Passivity of Metals in the Point Defect Model: Effect of Chloride [Part-III] Bosco Emmanuel, CSIR-CECRI, Karaikudi , India

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1 Paivity of etals in the Point Defect odel: Effect of hloride [Part-III] Bosco Eanuel, SIR-ERI, Karaiudi-3, India Abstract In this paper we study the effect of addition of chloride on the stability of the copact oxide layer pre-existing on a etal surface at a given ipreed potential and ph. The variant of the point defect odel [PD] advanced by us recently [, ] is used to construct a theory for the chloride-induced build-up of etal vacancies at the etal/fil interface and the chloride-induced diolution of the copact oxide layer. Under the quasi-steady-state approxiation the relevant oving boundary value proble is solved exactly and analytical expreions are found for the incubation tie, oxide diolution tie, and critical pitting potential, the tie evolution of the paive current density and the etal vacancy concentration and the dependence of these quantities on the chloride ion concentration. Soe diagnostics are also provided. The replaceent of reaction (3) of the original PD [3] by reaction (3 ) of the variant [, ] is shown to have iportant consequences for the chloride-ion effect. While the original PD invoed the Schotty-pair reaction to couple the chloride ion to the cation flux and to the etal vacancy generation by reactions () and (), the present odel couples the chloride ion directly to the etal vacancy annihilation by reaction (3 ) without invoing the Schotty-pair reaction. The anion flux-pinning by chloride is shown to be sufficient to destabilize the oxide layer. An interesting conclusion of the present wor is that thicer oxide layers are in general ore susceptible to pitting due to the chloride ion and thinner oxide layers destabilize by siple diolution in the presence of chloride. Introduction In our earlier preprints[,] we advanced a variant of the point defect odel [] which rectified a flaw in the original odel of acdonald et al [3] and further elucidated [] the tie dependence of the paive current density and barrier layer thicne during potential switching experients. In the present paper, which is Part-III of this series, we addre the following experient and wor out

2 the corresponding theory based on the corrected version of the point defect odel: For the copact oxide layer and a steady paive current density at a given ipreed potential and solution ph in the absence of any aggreive ion lie the chloride. Add chloride to the electrolyte ediu so that the chloride ion concentration switches abruptly to a predeterined value. onitor the transient response of the syste in ters of the current density and barrier layer thicne with a view to identify the critical pitting potential and the incubation tie Theory of icro-void Generation, ritical Pitting Potential and the Incubation Tie Following reference [] we postulate that the following reaction occurs at the fil/solution interface and it is at equilibriu with the equilibriu concentration given by equation (). l () * ( aq) l K [ l G exp ] Fφ f / s () Where is the concentration of at the fil/solution interface, Gthe * standard Gibbs free energy of reaction (), K has the activity corrections, lois a chloride ion occupying an oxygen lattice site and all other sybols have their * usual eanings. Unit activity of lois aued as in []. Now the rate of reaction () of the point defect odel, naely H H is pinned at. s R / ) (3)

3 given by equation (). This iplies that the flux of in the barrier with layer is pinned by the chloride. In the quasi-steady-state approxiation of [], the rate of reaction (3 ) q /. e will directly be controlled by R. This flux pinning by chloride has iportant consequences for icro-void generation and pitting as shown below. Siilarly the rates of reactions () and () will respectively be equal to the rates of reactions () and (5) in the quasi-steady-state. Even with the quasi-steady-state approxiation, the barrier layer thicne, the etal vacancy concentration and the current density will be seen to be tie-dependent. Tie Evolution of the etal acancy oncentration at the etal/fil Interface, Incubation Tie and Fil Diolution Tie At the etal/fil interface the rate of generation of the etal vacancy by reactions () and () and its annihilation by reaction (3 ) are given by Rate of generation of () q Rate of annihilation of. ( / ) ( / ) f s (5) The net rate of generation of at the etal/fil interface is: G q ( ). () ( / ) These etal vacancies diffuse into the etal and we need to solve the diffusion equation with a oving boundary at the etal/fil interface. The velocity v of the oving boundary at the etal/fil interface at x x ( is given by dxb ( v Ω. R3 (7) dt B

4 . Ω. (8) ( / ) which is a constant for a fixed potential, [ l ] and ph. The rate of change of the boundary layer thicne Lis dl dt. Ω 7 R ( / ) (9) R L () L L R t () L. as RLis a constant for case A. Note that when l is added to the syste initially at steady state, RLswitches fro zero to a negative value. For the quasi-steadystate approxiation, the Stephen proble for the diffusion of etal vacancy in the etal can be solved exactly and the solution is ( x, ( x x (, A.( exp{ D s t sx}) () B where sis a paraeter related to the velocity vof the oving boundary as [5] v s (3) D and Dis the diffusion coefficient of the etal vacancy in the etal phase. G A () v The incubation tie for pitting ay be evaluated by considering the tie evolution of the etal vacancy concentration at the oving etal/fil interface. Taing the liit x on either side of equation (), we obtain ( x, ( x x (, A (5) B ( x x (, A () B

