Langmuir 1989,5, 575-582 a ARGON COVEFIAQE .4.m
4
3 2
1 0
0
1
2
3
4
5
6
7
DISTANCE fR/ u)
Figure 9. 2D pair distribution functions for the first and third layers of the Arlgraphite system at 100 K. The first layer has a typical solidlike ordering, and the third layer has a typical fluid
form.
complete ~ e t t i n g . The ~ comparative plots of N ( z ) in Figures 5 and 6 are in good agreement; Le. they, like experiment, are very much alike. The upper layer maxima (Figure 7) and the spread of those peaks (Figure 8) as well as the populations of the layers (Table 111)indicate that the vertical structure of these three systems at 100 K is nearly the same. Another important feature is indicated in the 2D pair distribution functions of the individual layers at 100 K. Figure 9 shows the first layer of the argon film is quite solidlike even though the film is above its bulk triple point.
575
The third layer is still layered but has a very fluidlike character. This is in good agreement with the recent experiments of Zhu and Dash.3 Their heat capacity experiments indicate a layer by layer melting, which is in agreement with our simulations. It should be noted that since our simulation does not include zero-point effects and substrate-mediated forces, the temperature scale is not exactly the experimental one. However, sufficient analytic work14preceded these simulations to say that the model scales reasonably well to the experimental conditions of the thin film data of Zhu and Dash.3 The same behavior is shown in the results for the methane on both graphite and gold simulations. Also, the topmost regions of all three of these higher temperature films have lost most of their layered structure. The top region of the film has taken on an almost three-dimensional fluid character. In Table 11, the upper two peaks have widths at half-maximum (WHM) which are in excess of the root mean square displacements of the 3D solid. These features are consistent with the notion that all three films have the same growth character and the upper layer deposition from the vapor will be a nearly fluid surface.
Acknowledgment. I thank H. Taub, J. Larese, L. Passell, J. G. Dash, R. Evans, P. A. Monson, and L. W. Bruch for advice, instruction, and helpful discussions. I thank the University of Missouri-Kansas City, Computer Science Program, for the use of their Elxsi computer. Acknowledgement is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. Registry No. CH,, 74-82-8; Au, 7440-57-5; Ar, 7440-37-1; graphite, 7782-42-5.
Ellipsometric Study of Krypton, Methane, and Argon Films on Graphite: How Complete is Wetting?? H.S. Nham and G . B.Hess* Physics Department, University of Virginia, Charlottesville, Virginia 22901 Received October 27, 1988. In Final Form: February 13, 1989
An ellipsometric technique for measuring adsorbate coverage and a capacitance manometer were used to record numerous adsorption isotherms for krypton and methane on a graphite single surface. A range of temperatures was covered for which the saturated vapor pressure is a few millitorr to several torr. We also recorded a reflectance signal which gives complementary information on thick uniform films, as well as an indication of scattering by three-dimensional crystallites, when present on the surface. At low temperatures, a fairly uniform film grows rapidly at saturation to the equivalent of hundreds or (for krypton) sometimes thousands of layers, but it subsequently breaks up into strongly scattering crystallites. It is therefore unclear how thick a uniform film is stable. At higher temperatures, the film thickness for both adsorbates reaches a plateau at 8-12 layers, and the reflectance signal gives evidence for coexistence of three-dimensionalcrystallites. However, there are indications of A slow relaxation in the film, especially for krypton, raising the possibility that the equilibrium thickness could be larger than the observed plateau. Extrapolation of the measured chemical potentials at condensation of layers three through five suggests in the case of methane incomplete wetting consistent with the observed plateau level. More limited results for krypton are indecisive. A single argon isotherm closely resembles the plateau behavior of krypton.
Introduction Complete wetting of a substrate by an adsorbate means that an adsorbate film in equilibrium with ita three-di'Presented at the symposium on "Adsorption on Solid Surfaces", 62nd Colloid and Surface Science Symposium, Pennsylvania State University, State College, PA, June 19-22, 1988; W. A. Steele, Chairman. 0743-7463/89/2405-0575$01.50/0
mensional vapor grows uniformly over the substrate and increases in thickness continuously (or layer-by-layer) as a function of vapor pressure, the thickness diverging as the vapor pressure approaches saturation. Nonwetting or incomplete wetting means that three-dimensional droplets or crystallites coexist in equilibrium with vapor and with bare substrate or with substrate covered by an adsorbate film of finite thicknesi3.l The experimental distinction 0 1989 American Chemical Society
576 Langmuir, Vol. 5, No. 3, 1989
between complete and incomplete wetting becomes somewhat subtle if this finite thickness is more than 10 or 15 layers, as we shall discuss below. There has been considerable recent work on wetting of graphite and of chemically inert metal surfaces (relatively "strong", i.e., polarizable, substrates) by noble gases and simple molecular absorbates. Complete wetting by the liquid phase of the adsorbate has been reported for many of these systems, while wetting by the solid phase of the adsorbate is relatively rare: among adsorbates studied, only argon, krypton, and xenon have been thought to wet graphite at low temperature^.^,^ A liquid adsorbate should fail to wet if the adsorbate-adsorbate molecular interaction is stronger, in some appropriate measure, than the adsorbate-substrate intera~tion.~For a solid adsorbate, there may be the additional obstacle to wetting that the few-layer film may have structure or density incompatible with any plane of the bulk crystal, and the free energy cost of the restructuring or matching to these layers may exceed the gain from the substrate attractive p ~ t e n t i a l . ~The result for certain molecular adsorbates on graphite, such as ethylene6 and CF4r7,8is that at low temperatures a film of only one or two layers coexists in equilibrium with bulk solid. For spherical molecules on graphite, the possible mismatch is in the lattice parameter: The first layer or two is compressed by the excess holding potential of a strong substrate or modulated by the lateral potential. This will always produce some strain, which falls off less rapidly with distance from the interface than the holding potential, and so leads to incomplete ~etting.~JOThe limiting thickness, however, may be so large that experimental discrimination from complete wetting is difficult. Until quite recently, the completeness of wetting was often judged from the behavior of films of five or six layers.'l In this range, capillary condensation is becoming significant for powder substrates, and even with single-surface substrates a small degree of heterogeneity may overwhelm the relevant energy differences at slightly greater thicknesses. In this paper, we address the question of whether the behavior of certain solid adsorbates at thicknesses of about 10 layers (excess holding potential of order 0.5 K) indicates complete or incomplete wetting of graphite.
