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Prediction of Long-Term Corrosion Damage in High Level Nuclear Waste Disposal Systems

Digby D. Macdonald1 and George Engelhardt2

1Center for Electrochemical Science and Technology

Pennsylvania State University, 201 Steidle Bldg., University Park, PA 16802

2 OLI Systems Inc., 108 American Road, Morris Plains, NJ 07950

Tel: (814) 863-7772, Fax: (814) 863-4718, E-mail: ddm2@psu.edu Assuring the public of our ability to safely isolate High Level Nuclear Waste (HLNW) from the ecosphere over the long term represents one of the greatest technical challenges ever to face humankind. The principal difficulty is that the service life horizon is twice as far into the future (10,000 years) as recorded human history is in the past, and no direct experience exists with the degradation of engineering materials over that time period [1]. Indeed, some of the materials that are proposed for use in HLNW engineered barrier systems did not exist thirty years ago (e.g. Alloy C-22). A search of the literature reveals that no material that is currently contemplated for HLNW service has been investigated in a single corrosion study for more than a few tens of thousands of hours, or for more than a few one hundredths of one percent of the intended service life. Not only is the corrosion rate known over only a very small fraction of the service life, we cannot be sure that the mechanism of attack will remain the same as the system passes along the corrosion evolutionary path (CEP). Because the uncertainty of prediction in an empirical protocol scales with the power of each of the independent variables in the Dependent Variable (DV)/Independent Variable (IV) correlation, it is evident that the uncertainty grows rapidly over extended extrapolation. For example, the rate of propagation of a stress corrosion crack increases exponentially with potential, so that any uncertainty in the corrosion potential translates into very large uncertainty in the crack length over an extended extrapolation. The purpose of the present White Paper is to outline some of the important philosophical and practical issues that exist in the prediction of future behavior of physico-chemical systems in general and HLNW canister corrosion in particular. These issues are not just of academic interest, but will prove to have profound impact on how the public perceives, and indeed whether it accepts, YMP’s predictions of canister corrosion damage, and hence whether it feels assured that HLNW can be safely contained within the Yucca Mountain repository. Philosophical Basis for Predicting Future Behavior It is evident from the above that purely empirical methods cannot meet the challenge of assuring the public of the safe disposal of HLNW within the engineered barrier concept. In response to that conclusion, the author and his colleagues have initiated a program to develop deterministic models within the framework of Damage Function Analysis (DFA) [2-4] for predicting the accumulation of general and localized corrosion damage to Alloy C-22 in simulated HLNW repository environments. The ultimate goal is to develop deterministic models that capture the mechanistic essence of the damaging processes, that require minimal calibration, and that can be used to predict the evolution of corrosion damage over the requisite time to within the required engineering accuracy. It must be noted, however, that deterministic models enjoy little recognition in QA (Quality Assurance) protocols, where the prevailing philosophy appears to be: “If it hasn’t been directly measured, it cannot be real” (i.e., empiricism must prevail). We

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respectfully submit that the direct measurement of corrosion damage over all but a very small fraction of the CEP is physically impossible, so that empiricism cannot (by definition) provide an answer to the question at hand. In this regard, it is also important to note that there are good theories and bad theories, just as there are good data and bad data. To accept information as being “true”, simply because it was measured, is naïve at best and foolhardy at worst, and it largely negates the “scientific method” itself; that is, the process of prediction and refinement through testing and theoretical development that has been the hallmark of scientific endeavor throughout the ages. Determinism is the philosophy that posits that the future may be predicted from the past upon the basis of the natural laws, which are a summary of all scientific experience (not just experience with the corrosion of Alloy C-22 in HLNW systems, as is the case of empiricism). The effective application of determinism to predicting future behavior requires that: (1) The natural laws are time- and space-invariant (i.e., they will be as equally valid ten thousand years from now as they are today); (2) Valid mechanisms can be formulated for the damaging processes, and (3); The CEP is continuous (i.e., contains no singularities) and can be formulated (described). The Principle of Causality, which has been the foundation of scientific inquiry since the Ancient Greeks (Aristotle introduced the concept in his famous monograph, Physics, 2350 years ago!), together with the natural laws, ensures that the solution to the constitutive equations of a deterministic model are those that are physically real (this constraint does not exist in empiricism). Of the three prerequisites identified above, the second and third are the most challenging with regard to the present problem (the first can be accepted a priori, if a “natural law” is indeed a “law”). Thus, a valid mechanism is one that accounts for the known-facts, but that begs the question: “how is that to be established?” The answer is simply: “by comparison with experiment”. As noted above, we will only ever have experimental data that probe the system over the experimental time, but these data are invaluable if they are accurate and comprehensive for assessing and calibrating deterministic models.

