On the variation of work function with coverage for alkali-metal adsorption

L663

Surface Science 203 (1988) L663-L671 North-Holland, Amsterdam

SURFACE

SCIENCE

ON THE VARIATION FOR ALKALI-METAL G.E. RHEAD Department UK

LETTERS OF WORK FUNCTION ADSORPTION

WITH COVERAGE

*

of Physical

Chemistry,

Unioersity

of Cambridge, Lensfield Road, Cambridge CB2 IEP,

Received 14 April 1988; accepted for publication

26 May 1988

Data on the adsorption of gases on submonolayers of alkali metals support Sidorski’s suggestion that the minimum in the work function versus coverage (+( 13)) curve (at +,,,,. 0,) corresponds to a phase transition in which the dense monolayer structure is nucleated (condensation). Other experimental evidence is briefly reviewed. A simple physical argument shows that lateral restoring forces in a 2D dipole array disappear at 0,. The coverage range from 0, to the complete monolayer coverage may be described by a two-phase model which includes the effects of nuclei/island edges near 0,.

The variation of the work function ($) of a metal as a function of the coverage (0) of an alkali metal has been discussed for over fifty years [l-3]. Summaries of various theoretical aspects can be found, for example, in recent articles [4,5]. The subject is also treated in recently published general reviews on the work function of metals [6,7]. For most alkali-metal/metal substrate systems the +(f?) plot exhibits the well known form (fig. 1) in which there is, starting from zero coverage, a steep, near-linear, decrease in 9. This flattens off towards a minimum value, (p,,,, at a coverage 0,) which typically is about 60% of the dense complete monolayer coverage 8i. After 8, the work function rises towards a value sometimes associated with the work function of the bulk alkali, and which is usually considerably less than the clean substrate work function. Because plots for various systems show no discontinuities it is generally believed that they provide no evidence for phase transitions in the adsorbed layer and this possibility is not included in most theoretical descriptions. The purpose of this Letter is to support the idea put forward some 16 years ago, in particular by Sidorski [S], that there is in fact a phase transition precisely at 0, in which the compact monolayer phase is nucleated - in other * Permanent address: Laboratoire de Physico-Chimie des Surfaces, UniversitC Pierre et Marie Curie, ENSCP, 11 rue Pierre et Marie Curie, 75005 Paris, France.

0039-6028/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

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G.E. Rhead

/

Work functton

variation with alkali-metal

ldispersed dispersed

phase

1

0

1 ; dense I

I P

plu; phase,

I I I I I P

adsorption

PIA. I

Fig. 1. Schematic plot of work function (9) variations produced by the adsorption of an alkali metal with coverage 0 (curve (a)). 0,: complete dense monolayer coverage. It is considered here that 0, (minimum +) is the coverage at which the dense monolayer structure is nucleated. Curves (b) and (c): variations of $J with time (t) during adsorption of oxygen. The line (d) is tangential to curve (a) at 0,. Inset: Different systems may exhibit different variations in the high coverage range

words, there is the onset of 20 appropriate to treat the (p(e)

condensation. This suggestion (which makes it plot in two distinct parts) has received little

attention. Yet, as it will be argued below, considerable has been accumulated in the past decade to support

experimental evidence the view. Some of this

evidence has been discussed by Sidorski [9]. In addition recent results on the adsorption of gases on alkali metal (sub)monolayers appear especially relevant. A simple physical argument will be advanced that suggests that the existence of a minimum in the work function may necessarily imply that

