Lateral Compression of a Xe Film Physisorbed on Ag(111) - Langmuir

It was found that the compression in the first layer precedes the second layer adsorption. Using a simple model, we calculated the densities of the fi...
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Langmuir 2003, 19, 4627-4632

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Lateral Compression of a Xe Film Physisorbed on Ag(111) Sin Igarashi,*,† Aki Tosaka, Takato Hirayama,‡ and Ichiro Arakawa Department of Physics, Gakushuin University, 1-5-1, Mejiro, Toshima-ku, Tokyo 171-8588, Japan Received August 19, 2002. In Final Form: March 15, 2003 The growth and the structure of a Xe film physisorbed on a Ag(111) substrate have been investigated by means of ellipsometry and extremely low current low-energy electron diffraction (XLEED). Equilibrium between the Xe film and the coexisting three-dimensional Xe gas was maintained throughout the film growth. From a monolayer to a sufficiently thick film, the Xe film has a clear hexagonal structure whose directions of the unit vectors are coincident with those of the substrate. We have made a systematic observation of the change of the Xe-Xe spacing in the process of film growth. The Xe-Xe spacing just after the first layer condensation is a few percent larger than that of the bulk. While the pressure is increased or the temperature is lowered, the Xe-Xe spacing decreases gradually and reaches the bulk value before the second layer condensation. The second layer adatom density has been determined from ellipsometric and XLEED data. It was found that the compression in the first layer precedes the second layer adsorption. Using a simple model, we calculated the densities of the first and the second layer, which are consistent with our experimental results.

1. Introduction Physisorption systems on a microscopically smooth crystal surface have been studied for their interesting two-dimensional (2D) behavior. The 2D properties of a monolayer film, such as thermodynamics, surface structure, electronic structure, and so on, have been clarified by experimental observations and theoretical studies.1 A physisorbed film grows to a sufficiently thick one, almost bulk, by increasing the pressure of the surrounding threedimensional (3D) gas or by lowering the temperature of the system. The various parameters that characterize the 2D properties change into those of the bulk during the film growth. Studies of multilayer films have provided insight into the transition process from 2D film to bulk.2 The most fundamental and straightforward way for the experimental study of the film growth is the measurement of an adsorption isotherm which shows the relation between the amount of adsorbed molecules per unit area of the substrate surface and the equilibrium vapor pressure under constant temperature. Adsorption isotherms of various adsorbates on exfoliated graphite, which has a chemically inert and homogeneous surface with a large specific area, have been measured with the volumetry method, and the nature of phase transitions and phase diagrams have already been clarified.3 There are few effective probes, however, for the study of a thick film physisorbed on a surface of a metal single crystal. The helium-atom scattering studies of rare gas films on Ag(111)4 and Pt(111),5,6 which were performed * Corresponding author. † Present address: Department of Materials Science, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibarakiken 319-1195, Japan. Fax: +81-29-282-6716. E-mail: sin@ popsvr.tokai.jaeri.go.jp. ‡ Present address: Department of Physics, Rikkyo University, Tokyo 171-8501, Japan. (1) Bruch, L. W.; Cole, M. W.; Zaremba, E. Physical Adsorption: Forces and Phenomena; Clarendon Press: Oxford, 1997. (2) Hess, G. B. In Phase Transitions in Surface Films 2; Taub, H., Torzo, G., Lauter, H. J., Fain, S. C., Jr., Eds.; Plenum Press: New York, 1991; p 357. (3) Thomy, A.; Duval, X.; Regnier, J. Surf. Sci. Rep. 1981, 1, 1. (4) Gibson, K. D.; Sibener, S. J. J. Chem. Phys. 1988, 88, 7893.