In determinism, the unknown, unconstrained function, f, of its empirical counterpart, is replaced by a set of constitutive relationships (i.e., equations that describe how the mechanism describes the physico-chemical processes occurring in the system), the solution of which is constrained to a single, physically real value by the natural laws. Of course, if the mechanism is incorrect, the model will yield an incorrect answer, but experience has shown that the difference between the “true” value of the DV and that calculated from an inadequate physico-chemical mechanism is generally much smaller than that from an unconstrained empirical correlation, particularly in long extrapolations, provided that the prediction is constrained by the relevant natural law. In any event, a deterministic mechanism is continually modified (via the “scientific method”) to accommodate new experimental data and to render new predictions, with the result that the mechanism is continually refined. Eventually, the model may fail, because it can no longer make predictions that are in agreement with observation, or, if the model continues to make satisfactory predictions it may be accepted by the scientific community as being “correct”. The model can then be used to make predictions without the continual need to check the predictions against experiment. Clearly, in the case of HLNW isolation, the process described above must be carried out within the regime of available data, which is limited to only a small fraction of the repository lifetime. Extrapolation is then based upon the underlying theory; none in the case of empiricism and the natural laws in the case of determinism.

Finally, following the old adage that “theories explain but models calculate”, it is important to understand that all deterministic models must have a theoretical underpinning, although all theories need not be capable of calculation (the Theory of Evolution is a good example). Science and engineering are replete with deterministic models (theories) that are capable of precise calculation, including chemical equilibria (Mass Action and Chemical Thermodynamics), quantum mechanics (Hiesenberg’s Uncertainty Principle and Schroedinger’s Equation), activity coefficients (Debye-Huckel Theory), and relativistic mechanics (Theory of

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Relativity), so that the commonly expressed opinion that comparable calculations cannot be performed in a subject that is as complex as that which exist in corrosion science and engineering in general, and in the prediction of corrosion damage to HLNW canisters in particular, is unreasonable and inaccurate. The Nature of Data With regard to empirical models, only one type of data are important; the dependencies of the dependent variable(s) (DV, e.g., corrosion rate, corrosion potential) on various independent variables (IVj, e.g., time, pH, T, [Cl-]), such that a multivariate correlation