Experimental Method We obtain adsorption isotherms on a single cleaved surface of highly oriented pyrolytic graphite (HOPG) by measuring adsorbate coverage with a phase-modulated ellipsometric technique similar to that of Jasperson and Schnatterly.12 A spot on the graphite surface about 200 pm across is illuminated. Ellipsometric techniques measure the ratio p of the (complex) amplitude reflection (1)Recent reviews are given b y Dietrich, S. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J. L., Ed.; Academic Press: London, 1988; Vol. 12,Chapter 1. Ebner, C. In Chemistry and Physics of Solid Surfaces;Vanselow, R., Howe, R., Eds.; Springer-Verlag: Berlin, 1986;Vol. 5, Chapter 21. (2) Bienfait, M. Surf. Sci. 1985,162, 411. (3)Dietrich, S. ref 1, p 94. (4)Pandit, R.;Schick, M.; Wortis, M. Phys. Rev. B 1982,26, 5112. (5)Bienfait, M.;Seguin, J. L.; Suzanne, J.; Lerner, E.; Krim, J.; Dash, J. G. Phys. Rev. B 1984,29,983. (6)Kim, H.K.; Feng, Y. P.; Zhang, Q.M.; Chan, M. H. W. Phys. Reu. B 1988,37,3511. (7)Zhang, Q.M.;Kim, H. K.; Chan, M. H. W. Phys. Reu. B 1986,34, 8050. (8)Nham, H. S.; Drir, M.; Hess, G. B. Phys. Reu. E 1987,35, 3675. (9)Huse, D. A. Phys. Reu. B 1984,29,6985. (10)Gittes, F. T.;Schick, M. Phys. Reu. B 1984,30,209. (11)Thomy, A.; Duval, X. J. Chim. Phys. 1970,67,286;1969,66,1966. (12)Jasperson, S.N.;Schnatterly, S. E. Rev. Sci. Instrum. 1969,40, 761.
Nham and Hess
coefficients for light linearly polarized parallel (i' ) and perpendicular (i'J to the plane of in~idence.'~ $his is related to the real ellipsometric parameters A and p by ,
,ij =
~ ~ : ,=/ ipeiA '~
The Fresnel theory for reflection by plane parallel continuum layers can be used to relate these ellipsometric parameters to substrate and overlayer properties,13 the substrate being in this case a half space of refractive index (n + ik), covered by an overlayer of thickness d and refractive index nl. Alternatively, a thin overlayer can be represented by a surface polarizability at the substratevapor interface.14 The ellipsometer consists of the following sequence of optical elements: The light source is a diode laser with a wavelength of 780 nm and a collimated output of about 1 mw. The laser output is plane polarized at 45" to the plane of incidence on the sample. The laser beam first passes through a phase modulator, which has its axis in the plane of incidence. This modulator is a fused silica bar, which is optically isotropic; when strained, it becomes birefringent. The bar is mechanically driven at its fundamental axial resonance by a quartz transducer, cemented to one end. The relative phase delay between transmitted p- and s-polarized light is then
6(t) = A sin w t where A is proportional to the voltage applied to the transducer and w = 27rf, where f = 50 kHz is the resonant frequency. The phase-modulated light enters the cryostat through windows and is reflected from the sample at a 4 5 O angle of incidence. After exiting the cryostat, the light passes through a quarter-wavecompensator with a fast axis at an adjustable angle CY to the plane of incidence, through an analyzer fixed at 45" to the plane of incidence, and to a photodiode. Although stability is crucial, absolute alignment is not, unless we wish to make an absolute characterization of the substrate. In that endeavor, we are limited by imperfections, such as slight birefringence of the cell and cryostat windows. A Jones matrix analysis of this configuration, neglecting imperfections, yields for the normalized intensity at the detector
I' = ( ( p 2 - 1) sin 4a + 2(p2 + 1) 4p[cos 2a cos A sin2 2a sin A]sin 6 4p[-cos 2a sin A sin2 2a cos AICOS 6)/8 (1)
+
+
+
This is normalized to the intensity transmitted by the first polarizer, times li;J2. The dependence on modulator delay, 6, can be expanded in a Fourier series with Bessel function coefficients: m
COS
6 = Jo(A)
+ 2CJ2k(A) COS (%at) k=l
m
sin 6 = 2 C J 2 k + l ( A sin ) [(2k + l ) w t ] k=O
The amplitude is set at A = 138",for which Jo(A)= 0. We (13) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland: Amsterdam, 1977. (14)Siwkhin, D. V. Sou. Phys. JETP 1966,3,269. Dignam, M.J.; Fedyk, J. J. Phys. (Paris) Colloq. 1977,38, C5-57. (15)I I is normalized by Io with analog circuitry, provided that the Io signal exeeds 2 V, while below this level the normalization factor is fixed. For the data in Figure 2, this occurs when Io is less than 0.38scale units, which contributes to the attenuation of the oscillation in II on the right side.
