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Comprehensive nuclear materials 5 01 corrosion and compatibility Comprehensive nuclear materials 5 01 corrosion and compatibility Comprehensive nuclear materials 5 01 corrosion and compatibility Comprehensive nuclear materials 5 01 corrosion and compatibility Comprehensive nuclear materials 5 01 corrosion and compatibility Comprehensive nuclear materials 5 01 corrosion and compatibility Comprehensive nuclear materials 5 01 corrosion and compatibility
5.01 Corrosion and Compatibility S Lillard Los Alamos National Laboratory, Los Alamos, NM, USA ß 2012 Elsevier Ltd All rights reserved 5.01.1 Theory 5.01.1.1 5.01.1.2 5.01.1.3 5.01.1.4 5.01.1.5 5.01.1.6 5.01.2 5.01.2.1 5.01.2.2 5.01.2.3 5.01.2.4 References Introduction Half Cell Reactions Cell Potentials and the Nernst Equation Reference Electrodes and Their Application to Nuclear Systems The Thermodynamics of Corrosion from Room Temperature to the PWR Kinetics of Dissolution and Passive Film Formation Analytical Methods Introduction Potentiodynamic Polarization Electrochemical Impedance Spectroscopy Mott–Schottky Analysis Abbreviations BWR CNLS Boiling water reactor Complex nonlinear least squares fitting of the data EC Electrical equivalent circuit EIS Electrochemical impedance spectroscopy EPBRE External pressure-balanced reference electrode FFTF Fast Flux Test Facility HIC Hydrogen-induced cracking HIFER Hi-Flux Isotope Reactor IG Intergranular LBE Lead–bismuth eutectic PWR Pressurized water reactor SCC Stress corrosion cracking SS Stainless steel Symbols A C ci CR E EW Ecorr f Surface area Activity of species i Capacitance Concentration of species i Corrosion rate Potential Equivalent weight Corrosion potential Mass fraction ƒ F i icorr ji k L M MM n ND Q r R Rp RV S t ti T Vo z Z Z0 Z00 jZj b ba bc d 2 10 10 11 12 14 16 Fugacity Faraday’s constant Current density Corrosion current density Square root of À1 Rate constant Oxide thickness Molecular weight Metal cation Number of electrons Donor concentration Reaction quotient Rate of reaction Gas constant Polarization resistance Solution resistance Entropy of transport Time Transport number of species i Temperature Oxygen vacancy Charge Impedance Real part of the impedance Imaginary part of the impedance Magnitude of the impedance Symmetry factor Anodic Tafel slope Cathodic Tafel slope Double layer thickness Corrosion and Compatibility DCp Change in standard partial molar heat capacity DE0 Standard reduction potential DG Change in Gibbs energy DG0 Standard Gibbs energy DS0 Standard entropy change « Electronic charge Permittivity of space «0 f Applied potential h Overpotential u Phase angle r Material density v Frequency 5.01.1 Theory 5.01.1.1 Introduction Mars Fontana identified eight forms of corrosion in his book Corrosion Engineering1 and it is quite easy to find examples of almost all of these in nuclear reactors in both the primary and secondary cooling water systems For example, galvanic corrosion in zirconiumÀstainless steel couples,2,3 crevice corrosion in tube sheets4 and former baffle bolts,5 and pitting corrosion in alloy 600 steam generator tubes.6,7 Perhaps the most infamous form of corrosion observed in nuclear reactors is stress corrosion cracking (SCC), or environmental fracture, as we shall refer to it here, which has numerous examples in the literature Environmental fracture includes both intergranular SCC (IG), such as that which occurs in austenitic stainless steel, and hydrogen-induced cracking (HIC), frequently observed in nickel base alloys Failure by one of these mechanisms results from an interplay between stress, microstructure, and the environment (e.g., the electrochemical interface) The goal of this chapter is not to address each of the corrosion mechanisms outlined by Fontana individually, that will be accomplished in the following chapters Rather, this chapter is meant to provide the reader with the fundamental electrochemical theory necessary to critically evaluate the data and discussions in the corrosion chapters that follow In this section, we will review the fundamental theory of the electrochemical interface In the first three subsections, we review Half Cell Reaction, Cell Potentials and the Nernst Equation, and Reference Electrodes in Nuclear Systems In these sections, we develop the theory necessary to understand the role of electrochemical potential in environmental fracture and corrosion mechanisms For example, intergranular stress corrosion cracking (IGSCC) is only observed at potentials more positive than a critical value while HIC is only observed at potentials more negative than a critical value In the remaining two sections, we review the Thermodynamics from Room Temperature to the pressurized water reactor (PWR) and Kinetics of Dissolution and Passive Film Formation These sections should help the reader to understand the role of the passive film in the corrosion mechanism and the competition that occurs between film formation and metal dissolution rate As the fundamental role of irradiation in corrosion and environmental fracture mechanism is far from well established, in each section, we incorporate empirical irradiation data as examples and discuss concepts that are more broadly important to nuclear systems 5.01.1.2 Half Cell Reactions The electrochemical interface is characterized by an electrode (in this case a metal such as a cooling pipe) and an electrolyte (e.g., the cooling water in a reactor) While the bulk electrolyte contributes to variables such as solution chemistry and ohmic drop (solution resistance is discussed later in this chapter), it is the first nanometer of electrolyte that plays the most important role in electrochemistry In this short distance, referred to as the electrochemical double layer, a separation of charge occurs It is this separation of charge that provides the driving force (potential drop) for corrosion reactions For example, a 100 mV-applied potential across a typical double layer will result in an electric field on the order of 106 V cmÀ2 In the model proposed by Helmholtz,8 the double layer may be thought of as capacitor, with positive charge on the metal electrode and the adsorption of negatively charged cations on the solution side (Figure 1) The capacitance of the double layer is equal to that in its electrical analog e0D/d, where e0 is the permittivity of space, D is the dielectric, and d is the thickness of the layer For most electrochemical double layers, C is on the order of 10À6 F cmÀ2 Electrochemical reactions that take place in the double layer are reactions in