)N,1j,IV(fDV j == (1) can be formulated. If this function is linear, but is only known (has been established empirically) within the regime of the IVs, it may be used to effectively extrapolate the dependent variable over projections of the IVs, but generally over no more than two times the range over which the IV was varied in the calibration. This is because the errors due to uncertainties in the IVs generally scale with the power of the independent variable in the function, as noted above. However, if the correlation is non-linear (which is generally the case), and particularly if the series representation of the correlation with respect to a particular IV is divergent, the error in the DV can grow very rapidly, thereby rendering the prediction ineffective after only a short projection of the IV into the unknown regime. Projection of the IV over a factor of two, for a well-established correlation, is generally regarded as being feasible, over a factor of ten as being unreasonably optimistic, and anything over 100 as being nonsensical. Unfortunately, the empirical prediction of corrosion damage to HLNW canisters falls into this latter class. Returning now to the issue of data, it is important to understand that any deterministic model can be made to reproduce an experimental observation simply by calibration. Accordingly, comparison of the predicted behavior with a single (or a few) observation is not a valid test of any model (empirical or deterministic). A much better test is to compare the functional dependencies of the dependent variable (e.g., corrosion rate) on the various independent variables, as predicted by the model, with those established experimentally. The most efficient way of establishing these dependencies in the experimental data record is through the use of an Artificial Neural Network operating in the pattern recognition mode under supervised learning. This procedure has been carried out to establish correlations between Crack Growth Rate (CGR) and various independent variables (T, corrosion potential, pH, conductivity, etc.) in stress corrosion cracking in sensitized Type 304 SS in high temperature aqueous solutions [5]. This work showed that the deterministic Coupled Environment Fracture Model (CEFM) [6] is capable of reproducing the experimental correlations established by analyzing (often incomplete) data from widely disparate sources and hence demonstrated the remarkable ability of the CEFM to calculate crack growth rate in this steel in Boiling Water Reactor Coolant environments, even after being calibrated on only a single CGR datum. In the case of the general corrosion of Alloy C-22 in simulated HLNW environments, the data being obtained by the Lawrence Livermore National Laboratory (LLNL) represent an enormous resource for ANN analysis in establishing the required DV/IV correlations. While the ANN may be used to predict future behavior, it is important to recognize that the network does not contain a preconceived empirical or deterministic model and hence contains no “physics” of the system. In fact, this turns out to be an advantage, when compared with empirical models, in which the relationships are (often incorrectly) preconceived, but it is not for the case of deterministic models, in which the relationships exist upon the basis of the natural laws.

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Deterministic Predictions of Damage Over the past three years, the authors have developed a number of deterministic models for predicting the accumulation of general and localized corrosion damage over highly simplifies corrosion evolutionary paths (CEPs). While these calculations are far from the level of sophistication required for achieving the stated goal of convincing the public at large that the waste can be effectively isolated from the ecosphere for ten thousand years, they do illustrate some of the critical issues involved in the prediction of damage.

General Corrosion The General Corrosion Model (GCM) was developed as a deterministic model for calculating the rate of general corrosion of Alloy C-22 canisters in a Yucca Mountain-type repository [3]. The model is “deterministic”, because the partial currents are described in terms of accepted charge transfer theory (generalized Butler-Volmer kinetics) and the constraining natural laws are the conservation of mass, the conservation of charge, and Faraday’s law. The corrosion rate is then calculated at closely spaced “state points” over the CEP (Figure 1a), resulting in the corrosion rate (CR) versus time trajectories shown in Figure 1b. The CR over the three trajectories is then integrated to yield the corrosion loss plots shown in Figure 2. For the present purposes, we describe the evolutionary path in terms of the temperature, as predicted by researchers at the LLNL (Figure 1a) for a period of a million years. Three cases were defined: (1) Base Case, (2) Low Temperature Operating Mode (LTOM), and (3) High Temperature Operating Mode (HTOM), depending upon the mode of operation of the repository [1].

The Base Case and the HTOM display similar temperature profiles, in which the temperature rises to a maximum of about 160 oC soon after closure of the repository and then decreases with the decay in radionuclide activity in the waste. On the other hand, the LTOM, which corresponds to the scenario where closure of the repository is delayed until considerable decay of the most active radionuclides has occurred, displays significantly lower temperatures, with a maximum of a little over 85 oC. The corresponding [NaCl], [O2], and pH are calculated, assuming that the surface is covered with a thin layer (0.01-cm thick) of neutral, saturated sodium chloride solution.

The integrated damage is surprisingly monotonic with time and the model predicts that all three proposed operating modes will result in essentially identical damage. Thus, the model

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Figure 1. Evolutionary paths with respect to temperature and corrosion rate forAlloy C-22 in contact with saturated NaCl for the Yucca Mountain HLNWrepository for the three scenarios defined by the LLNL.

