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Study of disordered adsorbate layers on nickel (001) by helium atom scattering
Surface Science 117 (1982) 23-32 North-Holland Publishing Company
23
STUDY OF DISORDERED ADSORBATE (001) BY HELIUM ATOM SCATTERING J. IBAfiEZ,
N. GARCIA,
LAYERS ON NICKEL
J.M. ROJO and N. CABRERA
Depurtumento de Fisica Fundumental, Unioersidud Aut6noma de Madrid, Crmtohlanco, Madrid, Spcrin Received
14 September
1981; accepted
for publication
IO November
198 I
The intensity of a helium specular beam scattered from Ni( 100) with low concentration (0 = 0.03) of 0 and CO adsorbate atoms is found to oscillate with the angle of incidence. A simple theoretical model is proposed on the basis of the Kirchhoff approximation that is shown to fit well the data and leads to information about parameters of the corrugation potential of the surface. The electronic charge around an adsorbate atom of oxygen is found to protrude -0.30 A at the particle turning point level. The lateral spread of the charge corresponds to a surface of about 8 surface primitive cells.
1. Introduction In the past few years neutral atom scattering (NAS) has evolved from an odd technique that some people investigated from a fundamental point of view to a well accepted tool that is capable of probing static and dynamical properties of surfaces [l]. The elastic components of the scattered beams has been used in order to gain insight about the crystallography of the very first layer of clean and adsorbate-covered surfaces and in a number of cases a good agreement between theory and experiment has been achieved [2-61. Also, it has been proved [7], following earlier theoretical suggestions [8] that the analysis of the inelastic component can give much information about surface dynamics. All the work referred to above corresponds to surface periodic structures. It has been known for a long time that atom scattering is very sensitive to low concentrations of adsorbate atoms [9] and, in fact, the helium scattered specular beam has recently been used [lo] as a sensitive probe of hydrogen coverage on platinum for kinetic studies. Only very recently, it has been briefly reported [ 1 l] that NAS can be used in order to get information about surface electronic distributions around isolated surface atoms. In the present paper we give a full description of experiments along this line for oxygen and carbon monoxide adsorbed on Ni(OO1) and elaborate a simple theoretical model, based on the eikonal approximation, which is shown to be in good agreement with the experiments. We show that information concerning the geometry of 0039-6028/82/0000-0000/$02.75
0 1982 North-holland
the adsorbate isolated atoms can be inferred from these data and comparison for oxygen and carbon monoxide is made. It is worth remarking that isolated adsorbate atoms are physical entities that are not too dissimilar of defects like surface vacancies. Also, NAS is known to be very sensitive to surface disorder. Therefore studies, as the one reported here, may perhaps open new ways of attacking the really difficult problem of characterising surface defects in a solid.
2. Experimental The experimental set-up is shown in fig. 1. A nozzle source of helium [ 121 produces a rather monochromatic beam that impinges on the substrate maintained in ultrahigh vacuum (static pressure of the order of 2 X 10 _ ” Torr). The beam is chopped by means of a piezoelectric chopper and the scattered beams are detected with a rotating quadrupole with phase-sensitive techniques. Both in-plane and out-of-plane detection can be performed. The sensitivity of the detection is limited by noise coming mainly from the residual helium gas in the chamber and is of the order of 5 X 1O-4 of the incident beam. The value of the incident wavevector was measured to be il-,- 11 A’. The nickel (001) sample is in the form of a disc. Cleaning in the ultrahigh vacuum system has been performed by an alternation of argon bombardments and oxygen exposures at 900 K. After cleaning no traces of common contaminants (as sulfur or carbon) are visible in the Auger spectrum. However, after about 30 min segregated carbon began to appear in the surface. When that occurred, the experiment was interrupted and the sample cleaned before any more measurements were taken. In fact when some experience was gained, the intensity of the specular beam proved to be a much more sensitive technique for the detection of impurities than Auger spectroscopy. This is important because the experiments that we shall describe correspond to adsorbate coverages of the order of 0 = 0.03, that is not much larger than the detection limit of Auger spectroscopy. Under ordinary conditions the most conspicuous
leed.auger
system
ion pump
ion gun
Fig. I. Scheme of the experimental
to pumps
apparatus.
J. Ihmez
ef ui. / SIUC@of disordered udsorhcrte lqers
25
on Ni(OOl/
contaminant is hydrogen (CO partial pressure is kept below 2 X 10 -‘I Torr). In order to keep the surface free of hydrogen, the experiments have been performed above 370 K, as desorption of this gas was found to peak at about 360 K. At this temperature the desorption of CO was found to be negligeable. As a reference, we reach a value of the relative specular intensity I, = 0.5 for an incidence angle 8; = 70”. After polishing and subsequent introduction in the chamber, the intensity of the beam from the clean sample is lower (about a factor of 2) than its maximum value. Annealing the sample around 1400 K for a few minutes is required for the specular beam to reach its maximum intensity.
