ECORR

A reference electrode scanned along the metal surface will measure the series of (E x)n and (E M)n interface potentials. From these values, solution potentials (t))s) at the metal/solution interface may be calculated ( )s = -E ) and presented as in Fig. 4.6. When the anodic and cathodic sites are microscopic relative to the size and position of the reference electrode, identity of the anodic and cathodic sites on a macroscale is lost, and a single mixed or corrosion potential, Ecorr, is measured as discussed previously. There is essentially a uniform flux of metal ions from the surface, and cathodic reactants to the surface, which constitute anodic and cathodic currents. Since the relative areas to which these currents apply usually are not known, the total area is taken as the effective area for each reaction. It is these currents, however, that mutually polarize the anodic reaction potential from E M up to Ecorr and the cathodic reaction potential from E x down to Ecorr. 

---

Based on cathodic polarization curves, Dexter and Gao concluded that the increase of E for 316 stainless steel exposed to natural seawater was due to an increased rate of the cathodic reduction of oxygen at a given potential. It is not possible from Ecorr or polarization curves to decide whetlier the increase in Ecorr is due to thermodynamic effects, kinetic... 

Both Linhardt and Dickinson et al." demonstrated that microbi-ologically deposited manganese oxide on stainless and mild steel coupons in fresh water (Fig. 4) caused an increase in Ecorr and increased cathodic current density at potentials above -200 mYscE-" Biomineralization of... 

Figure 5. Evolution of cathodic response to 10 pA cm" galvanostatic pulse as Ecorr increases during biofouling of 316L stainless steel in fresh river water. Data shown by solid lines and circles indicate points generated from curve lit to Eq. (6). (Reprinted from Ref. 12 with permission from NACE International.)...

FIG. 25-11 Typical electrochemical polarization curve for an active/passive alloy (with cathodic trace) showing active, passive, and transpassive regions and other important features, (note pp = primary passive potential, Ecorr = freely corroding potential.)... 

Following Lowdin [7], we define the electron correlation energy, Ecorr, to be... 

Table 13 Empirical estimates of the correlation energy, Ecorr in atomic units. ...

In quantum chemistry, the correlation energy Ecorr is defined as Econ = exact HF- In Order to Calculate the correlation energy of our system, we show how to calculate the ground state using the Hartree-Fock approximation. The main idea is to expand the exact wavefunction in the form of a configuration interaction picture. The first term of this expansion corresponds to the Hartree-Fock wavefunction. As a first step we calculate the spin-traced one-particle density matrix [5] (IPDM) y ... 

However, it should not be surprising if the anodic and the cathodic Tafel plots do not intersect at E = Ecorr as the two reactions participating in the corrosion process are actually studied at potentials far removed from the corrosion potential. Moreover, it is not quite realistic to rely on the very simple model described here. Therefore, it appears more useful to record a complete current-potential characteristic and to attempt its interpretation in terms of simultaneous processes that can possibly be expected. Several practical examples have been extensively reviewed [93]. 

The terms aanodic and cathodic are the transfer coefficients [Eq. (7.143)] for the anodic and cathodic components of the corrosion reaction, respectively. Their values will depend upon the reactions making up the corrosion situation. If one assumes that a hydrogen evolution rate controlled by charge transfer is the cathodic reaction, acathodic = 1/2 and if, e.g., the metal dissolution is controlled by charge transfer to form a divalent cation, aanodic = 2. Then, from (12.37), the maximum value of V - Ecorr allowable for the approximation of Eq. (12.35) is... 

The 75 values listed under Ecorr and pH in Table P.3 are steady-state corrosion potentials as a function of pH, collected from the literature. 

Method Number of Number of configurations independent configurations E Eha Ecorr b / e V C 0oa/(eV)e... 

Since the problem of correlated motion of the N electrons cannot be dealt with adequately by the Hartree-Fock method, even in the limit of an infinite basis set (i.e., B —> oo), it is expected that the ground-state electronic energy and estimation of the first few excited-state energy levels of even small molecules can be several electron volts away from thermodynamic or spectroscopic reality the difference Eexp—EHF is often called the correlation energy Ecorr ... 

The dotted lines in Fig. 23 show the applied current densities observed if, after reaching points a and b respectively, the direction of the potential scan is reversed. In both cases, a hysteresis loop is generated. For case 2, a negative loop occurs, i.e., the current densities in the passive region on the reverse scan are less than those on the forward scan at the same potential. For case 3, a positive hysteresis develops. In both cases, the current eventually changes polarity (note the new Ecorr s ). Inspection of the two surfaces would reveal that while the case... 

Figure 3 Evans diagram illustrating the influence of solution velocity on corrosion rate for an anodic reaction under mixed charge transfer-mass transport control. The cathodic reaction shown is charge transfer controlled. Ecorr and imrr tyl is shown.

The corrosion potential, ECOrr, adopted by the system will be dictated by the relative kinetics of the anodic material degradation process and the cathodic reduction kinetics of the oxidant. While ECOrr yields no quantitative information on the rate of the overall corrosion process, its value, and how it changes with time, is a good qualitative indication of the balance in corrosion kinetics and their evolution with time. Thus a knowledge of ECOrr and its comparison to ther-... 

A preliminary knowledge of which reaction steps could be key in determining the overall corrosion rate can be assessed by measurements of Corr as a function of important system parameters, e.g., oxidant concentration, solution composition, temperature. The proximity of ACOrr to either eM/Mn+ or /Red can indicate which of the two half-reactions may be rate determining. This is illustrated in Fig. 3A, which shows an Evans diagram for the combination of a fast anodic reaction coupled to a slow cathodic one. The corrosion of iron or carbon steel in aerated neutral solution would be an example of such a combination. The anodic reaction requires only a small overpotential (1) = /Mn+ - Ecorr) to sustain the corrosion current, /COrr, compared to the much larger overpotential required to sustain the cathodic reaction at this current. The anodic reaction would... 

Figure 5 Evans diagram illustrating the influence on Icorr and ECorr of a corrosion product deposit that affects both the anodic and cathodic half-reactions. The solid lines are for no deposit the dashed lines illustrate the changes in the presence of the deposit.

Figure 6 Schematic showing the evolution of Ecorr and the reactions occurring with time for the oxidation of nuclear fuel (U02) in neutral noncomplexing solution. The lines marked by uranium phases show the equilibrium potentials for the formation of discrete phases Eq2/h2o is the system redox potential for these conditions.

Corrosion can be considered as a galvanic cell in which an anodic and cathodic half-reaction couple to yield the overall corrosion reaction, Fig. 8. The overall reaction proceeds at a rate /Corr (= h = /cI) at the corrosion potential, ECorr-... 

However, since this corrosion reaction is short-circuited on the corroding surface, no current will flow in any external measuring circuit. Consequently, a direct electrochemical measurement of the corrosion current (convertible to corrosion rate by the application of Faraday s law) cannot be made. Despite this limitation, electrochemical techniques can be used to decouple the two half-reactions, thereby enabling each to be separately and quantitatively studied. This involves the determination of the current-potential relationships for each half-reaction. Subsequently, the behavior under electrochemically unperturbed (open-circuit or natural corrosion) conditions can be reconstructed by extrapolation of these relationships to Ecorr-... 

The fuel corrosion potential, ECOrr, is computed from the relationship... 

---