An experimental investigation of the elastic scattering of He and H2 from Ag(111)

Surface Science 93 (1980) 47-63 0 North-Holland Publishing Company

AN EXPERIMENTAL INVESTIGATION He AND Hz FROM Ag( 111) *

OF THE ELASTIC SCATTERING OF

James M. HORNE, Steven C. YERKES and David R, MILLER ~e~art~~e~? of Applied Mecr~~n~csmd Engi~ee~ing Scierrces. University ~f~~~~~r~l~a rzt Sat2 Diego, La fofla, Califorrzia 92093, USA

Received 5 September 1979

Experimental diffraction probab~ities for 63 meV He and 66 mcV Hz scattering from Ag( 111) along the ( X12, direction are reported. Debye-Wailer experiments for the He/Ag( 111) system yield a mean well depth of 9.3 meV and an effective surface Debye temperature of 253 K.

1. Introduction

Elastic diffraction of light particles from single crystal surfaces has been observed for several systems and has provided some fundamental information on the gas-surface potential; although selective adsorption experiments provide more precise potential information [ 11. Debye-Waller measurements of the total inelastic scattering, or loss of elastic intensity, purports to provide indirect information on the average potential well depth and the surface Debye temperature [2]. Diffraction from metal surfaces has been difficult to observe and to date has been limited to the strongly corrugated W(112) [3], the stepped Cu(ll7) [4], and the smooth Ag(l11) [5,61. We have been interested in scattering from the Ag(l11) surface because it is relatively easy to clean and to maiIltain clean for several hours. Since little information on the intermolecular potentials for the light gases (He, H,, Dz) on Ag(l1 I) exists, it seems desirable to look at elastic scattering first. The first two diffraction experiments on Ag( 111) [.5,6] each provided a first order peak intensity for He and H,. Chow and Thompson [7] have subsequently completed a close-coupling calculation for the He/As system and found that, for their potential model, the two experiments could not be fit with the same potential paranleters. Their results do suggest that the silver surface is very smooth. Boato et al. [8] have since provided additional Ag(l11) data on first order He diffraction and second order H, diffrac-

* Research funded by National Science Foundation Grant DMR78-17176. 47

tion. We present here new data for He and H2 diffraction at several angles of incidence, including second order He diffraction. The focus of our experiments has been on He so that the He data are most complete. While the II, data makes an interesting comparison, theoreticians seem less inclined to study Hz at this time. We also present Debye-Waller data and elastic intensity corrections. Our procedures for determining quantitative scattering probabilities are discussed. Finally we tabulate our data for He and II, diffraction from Ag(l 11) in a form useful to theorcticians.

2. Apparatus, experimental

procedures,

and experimental

data

The components of our scattering apparatus, shown in fig. 1, have been described in detail previously [6.9,10]. It is unique in that the beam source is differentially pumped and rotates inside the scattering chamber, together with the target, while the detector remains fixed. The base pressure is less than 3 X lo-” Torr in the target chamber and is approximately 10 -’ Torr with the beam on. Table 1 gives dimensions of interest in the present experimerit. which are necessary to reduce the data. The epitaxially grown crystal is the same type as that used previously [6] and was cleaned in situ by cycles of ion bombardment (2 min. 950 V, 19 MA) and annealing (up to 600 K), and then cooled to about 140 K for the scattering experiment. We examine only scattering in the plane of the incident beam and the surface normal, with the beam incident along the (1 12) direction; the close packed

LN,

AUGER ELECTRON SPECTROMETER MASS

CHAMBER SOURCE

CHAMBER

SPECTROMETER

CHAMBER 2

SCATTERING CHAMBER

WINDOW

Fig. 1. Schematic

of experimental

apparatus;

see table 1 for critical

dimensions.