3. Results We have studied the variation of the helium specular peak as a function of ei after exposure of the Ni(lOO) face to oxygen and carbon monoxide in the tenth of a langmuir range. The exposure is calculated by integrating gauge records of gas pressure versus time and correcting for ionization probabilities. In order to obtain the coverage we have assumed a sticking coefficient of one for CO [ 131 and the values deduced by Holloway and Hudson [ 141 for oxygen
0.6
0.4
0.3
0.2
0.1
15
30
45
66
75
Bi
PI
Fig. 2. Experimental values of r for a carbon monoxide coverage 0 =0.025. Solid line: fitting with eq. (5) and Z(p)=h exp(--2p*/b*), h=0.59& b=5.4& a=7.8, Al/*=5XiO-“ A*. 0~7.5 meV. Dotted line: the same with D= 15 meV, h=0.50& AL/‘=3X lO-4 A*, 0=8.2, b=5.5 A.
J. Ihaner et.al. / Stucjs of disordered udwrbote
la_vers on Ni(OO1)
‘I
r
L
0.6
-
0.5
.
0.1
t
15
30
45
6%
75
BiP)
Fig. 3. Experimental values of r for an oxygen coverage of 0=0.034. Solid line: fitting for L)=7.5 meV with eq. (5) and Z(p) in the shape of a gaussian top, Z(p)=L(, exp(--2$/h’)--J,. h=d, -dz=0.31 A, a=5, h=4& A(/’ =2X 10v4 K. Dotted line: fitting for D= 15 meV, Z(p) in the shape of a paraboloid,
h=0.22,
0=4.3,
AU2 = I X 10d4 A2.
(it does not actually differ much from unity). We have used an average value of 0.95 in the 0 f 0 < 0.04 range. A typical run proceeds as follows: (a) The sample is cleaned and placed at a given angle Bi; the specular beam is recorded, I,. (b) Gas is admitted into the system until the desired exposure is reached; then the gas is pumped out. (c) Measurement of the intensity is made without moving the sample from its original position, 1. (d) The adsorbed gas is removed from the surface and the sample displaced to a new angle. This procedure has been found to be very reliable because the sample is practically not displaced during the adsorption. We have used a parameter r defined as r=r,
-I,/&),
(11
that is not sensitive to errors arising in the absolute deter~nation of either 1, or I such as those arising from beam sizes larger than sample dimensions near glancing angles. Fig. 2 shows the values of r as a function of Bi for a carbon monoxide coverage of 0 = 0.025 at 370 IL Notice the oscillation of the r versus ei curve. The curve has an absolute maximum near glancing incidence and shallow ~imum and maximum around 8, = 55” and ei = 35” repectively.
J. Ihunez et al. / St+v
of disordered udsorbute lqers
on Ni(oO1)
27
Fig. 3 shows the corresponding values for oxygen at 370 K for a coverage of 0 = 0.034. The shape of the curve differs markedly from that corresponding to CO. It is monotonically decreasing and levels off near glancing incidence. Experiments for different 0 have also been performed and they are described elsewhere [ 111. Let us just report here that for coverages as low as the ones discussed here non-linear effects in the r versus 0 dependence (for a given ei) are already noticeable.
4. Theoretical model A theoretical model, that will be shown to give good agreement with the experiments, has been derived on the basis of the Kirchhoff approximation [ 151. The validity of this approximation is discussed elsewhere [ 1 l] but let us just remark here that it is expected to hold in view of the small concentration of adsorbed atoms. We shall characterize impurities by a hard-wall corrugation function Z(R), where R is a two-dimensional coordinate parallel to the surface. The spatial extent of the impurity is represented by a non-dimensional parameter u equal to the surface actually covered by the adsorbate atom divided by the specific surface area bi (b, = nearest neighbour distance in nickel). On the basis of the Kirchhoff approximation the averaged specular coherent amplitude of the wave scattered from a flat metal surface at 0 K with a random set of adsorbate atoms (total coverage 0) is given by R=l-oO+zihexp[-iqZ(R)]
dR.
0’
The integral is extended to the surface area covered by the impurity. The parameter q is the momentum transfer of the incident particle and includes the effect [16] of an attractive well of depth D, q = 2[ k,2 cos28, + (2m/A2)
(3)
D] “2,
where m is the mass of the helium atom and fi the normalized Planck constant. Eq. (2) is very similar to the ones appearing in the diffraction of the light by apertures and its geometrical representation in the complex plane is of the form of a vibration curve. Let us define a complex number M M=
1 -&[hexp[-iqZ(R)] 0 0’
dR.
The scattered intensity I is obtained by multiplying AA*. Using the definition of it4 and taking the incident intensity 1, = 1, one immediately obtains r = 2~0
Re(M)
where Re stands
- e2a2 /MI’, for “real part of”.
(5)
For low coverages (00 < l), r is linear in 0. However, it must be realized that u can be large due to the considerable spread of the electronic charge around the impurity. In fact, as mentioned before, even in the range of a few hundredths of a monolayer the values of r are not simply proportional to 0. Several simple geometrical shapes (i.e. cylinder, cone) lead to integrals (2) with an analytical solution. For example for an impurity whose corrugation is in the shape of a paraboloid, Z(P)
=h[l-
(6)
(P/PM12]?
where p is a radial coordinate parallel resulting value of r is given by r = 2a@[ 1 - (sin
to the surface
and p’$ = (a/n)bi.
qh)/qh] .
the
(7)
The graph corresponding to eq. (7) is shown as a solid line in fig. 4. For the purpose of mathematical comparison,we have also represented the rather unrealistic limiting case of a cone. As expected, the oscillation of r versus 8; is smoothed with respect to the paraboloid case. The effect of changing the impurity height can be also easily visualized in the figure. From eq. (7) it is clear that for a given h the values of I span a given interval of the universal curve (solid line in fig. 4) between the limiting values to 8, = 90” and 0” respectively. Increasing h (@ )min and (@ ),,, corresponding
qh
-
10
5
Fig. 4. Plot of r as a function of qh (eq. (7)) for a paraboloid The upper segments (a-c) show the ranges of qh spanned D=7.5 meV.