which a transfer of charge (electrons) occurs There are two different types of cells in which electrochemical reactions may occur9: Electrolytic cells in which work, in the form of electrical energy, is required to bring about a nonspontaneous reaction Corrosion and Compatibility Metal Because the system cannot store charge, the electrons produced during the anodic reaction must be used This occurs at the cathode where typical reactions may include oxygen reduction: Excess negative charge Excess positive charge Bulk solution + - + - + - + - + - + + - + Acid: O2 þ 4Hþ þ 4eÀ ) 2H2 O - Base: O2 þ 2H2 O þ 4eÀ ) 4OHÀ + - ẵII ẵIII or hydrogen reduction: 2Hỵ ỵ 2e ) H2 fmetal ½IV From eqns [I] and [III], the general corrosion of an Fe surface in basic solution may then be written as: 2Fe ỵ O2 ỵ 2H2 O ) 2FeOHị2 fsolution Double layer Figure A diagram depicting the separation of charge at the electrochemical double layer and the associated potential drop (f) H2O 2H+ ClH2 H2O H+ H2O ClH2O Cl- 5.01.1.3 Cell Potentials and the Nernst Equation Oxide Fe For any chemical reaction the driving force, the Gibbs energy, may be written as10: Figure Diagram of what the anodic and cathodic reactions may look like on an iron surface depicting the separation of reactions and ionic conduction DG ẳ DG ỵ RT lnQ Voltaic cells in which a spontaneous reaction occurs resulting in work in the form of electrical energy Electrolytic cells cover a fairly large number of electrochemical reactions but may generally be thought of as ‘plating’ or ‘electrolysis’ type reactions and will not be treated here Corrosion reactions are voltaic cells and will be the focus of this chapter As in an electrolytic cell, voltaic cells are characterized by two separate electrodes, an anode and a cathode In corrosion, reactions at the anode take the form of metal dissolution, the formation of a soluble metal cation: Fe ) Feỵ2 ỵ 2e where Fe(OH)2 is the corrosion product An example of what the anodic and cathodic reactions on Fe electrode might look like is presented in Figure Though the anodic and cathodic reactions occur at physically separate locations, as shown in this figure, the reactions must be connected via an electrolyte (aqueous solution) Figure also suggests that corrosion reactions are controlled by variables such as mass transport (diffusion, convection, migration), concentration, and ohmic drop (resistivity of the electrolyte) These variables will be considered in our discussion of corrosion kinetics H+ Fe2+ e- ½V ½I ½1 where DG0 is the standard Gibbs energy, Q is the reaction quotient equal to the product of the activities (assumed to obey Raoult’s Law for dilute solutions and, thus, equal to the concentration) of the products divided by the reactants, R is the gas constant, and T is temperature The electrical potential, E, is related to the Gibbs energy of a cell by the relationship: nFE ẳ DG ẵ2 where n is the number of electrons participating in the reaction and F is Faraday’s constant For the reduction of hydrogen on platinum: ỵ ỵ e Ptị , H2gị Haq ½VI Corrosion and Compatibility The reaction quotient, Q (starting conditions) becomes: Q ẳ ẵfH2 1=2 ẵHỵ ½3 where fH2 is the fugacity of hydrogen gas Substituting eqns [2] and [3] into eqn [1], we find for the reduction of hydrogen on platinum that: " # RT ẵfH2 1=2 ẵ4 ln E ẳ DE ỵ ẵHỵ F where F is Faraday’s constant and DE0 is the standard reduction potential for the reaction in eqn [VI] Equation [10] is commonly referred to as the Nernst equation and defines the equilibrium reduction potential of the half cell and is pH dependent The Nernst equation is commonly expressed in its generalized form as: E ẳ DE ỵ RT ln½Q F ½5 5.01.1.4 Reference Electrodes and Their Application to Nuclear Systems In Equation [4], all of the parameters are easily calculated with one exception, DE0 Therefore, we define DE0 ¼ in eqn [4] for a set of specific parameters and refer to this cell as the standard hydrogen electrode (SHE): H2 pressure of atm, a pH ¼ 0, and a temperature of 25 C This provides a reference from which we can calculate the standard potentials for all other reduction reactions using eqn [5] These are referred to as standard reduction potentials and a few examples are provided in Table While the SHE is the accepted standard, from a practical standpoint, this reference electrode is difficult to construct and maintain As such, experimentalists have taken advantage of a number of other reduction reactions to construct reference electrodes for laboratory use The reaction selected typically depends on the application One common reference electrode is the silver–silver chloride electrode (Ag/AgCl) which is based on the reduction of Agỵ in a solution of potassium chloride: Agỵ ỵ e , Agsị ẵVII Agỵ ỵ Cl , AgClsị ẵVIII and the overall reaction being: Agsị ỵ Cl , AgClsị ỵ e ẵXI Table Standard reduction potentials for several reactions important to the nuclear power industry Reduction reaction Standard reduction potential (V) Au3ỵ ỵ 3e Au Cl2 þ 2eÀ ⇄ 2ClÀ O2 þ 4Hþ þ 4eÀ ⇄ 2H2O Agỵ ỵ e Ag Fe3ỵ ỵ e Fe2ỵ O2 ỵ 2H2O ỵ 4e 4OH AgCl ỵ e Ag ỵ Cl 2Hỵ ỵ 2e H2 (NHE) Ni2ỵ ỵ 2e Ni Fe2ỵ ỵ 2e Fe Cr3ỵ ỵ 3e Cr Zr4ỵ ỵ 4e Zr Al3ỵ ỵ 3e Al Liỵ ỵ e Li 1.52 1.36 1.23 0.80 0.77 0.4 0.22 0.0 À0.25 À0.44 À0.74 À1.53 À1.66 À3.04 The Nernst equation for eqn [XI] is equal to: ½aAgCl RT E ẳ DEAg=AgCl ỵ ln ẵaAg ẵaCl F ¼ DEAg=AgCl À ln½aClÀ ½6 where aClÀ is the activity of chloride and for which the concentration (mClÀ ) in molal (mol kgÀ1) is frequently substituted In the corrosion lab, the reference electrode is constructed by electrochemically depositing an AgCl layer onto a silver wire This wire is then placed in a glass capillary filled with a solution of potassium chloride the concentration of which then defines the cell potential (aClÀ in eqn [6]) One end of the capillary is sealed using a porous frit (typically a porous polymer) that acts as a junction between the solution of the reference electrode and the environment of the corrosion experiment While the Ag/AgCl reference electrode construction described above is straightforward for the lab, there are several obstacles that must be overcome before it can be used in a nuclear power plant setting, namely, radiation flux, pressure, and temperature As it turns out, the primary impact of ionizing radiation on laboratory reference electrodes relates to damage of the cotton wadding and polymer frits used in their construction and no change in cell potential occurs.11 As such, two approaches based on the Ag/AgCl reference electrode have been used to measure electrode potential in nuclear power reactors