under conditions far from equilibrium, exhibited layerby-layer growth up to a thickness of more than 20 layers. The isobar measurements of rare gas films physisorbed on Ag(111)7,8 using low-energy electron diffraction (LEED) showed the difficulty in achieving ideal layer-by-layer growth for films thicker than two layers under quasiequilibrium conditions. Dai et al.9,10 observed a Xe film thicker than 22 nm physisorbed on the Ag(111) surface under quasiequilibrium conditions. Using the LEED technique, Chesters et al.11 observed that the Xe monolayer on a Ag(111) surface was a triangular lattice which was incommensurate but aligned with the substrate at 77 K. The Xe-Xe spacing of 0.450 ( 0.003 nm is about 3% larger than that of the bulk (0.438 nm) at 77 K. Neither the rotated incommensurate structure predicted by Novaco and McTague12 nor a commensurate structure was observed. The experimental results have been interpreted as being due to the small corrugation of Ag(111) and the pinning of the overlayer at the step of the substrate. Leatherman et al.13 reported that surface steps play an active role in the determination of rotation angles for rare gas monolayers physisorbed on Ag(111). The change of the Xe-Xe spacing of Xe/Ag(111) was observed by Unguris et al. using LEED7 and by Dai et al. using X-ray diffraction.9 They observed the compression of a monolayer film only in isobaric growth under quasiequilibrium conditions. It was achieved using a (5) Kern, K.; David, R.; Palmer, R. L.; Comsa, G. Phys. Rev. Lett. 1986, 56, 2823. (6) Kern, K.; Zeppenfeld, P.; David, R.; Comsa, G. Phys. Rev. B 1987, 35, 886. (7) Unguris, J.; Bruch, L. W.; Moog, E. R.; Webb, M. B. Surf. Sci. 1979, 87, 415. (8) Unguris, J.; Bruch, L. W.; Moog, E. R.; Webb, M. B. Surf. Sci. 1981, 109, 522. (9) Dai, P.; Angot, T.; Ehrlich, S. N.; Wang, S.-K.; Taub, H. Phys. Rev. Lett. 1994, 72, 685. (10) Dai, P.; Wu, Z.; Angot, T.; Wang, S.-K.; Taub, H. Phys. Rev. B 1999, 59, 15464. (11) Chesters, M. A.; Hussain, M.; Pritchard, J. Surf. Sci. 1973, 35, 161. (12) Novaco, A. D.; McTague, J. P. Phys. Rev. Lett. 1977, 38, 1286. (13) Leatherman, G. S.; Diehl, R. D.; Karimi, M.; Vidali, G. Phys. Rev. B 1997, 56, 6970.

10.1021/la0264264 CCC: $25.00 © 2003 American Chemical Society Published on Web 05/02/2003

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constant flux of gas directed at the sample. The effective 3D gas pressure was determined by observing the temperature at which the flux was in equilibrium with the bulk Xe film. These experimental studies have utilized diffraction or spectroscopic techniques using photons, electrons, neutrons, and atoms as a probe, which may restrict the operating pressure or cause desorption and charging-up of the sample surface. We have developed an experimental apparatus for in situ observation of a physisorption system on a metal surface by ellipsometry and by extremely low current low-energy electron diffraction (XLEED). Both methods are suitable for the observation of physisorption systems because they have little influence on the sample. For Xe/Ag(111), we succeeded in observing the third layer condensation under equilibrium conditions and in determining the surface structure of thick films.14 Systematic observation under equilibrium conditions will clarify the transition process from 2D film to bulk. We chose Xe/Ag(111) as a target for several reasons: electron-stimulated desorption for Xe is much less than for Ar and Kr;15 a close-packed (111) surface of Ag is widely used as a substrate; the lateral variation (corrugation) in the Xe-Ag binding energy can be neglected.16 We observed the surface structure by XLEED while monitoring the film growth by ellipsometry from a submonolayer to a thick film where the equilibrium pressure was nearly equal to the bulk saturation vapor pressure. In a previous paper,14 we reported that a sufficiently thick Xe film has a clear (111) structure of face-centered cubic (fcc) crystal which keeps a relative orientation to the Ag(111) substrate. The results suggest that the structure of the film changes smoothly to that of the bulk without a strain in the film. Here we report how the Xe-Xe spacing of Xe/Ag(111) varies in the process of film growth.