Langmuir, Vol. 5, No. 3, 1989 577
Ellipsometric Study of Films on Graphite I I
-.cn c
I
I
i
I I I
0.8
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ea.
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0.5
0.8
0.4
I , (layers) Figure 1. Calculated locus of ellipsometer outputs IO and 11,as a function of film thickness, for a film of refractive index 1.30 on graphite. This is appropriate for krypton or methane films. The points are at 1W-A incrementa, and selected pointa are labeled in A. The ordinate Io is the dc output, a polarization-weighted reflectance. The abscissa Il is the normalized output at the modulation frequency, which is proportional to film thickness for values less than about 300 A. The scale in layers is appropriate in this range. In the experiment, the I, channel is saturated outside the band indicated by dashed lines.
use a low-pass filter to monitor the dc intensity Io and lock-in amplifiers at the fundamental and second harmonic frequencies to measure the components Zland 12, respectively. The corresponding Fourier components of I’ are
I‘o = ‘/,(p2 - 1) sin 4a
+ ‘/,(pz + 1)
+ sin2 2a sin A)Jl(A) 2a sin A + sin2 2a cos A)J2(A)
Z’l = -p(cos 2a cos A
Z ’2 = p(-cos
(2)
The compensator angle a is set near the value which nulls Ilfor the bare substrate. The effect of a very thin (compared to the wavelength) transparent film is to change A much more than p. That is, Ap, due to the film, is nearly orthogonal to jj. This would be exactly true for a dielectric substrate and is nearly true for a substrate, such as graphite, that has a dielectric constant large in magnitude compared to the films of interest.13 Therefore, the setting of a which nulls Il (a N 39O) also makes Il nearly maximally sensitive to film thickness. Thus, for thin films, Zl is proportional to coverage, and it provides our primary signal. In the usual mode of operation, the gain of the ac channel is regulated by a feedback circuit to maintain a constant dc component, so that the lock-in outputs are actually I1 = KlZ’i/Z’o I2
= KZZ’Z/I‘o
(3)
where Kl and K 2 are instrumental constants. The output of the dc channel is
Io = KolPJ2Z’,, (4) where KOis proportional to the laser intensity, detector sensitivity, and amplifier gain. The ellipsometer output (Il)at the modulation frequency is then a direct measure of the adsorbate coverage, provided the adsorbate film is
e
5
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0
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t
01
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I
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3
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18
Time ( m i d Figure 2. (a) Coverage signal Il and (b) reflectance signal Io vs time during adsorption and desorption of krypton on graphite at 58.4 K. Thick-film condensation takes place between A and B, reaching a thickness of about 4 pm, and evaporation between C and D. very thin compared to the wavelength of light. For thick uniform films, Zland the dc output Io are periodic functions of film thickness, with a period of order one-half wavelength. (These are forms of interference fringes in the film.) Figure 1shows a plot of Io versus 11,parameterized by the film thickness, as calculated for a uniform film of refractive index nl = 1.30 on graphite. In this calculation, as in the experiment, I I is normalized by I,,. Note that Iois only slightly affected by films of the order of 100 A. If three-dimensional crystallites with dimensions comparable to the wavelength or larger appear on the substrate, then there will be an additional reduction of Io due to the scattering of light out of the specular beam. Unless there is significant forward scattering, e.g., from flat platelets, or strong attenuation, the (normalized) Il signal should be unaffected. With the optical configuration adjusted to nearly null Zlfor the bare substrate, a large electronic gain can be used to resolve small changes in coverage. The ZI channel saturates at about +44 and -29 layers equivalent, as is seen in Figure 2a. Coverage isotherms are measured by regulating the temperature of the sample mount slightly colder than the surrounding cell and slowly admitting adsorbate gas through a leak valve. The gas pressure is monitored with a low-temperature capacitance diaphragm gauge. Adsorbate is then removed from the sample by cooling a separate copper probe in the cell below the temperature of the sample. All except the first layer can be desorbed from the sample in this way. Subsequent isotherms are obtained by heating the probe so as to raise the vapor pressure and distill adsorbate back to the sample and by admitting additional gas via the leak valve if required.