In the first approach, an internal reference electrode operates in the same high-temperature environment as the reactor In this case, one must consider the solubility of Corrosion and Compatibility Sapphire lid AgCl pellet Rulon adapter Compression fitting Sapphire container Pt cap Ni wire Alumina insulators Ceramic to metal braze Restrainer Ag/AgCl Kovar TIG weld 304SS Seal Coaxial cable Figure Diagram of an internal Ag/AgCl reference electrode used in BWRs Top end is inserted into the cooling loop, while the coaxial cable provides electrical connection Reprinted from Indig, M E In 12th International Corrosion Congress, Corrosion Control for Low-Cost Reliability; NACE International: Houston, TX, 1993; p 4224, with permission from NACE International Ag/Cl complexes that form as a function of temperature eqn [6].12,13 That is, reactions in addition to eqns [VIII] and [XI] must be considered From a construction viewpoint, the internal reference electrode consists of a silver chloride pellet on a platinum foil (Figure 3).14 External potential measurement is made via contact with a nickel wire which is connected to an electrometer via a coaxial cable The electrode is housed in a sapphire tube that is sealed via a porous sapphire cap In this configuration, there is no internal electrolyte per se Upon placing the electrode in a boiling water reactor (BWR), the porous cap allows the cooling water to penetrate the electrode and the potential is determined from eqn [6] and the solubility of AgCl in high purity water as a function of temperature.15 In the second approach, an external pressurebalanced reference electrode is used (EPBRE) In the EPBRE, the reference electrode is maintained at room temperature and pressure and the corresponding constants are used in eqn [6] The reference is connected to the high-temperature environment via a nonisothermal salt bridge sealed with a porous zirconia plug (Figure 4).16 As a result of this configuration, the EPBRE is not susceptible to Compression fitting 1/4ЈЈ NPT Pure water or 0.01 M KCl Glass wick 1/4ЈЈ OD SS tube Heat-shrinkable PTFE tube SS nut Rulon sleeve Zirconia plug Figure A diagram of a pressure-balanced reference electrode is used in BWRs Bottom of figure is sealed into pressure vessel via compression fitting while Ag/AgCl electrode (top) remains at room temperature and pressure Reprinted from Oh, S H.; Bahn, C B.; Hwang, I S J Electrochem Soc 2003, 150, E321, with permission from The Electrochemical Society potential deviations owing to the solubility of AgCl and its complexes as a function of temperature However, the temperature gradient between the reactor and the reference electrode results in a junction potential that must be subtracted from eqn [6] The corresponding thermal liquid junction potential (ETLJ)17 is given by: ð T2 tMỵ SMỵ tCl SCl dT ẵ7 ETLJ ẳ ỵ zMỵ zCl F T1 where t, S, and z represent the transport number, the entropy of transport, and the charge on the cation, respectively The symbol M in eqn [7] represents the metal in the chloride salt, MCl, and is commonly Li, Na, or K In addition to ETLJ, there is also the isothermal liquid junction potential, EILJ, which arises due to the differences in cation and anion mobilities through the porous frits and the fact that the electrolyte in the external reference (typically KCl) is vastly different from the reactor cooling water in which it is immersed17: RT T2 ti EILJ ẳ dlnẵai ½8 F T1 zi Corrosion and Compatibility where the subscript i denotes a species that may be transported through the zirconia plug and for a nuclear power reactor may include species ions as Agỵ, Cl, Hỵ, OH, Kỵ, and B(OH4)À It has been shown that both ETLJ and EILJ each increase by as much as 0.15 V over the temperature range of 25–350 C The result is a decrease in the measured potential of 0.30 V at 350 C While these junction potentials can be calculated and used to correct eqn [7], it has been shown that there is some deviation at higher temperatures (>200 C) and an experimental fitting procedure is the preferred method for calibration of the reference electrode reactions with two soluble species 3ỵ Fe ẵ11 Fe2ỵ ẳ Fe3ỵ ỵ e E ẳ 0:771 ỵ 0:059log Fe2ỵ solubility of iron and its oxides Fe ẳ Fe2ỵ ỵ 2e E ẳ 0:440 ỵ 0:0295logFe2ỵ ị 2Fe2ỵ ỵ 3H2 O ẳ Fe2 O3 ỵ 6Hỵ ỵ 2e E ẳ 0:728 0:177pH 0:059logFe2ỵ ị An atlas of electrochemical equilibria has been created by M Pourbaix for metals in aqueous solution at room temperature.18 This atlas contains potential– pH diagrams, so-called Pourbaix diagrams, which define three equilibrium thermodynamic domains for metals in aqueous solutions: immunity, passivity, and corrosion Immunity is defined as the state where the base metal is stable while corrosion is defined as the formation of soluble metal cations and passivity the formation of a stable oxide film Pourbaix’s derivation requires that the values of the standard chemical potential, m0, for all of the reacting substances are known for the standard state at the temperature and pressure of interest For chemical reactions at room temperature, the equilibrium conditions are defined by the relationship18: P nm ½9 logK ¼ 5708 and for electrochemical reactions at room temperature (Table 1) equilibrium is defined by: P nm ½10 E ¼ 96485n where K is the equilibrium constant for the reaction, m0 is in Joules per mole, v is the stoichiometric coefficient for the species, n is the number of electrons, 5708 is a conversion constant equal to RT/(log10e) where T is temperature (298.15 K) and R the ideal gas constant (8.314472 J (K mol)À1), and 96 485 is Faraday’s constant in J (mol V)À1 As an example of these diagrams, consider the iron–water system and the solid substances Fe, Fe3O4, and Fe2O3 Pourbaix18 defined the relevant equations for this system as: ẵ13 ỵ Fe ỵ 2H2 O ẳ HFeO ỵ 3H ỵ 2e E ẳ 0:493 0:089pH ỵ 0:0295logẵHFeO 5.01.1.5 The Thermodynamics of Corrosion from Room Temperature to the PWR ẵ12 ẵ14 ỵ 3HFeO ỵ H ẳ Fe3 O4 ỵ 2H2 O ỵ 2e E ẳ 1:819 ỵ 0:029pH 0:088logẵHFeO ẵ15 reaction of two solid substances 3Fe ỵ 4H2 O ẳ Fe3 O4 ỵ 8Hỵ ỵ 8e E ẳ 0:085 0:059pH ẵ16 2Fe3 O4 ỵ H2 O ẳ 3Fe2 O3 ỵ Hỵ ỵ 2e E ¼ 0:221 À 0:059pH ½17 An example of a simplified Pourbaix diagram for Fe at room temperature based on the reactions in eqns [11]–[17] is presented in Figure 5, where Eq [12] corresponds to figure line 23, [13] to line 28, [14] to line 24, [15] to line 27, [16] to line 13 and [17] to line 17 Note that Eq [11] is the boundary between Fe2ỵ and Fe3ỵ and was not drawn in the original figure In addition to the lines separating the domains for Fe, Pourbaix diagrams will typically include