5 where is the unifor concentration of the etal vacancy in the etal at the initial steady state. Using equations (),(8),and() in equation (), ( x x B (, Ω q Ω (7) The functional fors for and, for case A, are:. t exp{ a c ph}.exp{ b L( )} (8). exp{ a c ph} (9) Use equations (), (8) and (9) in (7) to obtain q x xb (, K K exp[ b RLt] () Ω ( where K K Ω exp[ a c ph ] exp[ a c Ω ph b L ] () () As RLis negative, it is interesting to note that the concentration of the etal vacancy at the etal/fil interface is an exponentially increasing function of tie with a tie constant which ay be identified with the incubation tie: T inc (3) b R L Using equations (9) and () and taing the reciprocal of (3) T bωr7 bω inc ( / ) [ l ] ()

6 where G Fφ f K exp / s (5) Equation () predicts that the reciprocal of the incubation tie is linear in the reciprocal of the chloride concentration with a negative slope and positive intercept that depends on the applied potential and ph. Fro equation () follows a siple equation for the tie required for the coplete diolution of the barrier oxide in the presence of chloride: T ΩR Ω 7 dis L L ( / ) [ l ] () It should be cautioned that this tie for coplete diolution of the barrier oxide is not to be confused with the incubation tie for pitting which is given by equation (). Note the functional siilarity of equations () and (). The place of bin equation () is taen by L in equation (). learly T inc will be saller than T dis if and when Lis larger than. In the opposite case fil diolution will b overtae pitting. As L increases linearly with the applied potential, pitting will be the failure ode for higher applied potentials and for lower applied potentials chloride-induced fil diolution will be favored. This conclusion is ade poible by the fact that bis eentially independent of the potential in the point defect odel [this independence was aued in the original PD and is predicted in the variant of the PD []]. ritical Pitting Potential In the present theoretical fraewor the critical pitting potential ay be identified as the potential above which there is a net etal vacancy generation at the etal/fil interface. This condition can be stated as: G > (7)

7 Thus the critical pitting potential is the solution of the equation G q ( ). ( / ) Use the nown fors of,, and and solve equation (8) for the critical pitting potential. Note, however, that involves the tie-dependent barrier-layer thicne L (. Just replace L( by L as the syste will be critical at a later tie t if it is critical initially. Interestingly this stateent allows for the poibility that a syste which is initially sub-critical ay becoe critical at a later tie. Thus a concept of dynaic criticality eerges fro the present odel. This concept ay be visualized by constructing a plot of potential versus tie based on equation (8). For each potential, chloride ion concentration and ph, there is a tie above which criticality sets in. This tie is not to be confused with the incubation tie or the fil-diolution tie but rather ars the initiation of the proce which terinates at the incubation tie or the fil-diolution tie. For oxides that are anionic conductors equation (8) ay be further siplified as (8) q ( / ). (9) After inserting the relevant functional fors and siplifying, there results PIT PIT.33log[ l ] αf a a (3) where PIT qk.33log ( / ) bl a G a Fφ f / αf s ( c c βf ) ph (3) Note we have set L L. (

8 Paive urrent Density Evolution on the Addition of hloride The general expreion for the paive current density is given by i F.{ δ ( ). J ( δ ). R7} (3) After inserting the relevant functional fors we obtain i J n F.{ δ. exp{ b L}exp{ brlt} δ. ( δ ). 7R} (33) [ l ] where the potential and ph dependent quantities are: exp{ a c ph} (3) exp{ a c ph} (35) 7 7 exp{ a7 c7 ph} (3) J ( a K exp αf) ( c βf) ph G Fφ f / s (37) As RLis negative the current density will rise with tie exponentially on the addition of chloride to the ediu. This rise will continue till the tie of coplete diolution of the oxide fil or pitting whichever is earlier. In addition equation (33) is not expected to hold very near to zero tie as the quasi-steadystate will tae soe tie to establish. onclusions In [] acdonald et al resorted to the Schotty-pair creation echanis in order to relate the action of chloride at the fil/solution interface on the etal vacancy generation/annihilation at the etal/fil interface. This was neceitated by the fact that the reaction (3) in the original point defect odel ied out the etal vacancy annihilation. However there is no real need to invoe Schotty-pair creation echanis as reaction (3 ) of the corrected PD naturally couples the action of chloride at the fil/solution interface and the etal vacancy annihilation at the etal/fil interface.

9 References D.D.acdonald, Electrochiica Acta 5()7-77. L.F.Lin,.Y.hao and D.D.acdonald, J.Electroche.Soc. 8(98) H.S. arslaw and J.. Jeager, onduction of Heat in Solids, xford, larendon Pre, 959, p.9 The defect reactions considered in the present paper are: etal Barrier Layer Porous Layer R Solution (). e () δ ( aq) ( δ ). e () i i.e (5) i δ ( aq) ( δ ). e i (3 ) q /. e () H H (7) ( δ e δ / H aq) H ( )