J. Phys. Chem. 1994, 98, 9486-9487
9486
Nature of Chemical Bonding in Highly Expanded Heavy Alkalis: Especially Cs and Rb G. R. Freeman* and N. H. Marcht Chemistry Department, University of Alberta, Edmonton, Alberta, Canada T6G 2G2, and Theoretical Chemistry Department, University of Oxford, 5 South Parks Road, Oxford OX1 3UB, England Received: May 27, 1994@
Experimental data are now available on the structure of heavy alkalis, and especially Cs, in highly expanded forms. First, the neutron diffraction experiments of Hensel and co-workers on expanded fluid Cs taken up the liquid-vapor coexistence curve toward the critical point show a dramatic decrease in coordination number but a relatively minor increase in the nearest-neighbor Cs-Cs bond length. Less extensive data for liquid Rb exhibit similar features. Subsequently, by deposition on semiconductor substrates, and in particular GaAs and InSb, one- and two-dimensional ordered structures of Cs have been established, with near-neighbor Cs distances substantially longer than in bulk Cs and being govemed by the geometry of the substrate. These experimental results and their relation to electrical conductivity are here analyzed in terms of a localized chemical bonding picture.
I. Introduction The pioneering experiments of Hensel and co-workers' have led to remarkable progress in understanding the structure of expanded liquid rubidium and cesium. In particular, neutron diffraction data are available from these studies on the static liquid structure factor S(q) for these two heavy alkalis, expanded by heating toward their critical points. For convenience we note here that the critical data of Rb and Cs are respectively T, = 2017 K, P, = 12.45 MPa, and d, = 290 kg/m3 and 1924 K, 9.25 MPa, and 380 kg/m3. The law of rectilinear diameters breaks down for these liquid metals and their vapors.la The data on the static structure factor S(q) and its Fourier transform g(r),the pair distribution function, were used by Hensel et al.lb to derive the characteristic changes of the microscopic structure and in particular the near-neighbor distance and the coordination number as a function of density. We shall return to the interpretation of these experimental data in the dense fluid state characterized by short-range order (SRO) below. However, from a different type of study, namely deposition of cesium on semiconductor crystal surfaces, data have subsequently become available on expanded Cs structures with long-range order (LRO). While this later study is partially about Cs in interaction with the semiconducting substrate, there is again important information about chemical bonding in expanded Cs, but now with LRO. We find it useful to discuss these data immediately below, before returning to the data on expanded alkalis in the fluid state with only SRO.
11. Low-Dimensional Expanded Cs with LRO, through Deposition on Semiconducting Substrates Whitman et aL2 have reported the structural properties of Cs adsorbed on room temperature GaAs( 110) and InSb( 110) surfaces as observed with scanning tunneling microscopy. What these workers demonstrate is that Cs initially forms long, onedimensional (1-D) zigzag chains on both surfaces. In particular, their Figure l(a) shows specifically a large-area image of Cs chains on GaAs( 1lo), including chains that are over 100 nm long. What their observations demonstrate in addition, that is
* Author to whom correspondence should be addressed at the University of Alberta. University of Oxford. Abstract published in Advance ACS Abstracts, August 15, 1994. +
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important in the present context, is that the chains tend to be separated by tens of nanometers and have no long-range order along the [Ool] direction, thereby establishing that they are truly 1-D structures. The higher-resolution image (their Figure l(b)) reveals that the Cs structures are zigzag chains of single atoms in registry with the GaAs( 110) surface. What needs especial emphasis in the present context is that the Cs-Cs nearest-neighbor (nn) distance in this structure is 0.69 nm, which is therefore considerably longer than the CsCs nm distance of 0.52 nm in bulk Cs. Whitman et aL2 also adsorbed Cs on the InSb( 110) surface, InSb being the 111-V semiconductor with the largest lattice constant: about 15% larger than that of GaAs. Again, the formation of Cs zigzag chains was observed, but now with increase of the Cs-Cs M distance to 0.80 nm. Though we shall return below in section IV to results found when additional Cs adsorption occurs on GaAs( 1lo), we want immediately to compare and contrast the above structures with deductions made from the diffraction experiments of Hansel et al.' on dense fluid Cs.