J&i. Home Table 1 Apparatus

et al. / .Clastie scatterir~x of’lfe

and If, from &(I

11)

49

parameters

Source pressure Source diameter Incident beam velocity (helium) Incident beam velocity (hydrogen) Incident beam speed ratio (helium) Incident beam speed ratio (hydrogen) Skimmer diameter Source to skimmer tip distance Skimmer tip to chopper blade distance Chopper blade to target distance Target to detector distance Aperture (1) diameter to detection chamber Target to aperture (1) distance Aperture (2) diameter to detection chamber Target to aperture (2) distance Effective aperture for mass spectrometer Chopper blade diameter at beam Chopper slot width Chopper speed Chopper gate time

(III)

4000-6000 Torr 0.002 cm 1.74 X lo5 cm/s 2.5 X lo5 cm/s 17* 1 13* 1 0.013 cm 0.89 cm 2.8 cm 4.8 cm 37.7 cm 0.29 cm 14.3 cm 0.50 cm 34.0 cm 0.51 cm 8.7 cm 0.056 cm 100-200 rev/s lo3octs

1 2

PLANE

(To)

.2 t

i-x400

Fi, Diffraction of 63 meV He from (lf!! neak was scanned.

Ag(ll1)

along

the (112)

direction;

only the top of the

50

J.,W Home

ct al. / t‘lartic

scattcrirlg

of He ad

H2 ,from Q/l

I I)

lattice parameter a = 2.88 ?i gives a grating of 2.49 ,& in the (112) direction. Angles are measured from the surface normal in degrees. The mass spectrometer multiplier output was processed, sequentially, by a Princeton Applied Research (PAR) 181 current-to-voltage amplifier, a PAR 113 amplifier, a PAR CW-1 boxcar integrator with a time gate of 1 ps ( see ref. [9]), and finally recorded on a Hewlett Packard chart recorder. Fig. 2 is an example of a chart recording of the signal versus angle. To obtain the signal-to-noise indicated took about two minutes to scan the specular peak and ten minutes for the (30) peak. We scanned very slowly at these angles in order to obtain the correct peak heights. Only the upper portion of the (10) peak was recorded. The signals have been normalized by the specular beam intensity and the ratio of

E,:63meV e,z50°

01 0

II0

200

300

400

500

600

700

T,(K)

Fig. 3. Debye-Wailer experiment, specular A&111); S and y’ are the slope and intercept

intensity versus for ln(Z(OO)/Zi).

surface

temperature

for He on

J.M. Horrle et al. /Elastic

scattering

of He arid

H, from Agflll)

51

6 5

4 ; s; 0

3

2

Fig. 4. Debye-Walk experiment, specular intensity versus surface temperature A&111); S and y’ are the slope and intercept for ln(I(OO)/Zi).

for He on

to incident beam intensity is given. The reduction of such data to quantitative scattering probabilities is given in the next section. Figs. 3 and 4 show one of the best and poorest Debye-Waller experiments, specular scattering probabilities versus surface temperature. If the Debye- Waller factor is valid one expects a linear relationship on this semi-log plot. Ideally, neglecting diffraction, if f(OO)/Zi is quantitative, the linear portions would extrapolate to 1 .O at T, = 0, as found by Armand et al. [ 111. Although surface roughness can lead to the deviations from this intercept indicated in figs. 3 and 4, we believe that slight misaligmnent would also easily account for them in our experiment. We rotated the crystal to measure the incident beam intensity and then rotated it back to specular to obtain Z(O0). Because of the narrowness of the incident and specular beams, an error of 0.25” in resetting the specular

I$. 5. Cube model for effect of adsorbate

on loss of speculur

helium

scattering

at low coverage.

specular angle could account for the observed deviations. We have obtained intercepts as high as 0.9 at the extrapolation to 7’, = 0. Fortunately. only the slopes are needed in the analysis. The Debye-Waller experiments were run by heating the crystal and taking data while it cools. The type of non-linearity at high temperatures shown in fig. 4 is usually attributed to anharmonic effects. The absence of a similar deviation in the data of fig. 3 may indicate that scattering at large glancing angles is more sensitive to these effects. The fall off at low temperatures seen in fig. 4 is, we believe due to surface contamination. One does expect non-linearities at low temperatures due to zero point vibrational (phonon) energies but we have calculated the expected deviation and they cannot account for the observed fall-off at low temperature IlO]. However, a simple classical calculation of the loss of specular scattering due to shadowing of the surface by an adsorbed molecule suggests that -1.5% contamination accounts for the loss of specular scattering observed in fig. 4 at low temperature. The model is depicted in fig. 5, which shows an adsorbate as a cube of side length C. It is assumed that helium atoms which strike the cubes are lost to the detector. For low fractional surface coverage x, x Q (1 + 2 tan Bi)-l, the fraction of incident beam effected, Ae, is given by AE