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predicts that a little less than 1.8-mm of Alloy C-22 will be lost over the 10,000-year life of the repository. This loss is judged to be modest compared with the wall thickness of the canister of 2 cm. In the authors’ opinion, localized corrosion, as discussed below, is a more likely mode of failure, particularly if the delayed repassivation constant for pits is small.

Of course, we hasten to stress that the calculations displayed above are very preliminary in nature, in that we do not yet possess a complete set of model parameter values for Alloy C-22 in all of the appropriate environments. Furthermore, little information is currently available on the chemical evolution of the repository environment (i.e., the CEP), particularly with respect to the chemical composition of the electrolyte layer that is postulated to exist on the canister surface.

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Figure 2. Evolutionary paths with respect to corrosion loss over the first ten thousand years for Alloy C-22 in contact with saturated NaCl for the Yucca Mountain HLNW repository for the three scenarios defined by the LLNL.

Pitting Corrosion A significant debate is currently taking place with regard to whether Alloy C-22

will suffer localized corrosion under Yucca Mountain-like environmental conditions within the design life of the repository. That Alloy C-22 can suffer various forms of localized attack (pitting corrosion and intergranular attack, at least) under sufficiently severe conditions is now firmly established by experiment (Figure 3) [4]. This figure displays a differential damage function for the pitting of Alloy C-22 after exposure in saturated NaCl solution at 80 oC for 180 days at an applied potential of 998 mVshe. The pits on the surface were found to extend to a little more than 31 µm in depth, but were characterized by a low aspect ratio (i.e., the pits are “open”).

Damage functions for shorter exposure times of 10 days and 45 days under the same exposure conditions were also measured, with the DFs having the same form, but extending to shallower depths into the alloy substrate. Note that great care was taken to exclude grain boundary ditching in the derivation of the damage function; however, intergranular attack is clearly evident and must be considered in any analysis of the localized corrosion behavior of Alloy C-22.

The potential at which these experiments were carried out is more than 700 mV more positive than the open circuit value observed under the same environmental conditions (approximately 250 mVshe), attesting to the extent of acceleration of the tests necessary in order to observe significant damage in laboratory times. The experimental differential damage functions were then used to extract values for various parameters in the Point Defect Model (PDM), which in turn were used to calculate the damage functions displayed in Figure 4 [4]. The conditions

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used in these calculations were selected to represent what might exist on the surface of an actual canister in service (in contact with a neutral, saturated NaCl brine), except that we assumed a potential of 400 mVshe versus the measured corrosion potential of about 250 mVshe. Accordingly, the conditions assumed in the calculations are less aggressive with respect to pH, but are more aggressive with respect to potential, than those employed in the experiments.

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Figure 3. Measured differential damage function for the pitting of Alloy C-22 in saturated NaCl (6.2 m), pH = 3, at 80 oC, and at a potential of 998 mVshe for 180 days, and a micrograph of the surface showing the form of attack.

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Figure 4. Predicted damage functions for the pitting of Alloy C-22 at one-, five- and ten-thousand years after exposure to brine (aCl- = 6.2) at pH = 7, and T = 100oC and as a function of the delayed repassivation constant, γ. Corrosion current density is chosen to be 10-7 A cm-2, and total possible number of stable pits is 5000 #/cm2.

