Two-dimensional phase formation

Fig. 171 The Frumkin isotherm with both negative and positive values of the parameter f. A negative value corresponds to attractive lateral interactions among adsorbed species, which may lead to two-dimensional phase formation. Dashed lines show the hysteresis loop which is expected in such cases.

As in the electrochemical case, the critical value of the interaction parameter is f = - 4. For more negative values, a hysteresis loop indicative of two-dimensional phase formation will be observed. 

Two-dimensional phase formation occurs preferentially when a strong suhstrate-metal interaction exists, a process that typically involves the formation of growth centers a few atoms thick, that expand and coalesce to form a monolayer that serves as a precursor deposit to subsequent two-dimensional metal layers. 

Often the peak current observed for formation of a U PD layer is found to be very narrow, as shown in Figure 12.2a, and this is generally assumed to represent two-dimensional phase formation. The formation of a two-dimensional phase is controlled by two opposing Gibbs energy terms. On the one hand we know that UPD must involve the formation of a chemical bond between atoms on the surface of the metal substrate and those in the UPD layer. This would lead to epitaxial deposition, which means that the structure of the deposited layer of atoms follows that of the particular crystal face exposed to the solution. However, this may not be the same as the most stable crystal structure of the metal deposited in the bulk form. Thus, lead on gold is much less likely to form a 2D phase than silver on gold, because the ratio of the crystal radii is only 1.002 for the Au/Ag couple, but 1.21 for the Pb/Au couple. 

The main idea of a lattice model is to assume that atomic or molecular entities constituting the system occupy well-defined lattice sites in space. This method is sometimes employed in simulations with the grand canonical ensemble for the simulation of surface electrochemical proceses. The Hamiltonians H of the lattice gas for one and two adsorbed species from which the ttansition probabilities 11 can be calculated have been discussed by Brown et al. (1999). We discuss in some detail MC lattice model simulations applied to the electrochemical double layer and electrochemical formation and growth two-dimensional phases not addressed in the latter review. MC lattice models have also been applied recently to the study the electrox-idation of CO on metals and alloys (Koper et al., 1999), but for reasons of space we do not discuss this topic here. 

The decomposition of this intermediate on both the Ni(llO) and Ni(lOO) surfaces occurred by an autocatalytic mechanism (99) for adsorbate coverages above about one-tenth of a monolayer. In fact, the decomposition rate was observed to accelerate isothermally as the reaction proceeded on both the Ni(l 10) and Ni(lOO) surfaces (98, 99) the rate of acceleration was more pronounced on the (110) surfaces. Furthermore, the intermediates were observed to form islands, as if a two-dimensional phase condensation occurred at about one-tenth monolayer coverage. The formation of this 2D condensed phase was clear indication of attractive interactions among the adsorbed species. 

Surface thermodynamics can explain some unusual shapes of the crystallites on the support, such as the extended planar structure, as well as the existence of a two dimensional phase on the support in equilibrium with the crystallites. It also allows one to derive an expression for the thickness of the planar crystallites. The two dimensional phase, which it predicts to exist, is responsible for the Ostwald ripening mechanism, by which the small crystallites lose atoms to the two dimensional phase and the large ones gain atoms from the two dimensional phase. The surface thermodynamics also provides an explanation for the dynamics of rupture of a thin film located on a support, thus shedding some light about the formation of Fe crystallites on alumina during heating in H2 in places in which no crystallites were present before (the specimen was previously heated in O2). 

The linear energy of the contact line between two-dimensional phases is only positive. Otherwise the mechanical equilibrium stability condition will be violated. This case is illustrated by examining the fluctuation formation of holes in bilayers. The linear energy of holes in between +6-10 12 J m 1 and +4.5-10 11 J m 1 (+6-10 7 dyn and +4.5-10 6 dyn). 

Upon the formation of two-dimensional phases a new interfacial quantity, the line tension enters the analysis. Phenomenologically the line tension is the onedimensional analogue of the Interfacial tension. It has the dimensions of a force and acts in the perimeter of three phase contacts. When it is positive it tends to... 

The method is based on the ability of TCNQ to react with bonded nitrogen compounds (secondary, tertiary amines) to form stable ion-radical salts (IRS) under mild conditions and with high yields. Completeness of formation of stable IRS has been monitored by ESR and electronic spectroscopy. One of the most important features of this method is the formation of two-dimensional phase by TCNQ anion-radicals on the surface, if bonded donor molecules are fixed at a small distance between their anchoring points, i.e. when separation between points of fixation is in the range 1-1.5 nm. ESR spectra of such samples contain an exchange-narrowed singlet with AH = 0.5 — 1.1 Gs, and g-factor 2.0025. Such spectra are typical for crystalline samples of IRS of TCNQ [25]. If bonded donor molecules are separated by as much as 2 nm or more, a distinct phase of TCNQ IRS is not formed. ESR spectra of such samples reveal either dipole-dipole broadening or hyperfine structure. 

A fiorther advantage of electrochemical in-situ SPM studies of two- and three-dimensional phase formation processes is the possibility of controlling accurately the supersaturation or undersaturation, Ap, which can be correlated, in the absence of other kinetic hindrances with overpotential and underpotential, respectively [11] ... 

If the oxide forms as a "monolayer," there is a question as to whether or not one can apply with some assurance these thermodynamic data, obtained on the bulk oxides. Some experimental evidence does indicate that for many metal-oxide systems the free energy of formation of the first monolayer is Indeed close to that observed for the bulk phase,(47) and hence no appreciable difference in the reversible potential should be expected. On the other hand, Vermilyea(48) has shown that, if the first monolayer forms by two-dimensional nucleatlon, the potential of the two-dimensional-film formation may be lower than that expected from the... 

The two-dimensional phase diagram of the monolayer of Xe adsorbed on graphite is displayed in Figs. 1 [6,8,14] and 2 [11,15,16] in two usital representations, coverage 0 vs. pressure and pressure vs. T. Fig. 2 extends the data of Fig. 1 to lower pressures and temperatures and allows the presentation of the second layer formation and of the bulk sublimation curve, as well. 

An alternative view on the UPD process provides the concept of substrate supported low-dimensional phase formation from Staikov, Budevski and LorenzThis concept explains unexpected stabilities of underpotential deposits. In this concept the UPD layer is considered to be a two-dimensional phase stabilized by the bond between substrate and UPD metal. A linear phase is the adsorption of atoms on steps and a phase of zero dimension is a group of atoms around a kink site position or around a surface dislocation. This concept is used to explain the positively shifted potentials in the cyclic voltammogram of UPD. Higher stabUily of the low-dimensional phase is described by introducing activities of atoms in the substrate-supported phase of lower dimension OMe,od> Me,id> d The deposition potential is given by the equation... 

The formalism of density functional theory (DFT) has received considerable attention as a way to describe the adsorption process at the fluid/solid interface. The older approach was to treat the adsorbate as a separate, two-dimensional phase existing in equilibrium with the bulk gas phase. This model works well in the monolayer region, but at higher surface concentrations the formation of multilayers requires the adoption of some sort of three-dimensional model to account for increasing adsorbate-adsorbate interaction and diminishing adsorption potential. 

The beginning of the growth process (cordierite or leucite glasses) is determined by a type of two-dimensional crystal formation. In other words, very flat crystallites initially grow on the surface of the base glass (Fig. 1-44). In a following reaction, this crystal phase was converted into a main crystal phase. 

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