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Figure 1. Schematic diagram of the experimental apparatus.

2. Experimental Section The experimental apparatus, shown schematically in Figure 1, has been described in detail previously.14,17 Here we briefly summarize the outline of the experimental apparatus and method. The silver single crystal was clamped on a sample holder as shown in Figure 2. The holder was attached to the thermal exchanger of a He-gas-flow cryostat. The temperature of the crystal was controlled in the range between 40 and 100 K by regulating the flow rate of cold He gas to the cryostat by an automatic valve. The sample temperature was determined from the saturation vapor pressure observed in an adsorption isotherm and from the table value of Leming and Pollack18 because it was difficult to measure the absolute and actual temperature of the surface by a thermocouple attached to the sample holder. We measured the difference between the true temperature of the surface and that of the sample holder to make a calibration table. The difference was 5.7 K at the surface temperature of 60 K. This calibration table made it possible to estimate the true surface temperature from the thermocouple throughout the experiments. The XLEED system and the ellipsometer are arranged to observe a physisorbed film simultaneously. The unique feature of the XLEED instrument is the pulse counting and position sensitive electron detector (model 3392A Open-Face MCP/RAE Sensor, Quantar Technology). The incident electron beam current was adjusted so that the total electron count became 105-106 (14) Igarashi, S.; Abe, Y.; Irie, Y.; Hirayama, T.; Arakawa, I. J. Vac. Sci. Technol., A 1998, 16, 974. (15) Moog, E. R.; Unguris, J.; Webb, M. B. Surf. Sci. 1983, 134, 849. (16) Cohen, P. I.; Unguris, J.; Webb, M. B. Surf. Sci. 1976, 58, 429. (17) Igarashi, S.; Abe, Y.; Hirayama, T.; Arakawa, I. Proceedings of the International Symposium on Polarization Analysis and Applications to Device Technology, 1996, Yokohama, Japan; SPIE-International Society for Optical Engineering: Bellingham, WA, 1996. (18) Leming, C. W.; Pollack, G. L. Phys. Rev. B 1970, 2, 3323.

Figure 2. Schematic diagram of the sample holder and thermal exchanger. The inset shows how the sample is attached to the sample holder. counts over the whole detector for 1 min of data accumulation, which is sufficient for a qualitative analysis of a LEED pattern. The beam current in this condition was about 0.1 pA. The thickness of an adsorbed film was determined from the ellipsometric parameters: “relative phase shift” ∆ and “amplitude reflectance ratio” ψ. The relative change in ∆, δ∆ ) |∆ - ∆0|, where ∆0 is the shift for the bare substrate, has been used as a monitor of the amount of adsorption in the ellipsometric studies of physisorbed layers on graphite19,20 and metal surfaces.21 According to the microscopic model formulated by Dignam and Fedyk,22 δ∆ is given by δ∆ ) cNR, where N is the amount of (19) Quentel, G.; Rickard, J. M.; Kern, R. Surf. Sci. 1975, 50, 343. (20) Volkmann, U. G.; Knorr, K. Surf. Sci. 1989, 221, 379. (21) Itakura, A.; Arakawa, I. J. Vac. Sci. Technol., A 1991, 9, 1779.

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adsorbate and R is the polarizability of the adatom. The coefficient c depends on the wavelength of light, the incident angle, and the complex refractive index of the substrate. Assuming that the polarizability is independent of the layer number and the adsorbate phase, we are able to determine the total amount of the adsorbate. As the density of the solid layer can be determined from the lattice constant obtained by XLEED, we can deduce the density of the 2D gas adsorbed on the solid layer.