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Each graph contains three DFs, corresponding to observation times of 1000, 5000, and 10,000 years, with the three graphs differing in the value adopted for the delayed repassivation constant, γ. (Note that delayed repassivation is the process whereby stable pits die). If repassivation does not occur (γ = 0), the deepest pit is predicted to extend about 2-cm into the alloy substrate after an exposure time under constant conditions of 10,000 years. In this case, the depth of the deepest pit is predicted to be comparable to the canister wall thickness, essentially corresponding to failure. Under strong repassivation conditions (γ = 0.1 year-1, bottom plots), all pits are predicted to die within the first depth increment, and hence the deepest pit is predicted not to exceed 1.0 mm in depth after 10,000 years of exposure; this corresponds to essentially no localized corrosion damage in light of the fact that general corrosion is predicted to thin the canister wall by about 1.8 mm (Figure 2) over the same exposure period. Recent analysis of the DFs obtained by the authors, in terms of Damage Function Analysis (DFA), suggests that the value of γ for this system is of the order of 200 year-1 [4]. This value signifies “strong delayed repassivation”, corresponding to much more severe repassivation conditions than those assumed in deriving the lower set of DFs shown in Figure 4. The predicted DF suggests that pitting will not be a factor in the accumulation of corrosion damage to the canister surface over the 10,000-year design life of the repository. It is stressed, however, that the DFs shown in Figure 4 are (to the author’s knowledge) the first deterministic predictions of pitting damage to Alloy C-22 under any environmental conditions, and hence the methodology is in its infancy. Furthermore, the delayed repassivation constant is tacitly assumed to be potential-independent, primarily because of the lack of experimental data that indicate otherwise, whereas the value corresponding to the corrosion potential (0.25 Vshe) may be substantially different from that measured at 0.998 Vshe.

The enormous impact that the delayed repassivation constant is predicted to have on the extent of development of pitting damage on a surface indicates new methods for corrosion control in this and other systems [7]. Thus, if methods can be devised for increasing the value of γ, localized attack may be effectively stifled, thereby rendering pitting corrosion to be not a threat to canister integrity. Although a satisfactory theoretical basis for delayed repassivation has yet to be developed, qualitative arguments suggest that γ might be increased by limiting the resources available to the pit on the external surface in the form of oxygen reduction, or by ensuring that the pit remains open, so that aggressive solutions are inhibited from forming within the cavity. The relatively high value for γ calculated from the experimental damage functions (~200 year-1) most likely reflects the open, low aspect ratio geometry of the pits that form on Alloy C-22 in low pH, saturated NaCl solutions at high anodic potentials. Clearly, we need to develop a sound theoretical basis for estimating γ, so that reasonable estimates may be made of this parameter in assessing the likelihood of the development of pitting corrosion damage to the canister surface.

One other aspect of the work described above needs to be mentioned and that is the extraordinary ability of deterministic models to translate experimental results from accelerated tests to the conditions of interest. Thus, the potential at which the experimental damage functions were derived lies within the transpassive region, but because DFA employs the PDM to describe the passivity breakdown process, and because the PDM accurately describes both the passive state and the transpassive state, translation of damage functions measured under accelerated conditions in the transpassive state in laboratory time to describe the accumulation of pitting damage in the passive state is justified. Recommended Research Thrusts As a result of our previous work, under DOE sponsorship [3,4], on the corrosion of Alloy C-22 in prototypical HLNW environments, we identify six research areas within which progress would significantly enhance our ability to predict the accumulation of general and localized corrosion damage over the 10,000-year isolation period. The principal areas are as follows:

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1. Definition of the Corrosion Evolutionary Path (CEP): No realistic prediction of

corrosion damage, deterministic or empirical, can be made without first defining the CEP. Currently, critics of DOE’s Yucca Mountain plan state that the problem is “unbounded” in terms of the environment and to a great extent this criticism is true. The CEP needs to be defined in terms of the variation of environmental parameters that impact the corrosion rate and hence the accumulated damage. These include temperature (Figure 1), pH, [Cl-], and ionic strength (solubility of oxygen and ion activity coefficients), to name but a few. Contact of the electrolyte film with the corroding surface must be incorporated in any model for the electrolyte as it moves along the CEP. The effective definition of the CEP will require the use of sophisticated geochemical codes for both the film itself and the near field environment, as well as a comprehensive database for the thermodynamic properties of ionic species in concentrated electrolyte solutions. Thermodynamic properties for many species may have to be re-determined experimentally, particularly those involved in complex equilibria involving mineralogical species at elevated temperatures.