the domains associated with water stability (oxidation and reduction) represented by the dashed lines marked a and b in Figure Upon inspection of this diagram one would conclude what is know from experience with Fe: that iron is passive in alkaline solutions and at higher applied potentials owing to oxide film formation while at more acidic solutions Fe is susceptible to corrosion owing to Fe2ỵ It is worth noting again that these potential–pH domains are defined solely by the thermodynamic stability of the species within them and these diagrams not consider kinetics which will be addressed later in this chapter This is important as while a species/reaction may be thermodynamically stable it may be kinetically hindered While the use of Pourbaix diagrams to characterize room temperature corrosion reactions is Corrosion and Compatibility 1.5 Fe3+ 1.5 Fe3+ 20 20 1.0 1.0 b Fe2O3 Fe2+ EH2 (200 ЊC) (V) 28 EH (25 ЊC) (V) 0.5 a 26 -0.5 17 Fe3O4 23 0.5 Fe2+ 26 13 -1.0 HFeO-2 17 Fe3O4 23 27 24 Fe Fe2O3 a -0.5 13 -1.0 b 28 Fe HFeO22- -1.5 -1.5 10 15 pH widespread, these diagrams and the method for generating them as presented thus far cannot be used at the higher temperatures associated with nuclear power reactors This is due to the lack of standard potentials at elevated temperature as required by eqns [9] and [10] (e.g., the application of Table to higher temperature) In the absence of these high-temperature thermodynamic data, Townsend19 used an extrapolation method introduced by Criss and Coble (the correspondence principle) The method allows for empirical entropy data of ionic species at 25 C to be extrapolated to higher temperatures In this method, the standard Gibbs free energy is calculated from the relationship: ð ÀT ðT 250 T 250 DC p T ịdlnT DC p T ịdT ẵ18 where DS is the standard entropy change and DC p is the change in standard partial molar heat capacity The potential–pH diagram for the Fe–H2O system and the solid substances Fe, Fe3O4, and Fe2O3 at 200 C calculated by Townsend is presented in Figure In comparison with the diagram at 25 C (Figure 5), the Fe2O3 and Fe3O4 regions are extended to lower pH and potentials As a result the area associated with corrosion at lower solution pH is decreased However, 24 10 15 pH Figure A simplified potential–pH diagram for the Fe–H2O system and the solid substances Fe, Fe3O4, and Fe2O3 at 25 C based on the reactions in eqns [11]–[17] Reprinted from Townsend, H E Corrosion Sci 1970, 10, 343, with permission from Elsevier DDG ị ẳ DT DS 250 ị ỵ 29 27 Figure The potential–pH diagram for the Fe–H2O system and the solid substances Fe, Fe3O4, and Fe2O3 at 200 C Most dramatic influence of increased temperature is the presence of a large region of soluble species (corrosion) at high pH Reprinted from Townsend, H E Corrosion Sci 1970, 10, 343, with permission from Elsevier the most notable change in the diagram is at high pH where the area associated with corrosion owing to the soluble HFeOÀ has increased dramatically The Criss and Coble method is limited, however, to the 150–200 C range and, to extend the Pourbaix to the temperatures of power reactors, Beverskog used a Helgeson–Kirkham–Flowers model to extend the heat capacity data to 300 C.20 Thus far, we have described a method for generating electrochemical equilibria diagrams and regions of passivity, corrosion, and immunity for pure metals from 25 to 300 C From an engineering standpoint, we would like to know this information for structural alloys such as austenitic stainless steels and super nickel alloys At temperatures near 25 C, the predominant oxide responsible for passivity is Cr2O3 and it is sufficient to rely only on the Cr potential–pH diagram for alloys with a high Cr content However, at higher temperatures other oxides form such as Fe(Fe,Cr)2O4, (Cr,Fe)2O3, (Cr,Fe,Ni)3O4, and (Cr,Fe,Ni)2O3, and it is desirable to know the thermodynamic stability of the alloy Beverskog has developed the ternary potential– pH diagrams for the Fe–Cr–Ni–H2O–H2 system for temperatures up to 300 C using heat capacitance data and the revised Helgeson–Kirkham–Flowers model described above.21 However, Fe–Cr–Ni phases lack thermodynamic data and the ternary oxides were, Corrosion and Compatibility npH H2CrO4(aq) HCrO4- Potential (VSHE) CrO42- where ia is the anodic current density, ka is the rate constant, co is the concentration of oxidized species, and DGa is the change in free energy for the anodic reaction Substituting G2a À G1a in eqn [20] for DGa in eqn [19], we express the anodic reaction rate as22: bịnF ẵ21 ia ẳ nFka cR exp RT Cr(OH)2+ NiCr2O4(cr) Cr2+ FeCr2O4(cr) -1 Cr2O3(cr) Cr(cr) -2 pH300 ЊC decreasing the barrier, that is, not all of the applied potential is dropped across the electrochemical double layer The rate (ra) of this reaction is expressed in the same, Arrhenius, form as for chemical reactions: DGa ½20 ¼ ia =nF ¼ ka co exp À RT 10 Figure Potential–pH diagram for chromium species in Fe–Cr–Ni at 300 C Concentration of aqueous species is 10À6 molal Reprinted from Beverskog, B.; Puigdomenech, I Corrosion 1999, 55, 1077, with permission from NACE International thus, not considered The diagrams assumed that the metallic elements in the alloy had unit activity, that is, equal amounts of iron, chromium, and nickel An example of the potential–pH diagram for chromium species in Fe–Cr–Ni at 300 C and aqueous species with a concentration of 10À6 molal is presented in Figure Unlike the Fe diagram, where the presence of soluble HFeO2À species increased with temperature (Figure 6), the diagram for Cr in Fe–Cr–Ni is dominated by passive region where the stable oxides of Cr2O3, FeCr2O4, and NiCr2O4 are formed 5.01.1.6 Kinetics of Dissolution and Passive Film Formation The study of dissolution kinetics, corrosion rate, attempts to answer the question: ‘‘What are the relationships that govern the flow of current across a corroding interface and how is this current flow related to applied potential?’’ Consider the anodic dissolution of a metal with an activation barrier equal to G1a ¼ nFE (eqn [2]) If we increase the driving force (potential) from its equilibrium condition, E0, to a new value, f, the new barrier is given by the relationship22: where (the overpotential) represents a departure from equilibrium and is equal to f À E0 We can derive a similar expression for the cathodic reaction22: bnF ẵ22 ic ẳ nFkc co exp À RT where ic is the cathodic current density, kc is the rate constant, and co is concentration of oxidized species Combining eqns [21] and [22] and rearranging them, we can write an expression for the total current, i: ð1 À bÞnF bnF exp ẵ23 i ẳ io exp RT RT where io is the exchange current density and is equal to Àb Àb nFkcc1Àb o ka cR This expression is commonly referred to as the Butler–Volmer equation To apply eqn [23] to corrosion reactions, we need to be able to relate to the corrosion potential, Ecorr , that is, as it stands the Butler–Volmer equation is derived for equilibrium conditions Returning to our definition of the overpotential ¼ f À E0, by both subtracting and adding Ecorr from the right side of this definition, inserting the resulting expression back into eqn [23] and rearranging we find22: ð1 À bÞF ðEcorr À Ea Þ icorr ¼ ia exp RT bF ¼ ic exp Ecorr Ec ị ẵ25 RT ẵ19 For small applied potentials around Ecorr , the Stern– Geary approximation of eqn [24] is used23: ba ỵ bc f Ecorr ị ẵ26 i ẳ 2:303icorr ba bc where b is the symmetry factor and reflects the fact that not all of the increase in potential goes to where ba and bc are defined as the anodic and cathodic Tafel slopes (discussed in Section Ga2 ¼ Ga1 À ð1 À bÞnF ðf À E0 Þ 0.4 0.1 0.35 Current density (A m-2) Potential (V vs SCE) Corrosion and Compatibility 0.3 0.25 0.2 Beam on at 100 nA ~540 s 0.15 0.1 500 1000 Time (s) 1500 2000 5.01.2.2) having units of volts and are empirical factors related to the symmetry factor by the relationships22: RT ð1 À bịnF bc ẳ 2:303 RT bnF Beam = 35 na Beam = 62 na Beam = 100 na -0.1 -0.2 Increasing radiation flux Increasing cathodic reaction rate -0.3 -0.4 -0.5 Figure Influence of proton irradiation on the Ecorr of a SS 304L electrode in dilute sulfuric acid, pH ¼ 1.6 The increase is caused by the production of water radiolysis products ba ẳ 2:303 ẵ27 ẵ28 As it relates to the nuclear power industry, eqn [24] not only relates the corrosion rate (icorr) to the applied potential, f, but it can also help us to rationalize other processes such as the influence of water radiolysis products on corrosion rate For example, it is generally observed that ionizing radiation (g, neutron, proton, etc.) increases Ecorr potential (Figure 8) and corrosion rate at Ecorr 24 The flux of ionizing radiation on the cooling water results in radiolysis, the breaking of chemical bonds During the course of water radiolysis, a wide variety of intermediate products are formed, such as O2À, eaq, and the OH radical.25 The vast majority of these species have very fast reaction rates so that the end result is a handful of stable species These stable products are typically oxidants, such as O2, H2, and H2O2 That is, these products readily consume electrons (eqns [II]–[IV]) and increase cathodic reaction rate (Figure 9) From eqn [25] we see that an increase in the cathodic reaction rate, ic, necessarily results in an increase in corrosion rate, icorr , consistent with the observation described While the development of dissolution kinetics is straightforward, the kinetics associated with passive -0.6 -0.2 -0.1 0.1 0.2 0.3 Potential (V vs SCE) 0.4 0.5 Figure Influence of proton irradiation on the cathodic reactions on a Au electrode in dilute sulfuric acid, pH ¼ 1.6 The increase is caused by the production of water radiolysis products film formation and breakdown are less well understood yet equally as important to our understanding of corrosion mechanisms One such example is the case of localized corrosion where the probability for a pit to transition from a metastable to a stable state is governed by the ability of the active surface to repassivate Another example is the initiation of SCC where passive film rupture results in very high dissolution rates and, correspondingly, crack advance rate which is controlled by the activation kinetics described above as the bare metal dissolves.26–28 During the propagation stage of SCC, the crack tip must propagate faster than (1) the oxide film can repassivate the surface and (2) the corrosion rate on the unstrained crack sides so that dissolution of the walls does not result in blunt notch To evaluate the role of repassivation kinetics in SCC and corrosion mechanisms in general, investigators set about measuring three critical experimental parameters, namely film: ductility,29,30 bare surface dissolution rates,31–33 and passive film formation rates34,35 for various alloys Each of these techniques involves the depassivation of a metal electrode using a tensile frame or a nano-indenter (in the case of ductility studies) or scratching/breaking an electrode (bares surface current density and repassivation studies) and measuring the resulting current transient as a function of time An example of a current transient for SS 304L in chloride solution is presented in Figure 10 The surface was under potentiostatic control and was bared using a diamond scribe The data were collected using a high-speed oscilloscope 10 Corrosion and Compatibility 7.0 ϫ 10−4 6.0 ϫ 10−4 Current (A) 5.0 ϫ 10−4 td tr 0.002 0.004 0.006 0.008 Time (s) 4.0 ϫ 10−4 3.0 ϫ 10−4 2.0 ϫ 10−4 1.0 ϫ 10−4 0.0 0.01 0.012 Figure 10 Scratch test current transient from a SS 304L electrode in 0.1 M NaCl The transient is characterized by a growth period, td, and a repassivation period, tr The transient is characterized by two separate processes, anodic dissolution and repassivation represented by td and tr in Figure 10 To analyze the repassivation rates, the period tr is typically fit to an expression and evaluated as a function of solution pH or electrode potential The most prolific work in this field is probably on the alloy SS 304L For this alloy, it has been proposed that the kinetics of film growth are controlled by ion migration under high electric field.36–38 The kinetics of high-field film growth were first proposed by Cabrera and Mott39 to obey the kinetic relationship: BV ẵ29 i ẳ Aexp L where i is the current density, V is the voltage, L is the oxide thickness, and A and B are constants 5.01.2 Analytical Methods 5.01.2.1 Introduction In this section, we will review the principle analytical methods used to probe the electrochemical interface In the Section 5.01.2.2 Potentiodynamic Polarization, we discuss linear polarization resistance and the practical application of corrosion kinetics, eqns [25] and [26] In that section, we also describe the salient points of the anodic polarization curve In the Section 5.01.2.3 Electrochemical Impedance Spectroscopy, we introduce an ac method for interrogating the electrochemical interface This technique is probably the most versatile experimental method available to scientists and researchers As it relates to nuclear reactors, this technique has the ability to subtract out the contribution of the solution resistance to