&Q

= _____

1 + 2 tan 0 i) _ ____ - X(1 + 2 tan ei) , nc2

(1)

where nc2 is the total scattering area. Eq. (1) indicates the sensitivity of helium scattering at glancing angles to surface adsorbates, or similar deviations to a smooth surface due to defects. At Bi = 80” and x = 0.01, AE = 0.12, a 12% effect on scattering intensity. For Bi = 50”, the case of fig. 3, the effect is only 3% for a 1% contamination. This model is similar to the one used by Goodman [12] to account for the effects of surface steps on the elastic specular intensity of H scattered from LiF.

J.M. Home

et al. /Elastic

scattering

of He and H, from A~(11 I)

Smith and Merrill [30] have also made detailed bates, but neglecting the reflected rays.

3. Data reduction

calculations

53

for spherical adsor-

and discussion of results

3. I. Elastic scattering The specular peak of fig. 2 is slightly broadened by inelastic effects with the peak height indicating that about 40% of the scattering is elastic, to within the energy resolution of our beam (MT/E - 16%). Inelastic effects are small and hopefully can be scaled out by the Debye-Waller analysis discussed in the next section. Even if there were no inelastic scattering there are several problems in obtaining quantitative cross-sections from data like that of fig. 2. Crystal imperfections such as steps can attenuate the beam. Lapajoulade et al. [11,13] have shown that these features can also lead to coherent interference effects. Their calculations suggest that such effects would be azimuthally dependent. We have studied the azimuthal angle dependence of our specular beam intensity and found negligible (
discuss some of the principle features of our calculation so that theoreticians might have some confidence in the final results we present below. We must transform among three coordinate systems to complete the problem: the incident beam, as seen from the source, the surface target area where all the scattering cross-sections and crystal geometry are described, and the detection system which determines if a particular scattering event is detected. It is necessary to transform among the three systems because the sc:lt tcring takes place over a large area of the crystal, especially at our glancing incident angle. and the scattering process is defined with respect to a local co-ordinate system fixed to a unit lattice. The cross-section of our incident beam is circular and to a very good approximation the divergence is that calculated from a point source seen through the skimmer opening. Our profile measurements show that the profile penumbra contains less than 3% of the incident beam. For a given incident angle on the crystal the beam projection onto the crystal is computed, a skewed ellipse in general. The incident beam is split into 72 equal parcels which splits the affected surface area into 72 segments. As the chopper slit moves across the incident beam various parcels start at different times; the beam centerline starting time is assigned as time zero. Since the time gate width of our boxcar detector is set at 1 MSand the chopper gating function is lo-20 ps it is clear that much of the beam cannot contribute to detected signal since the scattering is predominantly near-elastic. This has an effect of increasing the resolution of our elastic scattering experiment but at considerable loss in total signal compared to a dc or lock-in amplifier type of detection. There is a correspondence then to portions of the incident beam angular and velocity distribution, target areas at which a given velocity must strike to be able to reach the detector at the proper time (a small effect), and most importantly, the time at which the chopper slit is effective for the given parcel of incident beam. These correspondence, due to our time of flight detection, substantially reduce the number of trajectories we must compute to generate a total scattered signal at a given scattering angle. A trajectory is computed and successively checked to see if it passes through the three detection apertures and arrives at the correct time to be detected before it is weighted as a contribution to the total signal. The probabilities are then adjusted until the best agreement with the experimental data is obtained. If inelastic effects are to be considered a Debye-Waller correction is applied also, as discussed below. These computations are carried out uniformly to 1 /JS time and 0.1” angular resolution. When we proceed to inelastic experiments in the future the number of trajectories will substantially increase because the cross sections will be non-zero for large velocity changes at the surface. We anticipate a Monte Carlo type of numerical simulation in such inelastic cases. Before we proceed to the result of these calculations we briefly discuss our velocity distribution function. We use the one dimensional drifting Boltzmann distribution to experimentally fit the incident beam distribution and then to analyze our