3. Results Typical XLEED patterns of Ag(111) and Xe monolayer films on Ag(111) are shown in Figure 3. As seen from Figure 3b, the orientation of the Xe overlayer is aligned with that of the substrate, which agrees with the LEED observation by Chesters et al.11 Lowering the incident electron energy of the XLEED, we can clearly observe the six Xe spots of the Xe monolayer on Ag(111), as shown in Figure 3c. The Xe-Xe spacing is calculated from the average distance of Xe spots in the XLEED pattern using the Ag(111) pattern as a reference for a lattice parameter; the nearest neighbor distance of bulk Ag is 0.288 nm. The precision in determining the lateral spacing is estimated to be 1%, which is mainly due to the resolution and nonlinearity of the position sensitive electron detector of the XLEED system. Our interest is how the Xe-Xe spacing varies in the process of film growth. We have made a systematic observation of the change of the Xe-Xe spacing in one and two monolayer films at pressures between 10-7 and 10-2 Pa and at temperatures between 50 and 100 K. Throughout the film growth, the equilibrium between the gas phase and the adsorbed one was established either at a constant temperature (isothermal growth) or at a constant pressure (isobaric growth), which was confirmed by testing the reversibility of the layer condensations in the isothermal and isobaric growth conditions. It typically takes 6 h or more to obtain one isotherm or isobar. Figure 4a shows the change of the Xe-Xe spacing for the case of isothermal growth at 68.9 K together with the ellipsometric adsorption isotherm. To compare the results of the different growth modes (isothermal and isobaric growth), the abscissa is the chemical potential of the adsorbate, which is equal to that of the surrounding gas under equilibrium conditions. Assuming an ideal gas, we derive the chemical potential from the following formula:

[ (

µ ) kT ln

)]

3 p h2 /2 kT 2πmkT

(1)

where k is Boltzmann’s constant, h is Planck’s constant, m is the mass of a Xe atom, and p is the gaseous pressure. The ordinate of the adsorption isotherm is the relative phase shift, δ∆ ) |∆ - ∆0|, and the right ordinate is the relative expansion of the Xe-Xe spacing, (d - d0)/d0, where d is the Xe-Xe spacing of the film and d0 is that of the bulk (0.438 nm at 68.9 K23). Two vertical rises at -243 meV/atom (2.4 × 10-7 Pa) and -190 meV/atom (1.9 × 10-3 Pa) in the isotherm correspond to the first and the second layer condensation, respectively. As the Xe pressure approaches the saturation vapor pressure, δ∆ increases rapidly because of the formation of a 3D bulk film. The result for isobaric growth at 1 × 10-5 Pa is shown in Figure 4b. The first and the second layer condensations occur at almost the same chemical potentials as the isothermal growth, about -250 and -190 meV/atom, respectively. (22) Dignam, M. J.; Fedyk, J. J. Phys. 1977, 11, C5-57. (23) Korpiun, P.; Luscher, E. In Rare Gas Solids; Klein, M. L., Venables, J. A., Eds.; Academic Press: London, 1977.

Figure 3. (a) XLEED pattern of Ag(111) measured with an incident electron energy Ei of 119.9 eV at a temperature T of 68.5 K. The hexagonal diffraction pattern (dashed lines in the figure) indicates the structure of the Ag(111). (b) XLEED pattern of the Xe monolayer physisorbed on Ag(111) measured at T ) 66.1 K and Ei ) 105.5 eV. (c) XLEED pattern of the Xe monolayer physisorbed on Ag(111) measured at T ) 68.5 K and Ei ) 60.9 eV. The hexagonal diffraction pattern (dotted-dashed lines in the figure) indicates the structure of the Xe.

The Xe-Xe spacing just after the condensation of the first layer is a few percent larger than that of the bulk. At 68.9 K, the observed Xe-Xe spacing, d, is 0.447 nm, the Xe-Xe spacing of the bulk, d0, is 0.438 nm,23 and the relative expansion, (d - d0)/d0, is calculated to be 2.1%. The Xe-Xe spacing in the monolayer solid on Ag(111) was theoretically calculated by Bruch and Phillips24,25 along the 2D sublimation curve; they obtained values of (24) Bruch, L. W.; Phillips, J. M. Surf. Sci. 1980, 91, 1. (25) Phillips, J. M.; Bruch, L. W. J. Chem. Phys. 1985, 83, 3660.