polarization resistance measurements which, if not accounted for in highly resistive cooling water measurements will result in nonconservative corrosion rates In the final section, we introduce a more seldom used technique, Mott–Schottky analysis While this is by no means a common experimental method, it provides a conduit for the reader to become familiar with defects in the oxide film, their transport and ways to quantify it This has particular interest here as ionizing radiation may promote corrosion rates by increasing transport of these defects through the passive oxide film Regretfully, the scope of this chapter is limited, and we are not able to discuss the step-by-step details of the experimental methods that are used to make corrosion measurements A comprehensive guide to experimental methods in corrosion has been published by Kelly et al.40 as well as Marcus and Mansfeld41 while a more broad description of electrochemical methods has been published by Bard and Faulkner.42 The reader is also encouraged to become familiar with the equipment that is used to make electrochemical measurements and a good introductory chapter on this topic has been presented by Schiller.43 The most important instrument is, no doubt, the potentiostat While this instrument is the cornerstone of corrosion science, it does have its pitfalls including bandwidth limitations and the potential for ground loop circuits when used in conjunction with other equipment such as load frames, autoclaves and cooling loops The latter can be overcome using proper instrumentation such as potentiostat with a floating ground, or isolation amplifiers To investigate the influence of the neutron flux on corrosion rates and mechanisms, real-time in-situ corrosion measurements are often made ‘in-reactor’ or at neutron facilities such as Oak Ridge National Lab’s Hi-Flux Isotope Reactor (HIFER) and Argonne National Lab’s Fast Flux Test Facility (FFTF) Alternately, neutron damage can be simulated using ion beams As it relates to ion irradiation, this method provides opportunities for studying the interaction of the components of reactor environments (radiation, stress, temperature, aggressive media) that are not possible with in-reactor or neutron irradiation facilities For a full discussion of this topic, see Chapter 1.07, Radiation Damage Using Ion Beams To summarize these experiments, controlled Corrosion and Compatibility environmental cells are coupled to accelerator beamlines to study the interaction of the environment and irradiation on structural materials Corrosion at the substrate–environment interface is studied in real time by numerous electrochemical techniques including those described below With respect to dose, light ions can be used to reach doses up to $10 dpa in several days However, the depth of penetration is low (tens or micrometers), which puts unrealistic limitations on electrochemical cell construction Heavy ion irradiation can reach several hundred displacements per atom in a matter of days but the penetration depth is much less 5.01.2.2 Potentiodynamic Polarization During our development of Butler–Volmer reaction kinetics, we introduced the Stern–Geary approximation and defined Tafel slopes within the context of the symmetry factor without much further explanation To understand the empirical source of the Tafel slopes, we rearrange eqn [26] to define the polarization resistance Rp in units of O cm2: Rp ẳ ba bc DE ẳ 2:303icorr ba ỵ bc ị Di ẵ30 The Tafel slopes can be obtained from a plot of potential as a function of the logarithm of current density as shown for the cathodic curve in Figure 11 where bc has units of volts A similar anodic plot can be generated to obtain ba It is important to realize that these slopes are frequently not equal as they are related to separate mechanisms on the electrode surface From a plot of both the anodic and cathodic Tafel slopes, we can also obtain icorr (Figure 11) With knowledge of icorr , ba, and bc, the polarization iOH2 EH + + H h(mv) 20 10 Slope = Applied current curve Ecorr + M 20 20 iapp(cathodic) icorr E iOM resistance can then be determined from eqn [30] For small voltage perturbations, the slope of a plot of applied potential (DE ) versus the change in current density (Di ) is equal to Rp (Figure 12), often referred to as the linear polarization resistance as the slope is only linear for small voltage perturbations around Ecorr Errors not accounted for in eqn [30] include uncompensated solution resistance (RO) and choosing a scan rate that is too fast From a reactor standpoint, the value of RO in the cooling water or a simulant where the resistivity is high may be a significant contribution to the measured Rp and, therefore, result in a nonconservative corrosion rate, that is, the calculated corrosion rate will be too low For a complete standardized method of conducting potentiodynamic polarization resistance measurements and data analysis, the reader is referred to the appropriate ASTM standards G3, G59, and G102.44–46 Potentiodynamic polarization curves can also be used to assess corrosion rate as well as determine if a material is passive, active, or susceptible to pitting corrosion in a given environment Consider the curve in Figure 13 It plots the applied potential as a function of the log of the absolute value of the current density The corrosion potential and corrosion current density are shown at the intersection of the cathodic and anodic curves Mass loss (m, in grams) for a given period of exposure can then be 40 H+ /H2 11 DE Diapp 40 iapp(anodic) -10 Tafel region M - EM/M+ log iapplied Figure 11 Diagram depicting the cathodic polarization of an electrode near Ecorr Tafel extrapolation showing the determination of icorr is also presented Reprinted from Fontana, M G Corrosion Engineering; McGraw Hill: New York, 1986, with permission from McGraw Hill -20 h(mv) Figure 12 Diagram depicting the linear polarization for an electrode about Ecorr Slope, DE/Di, is equal to the polarization resistance Reprinted from Fontana, M G Corrosion Engineering; McGraw Hill: New York, 1986, with permission from McGraw Hill 12 Corrosion and Compatibility positive hysteresis in the reverse portion of the curve that is not observed in the case of solution oxidation or transpassivity Epit Potential Erepass 5.01.2.3 Electrochemical Impedance Spectroscopy Eflade ba ipass icorr bc Ecorr Log current density Figure 13 Diagram depicting the potentiodynamic polarization of an electrode far from Ecorr Relevant potentials and currents are defined in the text determined from the corresponding icorr using