient dots is much larger and the oscillation in intensity of W image points is much more pronounced with CH4. The transient image points cannot all be due to W-CH, mobile complexes, since their number far exceeded the amount of disorder (corrosion) of the W lattice. It appears therefore that CH4, or its dissociation products (CH,, CH,?) either by themselves or in combination with Ar, are at least transiently visible in Ar imaging. The result of raising the field to 2.9 V/A for 60 set is shown in fig. I4c.

ADSORPTIONSTUDIESINFIMWITH

Ar

IMAGING

225

The surface appears completely disordered. The onset field for rapid corrosion seems to be 2.5 V/A. These results also show that CH, or its decomposition products are present on the surface at 2.0 V/A, since corrosion occurred even after CH, pressure in the gas phase had been reduced to very low values by the getter pump. 3.5. HYDROGEN ADSORPTION Some experiments with H, adsorption were also carried out. No detectable changes in the image could be observed below or above 2.0 V/A, indicating that hydrogen is not visible, despite the fact that the results of Bell et a1.12) indicate that it should still be adsorbed at 1.8 V/A in the presence of Ar. 4. Conclusions 4.1. SURFACE RECONSTRUCTION The present experiments indicate rather clearly that reconstructive adsorption does not occur in the case of CO, and probably CH,. In the case of oxygen the results are ambiguous at high coverage but reconstruction seems to be slight or non-existent at low 8. In all cases the (110) plane seems not to reconstruct for T-c 300°K. It is not possible to make this statement much stronger, since reconstruction which left this plane densely packed might not be resolved, particularly if the loss of contrast persisted. However the structures postulated from LEED results for 0 on (110) by Germer and May 1) probably should have been resolvable, if present. Thus all that can be said is that gross rearrangements and disorder seem absent on this plane under almost all conditions. This is of course what one would expect, since the (I 10) plane is the most closely packed in bee structures, so that the activation energy for reconstructing it would be highest. 4.2. PROMOTEDFIELD DESORPTIONAND CORROSION It should be pointed out in connection with the previous heading that high fields could suffice in principle to cause surface rearrangement in the presence of an adsorbate, by facilitating the migration of metal ions outward and anions inward. Such a mechanism for oxidation was in fact proposed many years ago by Mott and Cabrera2g), in a different context, the field being supplied by dipole layers. In the present case the finite screening length of the surface would in fact denude metal ions, i.e., remove screening charge, and make such processes quite likely. Consequently reconstruction at high positive fields does not necessarily imply the same phenomenon at zero field. There seems little doubt from the present experiments that image gas

R.T. LEWIS AND R. GOMER

226

assisted (promoted) field desorption occurs, as also noted by many previous workersg-i4) at fields considerably lower than in vacuum, and further that these processes lead to considerable disordering of the surface. The reasons for promoted desorption are not completely understood. A detailed examination of collisional activation by Ar atoms hitting the surface with polarization energy $xF2 led Bell et aLiz) and Bassettii) to conclude that it was inadequate to explain promoted field desorption. There is also the possibility that electrons released by ionization of image gas can cause desorptionla). This would be particularly likely under high field conditions, which deform the relevant potential curvesBO). While most of the tunneling electrons arrive at the metal with zero kinetic energy, work by Jasonal) has shown that, above BIV in particular, there are secondary peaks in the ion energy distribution, corresponding to ionization at greater distances from the surface; this releases electrons with real kinetic energy. It is thus quite possible that electron impact desorption contributes appreciably to promoted field desorption. Further, it could also cause mobility of adsorbate or ad-complexes by excitation to repulsive states. It is known that conversion from virgin to beta-CO can be caused by electron impacts2); it is conceivable that excitations to an anti-bonding state, followed by reversion to the ground state, could lead to adsorbate displacement. Finally Miiller’s recent findingez) of a field induced image gas layer and of substrate-image gas compound ions suggests that the most important effect in promoted desorption is the formation of compound ions involving adsorbate, substrate, and image gas atoms. The transient formation of such ions, followed by decomposition, could also explain the apparent mobility of adsorbate-tungsten complexes. For instance it is possible that a WO-Ar ionic complex would disproportionate part of the time into a W atom left behind on the surface and an OAr+ ion. For present purposes the most important fact is that promoted desorption seems to lead to surface disorder, so that much of the effects attributed to adsorption in Holscher’s work7) for instance, must be blamed on desorption. It remains to ask why field desorption should cause surface disorder. In a general way this is easy to rationalize. Since the desorbing species is it is probable that the desorption act usually a W-adsorbate complex, initially involves more than one substrate atom, even if not all of these desorb. Thus displacements, as well as the plucking out of substrate atoms can occur. Further, the field effects already mentioned, will become more important as F is raised above the viewing, to the desorption field. 4.3. VISIBILITY OF ADSORBATES The results