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Figure 5. Adsorption isotherm (dots) and the density (closed circles) of the second layer of Xe/Ag(111) at temperatures of (a) 68.9 K and (b) 76.2 K. The dotted lines are guides to the eyes. The calculated results (thick solid curves) are located at a higher chemical potential. This is because the calculation does not include the contribution of a temperature. Figure 4. Adsorption isotherm (dots) and the relative expansion of Xe-Xe spacing of Xe/Ag(111) (closed circles) (a) at a temperature of 68.9 K and (b) at a pressure of 1 × 10-5 Pa.

0.445 nm at 30 K, 0.449 nm at 50 K, 0.457 nm at 80 K, and 0.462 nm at 90 K, which are systematically larger than the experimental results by Unguris et al.7 Our experimental result shows good agreement with the latter (e.g., 0.449 nm at 70 K7). The present result shows that on increasing the pressure (isothermal growth) or lowering the temperature (isobaric growth) the Xe-Xe spacing gradually decreases to that of the bulk before the second layer condensation and keeps the bulk value thereafter, which is consistent with the previous works.7,9 Then the layers which have the Xe-Xe spacing of the bulk are deposited successively after monolayer compression. Therefore the difference of interatomic spacing between Ag and Xe crystals does not impose a strain on the film. This supports our previous results14 that the surface of a sufficiently thick film is so flat as to allow clear diffraction spots and its orientation is aligned with the Ag(111) orientation. In the X-ray diffraction study,9 the Xe-Xe spacing has reached that of the bulk at bilayer onset. In the present experiments, the observed compression terminates around the midpoint (ca. -210 meV/atom) of the first plateau of adsorption isotherms and isobars which were determined by ellipsometry. As already mentioned in section 2, the total adsorbate density N is experimentally determined by ellipsometry. Assuming that the solid monolayer has no vacancies, we can obtain the monolayer density N1s from the Xe-Xe spacing measured by XLEED. The second layer density N2g ()N - N1s) in the region of the first plateau of the isotherms is then calculated, as shown by solid circles in Figure 5. The slope of N2g changes at around the midpoint of the plateau. This shows that the monolayer compression and adsorption of atoms on the monolayer film occur simultaneously after the first layer condensation, and after

Figure 6. Adsorption isosteres of Xe/Ag(111). The long-dashed, short-dashed, and dotted lines represent the condensation of the first, the second, and the third layer, respectively. The solid line of bulk sublimation is taken from ref 17.

the completion of the monolayer compression, only the second layer density increases with an increase in the chemical potential of the film. The large N2g near the second layer condensation is not clarified. The adsorption isosteres, which are derived from ellipsometric isotherms, are shown in Figure 6. From the slope of the lines in Figure 6, the isosteric heats of the first, the second, and the third layer condensations are calculated at q1 ) 208 ( 3 meV/atom, q2 ) 174 ( 3 meV/ atom, and q3 ) 173 ( 3 meV/atom, respectively. The latent heat of sublimation of bulk Xe is q0 ) 161 meV/atom.18 4. Calculation of Xe-Xe Spacing and Discussion The Xe-Xe spacing in the monolayer is determined by the Xe-Xe interaction in the presence of the silver surface. In a series of papers,24-28 Bruch and co-workers reported theoretical studies of the structural and the thermody-

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namical properties of Xe/Ag(111) in great detail. They have calculated the Xe-Xe spacing just after the layer condensation. There are, however, no theoretical studies for the transition process of Xe-Xe spacing from 2D film to bulk. In the following discussion, we will calculate the Xe-Xe spacing and its change during the film growth using a simple model of the interaction, where the zero-point energy and the thermal expansion are not taken into account. 4.1. Xe-Xe Spacing Immediately after the First Layer Condensation. In this subsection, we describe the interaction function we used and the calculation of equilibrium Xe-Xe spacing just after the first layer condensation. The interaction between an isolated pair of Xe atoms is represented by the Lennard-Jones (12, 6) potential, uLJ, 12