0
(solid line) and a cone (dotted line). by three different coirugations for
J. Ibune: et al. / St&
of disordered udsorhate Iuyers m Ni(001)
29
results in an increase of the total span (qh),,, - (qh),,, and a shift of ( qh),i, to the left. Values of r as a function of qh for three different values of the impurity height h are shown as inserts at the top of the figure (segments a, b, c). The potential well depth was taken D = 7.5 meV from data [6] for the system O/Ni( 110). Finally, the contribution from Debye-Waller factor changes upon adsorption will be taken into account. Physically it corresponds to the fact that adsorbate and substrate atoms vibrate with different amplitudes. As is well known, even in clean surfaces, controversy exists over the accurate description of Debye-Waller effects. Consequently, we have tried to incorporate in the simplest possible way the effect by defining a parameter AU2 = (u”)-
(u,‘),
(8)
where (u’) represents an averaged mean square amplitude (MSA) of vibration of the atoms of a surface partially covered with an adsorbate. Introduction of this temperature correction leads to a temperature dependent value of r r=
1 - (1 -rO)
exp(-q2
AU*),
(9)
where r0 now designs the corresponding value at 0 K given by eq. (5). The best value of AU2 is obtained by fitting the experimental data to eq. (9). However, it is worth pointing out that in the case of oxygen the order of magnitude of its fitted value of AU* = 2 X 10-4A2 (fig. 3) can be compared with the data existing in the literature for an ordered layer of oxygen on copper if one makes the simple assumption that (u2)=
U; + (1 - O)U&
where u& and U: are the MSA of gas and substrate Lapujoulade et al. [ 171
atoms.
From
the data of
3x10-3
the coverage,
1 X 1O-4
<3x
0, of our experiments
we obtain
10-4A2,
in fair agreement with our fitted value of 2 X 10 -“A2. For very low coverages (@a << 1) r=0[q2(U2-Uz)+2oRe(M)].
(101
Comparing eqs. (10) and (5) it is easy to see that the Debye-Wailer correction resembles a background in the r versus Bi curve. Because of the q2 factor this background increases with low Bi and is practically negligible near glancing incidence.
30
J. Ihmwr
et ul. / Stu&
of dmordered
udsorhute
lugers on N1(001)
5. Discussion We first want to remark that a simple explanation of the r versus Bi curve by a classical argument can be excluded. This argument is based on shadowing effects of the impurity and as a result, a monotonical increase of r versus oi would be expected. This is not observed for either of the two gases. We turn then to our model described in section4. For every gas, before trying to optimize the fitting, we shall prove that even a simple shape as the paraboloid is (with a minimum of adjustable parameters) gives at least a semiquantitative agreement with the experimental data. In this way,we can become convinced that the theoretical model proposed is a fair approach to the actual physical process. Then, we shall be in a good position to proceed to more accurate fittings by relaxing some degrees of freedom in the shape of the corrugation D(p). Following this scheme the univocity of the solution will become more clear. The main features of the experimental curve for carbon monoxide can be explained on the basis of the simple paraboloid of eq. (7). The average value of the curve for low 8; fixed the value of u whereas the height of the impurity controls the position of the features. In fig. 4 this corresponds to the upper segment a. The position of the maxima and minima is in fair agreement with the experiments but the oscillation amplitude tends to be larger than observed. As can be inferred from comparison of the different shapes in fig. 4 the amplitude of the oscillation can be decreased by using a steeper impurity shape. In order to improve the fitting we have used a gaussian. The best fitting for D = 7.5 meV is shown in fig. 2 as a solid line. Notice that the optimized impurity height does not change too much when going from one shape to the other. On the basis of these arguments we propose the corrugation has a height h = 0.59 * 0.04 A and covers about 8 primitive cells of the substrate. In the case of oxygen, the fact that only part of an oscillation is visible indicates that we are placed around the first maximum from the right in fig. 4. In fact, we can make a semiquantitative argument even on the basis of this simple shape. If one keeps the potential D = 7.5 meV the only possible fit corresponds to a segment like the one marked b in fig. 4, corresponding to h = 0.31 A. The steep descent corresponding to high values of qh (left side of the segment) is compensated by the Debye-Waller correction. On the other hand, values of h lower than 0.31 A lead to a very steep decrease of r for near glancing incidence (fig. 4, upper segment c). In fig. 3 the best fitting is shown by using again a gaussian with the same height 0.31 A. However, it is interesting to point out that another good fitting is possible, even with the simple paraboloid shape, if one assumes a higher potential well depth D. A higher D pulls up the r versus Bi curve at high 8; (segment C) and one can fit the data with a smaller h. An alternative fitting to the oxygen curve is shown in fig. 3 (broken line) with D = 15 meV and h = 0.22 A. In order to check the influence of such an assumption the data for CO have also been