J.M. Home et al. /Elastic scattering of He and Hz from &(I

I I)

55

experiment: flu) = C exp[-s2(u/u0-l)‘],

(2)

where C is a constant equal to the number density per unit speed for u = uo, s is the speed ratio, (mvi/2kT)“2, and uo the mean speed. Values of s and uo for the incident beam are given in table 1. In some instances researchers have an additional u2 weighting in front of the exponent, leading to a l/t4 pre-exponential when transforming to the f(t) time-of-flight function. This factor has been carried over from free-jet, nozzle beam technology [15] where it was originally, and correctly, used to characterize the three dimensional speed distribution of the elemental volume of gas in front of the skimmer inlet. In surface scattering experiments, where all of the collimated beam strikes the surface, we feel that is preferable to use one dimensional distributions. The difference for most incident beams at high (2 10) speed ratios is negligible. However, when researchers analyze scattered speed distributions from hot surfaces where s can be small (,<3) it is ambiguous to use other than onedimensional distributions at each angle along scattered rays. We show in fig. 6 results for a computation of the experiments of fig. 2. Two cases are shown. The dashed curve is a computation for a monoenergetic beam

Imol/I,= 0.2

(IO)

t,

L

,-x400

kx400

IO

20

30

I

1

I

\

50

40 .9

60

70

SK.400

CL I

L

-_L

0

I-‘ \

I II

Go,

60

\

90

S

Fig. 6. Numerical trajectory experiment simulating experiment of fig. 2. Dashed line is for monoenergetic beam. Solid line is full calculation (see text for details). Probabilities used are PR of table 2.

56

J.M. Home

et al. 1 Elastic scatteritlg o/He

ami II, from Ax(l I I)

(s + -), wherein the dispersion is due to the angular divergence of the incident beam, the chopper gating function, and the angular sensitivity of the detection system. The solid line is the full calculation with the correct incident speed distribution and fits the data of fig. 2 quite well. Some of the qualitative features of these numerical studies for our system arc: (i) most of our spreading for supraspecular (Or > Oi) scattered peaks comes from the angular divergence of the incident beam (Cl .O”); the effect of incident angular distributions is a narrowing of subspecular peaks and broadening of supraspecular peaks; (ii) the incident speed distribution broadens all peaks and the effect is increased for increasing Or and increasing diffraction order; (iii) slight tilting of the surface can cause a mean time shift in observed time-of-flight spectrum for perfectly elastic scattering. Results (i) and (ii) are obvious qualitatively upon differentiation of a simple one-dimensional diffraction relation: sin Br = sin Bi ? rIG,/ki ,

@a)

to give:

where ki = 2n/X is the incident wave vector and nG a reciprocal lattice vector. The result (iii) due to slight misalignment of the crystal has answered for us a long time bothersome laboratory problem. We sometimes observed constant time shifts up to 5 ~.ls in elastic specular beams compared to the incident beams with the identical time-of-flight system. These numerical trajectories show that slight (0.1”) tilts make the detector more sensitive to off-center parts of the crystal, which are struck by off-centerline parts of the incident beam, which are, in turn, gated by the chopper at a time different from that of true experimental time zero. The effect was particularly important to our in-plane detection system because we chop vertically through the beam and the crystal could be tilted out-of-plane. 3.2. Inelastic correction - Debye-

Waler

As we mentioned above the interpretation of the Debye-Waller experiment is subject to controversy in the case of atom-surface scattering. The exponential form of the inelastic attentuation of elastic scattering has been derived both quantummechanically [1,16-181 and semi-classically [19] and is analoguous to that obtained in LEED or neutron scattering [20] :