111. Modeling of Short-Range Order Using Chains (Coordination Number 2) in Dense Fluid Cs Near the Critical Density d, = 380 kg/m3 As already noted in section I, Hensel et al.lb derived both the nn bond length and the coordination number as a function of density d from neutron diffraction measurements of the dense fluid structure factor S(q). One of us3 earlier fitted their data for coordination number z by d=az+b (1) where a = 230 and b = -80, both in kg/m3. The relative constancylb of the nn distance as d is lowered lends strong support to the view that a chemical bond is the basic building block in these expanded fluid states. One of us has earlier noted,3 but for the lighter alkali Na, that the study of Malrieu et aL4 can be used to characterize this chemical bond. While their study3 was on crystalline Na, it is not as drastic as it might sound to adapt their study to the alkali fluids, since the arguments of Malrieu et aL4 rest purely on consideration of first and second neighbors to a chosen Na ion. These workers, following the ideas of Poshusta and Klein5 on
0022-3654/94/2098-9486$04.50/0 0 1994 American Chemical Society
Nature of Chemical Bonding in Highly Expanded Heavy Alkalis hydrogen, set up a Heisenberg Hamiltonian for Na, which was characterized by the 'E: and potential energy curves of the free-space diatom Naz. These were taken from the semiempirical study of Konawalow et aL6 and were then used4 to calculate the energy as a function of M distance for both a bodycentered cubic structure and a structure with lower coordination, namely simple cubic. We assume that this treatment3s4can be appropriately adapted to characterize the Cs chemical bond in terms of the corresponding potential energy curves of the Cs diatom. Returning now to eq 1, which yields z = 2 for the coordination number of fluid Cs at the critical density, for reasons discussed in refs 3 and 7, consistent with the results extracted from experiment by Hensel and co-workers,lb it has already been proposed3 that the coordination number is 2 (consistent with the existence of chains) in fluid Cs at density dc = 380 kg/m3. Returning to the data for Cs adsorbed on the semiconducting surfaces, it is natural again to assume zigzag chains, though the angle in these chains must clearly be >n/3 to yield a coordination number of 2, consistent with eq 1. Of course, for states with higher density, the coordination number increases and we shall return to discuss such states in comparison with the findings of Whitman et al.* for denser Cs adsorption in the summary below. Though the M distance in zigzag chains found by Whitman et aL2 is considerably longer than the chemical bond in fluid Cs, their 'expansion' of Cs is, of course, brought about the the substrate geometry. However, it is of interest, notwithstanding the marked differences between nn distances in fluid Cs (-0.56 nm) and Cs on GaAs (0.69 nm) and on InSb (0.80 nm), to consider the nature of the electrical conductivity associated with the 1-D Cs chain structures discussed above. Whitman et aL2 refer, in support of their experimental approach, to the work of Ferraz et al.' in relation to the proximity of bulk Cs to the metal-insulator transition. To probe for metallic characteristics, Whitman et al.2 measured the tunneling conductivity (reduction of the band gap) at zero bias, which is proportional to the density of states at the Fermi leveL8 Current versus voltage curves showed that the band gap of 1.45 eV of GaAs was reduced to 1.1 eV when 1-D chains were on the surface, which means that the 1-D Cs chain structures are insulating on GaAs( 1 Earlier, one of us3 had suggested the same conclusion from a chain model for the SRO in fluid Cs at the critical density, though there the Peierls transition was invoked to propose the identity of the metalinsulator transition and the critical point in fluid Cs (see also section IV below for the reasons behind such attempts to 'mimic' SRO by models with LRO character).