reported

here indicate

that oxygen

and CO are not visible,

ADSORPTION

STUDIES

but that CH, may be. The situation

IN FIM WITH

Ar IMAGING

227

for what may loosely be called electro-

negative adsorbates thus seems to be quite different from metallic ones, which image, provided they are not field desorbed at the viewing field. In addition, chemisorption can increase or decrease the visibility of substrate atoms, and in the case of 0 at high coverage, radically alter image contrast. It is not possible at this time to explain these phenomena, but some speculation about them may be warranted. The probability of field ionization near a substrate or adsorbate atom (or molecule) depends on the local field and on quantities like (g[Fexla)’ pa and (g[Fexlm)’ pm, where 18) stands for the wave function associated with the image gas orbital from which an electron makes a transition under the influence of the applied field F to either an adsorbate orbital la) or a metal orbital Im) and pa and P,,, are the local densities of state (in the meaning of the Anderson impurity model) and the metal densities of state respectively. In addition, ionization in front of an adsorbed entity will involve interference terms of the form (ml Fex lg) x (gl Fex la> and (4 Fex Id (4 Fex I@, each multiplied by an appropriate effective density term33). Because of energy conservation and the exclusion principle it is further necessary that transitions restrict themselves to ET E,, E, being the Fermi energy. The criteria for a high probability of ionization are thus (a) availability of empty orbitals with a high density of states near E,, (b) having high orbital density outward from the surface, and (c) maximum local field normal to the surface. It is easy to see why metallic adsorbates fulfill these criteria and why electronegative ones may not. In the former case there is, essentially by definition, a very broad local density of states extending above the Fermi level; there will generally be orbitals with the right properties, and there will be local field enhancement as well. In the case of electronegative adsorbates the position of virtual levels may be far from the Fermi surface; field enhancement is by no means guaranteed since the adsorbate may in fact act like a dielectric, and further, adsorbate orbitals need not point outward from the surface to an appreciable extent. Given our present state of ignorance about the details of chemisorption a more detailed discussion is not warranted at this time. It should be pointed out however that the problem of ionization in front of an adsorbate is intimately linked to that of field emission through an adsorbate, as also noted by Duke and Alferieffsa). As more information about the latter becomes available, it should be possible to become more specific about field ionization. It is also possible to see in a general way why adsorbates could alter the ionization probability of adjacent substrate atoms, since they can rehybridize the latter’s orbitals as well as change the local electric field. It is difficult to go from these generalities to the specific results encountered in this work. While it is not surprising that CO should have no

228

R. T.

LEWIS

AND R. GOMER

appropriate orbitals with adequate local density of states near E,, and while it may be that the affinity level of 0 lies mainly above E,, so that it contributes little it is hard to see why a high coverage of 0 atoms should reduce the contrast of the image so drastically. Since this effect does not occur with CO, it is probably not connected with the presence or absence of a field adsorbed Ar layer on a clean or chemisorbate covered surface, since CO and 0 would probably affect this about equally. It may be that at high coverages the combination of work function change (due to 0 adsorption) and applied field so shifts the effective 0 atoms potentials as to create very strong transmission resonances, of the kind discussed by Duke and Alferieffs4). If this were so the ionization probability near 0 atoms could be so strong, and overlap so strongly as to cause blurring. 5. Summary The present work indicates that Ar ion microscopy is capable of imaging clean surfaces with fairly high resolution, 4-5 A, and of providing some information on adsorption and reconstruction, although it appears that many adsorbates are not directly visible. In the case of CO at least the evidence points toward non-reconstructive adsorption on tungsten, surface disorder arising from subsequent field induced processes, which are not understood in detail. It is not likely that Ar field ion microscopy, even in conjunction with atom probe experiments, will be able to go much beyond this level of conclusion, since it seems very difficult to establish the correspondence between an image point and the entity field desorbed from that locus. Thus, even if an adsorbate sitting on top of the surface should give an image point, an adsorbate-substrate complex may desorb, and vice versa. Despite this limitation experiments of the kind described here help to resolve, in favorable cases, the problem of reconstructive chemisorption. Acknowledgments This work was supported in part by Contract AT(ll-1) 1383 with the U.S. Atomic Energy Commission. We have also benefited from facilities provided by the Advanced Research Projects Agency for Materials Research at the University of Chicago. References I) 2) 3) 4)