578 Langmuir, Vol. 5, No. 3, 1989
Nham and Hess
Possible heating of the substrate by the laser beam was checked by cycling the vapor pressure through a small range around a layer condensation step, alternately with full intensity and with the beam intensity attenuated by a factor of 2. No significant offset of the step pressure was observed. A data set under typical conditions gave an estimate of the heating at full intensity of 10 f 14 mK. Krypton Early volumetric adsorption isotherms for krypton on exfoliated graphite showed uniform films to at least five” to seven16layers at 77 K. A transmission electron microscope (TEM) study of krypton on natural graphite, cleaned by heating to 800 “C in vacuum, showed “layer by layer growth of nearly perfect crystals” at temperatures near 40 K.” More recently, the growth of various adsorbates on graphite at low temperatures has been studied by reflection high-energy electron diffraction (RHEED).5J8 Results for krypton indicate growth of uniform films up to at least the equivalent of 10 layers at 15-50 K. We have recorded more than 40 ellipsometric coverage isotherms for krypton at temperatures from about 57 K, where the saturated vapor pressure p o is 4 mTorr, to 80 K, where p o is about 3 Torr. Different behavior is found at low and high temperatures, but this does not appear to represent a transition in the equilibrium wetting properties: over the range 71-78 K, either behavior may be observed depending on other conditions, such as the amount of gas in the cell. Figure 2 is an example of the behavior at the lowest temperatures. Inflow of gas from the probe produces supersaturation at the graphite surface between points A and B ( t N 4-7 min). The large amplitude oscillation in both I , and Io indicates that an adsorbate film grows fairly uniformly to a thickness of over lo00 statistical layers (Ioreturns almost to its initial value after one cycle). Thereafter, attenuation of the oscillation and reduction of the mean value of Io indicate that the film thickness is becoming less uniform and the film is becoming sufficiently rough on a macroscopic scale to scatter diffusely most of the incident light. At point B, the adsorbate on the probe is exhausted, and from B to C conditions are static, with slow redistribution of adsorbate on the sample producing a further reduction in I,,. The negative value of II in this region presumably results from averaging over thicknesses ranging over several cycles of Figure 1. The number of cycles in AB (or CD) implies that the average adsorbate thickness is about 4 pm in this example. At point C, the probe has again cooled below the temperature of the sample and is drawing off adsorbate. The attenuated oscillations in I , (ref 15) between C and D show thinning of the average film thickness. The rapid recovery of Io near point D, accompanied by the positive swing of 11, indicates that the portions of the film with macroscopic thickness have largely disappeared, leaving transiently a film of about 40 layers. What does this tell about wetting? During rapid condensation}nearly uniform films up to hundreds of layers are seen to be at least metastable. However, this is essentially an observation about bulk growth kinetics. These films may not correspond to equilibrium, that is, the crystal form which minimizes interfacial energies. One thing which seems clear is that the first several layers for a suitable base for growth of macroscopic crystals. A t point (16) Data of Goffnet presented in: Thorny, A.; Duval, X.; Regnier, J. Surf. Sci. Rep. 1981, 1, 1. (17) Kramer, H. M. J . Crystal Growth 1976,33, 65. (18) Venables, J. A.; Seguin, J. L.; Suzanne, J.; Bienfait, M. Surf. Sci. 1984, 145,345.
- 1.0 - 0.9
4
0.8
C
AB 10
0
20
30
40
50
Time ( m i d
Figure 3. Coverage ZI(left scale) and reflectance signal Io (right scale) vs time during adsorption and desorption of krypton at 75.9 K. Reduction of Io indicates the presence of three-dimensional crystallites between points A and C. The leak valve was closed at B.