G.E. Rhead / Work function uariation with alkali-metal

adsorption

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condensation of the adsorbed layer will be initiated at this point. First, the evidence from different types of experiment will be briefly summarized. The adsorption of simple gases (oxygen, hydrogen) on adsorbed alkali metal layers shows an abrupt change of behaviour at 0,. Evidence to support this statement comes especially from measurements of the work function changes produced by gas adsorption. For example, in recent work on the oxidation of preadsorbed Cs and K layers on Ag(ll1) [lo], m which the adsorbate coverage was carefully calibrated by Auger spectroscopy, it was found that below 8, oxidation led to an increase in + whereas above 13, the work function first decreased on introduction of oxygen, went through a minimum, and then increased on further oxygen exposure. The behaviour is illustrated by the curves (b) and (c) in fig. 1. The increase in $I on oxidation was very small for alkali metal coverages just beyond 8, and increased with further increases in metal coverage. The change from no decrease to some decrease occurred precisely at 0,. Decreases in + on oxidation can be attributed to adsorption of oxygen in sites under the alkali metal [ll-141. Clearly there are most likely to be “underneath” sites if some of the metal is in a dense arrangement. The results indicated therefore, that the dense arrangement is nucleated at 8, and that the fraction of this arrangement increases until it reaches a maximum at 8 1’ The same conclusion can be drawn from published data on other systems. Some of the earliest observations of a switch in the direction of 9 changes on oxidation were made by Tishin and Tsarev [15] for the oxidation of barium on polycrystalline niobium. Chen and Papageorgopoulos [16] also concluded that for Na-covered W(112) “there is a critical couerage of Na beyond which 0 adsorption decreases the work function”. Desplat’s data for oxygen on Cscovered W(100) ([17,18], and especially fig. 3 of ref. [17]), give more quantitative evidence for this effect. Papageorgopoulos and collaborators have recorded similar data for the oxidation of Cs on MoS, substrates [19-211. There are also many isolated observations for different systems. For example Pirug et al. [22] found evidence for on-top adsorption of oxygen on K/Fe(llO) at low alkali coverage and underneath adsorption at a higher coverage but did not explore in detail the whole range of alkali coverage. Results for hydrogen adsorption on Mo(l10) with preadsorbed cesium [23] provide a confirmation of the interpretation of the oxidation experiments described above. For metal coverages below &,, hydrogen produces an increase in up;above 0, there occur decreases while at e,,, hydrogen produces no change in +. The increases in +I are due to adsorption of hydrogen underneath the bare parts of the substrate. However, once some of the surface is covered with islands of the compact arrangement of Cs there are sites on top of the alkali metal and hydrogen adsorption then produces increases in work function. Again, the data indicate that the transition occurs precisely at 0,. Similar effects were observed earlier for hydrogen on cesiated W(100) [24].

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G.E. Rhead / Work function varmtion wrth alkali-metal

adsorption

The possibility arises from these adsorption studies that the fractional coverage of the condensed phase may be evaluated from the work function variations. The results obtained in this way for Li/Ag(lll) [14], interpreted in terms of Li, clusters, suggest that this would be a valid procedure. LEED observations are compatible with the nucleation of the monolayer structure at t3,. The experimental correlation of LEED and work function measurements is not straightforward - and in fact there have been few well calibrated studies. Discrepancies may occur if the two techniques do not examine precisely the same part of the sample. Also, the coverage at which a particular structure is first present is not always easy to specify from visual observations. Such observations may be particularly difficult if, as is often the case with adsorbed alkali metals, there is a strong background intensity due to poor crystallization of the first adsorbed structure(s). LEED can readily detect a sharp transformation of one surface phase to another; it is less well adapted to observing the precise beginning of nucleation of a new structure. One of the few systems to have been examined with a view to making a careful correlation of structure and work function has been Cs/W(lOO). For this system different authors have firmly placed at 0, the change from a pattern associated with a low density arrangement to the first appearance of an additional pattern due to islands of the dense monolayer arrangement. MacRae et al. [25,26], Desplat [17,18] and Papageorgopoulos and Chen [24] all place the appearance of the hexagonal close-packed structure at 0,. Unfortunately the first interpretation of this structure ascribed it to the formation of a double layer [25,26]. This interpretation was corrected in the later work (see ref. [24] for a discussion) and with hindsight it can be seen that the Auger data (fig. 6 of ref. [26], fig. 6 of ref. [18]) clearly indicate simple monolayer adsorption. Another example is the recent study of Cs/Mo(llO), cited above [23], in which a weak pattern of the hexagonal close-packed structure also appeared immediately at 8,. Especially interesting, but more complex, is the system K/Cu(lOO) [27,28] for which there is evidence from LEED of condensation, nucleated at 0,, of a condensed phase which is a 2D liquid at the ambient temperature of observation. Evidence that condensation starts at e,,, can be found in changes in electron energy loss spectra. (Sidorski [8,9] discusses some of this evidence.) Some of the first recorded data on this point were for Cs/W(lOO) and were discussed by L,ander and Morrison [29]. MacRae et al. [25,26] showed that a 1.5 eV loss peak could be associated with a plasmon excitation in two-dimensional metallic cesium. This peak grew linearly from zero at B,, up to a maximum plateau value at the completion of the monolayer. Similar observations have been made for the alkali-earth barium on W(110) [30] and for Cs on Mo(ll0) 1231. Aruga et al. [28], for K on Cu(lOO), report a loss peak for which the energy