J. Ihunez et rrl. / Study of disordered udsorhate kqers on Ni(001)
31
fitted with D = 15 meV (dotted line, fig. 2). At present it is difficult to decide between these two possibilities. Whether or not as high values of D as the latter are realistic is doubtful but direct measurements are required. On the other hand,experiments described elsewhere [ 1 l] seem to suggest that a lower corrugation is more realistic. Therefore, we do not think that a definite answer can be given now. Let us finally discuss the physical meaning of all these parameters. One word of warning is necessary. One must not forget that NAS probes the electronic distribution at the turning point of the incident particle. Recently, Hamann [ 181has shown with a self-consistent calculation that this turning point (for H on Ni) is placed - 5 A above the level of the plane of the surface cores where equipotentials are very much smoothed down. Therefore our corrugation for CO and 0 are by no means small. In order to correlate these corrugations with geometrical distance between the surfaces cores, calculations of the type referred to [ 181 are required for isolated impurities. However, the well known fact that CO is adsorbed in an upright position on Ni is in good agreement with the observation of a corrugation about twice that of oxygen. We also want to point out that the large values of CI= 8 indicate that NAS is very sensitive to small concentration of adsorbates (and presumably also point defects) in the surface and suggests that this technique should be valuable for studying initial stages of adsorption and surface imperfections. Again, it is not straightforward correlating u at the scattering turning point with the actual spread of the impurity electronic charge over the surface. However, the high values of u suggest that this spread is important in agreement with recent calculations [ 191.
6. Conclusions The main conclusion of the present study is that elastic NAS can be used to obtain information not only about periodic overlayer but about the initial states of adsorption when the adsorbate atoms are isolated. A careful study of the curve can lead to obtention of geometrical parameters related to the corrugation potential. However, in order to compare this potential with intrinsic cyrstlllographic parameters realistic self-consistent calculations of charge densities [18] and potential above a surface with an adsorbate are urgently needed for a variety of systems.
Acknowledgements We thank A.M. Bar6 and R. Miranda for communication on his Debye-Waller
for discussions and J. Lapujoulade factor data. Financial support from
32
J. Ihuner
et aI. / Stu&
oj’ disordered
udsorhute
Ia~ers on Ni(OO1)
the Instituto de Estudios Nucleares (J.M.R.) the Joint Span-United Program and Comision Asesora Contract 4150/79 is acknowledged.
States
Note added in proof Formulas (2) and (5) are an approximation to the problem within the Eikonal approximation. A more general result will be presented elsewhere. Further calculations show that the conclusions and parameters given here are good.
References [l] [2] [3] [4] [5] [6] [7] [8] (91
[lo] [ 1I] [12] [13] [14] [15]
[16] [17]
[18] [19]
For a recent review, see H. Hoinkes, Rev. Mod. Phys. 52 (1980) 993. G. Boato, P. Cantini and L. Mattera, Surface Sci. 55 (1976) 141. N. Garcia, J. Chem. Phys. 67 (1977) 897; Phys. Rev. Letters 37 (1976) 912. G. Derry, D. Wesner, W. Carlos and D.R. Frankl, Surface Sci. 87 (1979) 629. M.J. Cardillo and G.E. Becker, Phys. Rev. Letters 40 (1977) 1148; 42 (1979) 508. K.H. Rieder and T. Engel. Phys. Rev. Letters 43 (1979) 373; 45 (1980) 824. G. Brusdeylins, R.B. Doak and J.P. Toennies, Phys. Rev. Letters 44 (1980) 1417. N. Cabrera, V. Celli and R. Manson. Phys. Rev. Letters 22 (1969) 346. D.L. Smith and R.P. Merrill, J. Chem. Phys. 52 (1970) 5861. B. Poelsema, G. Mechtersheimer and G. Comsa, in: Proc. 4th Intern. Conf. on Solid Surfaces, Cannes, 1980, p. 384. J. Ibahez. N. Garcia, J.M. Rojo and N. Cabrera. to be published. R. Campargue, in: Rarefied Gas Dynamics. Ed. J.H. de Leeuw (Academic Press, New York, 1966) Vol. 2, p. 279. K. Klier. A.C. Zettlemoyer and H. Leidheiser, J. Chem. Phys. 52 (1970) 589. P.H. Holloway and J.B. Hudson, Surface Sci. 43 (1974) 123. P. Beckman and A. Spizzichino, in: The Scattering of Light Electromagnetic Waves from Random Rough Surfaces, Eds. V.A. Fock and J.R. Wait (Pergamon. New York, 1963) ch. 6. p. 104. J. Beeby. J. Phys. C4 (1971) L359. J. Lapujoulade, Y. Le Corner, M. Lefort, Y. Lejay and E. Maurel, Phys. Rev. B22 (1980) 5740; J. Lapujoulade, Y. Lejay and G. Armand, Surface Sci. 95 (1980) 107. D.R. Hamann, Phys. Rev. Letters 46 (1981) 1227. J.M. Gallagher and R. Haydock, Surface Sci. 83 (1979) 117.