-10h
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-
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0 0 2
Langmuir, Vol. 5, No. 3, 1989 579
Ellipsometric Study of Films on Graphite
becomes macroscopically rough. The second distinctive behavior, favored by high temperatures and by low condensation rates, is illustrated in Figure 3. Gas was admitted through the leak valve. At point A, the pressure rise stops, Il peaks, and Io begins to decrease. At B, the leak valve was closed, causing an immediate drop in ZIto a plateau equivalent to approximately nine layers and initiating a slower relaxation of Io. One possible explanation for the failure to form a thick film might be that some spot on the sample mount is colder than the sample surface and is clamping the vapor pressure below the saturation value for the sample temperature. A temperature difference of 30 mK would be required to hold an inherently wetting film to nine layers. This is larger than we consider likely but cannot be ruled out. On the other hand, the reduction of Io by about 4% in the plateau region preceding point C is much larger than can be attributed to a uniform film of nine layers (from the calculation presented in Figure 1, it would require about 50 layers), so this reduction must be attributed to scattering by macroscopic crystallites of krypton, possibly nucleated on substrate defects. The coexistence of macroscopic crystallites (indicated by Io) with a stable film of 9 f 1 layers (indicated by 11)under nearly static conditions is direct evidence of incomplete wetting at this level. Another approach to the study of wetting is to determine the chemical potential pn at which the nth discrete layer condensation is observed, relative to the chemical potential po of bulk solid-vapor equilibrium: (5) where p,, and p o are the corresponding vapor pressures; the vapor is treated as an ideal gas. The simplest model for a wetting film is a slab with the same properties as bulk solid adsorbate but in the attractive potential of the substrate. In this model ce
p,
- p, = V , = -3C3do
(ndl m=O
+
(6)
where V,, is the potential of a molecule in the nth layer due to the graphite substrate, less the potential which would exist if the graphite were replaced by solid krypton. The limit p, should equal po for complete wetting but po < pmif wetting is incomplete. The layer-sum form in eq 6 is appropriate for graphite, but the coefficient C3is taken to represent the difference between graphite and solid krypton. The length do is the graphite layer spacing, and dl is the krypton monolayer thickness. In favorable pagges, five- or six-layer steps can be resolved in adsorption and six or seven in desorption. The adsorption steps beyond the second layer are much less vertical than the desorption steps (about 5 K width versus 0.4 K, for layers three and four) for krypton, apparently due to slow kinetics associated with relaxation of the solid film. Chemical potentials are taken at the bases of the steps, the point which shows least hysteresis (about 0.4 K). The data from two recent runs are shown in Figure 4. The second layer cannot be included in a satisfactory fit to eq 6 for any adsorbate we have studied on graphite (p2 is too high). Fits to steps 3 , 4 , and 5 for three isotherms below 63 K are consistent with extrapolation to complete wetting (pm= po) or to a maximum equilibrium film thickness as thin as about nine layers (pm- po I0.5 K).
Methane Methane on graphite has been studied extensively in the multilayer regime. Volumetric isotherms of Thomy and
I
I
I
I
I
U I
I
2
4
6
50 40
30 20 10
0 -10
-20
-30
I
0
8
Time ( m i d Figure 5. Coverage signal vs time during adsorption and desorption of methane at 57.6 K. A strongly scattering thick film is present in the region in which ZI is negative.
Duval" showed at least five discrete layers below saturation at 77.3 K. Inaba and Morrison reported, on the basis of three isotherms, a maximum of three layers at 65 K and a wetting transition at 75.5 K.le This is in conflict with other experiments at lower temperatures. Heat capacity measurements of Kim et al.%were interpreted as showing uniform film growth up to at least 14 layers in the temperature range 20-40 K: the orientational ordering peak differs from bulk behavior up to at least this thickness, and there is no sign of layer transitions. RHEED measurements between 14 and 40 K showed evidence of flat films up to nearly 15 layers but bulk crystallites (with faces not parallel to the substrate) for 15 or more statistical layers.2l Substrate LEED spot attenuation showed a minimum of four discrete layers at 35-40 K.21 At higher temperatures, approaching 90.5 K, Pettersen et have interpreted their heat capacity data as indicating uniform solid films up to at least 18 layers thick. We have recorded more than 100 isotherms for methane on graphite between 42 and 76 K. The qualitative behavior is similar to that reported for krypton but with a greater tendency to give a plateau rather than form a (probably metastable) thick layer. That is, in the higher temperature regime above about 61 K, a plateau in the coverage is observed even in passes with large condensation rate. Figure 5 is typical of the low-temperature regime: a film of several hundred statistical layers condenses and then breaks up into three-dimensional crystallites. In the interval in which 1,is negative, Io (not shown) is attenuated by 85%, presumably due to scattering. On evaporation, a much thinner film is left transiently as the scattering crystallites disappear. Nearly all isotherms taken above 61 K are similar to Figure 6. In some cases a much more extended flat plaal.22123
(19) Inaba, A.; Morrison, J. A. Chem. Phys. Lett. 1986, 124, 361. (20) Kim, H.K.; Zhang, Z. M.; Chan,M. H. W. J.Chem. SOC.,Faraday Trans. 2 1986,82, 1647. (21) Krim, J.; Gay, J. M.; Suzanne, J.; Lerner, E. J. Phys. (Les UliS, Fr.) 1986, 47, 1757. (22) Pettersen, M. S.;Lysek, M. J.; Goodstein, D. L. Surf. Sei. 1986, 175, 141. (23) Lysek, M.J.; Pettersen, M. S.;Goodstein, D. L. Phys. Lett. 1986, 115, 340.
580 Langmuir, Vol. 5, No. 3, 1989
10 -
Nham and Hess 0
I
I
-10
-20 1.00
;c;.; .-c =I
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4
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0
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-70 0
10
20
30
40
Time (min) Figure 6. Coverage I I (left scale) and reflectance signal Io (right scale) vs time during adsorption and desorption of methane at 75.0 K. The supply of methane from the warming probe was exhausted at point B.