G.E. Rhead / Work function variation with alkali-metal

adsorption

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plot goes through a minimum at 8, while the intensity-versus-coverage exhibits a change in slope. The coverage dependence of the EEL spectra were found to be similar to those reported earlier for Na and K on Ni(lOO) [31,32]. Comparable variations were observed by Hohlfeld et al. [33] for Cs on Al(111). Rangelov and Surnev [34] have found sharp changes close to 0, in the energy of core level excitations for Na, K and Cs on Ru(001) and have commented on the possible connection with metallization of the layers. In a different type of experiment Lindgren and Wallden [35] describe changes in the plasmon energy loss on coadsorbing oxygen with Cs on Cu(ll1). This effect is “observed for coverages above a critical value corresponding to around 60% of a close-packed (Cs) monolayer”. Observations of a variety of other phenomena also point to sharp changes at 0,. (Again, some of these were noted by Sidorski [8,9].) For example the temperature required to equilibrate small doses of potassium on a field-emitter tip drops sharply at (3, [36]. This effect can be ascribed to the presence of dense nuclei, to which the added potassium migrates. The variation of the sticking coefficient of a coadsorbed gas as a function of the alkali coverage may change sharply at 6,. Such an effect has been observed for hydrogen on cesiated Mo(ll0) [23]. For the same system the thermal desorption of hydrogen shows a change of behaviour at 8,. A comparable sharp change in the variation of the sticking coefficient for oxygen on potassium-covered Fe(ll0) has also been observed [22]. There may also be changes in the heat of adsorption of the alkali as the coverage passes through 0,. For example, an inflection is observed in the heat-versus-coverage plot for Ba on W(110) [30]. (In terms of the ideas expressed below this may be related to the absence of lateral inter-dipole restoring forces at em.) While it is generally acknowledged in the literature that partial coverage by the dense monolayer structure is not seen before e,,,, and that the structure is obviously present before the whole surface is covered at 8,, it can be seen from the whole of the experimental results cited above that much evidence has been accumulated since Sidorski’s publication [8] to endorse the suggestion that 8, corresponds precisely to the point at which the dense phase is nucleated. Yet this idea has not been incorporated in theoretical work. Theoretical treatments of the variation of work function due to alkali metal adsorption are discussed in many articles and reviews (see, for example, refs. [4-71). Briefly, and in simple terms, it is a question of describing, as a function of coverage, the changes in electronic structure due to the competing effects of (“vertical”) ionic binding of the adatoms to the substrate and the lateral interactions between adatoms that ultimately lead to condensation. At low coverages there is considered to be an assembly of positive-outward dipoles (dispersed phase) in which the mean lateral spacing is determined by repulsive lateral dipole interactions. As the coverage increases there is a “depolarization”

GE. Rhead / Work function vnrtation with alkali-metal

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adsorption

effect [3,37,38] leading to less rapid decreases in +. The minimum is reached and beyond that the work function rises to a value that is considered to approach that of the bulk alkali metal. Analytical techniques and models have been Lang [39] (the “jellium” continuous

homogeneous

of Gurney’s

approach

[41] (analytical gas). These proposed

distributions);

[3] in treating

methods

Muscat

in particular

by

layers are assimilated

to

and Newns [40] (an extension

“polarization”);

Yamauchi

and Kawabe

in terms of the theory of an inhomogeneous

theoretical approaches that a minimum in

significance

developed

model in which the charged

electron

will not be reviewed here. Instead it is the ~(0) curve may have a fundamental

that has been overlooked,

and which may confirm

condensation is nucleated at 0,. The following starting point for a more rigorous and detailed

the view that

ideas are offered treatment.

as a possible

The ~(8) plots for alkali-metal adsorption are generally smooth with d+/de I e, = 0. At 0,, therefore, adding or subtracting alkali adatoms (ideally, infinitesimal changes) causes no change in the work function. On the low coverage

side of 13,,,, and in terms

adsorbed

layer, this means that changing

change

in the lateral

field. Such a change between

dipoles

spacing

produces

in laterally required condition

but

interactions in coverage

dipole

the density

with other also implies

field model

of dipoles

dipoles a change

field does

not change

The lateral

restoring

displacing

any dipole is therefore the dispersed

modify

in the average

the dipole

of the

causes no net

that would

no change in energy.

to maintain

since

of the surface

the

spacing

this change

in

force experienced

zero. Since these lateral forces are

phase their absence

would appear

to be a

for condensation.