6

[(σr) - (σr) ]

uLJ ) 4

where r is the distance between two Xe atoms,  is the depth at the potential minimum, and σ is the pair separation at which uLJ changes from positive to negative. The parameters  and σ for Xe are 20.0 meV and 0.398 nm, respectively, which are adopted from Barnardes.29 The summation for the fcc lattice of 3D bulk Xe provides an equilibrium interatomic distance of 0.434 nm, which is consistent with the results of X-ray measurements of Sears and Klug30 in the low-temperature region. The equilibrium distance for the isolated 2D Xe layer is estimated in the same manner. In this case, we considered a 2D hexagonal Xe slab with an infinite area and a monatomic thickness. The calculated result was 0.442 nm, which is 1.8% larger than that of the 3D bulk Xe. Finally, we consider a Xe monolayer film physisorbed on Ag(111) by putting an isolated Xe slab on the Ag surface. The interaction potential for the Xe atoms adsorbed on Ag(111), u11, is calculated from the sum of the LennardJones (12, 6) potential, uLJ, the interaction between dipoles induced by the substrate, udipole, and the McLachlan interaction, uM, which accounts for a substrate-mediated three-body interaction. The interaction of a pair of dipoles, udipole, at separation r is expressed as

udipole )

µ02 4π0r3

where µ0 is the dipole moment associated with Xe atoms on the surface ()0.2 D31), and 0 is the permittivity of a vacuum. We use the McLachlan interaction32 for the long-range dispersion force between adatoms with the substrate which is treated as a continuum. In this model, besides the fluctuating dipoles on the adatoms, there are images of these dipoles in the substrate. The McLachlan expression, uM, for the substrate-mediated dispersion energy for two identical adatoms is (26) Bruch, L. W.; Cohen, P. I.; Webb, M. B. Surf. Sci. 1976, 59, 1. (27) Bruch, L. W.; Unguris, J.; Webb, M. B. Surf. Sci. 1979, 87, 437. (28) Bruch, L. W. Surf. Sci. 1983, 125, 194. (29) Barnardes, N. Phys. Rev. 1958, 112, 1534. (30) Sears, D. R.; Klug, H. P. J. Chem. Phys. 1962, 37, 3002. (31) Behm, R. J.; Brundle, C. R.; Wandelt, K. J. Chem. Phys. 1986, 85, 1061. (32) McLachlan, A. D. Mol. Phys. 1964, 7, 381.

{

}

4z2 1 1 4 1 - 2 uM ) Cs1 3 2 - Cs2 2 2 3 2 3 r (r + 4z ) / r + 4z2 (r + 4z2)3 for adatoms at a height z above the image plane and at a lateral separation r. The coefficients Cs1 and Cs2 are given in terms of the dielectric constant of Ag and the electric dipole polarizability of Xe, Cs1 ) 0.114 meV‚nm6 and Cs2 ) 0.0842 meV‚nm6.28 We use the value z ) 0.20 nm,26 which is estimated from the spacing between Xe adatoms and Ag substrate determined by LEED I-V curves. The summation of these three interactions for a triangular Xe lattice on Ag(111) provides the lateral binding energy of 54.37 meV/atom and an equilibrium interatomic distance of 0.448 nm, which is 3.2% larger than that for the bulk, 0.434 nm. 4.2. Lateral Compression of the Xe Film. To evaluate how the densities of the first layer and the second layer change as the chemical potential of the adsorbate is increased, we calculate the total energy of the adsorbate as a function of the adsorbate density in a monolayer solid and a 2D gas physisorbed on the monolayer film. The most energetically favorable densities of the first layer, N1s, and the second layer, N2g, are calculated at a given total adsorbate density, N ) N1s + N2g. The total energy of the adsorbate is calculated from the interactions between adatoms and between an atom and the substrate. The in-plane interactions, u11, between adatoms in the first layer are mentioned in section 4.1. The out-of-plane interaction, u12, between the atoms in the first and the second layer is represented by the Lennard-Jones potential assuming that the latter is deposited in the 3-fold site on the first layer. The interaction between a Xe atom in the first layer and the Ag substrate, v1, is deduced using the estimation of Suzanne et al.,33 which is