teau is observed after the cessation of condensation than is observed in this example. The film never becomes much thicker than the plateau level, which is between 8 and 12 layers. The reduction of Io is again too large to be due to a uniform film of this thickness and must be attributed to scattering by three-dimensional crystallites. The reason why this attenuation does not become greater than the order of 10% is not clear, but it may be that there are more nucleation sites for unstrained three-dimensional growth on the copper sample mount than on the graphite cleavage plane. We never resolve layer steps all the way to the plateau level in either condensation or evaporation, although layers have been resolved to comparable thickness in liquid films (e.g., ethane"). When resolved, steps beyond the fifth are often reduced in height. We believe this is due to slow kinetics associated with lattice parameter relaxation when a layer is added. The result is that the (n+l)st layer begins to form (at a well-defined chemical potential, presumably over relaxed portions of the nth layer) before the nth layer is complete. We have converted the ZIsignal to a layer-number scale based on the height of the third to fifth layer steps. Extrapolation of this scale to the plateau level is uncertain by a significant fraction of a layer. The plateau level shows some variability from isotherm to isotherm, and histograms do not reveal clustering corresponding to integer differences in layer number. This may be the result of a small but variable contribution to ZIfrom thick crystallites. However, an indication that this contribution is not of major importance is that the ZI plateau can remain very flat while the reduction of Io decreases by as much as from 12% to 1%, presumably due to annealing or sublimation of crystallites. In three different runs, the distribution of plateau heights was 8.5 f 0.9 extrapolated layers over 57-72 K, 8.8 f 0.4 layers over 68-73 K, and 10.4 f 1.0 layers over 71-76 K. In a few cases, the plateau decreased by a step of monolayer size just at the start of evaporation. Chemical potentials at condensation of the third through sixth layers, relative to bulk solid, are plotted in Figure 7. The negative slopes of the layer lines indicate that the partial entropy at layer condensation is less than the bulk entropy at the same temperature but by an amount which (24) Nham, H.S.;Hess, G . B. Phys. Rev. E 1988, 38,5166.
-80 1
I
I
50
60
e,% 70
2 80
T (K) Figure 7. Chemical potential at layer condensation, relative to bulk solid, vs temperature for methane on graphite. Data for layers two through six are indicated by different symbols and are labeled on the right. The increased scatter at the lowest temperatures reflects sensitivity to manometer noise at low pressures. becomes small (IO.lkB per molecule) for the higher layers. These layer chemical potentials can be fit to a modified Frankel-Halsey-Hill model, similar to that described above for krypton. For comparison with this model, we grouped the data above 55 K into seven temperature intervals and made a fit to the averages for each interval. The data are consistent with the model, and the principal result is that the asymptotic chemical potential p, of the layered f i i is larger than the bulk solid chemical potential po by 0.46 f 0.21 K. The quoted uncertainty is the standard deviation for the distribution of the seven fits, only one of which is consistent with p, - cc, = 0. This result suggests incomplete wetting at the level of 8-11 layers (pn - po = 0 for n = 8-11), in agreement with the observed behavior in saturation. There is a marginally significant trend toward smaller p, - po (hence larger n) with increasing temperature. This is for condensation. There is some hysteresis on desorption, which occurs at a lower chemical potential by about 0.4 K (third layer), 0.3 K (fourth layer), or 0.1 K (fifth layer). The chemical potentials on desorption of higher layers can be determined accurately only in passes for which there was little excess adsorbate in the cell; otherwise, evaporative cooling offsets the sample temperature significantly. Thus there are only limited data for determifling p, from desorption, but the hysteresis values cited above do not lead to a significant offset. As for krypton, the widths of the higher steps are greater in adsorption than in desorption, but the effect is much less pronounced. The average adsorption (desorption) widths for isotherms above 70 K are as follows: third layer, 0.3 K (0.4 K); fourth layer, 0.9 K (0.2 K); fifth layer, 0.6 K (0.3 K). In addition, the third layer is often split, at a fraction of its height which varies from run to run, by typically 0.6 K in adsorption and 0.8 K in desorption. This occurs over a wide temperature range. Although not as conspicuous, similar splitting is also found in the second and fourth layers. When the third layer is split at 25% of its height, the fourth is split at 75%, suggesting that the effect producing the splitting is shifting p3 and p4 in opposite directions. We do not understand the origin of this, although impurity segregation or stacking fault effects
Langmuir, Vol. 5, No. 3, 1989 581
Ellipsometric Study of Films on Graphite I
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3
32
Time ( m i d Figure 8. Coverage I , (left scale) and reflectance signal Io (right scale)vs time during adsorption of argon at 64.7 K. The leak valve was c l d at point B. Desorption,not shown, was done at a higher
temperature.
seem possible. We have observed no similar splitting with any other adsorbate.