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IV. Discussion and Summary It seems to be established beyond reasonable doubt that the basic building block for the structure of the expanded liquid metals Cs and Rb is a chemical bond with a rather constant length, -0.54-0.57 nm. If one follows the approach of Warren and Mattheiss9in using LRO models to mimic the local coordination in the fluid, then in conjunction with eq 1, which gives z = 2 at d,, one would naturally, in view of the discussion of the semiconductor substrate adsorption in section 11, adopt a largely 1-D model of zigzag chain^,^ with a nn distance -0.57 nm. The findings of Whitman et aL2 would then suggest that the fluid at this density would be insulating even though their M distances are somewhat larger. This would be consistent with experiment, which currently does not distinguish clearly the metal-insulator transition and the critical point in Cs.Ib
J. Phys. Chem., Vol. 98, No. 38, 1994 9487 Raising the density and using the structure data of Hensel et al.Ib at T = 1923 K, with number density = 2.7 x atom/ m3, Ascough and Marchlo have extracted an effective pair potential $(I), using the procedure proposed by Johnson and March." This potential has a sharp minimum at the nn distance 0.56 nm followed by a repulsive region out to -0.9 nm. Clusters with roughly equal bond lengths would be favored by this pair interaction, separated by substantial distances. Equation 1 predicts that this state has a coordination number near 3, and we now return to the study of Whitman et a1.2 On allowing additional adsorption on GaAs(110) beyond that leading to the zigzag chains described in section 11, Whitman et al. observe the formation of a 2-D overlayer consisting of five-atom Cs trapezoids arranged in a c(4 x 4) superlattice. It is true that the nn distance in their work is now shorter than that in bulk Cs, but there is space between these trapezoids. These configurations have an average coordination of -3. As Whitman et point out, nearly identical planar Cs clusters are also stable in the vapor p h a ~ e . ~ ~ . ~ ~ To summarize, the main purpose of the present work is to emphasize considerable similarities of the chemical bonding of the heavy alkalis (particularly Cs) in situations with SRO only (dense fluids) and in adsorption on semiconducting substrates. Local coordination appears to exhibit similar trends with density. In the liquid state, the bond length remains remarkably constant as the density is varied from the normal melting point of Cs to about twice the critical density. Of course, with Cs on the substrate, the nn distance is imposed on the Cs configuration by the substrate geometry. Nevertheless, in both InSb and GaAs, at low coverage, the Cs atoms take up zigzag chain configurations with low coordination number, just as found in the expanded liquid phase. The nn distances here are substantially larger than those in bulk Cs, so that again we are dealing with highly expanded states. Even at monolayer coverage, with a shorter Cs-Cs bond length now than in bulk Cs, there seems still a close relation between local coordination behavior and that found for Cs clusters in the vapor phase. It will clearly be of interest to extract pair potentials1° at other densities from liquid structure data, as these potentials, in the metallic fluid phase, are known to have essential density d e p e n d e n ~ e . ~ ~ , ' ~
References and Notes (1) (a) Jiingst, S.;Knuth, B.; Hensel, F. Phys. Rev. Lett. 1985,55, 2160. (b) Winter, R.; Hensel, F. Phys. Chem. Liq. 1989, 20, 1. (2) (a) Whitman, L. J.; Stroscio, J. A.; Dragoset, R. A.; Celotta, R. J. Phys. Rev. Lett. 1991,66, 1338. (b) First, P. N.; Dragoset, R. A.; Stroscio, J. A.; Celotta, R. J.; Feenstra, R. M. J . Vac. Sei. Technol. 1989, A7, 2868. (3) March, N. H. (a) Phys. Chem. Liq. 1989, 20, 241; (b) J . Math. Chem. 1990,4,271. (4) Malrieu, J. P.; Maynau, D.; Daudey, J. P. Phys. Rev. 1984, B30, 1817. (5) Poshusta, R. D.; Klein, D. J. Phys. Rev. Lett. 1982, 48, 1555. (6) Konowalow, D. D.; Rosenkrantz, M. E.; Olson, M. L. J. Chem. Phys. 1980, 72, 9612. (7) Ferraz, A.; March, N. H.; Flores, F. J . Phys. Chem. Solids 1984, 45, 627. ( 8 ) Stroscio, J. A.; Feenstra, R. M.; Fein, A. P. Phys. Rev. Lett. 1986, 57, 2579. (9) Warren, W. W.; Mattheiss, L. F. Phys. Rev. 1984, B30, 3103. (10) Ascough, J. A.; March, N. H. Phys. Chem. Liq. 1990, 21, 251. (11) Johnson, M. D.; March, N. H. Phys. Lett. 1963, 3, 313. (12) Krauss, M.; Stevens, W. J. J . Chem. Phys. 1990, 93, 8915. (13) Bonacic-Koutecky, V.; Fantucci, P.; Boustani, I.; Koutecky, J. In Studies in Physical and Theoretical Chemistry;Elsevier: Amsterdam, The Netherlands, 1989; Vol. 62, p 429. (14) See, for example: March, N. H. In Liquid Metals: Conceprs and Theory; Cambridge University Press: Oxford, U.K., 1990. (15) (a) Hafner, J.; Heine, V. J. Phys. F Met. Phys. 1983, 13, 2479. (b) Young, W. H. Rep. Prog. Phys. 1992, 55, 1 .
