Kink site position

Deposition of Me on a 3D native bulk phase proceeds by incorporation of atoms in kink site" positions as a final step of the overall reaction (1.1) (cf. Section 2.1). In contrast. Me dissolution can also take place at all sites where lattice atoms are more loosely bound to the crystal than kink atoms. Usually dissolution starts, in addition to the kink sites, at crystal edges and corners, or at surface defects and inhomogeneities. Therefore, the Me deposition-dissolution processes are not necessarily symmetric. At the Nernstian equilibrium potential, equality... 

Among the different surface atom positions illustrated on Fig. 2.8, the kink site position, or the half crystal position, as introduced independently by Kossel [2.12] and Stranski [2.13], has a special significance for the definition of the equilibrium conditions (vapor pressure, equilibrium concentration, equilibrium electrode potential, etc.) of the infinitely large (bulk) crystal. 

RT In vwinif represent the enthalpic and entropic contributions, respectively. The separation work of an atom from a kink site position into a vacuum is equal to the sublimation enthalpy, AsubA, of the crystal assumed as infinitely large ... 

In this equation, Aads f corresponds to the enthalpy difference between occupied and unoccupied adsorption sites and contains Meads-s be difference of the solvation enthalpies of Meads and S. Asub is the sublimation enthalpy, which is related to the interaction enthalpy per Me bond, Hle-Me, approximated as y/i in the case of first nearest neighbors (cf. eqs. 2.2 and 2.3). The terms and Vads represent the mean vibrational volumes of an atom in a kink site position or in an adatom position, respectively [3.269]. They are related to the mean atomic vibration frequencies in the 3D Me bulk lattice and in the Meads overlayer, respectively. 

Results are presented for stepped surfaces with terrace orientations (100) and (111) on Pt and (001) on Ru. In fact, these planes, together with various others, form the surface of a field emitter tip which can be regarded as a catalyst particle with a diameter of about 20 to 200 nm. Although our probe hole measurements sample only a few atomic sites (up to about 200) the detailed crystallography of the probed area, i.e. terrace widths and step site symmetries, is not known because the concomitant removal of substrate atoms by field evaporation (from kink site positions) during the measurements causes continuous alterations of the morphology. 

The adsorbed metal ion is called an adatom. From the ad-atom position, the cation is transported by surface diffusion to a position at which it is already part of the growing metal structure (Step 3, Eq. 2). This position is called the kink site position (HalbkristaUage Mei/2). Step 3 is accompanied by transfer of z - X) electrons. 

On a real surface the atoms undergo reorientation processes, which lead to changes in the distribution of energies between different bonds. The bond of an atom in a kink site position (the calculation will be described in the next chapter) can differ from the ideal value. 

In the process of sublimation the atom is separated from a special position on the surface, the kink site position (half crystal position). In the ideal kink site position the... 

The Gibbs energy of an atom in the ideal kink site position is the characteristic value for the molecular interaction of the atom with the bulk matrix. It takes into account bond strengths among first, second, and further neighbors. It is exactly one half of the lattice energy. 

The enthalpy of an atom in an ideal kink site position is... 

Values of energies of atoms in ideal kink site positions and bond energies between two metal atoms were summarized for transition and main group metals in Table 2.3. On the real surface, the bond energies in kink site positions and the bond energies between two neighbors can differ from the ideal model values because of relaxation processes on the surface. 

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... 

In the following treatment, the density of kink site positions is considered to be in equihbrium with the ad-atom concentration and with the ion concentration in the electrolyte. This is shown in Figure 7.11. 

In this diagram the reaction of an ad-atom with the kink site position is reversible. But in the kink site position an atom may return to its previous position by separation from the kink site position, or it may become fixed in the crystal lattice by the next atom deposited in the kink site position. The built-in process is then completed. In this model, the kink site position has a similar function as the transition state in the theory of chemical reactions. 

Finally, the crystallization exchange current density was calculated and interpreted as the rate of deposition and separation of ad-atoms into kink site positions. 

In the following section, a statistical description of the surface processes will be presented. This is based on the definition of a residence time of an atom in a kink site position. 