Remaining

with the dipole

model,

we can envisage

fluctuation which increases the density which there is a switch in the dominant

that at 0,

any local

will lead to a “run away” effect interaction from ionic (“vertical”)

in to

metallic (lateral) and a local condensation to the compact metallic phase. Sidorski [8,9] has suggested that such a process would have the characteristics of a Mott transition [42,43] in a two-dimensional form. In the model proposed here nuclei of the dense metallic phase

in which

the average

phase are formed

adatom

spacing

in a “sea”

of the dispersed

has the minimum

value corre-

sponding to (3,. What can be said about the zero slope of (p(8) on the high coverage side of e,,,? It is hard to speculate without information on the type of metallic nuclei that are formed. One can imagine the successive formation of dimers, trimers and larger clusters. The zero slope might be due to the initial formation of singly ionized dimers (Me:) On the other hand, closer non-zero

having the same dipole strength as the monomer. experimental observations may reveal cases of

slopes on the high-coverage side of 0,. between 0, and 8, is, according to the model

The region

presented

here,

G.E. Rhead / Work Junction variation with alkali-metal

adsorption

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essentially a two-phase region in which the coverage corresponds to appropriate fractions of the two extreme concentrations. In a first approximation the work function at any particular coverage might be considered as a weighted sum of the work functions of the two extreme structures (assuming the particular measurement technique gives the average of a “patchy” surface). On this basis there would be a linear variation between 6, and 8,. But for low concentrations of the dens phase, near S,, there will be effects of the edges of the dense nuclei/islands and these will tend to decrease $ (as illustrated by the work of Besocke and Wagner [44,45]). The result would be a departure from linearity near 19, but a fairly linear increase from say 0, + 0.6(8, - 8,) to 0,. This type of variation does correspond to the form recorded for many systems. The effect of island edges would correspond to the gap between line (d) and curve (a) of fig. 1. This model is different from that proposed by Sidorski and Wojciechowski for the high coverage region in which the layer was considered to have a continuously varying lattice parameter [46]. The shape of the curve between 0, and a1 will depend on the relative values of +,,, and +i, the work function at the monolayer coverage. Very shallow minima may occur (curve (e), inset fig. 1) and the possibility of +, < (P, (curve (f), inset fig. 1) cannot be excluded. Indeed, the results obtained by Gupalo et al. [47] for lithium on Mo(112) correspond precisely to such a variation. Most investigations of alkali metal absorbate structures and induced work function changes have been limited to room temperature observations. The simplified picture presented in fig. 1 is intended to represent those conditions. At low coverages there may be more than one dispersed phase and at low temperatures the surface phase diagram may be more complex, as noted by Doering and Semancik [48] in their LEED study of Na/Ru(OOl). For some systems there may be more than one condensed phase. Also, as cited above, there is at least one case, K/Cu(lOO) [27,28], where the condensed phase is liquid at ambient temperature. These observations do not contradict the general arguments presented here. It is important to note that where two intimately mixed surface phases are present the LEED pattern may actually give the average crystalline parameters, and these may appear to vary continuously with coverage when in fact it is the proportion of the two structures that is changing. Such an effect has been observed, for example, for adsorbed binary metallic monolayers [49]. As more surface phase diagrams for alkali adsorbates becomes available it would be interesting to correlate them with work function measurements. To summarize, there appears to be abundant experimental evidence for the nucleation of condensation of the alkali adsorbate at 0,. Further experimental studies might be oriented to test, specifically and critically, this conclusion. The zero slope of the +(8) curve at 0, may have a special physical significance that has apparently been previously overlooked. The two regions of

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G. E. Rhend / Work function variation with alkali-metal

adsorptron

coverage, 0 = 0 to 0, and 6, to 0, apparently require different types of theoretical modelling. The structural model proposed here for the 8, to 8, region can be tested experimentally by various surface techniques and particularly by gas adsorption as a means of detecting the fraction of condensed phase. I thank Dr. Richard Lambert for hospitality and encouragement, members of his laboratory, particularly Deborah Jatfey, for stimulating discussions, and the British Council for an Academic Travel Grant.