Argon Argon is another solid adsorbate which has been thought to completely wet graphite. RHEED18i26and TEMl’ experiments support this view, although the published data are sketchy. A heat capacity studyMin the range 60 < T < 90 K showed no sign of bulk nucleation up to at least 11 layers, where the melting peak was still distinctly below that of bulk argon. However, a recent graphite fiber microbalance experiment2’ finds incomplete wetting below the triple point and only four layers at saturation at 61 K. We have recorded a single argon isotherm at 64.7 K, for which the time dependence of Zland Io is shown in Figure 8. The behavior is very similar to the krypton isotherm in Figure 3. At least five clear layer steps are seen in adsorption and seven in desorption (not shown). After the leak valve was closed at point B, Il settled to a plateau equivalent to about 11 layers. The vapor pressure was not measured beyond the vicinity of the second step; the pressure at the second step agrees with previous measurement~.~’
Discussion Incomplete wetting of a strongly attractive substrate is expected when the free energy per molecule of the film as a function of thickness is larger at some thickness than the free energy of the bulk phase of the adsorbate. Then the bulk phase can coexist in equilibrium with a film of some finite thickness. For some adsorbates, such as ethylene or tetrafluoromethane at low temperatures, this occurs at one or two layers and is the result of a structural incompatibility between the first few layers of the film and the three-dimensional crystal. For spherical or quasi-spherical molecules, such as those studied here, this is unlikely, but (25) Seguin, J. L.; Suzanne, J.; Bienfait, M.; Dash, J. G.; Venables, J. A. Phys. Reo. Lett 1983,51,122. (26) Zhu, D. M.; Dash, J. G. Phys. Reo. Lett. 1986,57,2959; Phys. Reo. E 1988,38, 11673. (27) Bruechi, L.; Tono, G.; Chan, M. H. W. Europhys. Lett. 1988,6, .Ul -_-.
(28) Birgeneau, R. J., private communication.
a remaining possible difficulty is a mismatch of the lattice parameter^.^^ Unless the integral of the excess substrate potential is zero, the film will be strained due to the substrate interaction, and the strain energy will decrease less rapidly than the excess potential energy with increasing film thickness, leading to incomplete ~etting.~JOThe primary determining parameter is the ratio R of the integrated strengths of the adsorbate molecule-substrate and the adsorbate-adsorbate potentials (one possible explicit definition is given in ref 10). Gittes and Schick’O have made quantitative estimates which show there is a substantial range of R (about 1.5-3.5) for which the equilibrium thickness exceeds 20 layers. Xenon ( R = 1.51, krypton (1.6), argon (1.8), and neon (2.6) lie in this range, spanning it from the “weak substrate” to the “strong substrate” sides. Methane falls between argon and neon (R N 2.0) on this scalea5There is some uncertainty in the exact values of R which are appropriate for use with this model, but the very steep predicted increase in equilibrium layer number with R would make it very implausible that all three adsorbates which we have studied should wet to just 10 f 2 layers. Specifically, n increases from 10 to 40 as R goes from just 1.25 to 1.5 in the elastic model result shown in Figure 3a of ref 10. The “strong substrate” side is less steep but would require large adjustments of R. We have already noted that the very thick, optically uniform films which we observed transiently on condensation at low temperatures (e.g., Figure 2), while distinguishing these adsorbates from certain others such as CF4, do not provide any quantitative limits on the equilibrium thickness. The plateau behavior (Figures 3,6, and 8) gives evidence for the stable coexistence of moderately thick films with three-dimensional crystallites. However, there are indications, particularly in the case of krypton, that condensing layers relax to equilibrium only slowly. This is apparent in rounding of the upper part of the layer steps, as for instance the third layer in Figure 3. This is hysteretic and not a simple exponential relaxation in time. Furthermore, the heights of steps beyond about the fourth became successively smaller on the adsorption side, but not to the same degree on the desorption side, as though one layer were not yet completed when the next began to condense. This makes it plausible that the film reaches the thickness of the plateau with excess strain, and this excess does not relax on the time scale of the experiment. The relaxation might be this slow if it requires motion of dislocations, as suggested by Kramer.l’ X-ray diffraction by multilayer xenon films shows that stacking faults are prevalent in that system.28 If the excess strain raises the chemical potential by about 0.5 K, it could account for the film thickness plateaus observed. Although the mechanism interfering with rapid equilibration remains obscure, it seems clear that the plateau must be a lower limit on the equilibrium film thickness at saturation. In conclusion, we find for krypton a lower limit for the equilibrium film thickness at saturation of about nine layers over the temperature range studied. This is very similar to the limit found in the RHEED experiment5J8 at lower temperatures. For methane, the lower limit is 8-1 1 layers, increasing weakly with temperatures over the range 57-76 K. This result does not agree with conclusions drawn from earlier, much more limited isotherm meas u r e m e n t ~but ~ ~is consistent with other experiments. I t gives a weaker limit than the heat capacity studies at lower20and at higher22*23 temperatures but is more direct and avoids uncertainties associated with capillary condensation. It is also a somewhat weaker limit than was reported for low temperatures from RHEED.21 The layer
582
Langmuir 1989,5, 582-588
chemical potential data for methane are at least suggestive of incomplete wetting in equilibrium: p.. seems to be significantly above po when extrapolated from the desorption as well as the adsorption data. Our single argon isotherm gives a lower limit of approximately 11 layers. The disagreement with the graphite fiber experiment2' remains unexplained but is consistent with other experiments.
Acknowledgment. We thank M. H. W. Chan and G. Torzo for helpful discussions. We thank G. Reynolds for assistance with the argon measurements. This work was supported by the National Science Foundation, Low Temperature Physics Program, Grant No. DMR 8617760. Registry No. Kr, 7439-90-9; Ar, 7440-37-1; CHI, 74-82-8;
graphite, 7782-42-5.