23
STUDY OF DISORDERED ADSORBATE (001) BY HELIUM ATOM SCATTERING J. IBAfiEZ,
N. GARCIA,
LAYERS ON NICKEL
J.M. ROJO and N. CABRERA
Depurtumento de Fisica Fundumental, Unioersidud Aut6noma de Madrid, Crmtohlanco, Madrid, Spcrin Received
14 September
1981; accepted
for publication
IO November
198 I
The intensity of a helium specular beam scattered from Ni( 100) with low concentration (0 = 0.03) of 0 and CO adsorbate atoms is found to oscillate with the angle of incidence. A simple theoretical model is proposed on the basis of the Kirchhoff approximation that is shown to fit well the data and leads to information about parameters of the corrugation potential of the surface. The electronic charge around an adsorbate atom of oxygen is found to protrude -0.30 A at the particle turning point level. The lateral spread of the charge corresponds to a surface of about 8 surface primitive cells.
1. Introduction In the past few years neutral atom scattering (NAS) has evolved from an odd technique that some people investigated from a fundamental point of view to a well accepted tool that is capable of probing static and dynamical properties of surfaces [l]. The elastic components of the scattered beams has been used in order to gain insight about the crystallography of the very first layer of clean and adsorbate-covered surfaces and in a number of cases a good agreement between theory and experiment has been achieved [2-61. Also, it has been proved [7], following earlier theoretical suggestions [8] that the analysis of the inelastic component can give much information about surface dynamics. All the work referred to above corresponds to surface periodic structures. It has been known for a long time that atom scattering is very sensitive to low concentrations of adsorbate atoms [9] and, in fact, the helium scattered specular beam has recently been used [lo] as a sensitive probe of hydrogen coverage on platinum for kinetic studies. Only very recently, it has been briefly reported [ 1 l] that NAS can be used in order to get information about surface electronic distributions around isolated surface atoms. In the present paper we give a full description of experiments along this line for oxygen and carbon monoxide adsorbed on Ni(OO1) and elaborate a simple theoretical model, based on the eikonal approximation, which is shown to be in good agreement with the experiments. We show that information concerning the geometry of 0039-6028/82/0000-0000/$02.75
0 1982 North-holland
the adsorbate isolated atoms can be inferred from these data and comparison for oxygen and carbon monoxide is made. It is worth remarking that isolated adsorbate atoms are physical entities that are not too dissimilar of defects like surface vacancies. Also, NAS is known to be very sensitive to surface disorder. Therefore studies, as the one reported here, may perhaps open new ways of attacking the really difficult problem of characterising surface defects in a solid.
2. Experimental The experimental set-up is shown in fig. 1. A nozzle source of helium [ 121 produces a rather monochromatic beam that impinges on the substrate maintained in ultrahigh vacuum (static pressure of the order of 2 X 10 _ ” Torr). The beam is chopped by means of a piezoelectric chopper and the scattered beams are detected with a rotating quadrupole with phase-sensitive techniques. Both in-plane and out-of-plane detection can be performed. The sensitivity of the detection is limited by noise coming mainly from the residual helium gas in the chamber and is of the order of 5 X 1O-4 of the incident beam. The value of the incident wavevector was measured to be il-,- 11 A’. The nickel (001) sample is in the form of a disc. Cleaning in the ultrahigh vacuum system has been performed by an alternation of argon bombardments and oxygen exposures at 900 K. After cleaning no traces of common contaminants (as sulfur or carbon) are visible in the Auger spectrum. However, after about 30 min segregated carbon began to appear in the surface. When that occurred, the experiment was interrupted and the sample cleaned before any more measurements were taken. In fact when some experience was gained, the intensity of the specular beam proved to be a much more sensitive technique for the detection of impurities than Auger spectroscopy. This is important because the experiments that we shall describe correspond to adsorbate coverages of the order of 0 = 0.03, that is not much larger than the detection limit of Auger spectroscopy. Under ordinary conditions the most conspicuous
leed.auger
system
ion pump
ion gun
Fig. I. Scheme of the experimental
to pumps
apparatus.
J. Ihmez
ef ui. / SIUC@of disordered udsorhcrte lqers
25
on Ni(OOl/
contaminant is hydrogen (CO partial pressure is kept below 2 X 10 -‘I Torr). In order to keep the surface free of hydrogen, the experiments have been performed above 370 K, as desorption of this gas was found to peak at about 360 K. At this temperature the desorption of CO was found to be negligeable. As a reference, we reach a value of the relative specular intensity I, = 0.5 for an incidence angle 8; = 70”. After polishing and subsequent introduction in the chamber, the intensity of the beam from the clean sample is lower (about a factor of 2) than its maximum value. Annealing the sample around 1400 K for a few minutes is required for the specular beam to reach its maximum intensity.