2. Continued Development of Deterministic Theories and Models for General

Corrosion: While the GCM, which is based on the Mixed Potential Model (MPM) [8] that was previously developed and successfully used for calculating corrosion potentials and general corrosion rates of Type 304 SS in Boiling Water Reactor primary coolant circuits, yields realistic values for the accumulated damage (1.8 mm in 10,000 years, Figure 2), corresponding to an average corrosion rate of 0.18 µm/year, there are a number of ways in which the model may be significantly improved. Thus, in the present GCM, the passive film is assumed to comprise only of the barrier layer and no account is taken of the formation of the outer layer via the precipitation of oxides, hydroxides, and oxyhydroxides at the barrier layer/solution interface. The outer layer may also contain alien species (e.g., mineral salts) that are incorporated as it forms on the surface. In any event, the formation of the outer layer may result in the corrosion rate being considerably reduced, particularly at long exposure times, by restricting access of the cathodic depolarizer (e.g., O2) to the surface, or by inhibiting the dissolution of the barrier layer, or both, thereby leading to a reduction of the accumulated damage. This is a possible explanation of the steady decrease with exposure time in the corrosion rate of Alloy C-22, as determined by weight loss over a 5-year period at LLNL. A second issue that requires attention involves the role of the barrier layer in the kinetics of the cathodic reactions. Thus, current charge transfer theory posits that the transfer of charge carriers across a passive film occurs by direct or indirect quantum mechanical tunneling of electrons or electron holes, the probability of which is a very sensitive function of the potential profile. Thus, any realistic calculation of the tunneling probability, and hence of the exchange current density, for a redox reaction (e.g., O2 reduction), will require significant revision of current charge transfer theory, for which a Nobel Prize was awarded just a few years ago.

3. Continued Development of Deterministic Theories and Models for Localized

Corrosion: The theory for passivity breakdown, in the form of the Point Defect Model (PDM) [7] is well developed and has been tested extensively without failure to date. However, the current theory addresses only constant environmental conditions and hence is not ideally suited for calculating the nucleation rate of pits along a CEP where the conditions change with time. The road to generalizing the PDM to accommodate variable conditions has been examined and defined [4], and we see no major impediment to modifying the current theory to accomplish that task. Furthermore, methods have been

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developed recently for examining the role of aggressive species, such as Cl-, in great detail and, when applied to passivity breakdown on nickel in chloride-containing solutions, confirmed that chloride ion catalyses the ejection of cations from the barrier layer with the concomitant generation of cation vacancies. Because Alloy C-22 is a nickel-based alloy, albeit one whose passive film at low voltages is n-type in electronic character, rather than p-type, as is that on nickel, it is expected that the mechanism of passivity breakdown will be the same, but this needs to be demonstrated experimentally. (It is important to note that the passive film on Alloy C-22 becomes p-type at voltages above about 0.6 Vshe). Also, while the current, “coupled environment” models for pit (and crack) growth are highly deterministic and are well founded in electrochemical, dilute solution, and mass transport theory [9], they need to be rendered more sophisticated by the inclusion of concentrated solution theory, for example. Perhaps the greatest needs are the development of firm theoretical bases for prompt and, in particular, delayed repassivation. That delayed repassivation, which describes the death of stable pits, has a profound impact on the development of localized corrosion damage is clearly evident from the simulated damage functions plotted in Figure 4.