Figure 7.13 shows the (100) surface of a metal crystallizing in the face-centered cubic lattice. Three planes of atoms and a step running in the [110] direction are shown. On the step a kink site position is shown. 

Ad-atoms can be deposited into a kink site position either directly or via a step position. Otherwise, the atom in a kink site position can be separated from the kink site position to a step position or to an ad-atom position as shown in Figure 7.13. 

There is, in principle, the direct transfer between kink site position and electrolyte. This process, which must be taken into account at larger overpotentials, will not be discussed further. 

The transfer of an ad-atom into a kink site position can be described by a reaction of a metal ion with a kink site position... 

The separation from a kink site position is a reaction of first order. The reaction rate is given by the rate equation... 

What happens to an atom in the kink site position This may be determined by the time interval in which the atom stays in the kink site position. This time is called residence time in the kink site position (in German Verweilzeit )- The residence time is the statistical average of the time between the arrival of the atom in the kink site position and its separation from the kink site position. During the residence time the process of separation from the kink site position competes with the arrival of new atoms. The residence time t in a kink site position is given by the reciprocal value of the rate constant of separation. 

The pre-exponential factor kg is approximately the oscillation frequency of the atom in the kink site position. An estimated value of 10 can be used. 

Comparison of the dynamic of some metals with cep and hep structures rate constants of separation from kink site positions (calculated with the assumption that the activation energy is proportional to the cleavage of one bond nd residence time t... 

DENSITY OF KINK SITE POSITIONS 7.4.1 Equilibrium conditions... 

In a first approximation it can be assumed that the density of kink site positions is in equilibrium with the ad-atom concentration. More generally, all partial reactions are in equilibrium at the Nemst potential. The following equation describes equilibrium between ions in the electrolyte and atoms in kink site positions ... 

This reaction expresses the repeating nature of the reaction of an ion with a kink site position A that forms a new kink site position AA. The equilibrium constant Kf is related to the rate constants and by the following equation ... 

The density of kink site positions A and AA at equilibrium potential is [ksp]Q. For equilibrium conditions one gets, Thus it follows with Eq. (7.25) ... 

With Avogadro s number and F the Faraday constant. The density of kink site positions at the equilibrium potential [ksp] is given by the product of exchange current density and residence time. This equation will be discussed in the next section. 

The residence time provides a measure of how long an atom can stay in a kink site position. The next atom accumulated in the kink site position determines its future. Therefore one has to compare residence time and rate of deposition. 

Dividing Eq. (7.35) through the density of kink site positions [A p], the number of atoms arriving during the residence time per kink site position is obtained... 

If is much smaller than [ksp], the number of kink site positions decrease, because the renewal of the kink site positions by accumulation of metal ions is so slow that more and more kink site positions disappear because of the natural surface reconstruction. If is much larger than [ksp], however, the number of kink positions will increase because new surface structures can develop. Thus one can say for stationary conditions that N,should approach the value = 1. The density of kink site positions [fop] finally therefore approach the value... 

A special situation that can cause stationary conditions is at the electrochemical equilibrium potential (Nemst potential). The current density at the Nemst potential is the exchange current density The density of kink site positions [fopJo is therefore proportional to the product of exchange current density Iq and residence time, as was already shown in Eq. (7.34). 

Exchange current densities have been determined for many metals. Using ig values from the literature and the values for the residence times presented in Table 7.1 a rough estimation of the order of magnitude of the density of kink site positions at the Nemst potential is possible. Examples are presented in Table 7.2. 

The calculation of [fop], takes into account the nature of the metal (by r) and the electrochemical conditions (by if). The value of ig reflects the different experimental parameters like electrolyte composition, and additives, etc. Therefore, the values of the density of kink site positions provide an image of the surface dynamic at equilibrium conditions. While the absolute values might be questionable, the comparative nature of the described procedures allows at least a comparison of the dynamics of experimental systems. The values for Ag reflect the density of kink site positions for three experimental conditions. The largest value of 5 X lO cm corresponds to one of the highest experimental exchange current densities observed. In this case, [fopJo approaches the surface density of atoms on... 

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