3. Results We have studied the variation of the helium specular peak as a function of ei after exposure of the Ni(lOO) face to oxygen and carbon monoxide in the tenth of a langmuir range. The exposure is calculated by integrating gauge records of gas pressure versus time and correcting for ionization probabilities. In order to obtain the coverage we have assumed a sticking coefficient of one for CO [ 131 and the values deduced by Holloway and Hudson [ 141 for oxygen
0.6
0.4
0.3
0.2
0.1
15
30
45
66
75
Bi
PI
Fig. 2. Experimental values of r for a carbon monoxide coverage 0 =0.025. Solid line: fitting with eq. (5) and Z(p)=h exp(--2p*/b*), h=0.59& b=5.4& a=7.8, Al/*=5XiO-“ A*. 0~7.5 meV. Dotted line: the same with D= 15 meV, h=0.50& AL/‘=3X lO-4 A*, 0=8.2, b=5.5 A.
J. Ihaner et.al. / Stucjs of disordered udwrbote
la_vers on Ni(OO1)
‘I
r
L
0.6
-
0.5
.
0.1
t
15
30
45
6%
75
BiP)
Fig. 3. Experimental values of r for an oxygen coverage of 0=0.034. Solid line: fitting for L)=7.5 meV with eq. (5) and Z(p) in the shape of a gaussian top, Z(p)=L(, exp(--2$/h’)--J,. h=d, -dz=0.31 A, a=5, h=4& A(/’ =2X 10v4 K. Dotted line: fitting for D= 15 meV, Z(p) in the shape of a paraboloid,
h=0.22,
0=4.3,
AU2 = I X 10d4 A2.
(it does not actually differ much from unity). We have used an average value of 0.95 in the 0 f 0 < 0.04 range. A typical run proceeds as follows: (a) The sample is cleaned and placed at a given angle Bi; the specular beam is recorded, I,. (b) Gas is admitted into the system until the desired exposure is reached; then the gas is pumped out. (c) Measurement of the intensity is made without moving the sample from its original position, 1. (d) The adsorbed gas is removed from the surface and the sample displaced to a new angle. This procedure has been found to be very reliable because the sample is practically not displaced during the adsorption. We have used a parameter r defined as r=r,
-I,/&),
(11
that is not sensitive to errors arising in the absolute deter~nation of either 1, or I such as those arising from beam sizes larger than sample dimensions near glancing angles. Fig. 2 shows the values of r as a function of Bi for a carbon monoxide coverage of 0 = 0.025 at 370 IL Notice the oscillation of the r versus ei curve. The curve has an absolute maximum near glancing incidence and shallow ~imum and maximum around 8, = 55” and ei = 35” repectively.
J. Ihunez et al. / St+v
of disordered udsorbute lqers
on Ni(oO1)
27
Fig. 3 shows the corresponding values for oxygen at 370 K for a coverage of 0 = 0.034. The shape of the curve differs markedly from that corresponding to CO. It is monotonically decreasing and levels off near glancing incidence. Experiments for different 0 have also been performed and they are described elsewhere [ 111. Let us just report here that for coverages as low as the ones discussed here non-linear effects in the r versus 0 dependence (for a given ei) are already noticeable.
4. Theoretical model A theoretical model, that will be shown to give good agreement with the experiments, has been derived on the basis of the Kirchhoff approximation [ 151. The validity of this approximation is discussed elsewhere [ 1 l] but let us just remark here that it is expected to hold in view of the small concentration of adsorbed atoms. We shall characterize impurities by a hard-wall corrugation function Z(R), where R is a two-dimensional coordinate parallel to the surface. The spatial extent of the impurity is represented by a non-dimensional parameter u equal to the surface actually covered by the adsorbate atom divided by the specific surface area bi (b, = nearest neighbour distance in nickel). On the basis of the Kirchhoff approximation the averaged specular coherent amplitude of the wave scattered from a flat metal surface at 0 K with a random set of adsorbate atoms (total coverage 0) is given by R=l-oO+zihexp[-iqZ(R)]
dR.
0’
The integral is extended to the surface area covered by the impurity. The parameter q is the momentum transfer of the incident particle and includes the effect [16] of an attractive well of depth D, q = 2[ k,2 cos28, + (2m/A2)
(3)
D] “2,
where m is the mass of the helium atom and fi the normalized Planck constant. Eq. (2) is very similar to the ones appearing in the diffraction of the light by apertures and its geometrical representation in the complex plane is of the form of a vibration curve. Let us define a complex number M M=
1 -&[hexp[-iqZ(R)] 0 0’
dR.
The scattered intensity I is obtained by multiplying AA*. Using the definition of it4 and taking the incident intensity 1, = 1, one immediately obtains r = 2~0
Re(M)
where Re stands
- e2a2 /MI’, for “real part of”.
(5)
For low coverages (00 < l), r is linear in 0. However, it must be realized that u can be large due to the considerable spread of the electronic charge around the impurity. In fact, as mentioned before, even in the range of a few hundredths of a monolayer the values of r are not simply proportional to 0. Several simple geometrical shapes (i.e. cylinder, cone) lead to integrals (2) with an analytical solution. For example for an impurity whose corrugation is in the shape of a paraboloid, Z(P)
=h[l-
(6)
(P/PM12]?
where p is a radial coordinate parallel resulting value of r is given by r = 2a@[ 1 - (sin
to the surface
and p’$ = (a/n)bi.
qh)/qh] .
the
(7)
The graph corresponding to eq. (7) is shown as a solid line in fig. 4. For the purpose of mathematical comparison,we have also represented the rather unrealistic limiting case of a cone. As expected, the oscillation of r versus 8; is smoothed with respect to the paraboloid case. The effect of changing the impurity height can be also easily visualized in the figure. From eq. (7) it is clear that for a given h the values of I span a given interval of the universal curve (solid line in fig. 4) between the limiting values to 8, = 90” and 0” respectively. Increasing h (@ )min and (@ ),,, corresponding
qh
-
10
5
Fig. 4. Plot of r as a function of qh (eq. (7)) for a paraboloid The upper segments (a-c) show the ranges of qh spanned D=7.5 meV.