References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]

I. Langmuir, J. Am. Chem. Sot. 54 (1932) 2798 J.B. Taylor and 1. Langmuir, Phys. Rev. 44 (1933) 423. R.W. Gurney, Phys. Rev. 47 (1935) 479. J.P. Muscat and I.P. Batra, Phys. Rev. B 34 (1986) 2889. P.A. Serena, J.M. Soler, N. Garcia and I.P. Batra, Phys. Rev. B 36 (1987) 3452. J. H61z.l and F.K. Schulte, Work Function of Metals, in: Springer Tracts in Modern Physics, Vol. 85, Eds. G. Hohler and E.A. Niekish (Springer, Berlin, 1979). A. Kiejna and K.F. Wojciechowski, Progr. Surface Sci. 11 (1981) 293. Z. Sidorski, Acta Phys. Polon. A 42 (1972) 437. Z. Sidorski, Appl. Phys. A 33 (1984) 213. C. Argile and G.E. Rhead, Surface Sci. 203 (1988) 175. C.A. Papageorgopoulos and J.M. Chen, J. Vacuum Sci. Technol. 9 (1972) 570. C.A. Papageorgopoulos and J.M. Chen, Surface Sci. 52 (1975) 40. J.L. Desplat and C.A. Papageorgopoulos, Surface Sci. 92 (1980) 97. S.D. Parker and G.E. Rhead, Surface Sci. 167 (1986) 271. E.A. Tishin and B.M. Tsarev, Soviet Phys-Solid State 11 (1969) 931. J.M. Chen and C.A. Papageorgopoulos, Surface Sci. 26 (1971) 499. J.L. Desplat, Surface Sci. 34 (1973) 588. J.L. Desplat, Japan, J. Appl. Phys. Suppl. 2, Pt. 2 (1974) 177. C.A. Papageorgopoulos, Surface Sci. 75 (1978) 17. S. Ladas, S. Kennon and C.A. Papageorgopoulos, Surface Sci. 162 (1985) 279. S. Kennon, S. Ladas and C. Papageorgopoulos, Surface Sci. 164 (1985) 290. G. Pirug, G. BrodCn and H.P. Bonzel, Surface Sci. 94 (1980) 323. M.L. Ernst-Vidalis, M. Kamaratos and C.A. Papageorgopoulos, Surface Sci. 189/190 (1987) 276. C.A. Papageorgopoulos and J.M. Chen, Surface Sci. 39 (1973) 283,313. A.U. MacRae, K. Mtiller, J.J. Lander, J. Morrison and J.C. Phillips, Phys. Rev. Letters 22 (1969) 1048. A.U. MacRae, K. Miiller, J.J. Lander and J. Morrison, Surface Sci. 15 (1969) 483. T. Aruga, H. Tochihara and Y. Murata, Surface Sci. 175 (1986) L725. T. Aruga, H. Tochihara and Y. Murata, Phys. Rev. B 34 (1986) 8237. J.J. Lander and J. Morrison, Surface Sci. 14 (1969) 465. D.A. Gorodetsky and Yu. P. Melnik, Surface Sci. 62 (1977) 647. S. Anderson and V. Tostell, Surface Sci. 46 (1974) 625. S. Anderson and V. Tostell, Faraday Disc. Chem. Sot. 60 (1975) 255. A. Hohlfeld, M. Sunjic and K. Horn, J. Vacuum. Sci. Technol. A 5 (1987) 679.

G.E. Rhead / Work function variation with alkali-metal [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] 1451 [46] [47] [48] [49]

adsorption

L671

G. Rangelov and L. Surnev, Surface Sci. 185 (1987) 457. S.A. Lindgren and L. Wallden, Phys. Rev. B 22 (1980) 5967. L.D. Schmidt and R. Comer, J. Chem. Phys. 42 (1965) 3573. J. Topping, Proc. Roy. Sot. London A 114 (1927) 67. T.A. Flaim and P.D. Ownby, Surface Sci. 32 (1972) 510. N.D. Lang, Phys. Rev. B 4 (1971) 4234; Solid State Commun. 9 (1971) 1015. J.P. Muscat and D.M. Newns, Solid State Commun. 11 (1972) 737; J. Phys. C (Solid State Phys.) 7 (1974) 2630. H. Yamanchi and U. Kawabe, Phys. Rev. B 14 (1976) 2687. N.F. Mott, Phil. Mag. 6 (1961) 287. N.F. Mott, Rev. Mod. Phys. 40 (1968) 677. K. Besocke and H. Wagner, Phys. Rev. B 8 (1973) 4597. K. Besocke and H. Wagner, Surface Sci. 53 (1975) 351. 2. Sidorski and K.F. Wojciechowski, Acta Phys. Polon. A 40 (1970) 661. M.S. Gupalo, V.K. Medvedev, B.M. Palyukh and T.P. Smereka, Soviet Phys.-Solid State 21 (1979) 568. D.L. Doering and S. Semancik, Surface Sci. 129 (1983) 177. C. Argile and G.E. Rhead, Surface Sci. 78 (1978) 125.