Z/Z,= exp[-((u.ak)‘)],

(4)

where I, is the elastic intensity if no inelastic scattering occurs, u is the surface atom thermal displacement, usually taken normal to the surface, and Ak the change in wavevector of the gas atom. For atom-surface scattering, the interpretation of both u and Ak has been subject to controversy. Much discussion has developed over

J.M. Home et al. /Elastic

scattering

ofHe and Hz from Ag(l1 I)

57

Beeby’s 1211 calculation which showed that the attractive part of the potential is thermally averaged and conservative, and therefore serves simply to accelerate the atom into the repulsive part of the potential where the inelastic exchange then occurs. Beeby suggested, therefore, that the normal component of k should be corrected by acceleration to the potential minimum. Goodman [22] has questioned the validity of evaluating k at the potential minimum where most experimentalists apply Beeby’s correlation, while Masel [23] suggests that it is valid provided there is little distortion as the repulsive potential moves and that multiple scattering is negligible. The experiment by Hoinkes et al. [24] for the H/LiF system was qualitatively successful in showing that the well depth obtained from Beeby’s correction to the Debye-Waller analysis did agree with the potential obtained from selective adsorption experiments. At the other extreme, Krishnaswamy et al. [25] recently found for the He/NaF system that the Debye-Waller theory was only applicable for more glancing angles (6, > 4.5’) and that no Beeby correction was required at all. The evaluation of U, related to a surface Debye temperature, is likewise unclear at this time because of the larger size of the incident gas atom, discussed below. Whether or not a quantitative understanding of the two parameters, “effective” surface Debye temperature and thermally averaged potential well depth, obtained from a Debye-Waller experiment exist, the Debye-Waller correction still stands as the easiest way to scale inelastic effects. In our experiments with Ag(lll) the Beeby corrected Debye-Waller analysis is consistent with our data and we have therefore used it to scale out inelastic effects. Assuming u is normal to the surface and evaluating Ak at the potential minimum, following Goodman [22], eq. (4) can be written, in the high temperature limit, for any elastic diffraction peak: / I,=exp

24Mg(Ei COS'Oi+ D) ------i,ksi;f

__-

(5)

i where Ms, S is the gas (g) or surface (s) atom mass, Ei the incident energy, D the gas-solid potential well depth, kB is Boltzmann’s constant, T, the surface temperature, Oi, f the incident (i) and final (f) angles, measured from the surface normal. The second factor in brackets is unity for specular scattering and is the angle correction factor for diffracted beams where the Beeby correction is applied to the normal component of k [22]. Our measurements of 0, and D are based only on specular data, but when applying the result to diffracted beams we have included the angle correction factor. We have not yet completed Debye-Waller experiments on the diffraction peaks, which would be very informative. From specular data such as in figs. 3 and 4 we obtain slopes S = A(Et cos28i) + B, where A = -24M,/(kBM,O~) and B = AD. A plot of these slopes versus (Eicos’Bi) is shown in fig. 7. The slope and intercept of this plot then yields A and B and hence

58

-7

-

-6 -

,I, 0

I,,, 5

,I,, IO

I,,, 15

I,,, 20

,, 25

E, COS’8, (meV1 Fig. 7. Debye-Walk

slope and intercept

slopes versus the normal of the solid line.

component

of incident

energy;

A and B are the

0” and D. For our data we obtain D= 9.3 ? 1.2 meV and 0~) = 253 + 10 K. Because we obtained data at only one large value of (Eicos’@i), although they are our best data and were repeated twice, the 5 values given are based on only the lower 4 points shown, so that they represent the maximum uncertainty for our data. Our result for the well depth is slightly larger than recent theoretically estimated values, 6.5 meV [26] and 8.5 meV [27]. Our value for the effective surface Debye temperature 0~ is larger than the bulk value (225 K) and much larger than the surface 0 D obtained from LEED (15.5 K). Similar large 8~ have been obtained in atom-surface scattering for H/LiF(lOO) [24] He/LiF(lOO) [28], He/W(ll2) [3], and He/Cu(lOO) [11,29]. Several researchers [3,24,29] have attributed the apparent anomaly to the non-zero size of the gas