0
(solid line) and a cone (dotted line). by three different coirugations for
J. Ibune: et al. / St&
of disordered udsorhate Iuyers m Ni(001)
29
results in an increase of the total span (qh),,, - (qh),,, and a shift of ( qh),i, to the left. Values of r as a function of qh for three different values of the impurity height h are shown as inserts at the top of the figure (segments a, b, c). The potential well depth was taken D = 7.5 meV from data [6] for the system O/Ni( 110). Finally, the contribution from Debye-Waller factor changes upon adsorption will be taken into account. Physically it corresponds to the fact that adsorbate and substrate atoms vibrate with different amplitudes. As is well known, even in clean surfaces, controversy exists over the accurate description of Debye-Waller effects. Consequently, we have tried to incorporate in the simplest possible way the effect by defining a parameter AU2 = (u”)-
(u,‘),
(8)
where (u’) represents an averaged mean square amplitude (MSA) of vibration of the atoms of a surface partially covered with an adsorbate. Introduction of this temperature correction leads to a temperature dependent value of r r=
1 - (1 -rO)
exp(-q2
AU*),
(9)
where r0 now designs the corresponding value at 0 K given by eq. (5). The best value of AU2 is obtained by fitting the experimental data to eq. (9). However, it is worth pointing out that in the case of oxygen the order of magnitude of its fitted value of AU* = 2 X 10-4A2 (fig. 3) can be compared with the data existing in the literature for an ordered layer of oxygen on copper if one makes the simple assumption that (u2)=
U; + (1 - O)U&
where u& and U: are the MSA of gas and substrate Lapujoulade et al. [ 171
atoms.
From
the data of
3x10-3
the coverage,
1 X 1O-4
<3x
0, of our experiments
we obtain
10-4A2,
in fair agreement with our fitted value of 2 X 10 -“A2. For very low coverages (@a << 1) r=0[q2(U2-Uz)+2oRe(M)].
(101
Comparing eqs. (10) and (5) it is easy to see that the Debye-Wailer correction resembles a background in the r versus Bi curve. Because of the q2 factor this background increases with low Bi and is practically negligible near glancing incidence.
30
J. Ihmwr
et ul. / Stu&
of dmordered
udsorhute
lugers on N1(001)
5. Discussion We first want to remark that a simple explanation of the r versus Bi curve by a classical argument can be excluded. This argument is based on shadowing effects of the impurity and as a result, a monotonical increase of r versus oi would be expected. This is not observed for either of the two gases. We turn then to our model described in section4. For every gas, before trying to optimize the fitting, we shall prove that even a simple shape as the paraboloid is (with a minimum of adjustable parameters) gives at least a semiquantitative agreement with the experimental data. In this way,we can become convinced that the theoretical model proposed is a fair approach to the actual physical process. Then, we shall be in a good position to proceed to more accurate fittings by relaxing some degrees of freedom in the shape of the corrugation D(p). Following this scheme the univocity of the solution will become more clear. The main features of the experimental curve for carbon monoxide can be explained on the basis of the simple paraboloid of eq. (7). The average value of the curve for low 8; fixed the value of u whereas the height of the impurity controls the position of the features. In fig. 4 this corresponds to the upper segment a. The position of the maxima and minima is in fair agreement with the experiments but the oscillation amplitude tends to be larger than observed. As can be inferred from comparison of the different shapes in fig. 4 the amplitude of the oscillation can be decreased by using a steeper impurity shape. In order to improve the fitting we have used a gaussian. The best fitting for D = 7.5 meV is shown in fig. 2 as a solid line. Notice that the optimized impurity height does not change too much when going from one shape to the other. On the basis of these arguments we propose the corrugation has a height h = 0.59 * 0.04 A and covers about 8 primitive cells of the substrate. In the case of oxygen, the fact that only part of an oscillation is visible indicates that we are placed around the first maximum from the right in fig. 4. In fact, we can make a semiquantitative argument even on the basis of this simple shape. If one keeps the potential D = 7.5 meV the only possible fit corresponds to a segment like the one marked b in fig. 4, corresponding to h = 0.31 A. The steep descent corresponding to high values of qh (left side of the segment) is compensated by the Debye-Waller correction. On the other hand, values of h lower than 0.31 A lead to a very steep decrease of r for near glancing incidence (fig. 4, upper segment c). In fig. 3 the best fitting is shown by using again a gaussian with the same height 0.31 A. However, it is interesting to point out that another good fitting is possible, even with the simple paraboloid shape, if one assumes a higher potential well depth D. A higher D pulls up the r versus Bi curve at high 8; (segment C) and one can fit the data with a smaller h. An alternative fitting to the oxygen curve is shown in fig. 3 (broken line) with D = 15 meV and h = 0.22 A. In order to check the influence of such an assumption the data for CO have also been