Faraday’s Law, for a pure metal40: icorr t EW ½31 FA where t is time in seconds, icorr has units of A (cmÀ2), A is surface area, and EW is equivalent weight and is equal to molecular weight (M) divided by the number of electrons in the reaction Similarly, for an alloy: m¼ EW ¼ P n i i fi =Mi ½32 where the subscript i denotes the alloying element of interest and f is the mass fraction of that element in the alloy From Faraday’s law, it is also possible to calculate corrosion rate, the penetration depth owing to corrosion over a period of time in units of mm yearÀ1 (CR): CRmm yearÀ1 ¼ 3:27 Â 103 icorr EW r ½33 where r is the material density in g cmÀ3 Other critical parameters in Figure 13 include the Flade potential (EFlade) which marks the critical potential necessary for passive film formation, the passive current density (ipass), the pitting potential (Epit), and the repassivation potential (Erepass) With respect to EFlade, this active to passive transition is not observed for materials that are spontaneously passive in a given environment such as SS in a BWR In such a case, the current would be limited by the film dissolution current (ipass) As it relates to Epit, the onset of localized corrosion is characterized by a sharp increase in current at a given potential As such, materials that are more susceptible to pitting have lower Epit values Pitting is also characterized by a While potentiodynamic polarization is typically considered a destructive technique, that is, it alters the surface of the corrosion sample, electrochemical impedance spectroscopy (EIS) is a powerful nondestructive technique for obtaining a wealth of data including Rp.47 Further, this technique has the ability to subtract out the uncompensated solution resistance (RO) from the measurement which, for highly resistive reactor cooling water environments, is a significant advantage In EIS, a small sinusoidal voltage perturbation (10 mV) is applied across the electrode interface over a broad frequency range (mHz to MHz) By measuring the transfer function of the applied voltage to the system current, the system impedance may be obtained For corrosion systems, the impedance (Z) is a complex number and may be represented in Cartesian coordinates by the relationship: Zoị ẳ Z0 ỵ Z00 ẵ34 where o is the applied frequency in radians, Z0 is the real part of the impedance, and Z00 is the imaginary part of the impedance, and the magnitude of the impedance jZj is given by: q ẵ35 jZj ẳ Z0 ị2 þ ðZ00 Þ2 In its simplest form, the electrochemical interface can be thought of as an electrical equivalent circuit (EC): a resistor (R) with an impedance Z(o) ¼ R and a capacitor (C) with Z(o) ¼ 1/joC where j is the square root of À1.48 Thus, the impedance of a resistor is purely real and independent of frequency while the impedance of a capacitor is purely imaginary and inversely proportional to frequency With respect to the electrochemical interface, the polarization resistance is in parallel with the double layer capacitance (Cdl, owing to adsorption of charged anions/cations in the electrolyte) These two components act in series with the solution resistance, RO as seen in the EC in Figure 14 This circuit is referred to as a simple Randles circuit and represents an ideal interface Commonly, however, Cdl does not behave as an ideal capacitor and its impedance is better represented by the expression Corrosion and Compatibility 13 -6 ϫ 104 Rp RW -5 ϫ 104 -4 ϫ 104 Figure 14 Simplified Randles equivalent circuit of an electrochemical interface where Rp is the polarization resistance, Cdl is the double layer capacitance, and RO is the geometric resistance associated with the solution resistance ZЈЈ (W) Cd1 -3 ϫ 104 -2 ϫ 104 -1 ϫ 104 105 ϫ 104 ϫ 104 ϫ 104 ϫ 104 ϫ 104 ϫ 104 ZЈ (W) Rp + RW Figure 16 Nyquist format for data in Figure 15 where Rp ¼ Â 104 O, Cdl ¼ Â 10À6, and RO ẳ 200 O 104 |Z| (W) Zoị ẳ 1=C j oÞa 103 RW 102 10-3 10-2 10-1 100 101 102 (a) Frequency (Hz) 103 104 105 -10 Q (Њ) -30 -40 -50 -70 wmax -80 -90 10-3 10-2 10-1 100 101 102 (b) Frequency (Hz) where a is typically found to be between 0.5 and The element that represents this behavior is known as a constant phase element (Ccpe).49 The response of a simple Randle’s circuit as a function of frequency is shown in Figure 15(a) and 15(b) These plots are referred to as the Bode magnitude plot (eqn [35]) and the Bode phase plot50 where the phase angle, y, is equal to: 00 Z ½37 y ¼ tanÀ1 Z0 This phase angle is a result of the double layer capacitance where the current leads the applied ac voltage perturbation as is the case for pure capacitors The parameters Rp and RO may be determined graphically from the Bode magnitude plot as shown in Figure 15(a) while Cdl is determined from the graphical parameter omax (converted to radians, 2pf) in Figure 15(b) and the relationship40: q ỵ Rp =RO ẵ38 Cdl ẳ omax Rp -20 -60 ½36 103 104 105 Figure 15 (a) Bode magnitude and (b) Bode phase plots Data were generated from an electrical equivalent of a simplified Randles circuit (Figure 13) where Rp ¼ Â 104 O, Cdl ¼ Â 10À6, and RO ¼ 200 O Alternately, the data may be presented using the Nyquist format which plots the imaginary impedance as a function of the real impedance as seen in Figure 16 (sometimes referred to as a Cole–Cole plot) As graphical analysis is somewhat imprecise, commercially available complex nonlinear least squares fitting of the data (CNLS) is commonly used to obtain these parameters (Figure 17) 14 Corrosion and Compatibility |Z| exper |Z| fit 102 ROX RW -10 |Z| (W m2) -30 Q exper Q fit -40 -50 100 Q (degrees) -20 101 -60 COX Figure 19 Equivalent circuit of an oxide-covered metal in liquid PbBi eutectic (LBE) where Rox is the resistance of the passive film, Cox is the double layer capacitance of the oxide, and RO is the geometric resistance associated with the LBE -70 10-1 10-3 10-2 10-1 100 101 102 -80 103 Frequency (Hz) Figure 17 Bode magnitude and Bode phase plots for SS 304L during proton irradiation in a pressurized deionized cooling water loop at 125 C showing experimental data and complex nonlinear least squares fit of equivalent circuit in Figure 14 Corrosion rate (mm year −1) 6.0 5.0 4.0 3.0 Photons Neutrons 2.0 1.0 Protons 20 100 120 40 60 80 Flux (particles m–2 per proton) 140 Figure 18 Corrosion rate as a function of particle flux for a SS 304L electrode during proton irradiation in a pressurized deionized cooling water loop at 125 C EIS has been used successfully to investigate the passive films on Zr alloys,51–53 SS 304L,54 and nickel base alloys55 in environments that simulate reactor cooling water