J.M. Home et al. /Elastic scattering of He and H2 from .&(I 1 I)

59

atom. Since the atom interacts simultaneously with several surface atoms the time average surface displacement contains terms which correlate the motion of neighbouring surface atoms [29]. Put another way, the incident gas atom sees a smoother potential, smaller u, than would be expected by interactions with a single oscillating atom, so that parameter 8, extracted by eq. 5 is larger. Armand [29] has shown that when the correct displacement correlation is used, the tin’s are consistent with LEED data. We have used the D and or, parameters in eq. (5) to scale out inelastic effects from our diffraction intensity data. For H2 data we have used the same or, but we assumed D = 22 meV as suggested by Weinberg [2]. A value of D = 15 meV would change the results given below for Hz by about 10%. We have not completed H2 Debye-Waller type experiments. 3.3. Tabulation of results and discussion Table 2 gives our results for the elastic scattering probabilities of He and H2 from Ag(ll1) along the (11% direction. Three probabilities are given. PE is the Table 2 Summary of results Gas

T,

tli

ef

h,

149 149 155 155 155 155 151 151 151 138 138

35 35 50 50 50 50 80 80 80 80 80

21 35 18.5 33 50 82 33 48.5 80 48.5 80

00)

161 161 161 159 159 151 151 138 138

35 35 35 50 50 80 80 80 80

16 35 61.5 28 50 43.5 80 43.5 80

(10)

n)

PE

PR

‘)

a)

PRD

PRdPRD(00)

a)

WI

He He He He He He He He He *He *He Hz Hz Hz HZ HZ Hz Hz *Hz *Hz

po, (20)

00) (00)

(10)

(20)

(10) (00)

00) (00) (00) (10)

(TO) (00)

(i0) (00)

00) (00)

1.66 x 0.12 3.48 x 8.87 x 0.195 7.69 x 1.21 x 2.22 x 0.327 3.1 x 0.54 3.33 x 0.127 1.41 x 2.54 x 0.203 6.15 x 0.279 9.5 x 0.32

IO-4 lo-’ lo-’ lo-’ 10-4 10-4 10-4 10-s 10-4 1O-3 lo4 10-4

2.51 x 0.12 8.63 x 1.44 x 0.195 7.4 x 4.74 x 5.24 x 0.327 7.3 x 0.54 5.33 x 0.127 4.23 X 4.57 x 0.203 1.68 x 0.279 2.6 x 0.32

104 lo-’ 10-4 10-4 10-4 IO+ 104 10-s lo-’ 10-s 10-a 1O-3

1.0 x 0.4 1 2.96 x 4.32 x 0.471 1.25 x 9.39 x 8.94 x 0.43 1.2 x 0.69 1.4 0.30 8.13 9.93 0.38 2.71 0.37 4.0 0.42

10-j lO-4 lo4 10-s 10-4 IO4 10-4

x 10-2 x 10-j x 10-s x 1O-3 x 10-s

2.44 1.0 6.28 9.17 1.0 2.65 2.18 2.08 1.0 1.74 1.0 4.67 1.0 2.71 2.61 1.0 7.32 1.0 9.52 1.0

x 1O-3 x 1O-4 x 104 X 1O-3 x 1O-3 x 1O-3 x 10-a x 1O-2 x 1O-2 x 1O-2 x

1O-3

x lO-3

a) PE is probability based on peak height; PR is corrected for apparatus velocity and angular resolutions; PRD is corrected for resolution and inelastic effects (Debye-Wailer) and would correspond to the extrapolation to T, = 0.