J. Ihunez et rrl. / Study of disordered udsorhate kqers on Ni(001)
31
fitted with D = 15 meV (dotted line, fig. 2). At present it is difficult to decide between these two possibilities. Whether or not as high values of D as the latter are realistic is doubtful but direct measurements are required. On the other hand,experiments described elsewhere [ 1 l] seem to suggest that a lower corrugation is more realistic. Therefore, we do not think that a definite answer can be given now. Let us finally discuss the physical meaning of all these parameters. One word of warning is necessary. One must not forget that NAS probes the electronic distribution at the turning point of the incident particle. Recently, Hamann [ 181has shown with a self-consistent calculation that this turning point (for H on Ni) is placed - 5 A above the level of the plane of the surface cores where equipotentials are very much smoothed down. Therefore our corrugation for CO and 0 are by no means small. In order to correlate these corrugations with geometrical distance between the surfaces cores, calculations of the type referred to [ 181 are required for isolated impurities. However, the well known fact that CO is adsorbed in an upright position on Ni is in good agreement with the observation of a corrugation about twice that of oxygen. We also want to point out that the large values of CI= 8 indicate that NAS is very sensitive to small concentration of adsorbates (and presumably also point defects) in the surface and suggests that this technique should be valuable for studying initial stages of adsorption and surface imperfections. Again, it is not straightforward correlating u at the scattering turning point with the actual spread of the impurity electronic charge over the surface. However, the high values of u suggest that this spread is important in agreement with recent calculations [ 191.
6. Conclusions The main conclusion of the present study is that elastic NAS can be used to obtain information not only about periodic overlayer but about the initial states of adsorption when the adsorbate atoms are isolated. A careful study of the curve can lead to obtention of geometrical parameters related to the corrugation potential. However, in order to compare this potential with intrinsic cyrstlllographic parameters realistic self-consistent calculations of charge densities [18] and potential above a surface with an adsorbate are urgently needed for a variety of systems.
Acknowledgements We thank A.M. Bar6 and R. Miranda for communication on his Debye-Waller
for discussions and J. Lapujoulade factor data. Financial support from
32
J. Ihuner
et aI. / Stu&
oj’ disordered
udsorhute
Ia~ers on Ni(OO1)
the Instituto de Estudios Nucleares (J.M.R.) the Joint Span-United Program and Comision Asesora Contract 4150/79 is acknowledged.
States
Note added in proof Formulas (2) and (5) are an approximation to the problem within the Eikonal approximation. A more general result will be presented elsewhere. Further calculations show that the conclusions and parameters given here are good.
References [l] [2] [3] [4] [5] [6] [7] [8] (91
[lo] [ 1I] [12] [13] [14] [15]
[16] [17]
[18] [19]
For a recent review, see H. Hoinkes, Rev. Mod. Phys. 52 (1980) 993. G. Boato, P. Cantini and L. Mattera, Surface Sci. 55 (1976) 141. N. Garcia, J. Chem. Phys. 67 (1977) 897; Phys. Rev. Letters 37 (1976) 912. G. Derry, D. Wesner, W. Carlos and D.R. Frankl, Surface Sci. 87 (1979) 629. M.J. Cardillo and G.E. Becker, Phys. Rev. Letters 40 (1977) 1148; 42 (1979) 508. K.H. Rieder and T. Engel. Phys. Rev. Letters 43 (1979) 373; 45 (1980) 824. G. Brusdeylins, R.B. Doak and J.P. Toennies, Phys. Rev. Letters 44 (1980) 1417. N. Cabrera, V. Celli and R. Manson. Phys. Rev. Letters 22 (1969) 346. D.L. Smith and R.P. Merrill, J. Chem. Phys. 52 (1970) 5861. B. Poelsema, G. Mechtersheimer and G. Comsa, in: Proc. 4th Intern. Conf. on Solid Surfaces, Cannes, 1980, p. 384. J. Ibahez. N. Garcia, J.M. Rojo and N. Cabrera. to be published. R. Campargue, in: Rarefied Gas Dynamics. Ed. J.H. de Leeuw (Academic Press, New York, 1966) Vol. 2, p. 279. K. Klier. A.C. Zettlemoyer and H. Leidheiser, J. Chem. Phys. 52 (1970) 589. P.H. Holloway and J.B. Hudson, Surface Sci. 43 (1974) 123. P. Beckman and A. Spizzichino, in: The Scattering of Light Electromagnetic Waves from Random Rough Surfaces, Eds. V.A. Fock and J.R. Wait (Pergamon. New York, 1963) ch. 6. p. 104. J. Beeby. J. Phys. C4 (1971) L359. J. Lapujoulade, Y. Le Corner, M. Lefort, Y. Lejay and E. Maurel, Phys. Rev. B22 (1980) 5740; J. Lapujoulade, Y. Lejay and G. Armand, Surface Sci. 95 (1980) 107. D.R. Hamann, Phys. Rev. Letters 46 (1981) 1227. J.M. Gallagher and R. Haydock, Surface Sci. 83 (1979) 117.