L. H. Germer and J. W. May, Surface Sci. 4 (1966) 452. P. J. Estrup and J. Anderson, J. Chem. Phys. 45 (1966) 2254. E. Bauer, Surface Sci. 5 (1966) 152. J. C. Tracy and J. M. Blakely, Surface Sci. 15 (1969) 257.

ADSORPTION

STUDIES

IN FIM WITH

Ar

IMAGING

229

5) E. W. Miiller and T. T. Tsong, Field Zon Microscopy (American Elsevier, New York, 1969). 6) G. Ehrlich and F. G. Hudda, J. Chem. Phys. 36 (1962) 3233; G. Ehrlich, J. Chem. Phys. 36 (1962) 1171; G. Ehrlich, Discussions Faraday Sot. 41 (1966) 7. 7) A. A. Holscher and W. H. M. Sachtler, Discussions Faraday Sot. 41 (1966) 29. 8) E. W. Miiller, Z. Elektrochem. 59 (1955) 372. 9) E. W. Miiller, in: Structures and Properties of Thin Films, Eds. C. A. Neugebauer, J. B. Newkirk and D. A. Vermilyea (Wiley, New York, 1959) p. 476. 10) E. W. Mtiller, J. A. Panitz and S. B. McLane, Rev. Sci. Instr. 39 (1968) 83. 11) D. W. Basset, Brit. J. Appl. Phys. 18 (1967) 1753. 12) A. E. Bell, L. W. Swanson and D. Reed, Surface Sci. 17 (1969) 418. 13) G. Ehrlich and F. G. Hudda, Phil. Mag. 8 (1963) 1587. 14) S. S. Brenner and J. T. McKinney, Surface Sci. 20 (1970) 411. 15) R. Gomer, Field Emission and Field Zonization (Harvard Univ. Press, Cambridge, Mass., 1961). 16) P. J. Turner, P. Cartwright, M. J. Southon, A. van Oostrom and B. W. Manley, J. Sci. Instr. 2 (1969) 731. 17) R. Lewis and R. Gomer, Appl. Phys. Letters 15 (1969) 384. 18) A. van Oostrom, in: Seventeenth Field Emission Symp., New Haven, Corm., 1970. 19) A. van Oostrom, Philips Res. Rept. 25 (1970) 87. 20) 0. Nishikawa and E. W. Miiller, J. Appl. Phys. 35 (1964) 2806. 21) S. S. Brenner and J. T. McKinney, in: Sixteenth Field Emission Symp., Pit&burg, Pa., 1969. 22) E. W. Mtiller, S. B. McLane and J. A. Panitz, Surface Sci. 17 (1969) 430; E. W. Miiller and S. V. Krishnaswany, in: Thirtieth AnnualPhysical Electronics Conf., Milwaukee, Wis., 1970; T. T. Tsong and E. W. Miiller, Phys. Rev. Letters 25 (1970) 911. 23) M. G. Inghram and R. Gomer, Z. Naturforsch 10a (1955) 864. 24) D. Newns, Phys. Rev. Bl (1970) 3304. 25) C. Kohrt and R. Gomer, J. Chem. Phys. 52 (1970) 3283. 26) T. Engel and R. Gomer, J. Chem. Phys. 52 (1970) 1832. 27) C. Kohrt and R. Gomer, Surface Sci. 24 (1971) 77. 28) T. Engel and R. Gomer, J. Chem. Phys. 50 (1969) 2428. 29) N. F. Mott and N. Cabrera, Rept. Progr. Phys. 12 (1948) 163. 30) D. Menzel and R. Gomer, J. Chem. Phys. 41 (1964) 3311. 31) A. Jason, Phys. Rev. 156 (1967) 266. 32) D. Menzel and R. Gomer, J. Chem. Phys. 41 (1964) 3329. 33) D. Penn, M. H. Cohen and R. Gomer, to be published. 34) M. E. Alferieff and C. B. Duke, J. Chem. Phys. 46 (1967) 938.