60

J.M. Home

ct al. /Elastic

sc’attcrirlg

of He and tj,

fkm

A~(11 I)

probability based only on raw experimental peak height data l/It. PII is the probability obtained by correcting Z/Zt for the experimental speed and angular resolutions using the numerical trajectory calculations described above. PRD is the final probability obtained after correcting PK for inelastic effects, using the DebyeWaller analysis and represents the expected results for a cold, perfectly elastic lattice. Despite the fact that the angle dependence of the Debye-Waller angular correction in eq. (5) has not been experimentally tested we feel theoreticians should compare their elastic scattering from cold, rigid lattice calculations with P ~1). Finally the ratio of diffracted to specular probability PK,)/P&OO) is given for convience. A measure of our reproducibility is obtained by comparing our original data [6] at 8i = 80” (indicated by an asterisk in table 2) with the newer data. These runs were more than six months apart on two different crystals. For He the change in PKIl is about 40% at specular and 26%’ for the (CO) peak. For H, the changes were 12% and 32% for specular and (TO) respectively. The differences could be due to differences in surface quality, alignment, or detector stability. Normalizing to specular, PRD/PR1,(OO). gives differences of about lC% and 7% for He (TO) and Hz (i-0) peaks, which are acceptable variations.

5r,

He - Ag(lIl)

+

1

A +

Fig. 8. Normalized first order diffraction probability related to the change in normal tum, qZ, for He on Ag(ll1). a are (10) data; -i are (10); + arc Genoa data of ref. [8].

momen-

J.M. Home et al. / Elastic scattering of He and 112 from &(I 11)

61

A second point of interest is the rather large probability for second order diffraction compared to first order for He. For the Bi = 50” case PKD(~O)/PRI)(iO) = 0.69 and for the Bi = 80” case the ratio 1.05. While the Debye-Waller angular corrections used may be incorrect for these peaks it is still apparent from the PR values that second order probabilities are within 50% of first order. This result may suggest that perturbation theoretical treatments for Ag(l11) may be inappropriate for He at these energies. Boato et al. [B] report a much smaller second order probability for H, at Bi = 30”, P(jO)/P(iO) - 0.02 and P(ii)/P(iO) - 0.05. We were unable to clearly resolve a second order H2 peak, but based on one experiment at Bi = 50”, we feel the probability, PE, was less than 5 X IO-‘. Additional second order data would clearly be desirable. Boato et al. [B] found a qualitative correlation of increasing diffraction probability with increasing perpendicular momentum transfer qZ f ki(cos Bi + cos 0,). Because most of their first order diffraction data were conveniently summarized this way, for comparison we have replotted in figs. 8 and 9 their data, extracted from fig. 3 of ref. [B], together with our first order data. We have used PRD/ PRD(OO) for the normalized, first order probability P(lO)/P(OO). Both sets of data

5

Hz

- Ag(lIl) 0 (I 1%

i 4c

N

0

*

3

Ld

2

1.

0

c

2

I 0

I

0’

+

A

+

I

’

’

IO

20

30

++

’ 40 tqz/2j2

t

4

50

60

1

70

00

,

90

a-2

Fig. 9. Normalized first order diffraction probability related to the change in normal tum,q,, for H, on Ag(ll1). a are (IO) data; o are (10); + are Genoa data of ref. [8].

momen-

show that our probabilities agree within factors of two, which is quite satisfying considering the differences in experimental facilities and techniques. The most significant qualitative difference indicated in the graphs is that we show a substantial increase in probability at low qz for helium. We run our experiments at more glancing angles (35”-80”) than does the Genoa group (11%30’) and this will cause our results to be more sensitive to the attractive potential, especially at low qz. Indeed, theory [ 181 does not prescribe a simple quadratic dependence on qz over as wide a range of parameters as covered by our two groups. In summary. we have provided additional elastic diffraction data. corrected for the effects of apparatus resolution and inelastic scattering. which compare favorably with that of the Genoa group. Hopefully enough data now exist to encourage theoreticians to provide some insight. Particularly interesting would be theoretical calculations of selective adsorptions using well depths up to the 9.5 meV suggested by our Debye-Waller data. Since such an experiment would provide the best information on the He-Ag potential. and Chow and Thompson [7] have already indicated that the selective adsorptions are quite narrow, experimentalists would benefit from a theoretical indication of what the optimum experimental conditions might be.

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scatterirlg of He arld H2 from Ag(l I I)

63

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