systems In addition, it has also been used to measure the real-time corrosion rates of materials during irradiation Lillard et al.56,57 measured the corrosion rate of materials as a function of immersion time in a deionized water cooling loop during proton irradiation In that work, radiationhardened probes made from Alloy 718, SS 304L, and Al 60 601 were exposed to a proton beam at various current densities The impingement of the beam on the probes resulted in a mixed neutron, photon, and proton flux It was shown that corrosion rate was almost linear with photon and neutron flux as compared to proton flux where anomalies existed at intermediate fluxes (Figure 18) The data were ultimately used to extrapolate lifetimes for accelerator materials In other studies, EIS has also been applied to investigate passive films on metals in sodium (Na)cooled and lead–bismuth (LBE) systems that simulate reactor environments The equivalent circuit (EC) used to model the data is similar to the simplified Randles circuit; however, in this case, there is no electrochemical double layer, only the impedance and capacitance associated with the oxide (Figure 19) In this EC, Rox is the dc resistance of the oxide, Cox is the oxide capacitance, and RO is the geometric resistance associated with the liquid metal (Na or LBE) In one such study, Isaacs investigated the capacitance of anodized films on Zr in liquid Na In that study, it was shown that both Rox and Cox were a function of Na temperature between 50 and 400 C Lillard et al.58 reported similar trends for HT-9 in LBE At constant temperature, Rox and Cox for HT-9 in LBE were a function of immersion time (Figure 20) The data were used to calculate oxide thickness as a function of time In addition, Rox was related to ionic transport through the film and corrosion rates were calculated using Wagner’s oxidation theory Upon irradiation in a proton beam, this rate fell even further.59 Additional information about leadÀeutectic coolants may be found in Chapter 5.09, Material Performance in Lead and Lead-bismuth Alloy 5.01.2.4 Mott–Schottky Analysis The formation and growth of passive oxide films is driven, fundamentally, by interfacial reactions and defect, electron and ion transport processes Yet the Corrosion and Compatibility 105 ROX 15 5.5 ϫ 1010 101 5.0 ϫ 1010 104 Prior to irradiation Fit Beam on Fit 10–1 101 C-2 (cm4 F-2) ROX (W cm−2) Rp = 0.9 ´ t1.7 102 COX (nF cm–2) 100 103 4.5 ϫ 1010 4.0 ϫ 1010 3.5 ϫ 1010 10–2 COX 100 10–1 –50 50 100 Immersion time (h) 150 3.0 ϫ 1010 10–3 200 2.5 ϫ 1010 -0.2 0.2 0.4 0.6 0.8 Potential (V vs SCE) Figure 20 Impedance capacitance for the oxide on an HT-9 steel as a function of immersion in liquid PbBi eutectic Reprinted from Lillard, R S.; Valot, C.; Hanrahan, R J Corrosion 2004, 60, 1134, with permission from the author Figure 21 Mott–Schottky plots for a SS 304L electrode in dilute sulfuric acid, pH ¼ 1.6 Before and after proton irradiation Reprinted from Lillard, R S.; Vasquez, G J Electrochem Soc 2008, 155, C162, with permission from the author nature and relative importance of these processes are still far from being understood Key to oxide growth, and, therefore, passivation, is the mobility of these defects, specifically vacancies Under irradiation, however, the defect properties of the oxide are undoubtedly changed, and the extent of corrosion is related both to the microstructure and transport properties of defects One way to probe the transport properties of the oxide film is by using Mott–Schottky theory Returning to our discussion of EIS above, the oxide capacitance may be obtained at high frequency from the relationship depends on what type of semiconductor the oxide is (p vs n) and this effects the sign of the slope Lillard used Mott–Schottky analysis to examine the influence of proton irradiation on defect generation and transport in the oxide film on SS 304L.61 The passive film on SS 304L is an n-type semiconducting oxide and the major defect is the oxygen vacancy which acts as an electron donor According to the Point Defect Model62 for oxide growth, oxygen vacancies are produced at the metal–film interface by the injection of a metal atom into the oxide lattice: Z00 ðoÞ ẳ 1=oC or C ẳ 1=oZ00 olim ị ẵ39 By measuring Z00 as a function of applied dc voltage at the high frequency limit (olim) and calculating the film capacitance from eqn [39], it is possible to evaluate donor concentration (ND) in the oxide film from the well-known Mott–Schottky relationship: kT ẵ40 ẳ 2=ee N U U D fb C2 q where e0 is the permittivity of space and is equal to 8.854 Â 10À14 F cmÀ1, e is the electronic charge and is equal to 1.602 Â 10À19 C, U is the applied potential in V, Ufb is the flatband potential in V, kT/q is equal to 25 mV at 25 C, and ND is the donor concentration (oxygen vacancies) in cmÀ3.60 ND is the slope of a plot of 1/C2 versus applied potential The type of defect m ! MM ỵ x=2ịVo þ xeÀ ½41 where m is a metal atom, MM is a metal cation, Vo is a oxygen vacancy, eÀ is an electron, and x is the stoichiometric coefficient In pH 1.6 H2SO4, it was found that the cation vacancy concentration in the oxide increased from 2.94 Â 1021 in the absence of irradiation to 3.41 Â 1021 during irradiation (Figure 21) It was proposed that the film on SS 304L is composed of an inner Cr-rich p-type semiconductor and an outer Fe-rich n-type semiconductor This bilayer film results in a p–n junction where the two layers meet On the p side of the junction, there is a surplus of holes, while on the n side of the junction, a surplus of electrons exists The energy bands are such that it is ‘uphill’ (an increase in energy) for electrons moving across the junction (from the n side to the p side) On a related topic, a discussion of defects in bulk oxides can be found in Chapter 1.02, Fundamental Point Defect Properties in Ceramics 16 Corrosion and Compatibility References 33 34 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Fontana, M G Corrosion Engineering; 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Nature 1 958 , 181, 8 35 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 Frankel, G S.; Jahnes, C V.; Brusic, V V.; Davenport, A J J Electrochem Soc 19 95, 142,... and defect, electron and ion transport processes Yet the Corrosion and Compatibility 1 05 ROX 15 5 .5 ϫ 1010 101 5. 0 ϫ 1010 104 Prior to irradiation Fit Beam on Fit 10–1 101 C-2 (cm4 F-2) ROX (W... = 0.9 ´ t1.7 102 COX (nF cm–2) 100 103 4 .5 ϫ 1010 4.0 ϫ 1010 3 .5 ϫ 1010 10–2 COX 100 10–1 ? ?50 50 100 Immersion time (h) 150 3.0 ϫ 1010 10–3 200 2 .5 ϫ 1010 -0.2 0.2 0.4 0.6 0.8 Potential (V vs