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A Fourier analysis technique has been used to solve the p.roblem of the potential distribution around a long narrow scratch in a passzve film on an electrode surface. Analytic solutions have been obtained for situations where linear polarization kinetics may be assumed for the unscratched region, and where the current density is constant over the scratch and very much greater than the current density over unscratched regions. If the half-width l of the scratch is very much smaller than the Wagner polarization parameter for the unscratched region Lc, a simple expression is obtained for the potential distribution close to the scratch. There is a small additional increase in e!ectrode potential at the scratch, but the main increase in potential is over a distance characterized by Lc and not by the size of the scratch. The potential within the electrolyte and along the electrode depends mainly on the logarithm of distance from the center of the crack. There is an angular dependence of the potential only for distances < 21 from the center of the scratch.

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A technique using integrals of Bessel functions has been used to calculate the effect of an anodic current distribution of the form Ja ----jm(flo -~-fllr2/a 2 + ~2r4/a 4) within the pit on the potential distribution in the plane of the electrode surface, and analytic solutions have been obtained for situations where linear polarization kinetics may be assumed. If the radius of the pit is small compared to the Wagner polarization parameter Lc for the unpitted electrode, the potential distribution is independent of the polarization parameter, and thus insensitive to the assumption of linear kinetics. The potential within the pit depends mainly on the value of the total current flowing from the pit, and is less sensitive to the form of the current distribution. The potential outside the pit on the surface of the electrode depends on the mean current density and is virtually unaffected by the form of the current distribution.In a recent paper (1) a Fourier integral technique has been used to calculate the distribution of potential around a scratch in a passive film. This has been extended (2) to cylindrical coordinates to calculate the variation in potential around a pit, assuming that the current density flowing from the pit is uniform across the pit. Here this method of solution is extended to allow for a variation in the current density across the pit. As in Ref.(2) it is assumed that the pit (the anode) is very small compared with the rest of the electrode, which may be treated as infinite, so that integration may be used as in Ref.(2-4) instead of summation, which is necessary for finite systems with this geometry (5-7). Mathematical ModelAs in Ref.(2) the problem considered is that of an infinite plate perpendicular to the z-axis at z ----0 with a small pit of radius a at the origin r ----0. The general solution for the distribution of the electrostatic potential P is given from the Laplace equation with the boundary conditions that P is a constant at z ----~, and that the solutions are symmetric about r --0. This requires that P(r, z) is of'the form P(r,z) = Bo + ~" B(t)Jo(rt)e-ztdt[1] ~, o where Jo( ) is a Bessel function of the first kind of order zero, and where the constant Bo and the function B(t) have to be determined from the boundary conditions at the electrode surface. If the change in potential is small, linear polarization kinetics may be assumed as in Ref. (1) and (2) and as in the solutions of Waber and his associates (8-13) for strip geometry and by Gal-Or et al. (5) and McCafferty (6, 7) for circular geometry. The current density at the electrode surface is given by j(r) = -~ [21 0Z s=O where ~ is the conductivity of the electrolyte. This has to satisfy the electrochemical relations for the electrode, which if linear polarization kinetics are assumed is of the form Key words: anodic current distribution, pitting, integral of Bessel functions. j* = ~ (E* --Ec) [S]where Ec is the free corrosion potential and Lc the Wagner polarization parameter (14) for the unpitted area (the cathode), and E*, the...

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