hg ≈ u2D + q1 where hg ()5/2 kT) is the enthalpy of the 3D gas in equilibrium, and q1 is the isosteric heat of the first layer of Xe/Ag(111), which is determined in the present work to be 208 meV/atom (section 3). The energy of adsorbed phase, u2D, is represented by the sum of three terms, which is

u2D ) u11 + v1 + uvib where uvib ()∫Cp dT ≈ 22 meV/atom33) is the vibrational energy of the adsorbed atoms. The interaction energy, v1, is then calculated at 153 meV/atom. The interaction between a Xe atom in the second layer and the Ag substrate, v2, is calculated from the equation

v2 ) -

C3 (z + l)3

where z is the distance between the adatom in the first layer and the substrate which was used in the McLachlan expression, l ()x2/3r) is the distance between the first and the second layer, and the coefficient C3 ()3.51 meV‚ nm3 28) is given by the dielectric constant of Ag and the polarizability of Xe. The total energy of the adsorbate is then calculated from the sum of u11, u12, v1, and v2 as a function of the (33) Suzanne, J.; Coulomb, J. P.; Bienfait, M. Surf. Sci. 1974, 44, 141.

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density of the second layer, N2g, and the value of N2g which minimizes this energy is plotted by thick dashed curves in Figure 5. Just after the first layer condensation, the adsorbate merely consists of the atoms in the first layer whose Xe-Xe spacing is 0.448 nm, and the total energy of the adsorbate is calculated at 207 meV/atom. When the total energy increases, the compression in the first layer (increase in N1s) is preferred rather than the adsorption on the second layer (increase in N2g). At N ) N1s ) 6.28 nm-2, the Xe-Xe spacing is 0.429 nm and the energy is 202 meV/atom. After this point, N1s is constant and N2g increases with the total energy of the adsorbate. The calculated chemical potential just after the first layer condensation (-207 meV/atom) is larger than that found in our experiments (e.g., -243 meV/atom at 68.9 K and -248 meV/atom at 76.2 K). Our calculation does not include the contribution of a temperature. Using our adsorption isosteres (Figure 6) and eq 1, we can extrapolate the chemical potential of the first layer condensation at 0 K (-208 meV/atom), which agrees with our calculated value. The following question still remains. Although the experimental curves in Figure 5 show that the second layer adsorption occurs simultaneously with the first layer compression, it does not appear in our calculated curve. We believe our calculation will work well if an entropy effect is suitably incorporated in the model. 5. Summary We have made a systematic observation of the change of the Xe-Xe spacing in one and two monolayer films of

Igarashi et al.

Xe/Ag(111) at pressures between 10-7 and 10-2 Pa and at temperatures between 50 and 100 K by means of ellipsometry and XLEED. The Xe-Xe spacing just after the condensation of the first layer is a few percent larger than that of the bulk. When the pressure is increased or the temperature is lowered, it gradually decreases to that of the bulk before the second layer condensation and keeps the bulk value thereafter. The layers which have the XeXe spacing of the bulk are deposited successively after the monolayer compression. Using a simple model, we evaluate the Xe-Xe spacing in the first layer and the lateral compression of the Xe monolayer. The calculated relative expansion just after the first layer condensation agrees with our experimental results. The calculation of the densities of the first layer and the second layer shows that the monolayer compression terminates in advance of the second layer adsoption. Acknowledgment. The authors thank Professor Masaki Yamamoto and Dr. Akiko Itakura for helpful discussions throughout the course of the work. One of the authors (S.I.) greatly appreciates the financial support from the Nomura Foundation. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports, and Culture, Japan. LA0264264