4. Neural Network Analysis of Existing and Future Empirical Databases: Very large databases are currently being generated at the LLNL, and elsewhere, on the corrosion behavior of Alloy C-22 in a variety of environments related to the disposal of HLNW in Yucca Mountain-type repositories. Analysis of the data appears to be restricted to the development of empirical relations between various dependent and independent variables, from which the corrosion loss may be extrapolated over the 10,000-year isolation period (although this has been debunked above). However, the databases are expected to contain a great deal of mechanistic information that, because of the multivariate nature of the problem, remains hidden within the complex, non-linear relationships between the dependent and independent variables. These relationships need to be carefully defined by using Artificial Neural Networks (ANNs) operating in the pattern recognition mode and trained under supervised learning protocols. Once defined, the relationships need to be used to assess various existing, deterministic models for predicting the dependent variable and to guide the modification and development of more advanced models. The ANNs may be used themselves to predict damage; their advantage in the empirical sense being that they do not contain any preconceived mathematical or physical model. Finally, ANNs are powerful tools for assessing the relative importance of various independent variables and hence for recognizing where emphasis should be placed in experimental programs.

5. Continued Experimental and Theoretical Investigation of the Passive and

Transpassive States on Alloy C-22: As noted above, the PDM has been demonstrated to account for the passive and the transpassive states within a single theoretical framework [2]. However, the predictions of the model have not been tested extensively, because of the lack of experimental data. The experimental data required are essentially those described in Item 6 below, as determined by Electrochemical Impedance Spectroscopy (EIS), but care must also be taken to carefully define the steady state. From a theoretical viewpoint, we need to identify the major defect within the barrier layer in the passive state (oxygen vacancy of metal interstitial) and transpassive state (cation vacancy), measure the rate of dissolution of the barrier layer and its dependence on pH, determine the impact of the various independent variables on the properties of both the passive and transpassive states, and defining the role of the outer layer in determining the corrosion rate. If necessary, the PDM must be modified to account for these data, if the present model fails to do so.

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6. Continued Determination of Fundamental Model Parameters: All deterministic models require that values for various model parameters be determined by independent experiment, if possible. If that is not possible for any given parameter, then the value may be determined by calibration of the model against DV(IV). It turns out that all but one of the parameters contained within the PDM, which yields the nucleation rate, may be determined using EIS. The values are determined by fitting the PDM to impedance data measured over a wide frequency range (typically 1 mHz to 10 kHz) as a function of voltage, pH, T, [Cl-], etc. To date, we have determined values for the various parameters at a single temperature (80 oC), [Cl-] (6.2 m), and pH (3) values, with the initial work being done to demonstrate the feasibility of the method. The one remaining parameter, the change in standard Gibbs energy for the absorption of a chloride ion into a surface oxygen vacancy, is readily determined by calibration.

The authors gratefully acknowledge the support of this work by the Department of Energy, Nuclear Energy Research Initiative, under Contract No. DE-FG03-99SG21884 to SRI International, and by DOE’s Yucca Mountain Project through Subcontract A20257JG1S to DDM via Innovative Design Technologies Inc.

1. G. Gordon, Corrosion, 58, 811 (2002). 2. G. R. Engelhardt, G. R. and D. D. Macdonald, Corrosion, 54, 469-479 (1998). 3. D. D. Macdonald, “The Holy Grail: Deterministic Prediction of Corrosion Damage

Thousands of Years into the Future”, Proc. Europ. Corros. Fed, in press (2003). 4. D. D. Macdonald, G. R. Engelhardt, P. Jayaweera, N. Priyantha, and A. Davydov, “The

Deterministic Prediction of Localized Corrosion Damage to Alloy C-22 HLNW Canisters”, Proc. Europ. Corros. Fed, in press (2003).

5. P-C. Lu and M. Urquidi-Macdonald, “Prediction of IGSCC in Type 304 SS Using Artificial Neural Networks”, CORROSION/94, Paper 103, 21 pp, Baltimore, MD, March 1994.

6. D. D. Macdonald, P. C. Lu, M. Urquidi-Macdonald, and T. K. Yeh. Corrosion, 52, 768 (1996).

7. D. D. Macdonald, Pure Appl. Chem., 71, 951 (1999). 8. D. D. Macdonald, Corrosion, 48(3), 194 (1992). 9. G. R. Engelhardt, D. D. Macdonald, and M. Urquidi-Macdonald, Corros. Sci., 41, 2267

(1999).