Phase Diagrams of K and Cs on Cu(110) and Cu(111) Surfacest W. C. Fan and A. Ignatiev" Department of Physics, University of Houston, Houston, Texas 77204 Received October 27, 1988. I n Final Form: February 24, 1989
The ordered phases of K and Cs overlayers on the Cu(ll0) and Cu(ll1) substrates have been studied with low-energy electron diffraction (LEED) at temperatures between 80 and 400 K. The K and Cs on the Cu(ll0) surface form quasi-hexagonal (QH) structures. These QH structures grow on the 80 K Cu(ll0) surface in the [lo] direction as the coverage increases. At temperatures above 150 K, the alkali-metal overlayers induce Cu(ll0) surface reconstructions. The depositions of the K and Cs on the 80 K Cu(ll1) surface result in orientationally ordered overlayers, which grow as a function of coverages. The coverage-temperature dependence of the observed ordered overlayer phases is described in the phase diagrams for the K and Cs systems. Introduction The adsorption of alkali metals on transition-metal surfaces has been an interesting research subject for many years.l These studies were motivated by the need to examine electronic and atomic structural properties as related to the application of the alkali-metal adsorbates in catalytic reactions. Recent studies have shown some interesting electronic properties induced by alkali-metal adsorbates, such as decreases of the work function and a shift of electronic surface states.2 These electronic properties accompanying alkali-metal adsorption have recently had successful theoretical e x p l a n a t i ~ n . ~ ? ~ Besides studies of electronic phenomena, a variety of atomic structures of the alkali-metal overlayers have been also observed as a function of coverage and temperature. For example, incommensurate structures of alkali overlayers have been grown on various substrate^.^,^ These interesting atomic structures are good candidates for the study of order-disorder transitions6-10in two dimensions. The order-disorder transition of an orientationally ordered incommensurate structure is of additional interest since adatoms of the incommensurate phase may realize a "2-D solid" structure. Furthermore, a number of surface reconstructions induced by adsorbates have been reported recently, such as alkali metals on Ni(ll0) and Ag(llO)." One interesting reconstruction in those systems is the (1x2) reconstruction of a number of fcc (110) metal surface^.'^-'^ Three simple models for the (1x2) reconstructed surface structure have been proposed in the published literat~re.'~-'~ These are the "missing-row" model, "row-paring" model, and 'Presented at the symposium on "Adsorption on Solid Surfaces", 62nd Colloid and Suface Science Symposium, Pennsylvania State University, State College, PA, June 19-22, 1988; W. A. Steele, Chairman. 0743-7463/89/2405-0582$01.50/0
"sawtooth" model. LEED dynamical c a l ~ u l a t i o n s ~ in-~ J ~ dicate that the (1x2)reconstruction is consistent with the "missing-row" model or the "row-paring" model. Recent theoretical calculation^'^ for the Pt(ll0) surface using the embedded atom method have also shown that the (1x2) reconstruction is favored by the "missing-row" structure as compared to the "sawtooth" structure. In this paper, the growth and the order-disorder phase transitions of alkali-metal overlayers on the Cu(ll1) and Cu(ll0) surfaces are described through quantitative LEED measurements. In addition to the overlayer structures, the reconstruction of the Cu(ll0) surface under Cs and K adsorption is also described in this paper. Experimental Section The experiments were carried out in an ultra-high-vacuum (1)Gerlach, R. L.; Rhodin, T. N.'Surf. Sci. 1969,17,32. (2)Soukiassian, P.; Riwan, R:; Lecante, J.; Wimmer, E.;Chubb, S. R.; Freeman, A. J. Phys. Rev. B 1985,31,4911. (3)Soukiassian, P.; Riwan, R.; Lecante, J.; Guillot, C.; Chauveau, C. Bull. Am. Phys. SOC.1983,28, 261. (4)Doering, D. L.; Semancik, S. Surf. Sci. 1986,175,L730; Phys. Rev. Lett. 1984,53,66; Surf. Sci. 1983, 129,177. (5)Aruga, T.; Tochihara, H.; Murata, Y. Phys. Rev. Lett. 1984,52, 1794. ( 6 ) Kosterlitz,J. M.; Thouless, D. J. J. Phys. C. 1972, 6,1181. (7) Nelson, D. R.; Halperin, B. I. Phys. Reu. B 1979,19,2457. (8)Young, A. P. Phys. Reu. B 1979,19, 1855. (9)Sachdev, S.Phys. Reu. B 1984,31,4476. (10)Bedanov, V. M.; Gadiyak, G. V.; Lozovik, Y. E. Sou. Phys. JETP 1985,61,967. (11)Hayden, B. E.;Price, K. C.; Davie, P. J.; Paolucci, G.; Bradshaw, A. M. Solid State Commun. 1983,48,325. (12)Kleinle, G.; Penka, V.; Behm, R. J.; Ertl, G.; Moritz, W. Phys. Reu. Lett. 1987,58, 148. (13)Dobler, U.;Baberschke, K.; Vvedensky, D. D.; Pendry, J. B. Surf. Sci. 1987,178,679. (14)Moritz, W.;Wolf, D. Surf. Sci. 1985,163, L655; Surf. Sci. 1979, 88.L29. (15)Daw, M. S.;Foiles, S. M. J. Vac. Sci. Technol. A. 1986,4,1412.
0 1989 American Chemical Society
