Pitting theories

We describe here an experiment which indicates that the dislocation etch pit theory is a useful tool in interpreting formation of... 

In the following, some experimental results pertaining to these concerns are presented, making the relation between pitting theories and practical behavior more realistic and motivating future works to shed light on some poorly understood domains. 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

The usual context for linear response theory is that the system is prepared in the infinite past, —> -x, to be in equilibrium witii Hamiltonian H and then is turned on. This means that pit ) is given by the canonical density matrix... 

Pontiff, D., and J. Sammons, Theory, Design and Operation of an Environmentally managed Pit System, First International Symposium on Oil and Gas Exploration Waste Management Practices, pp. 997-987, 1990. 

Unfortunately, there is no general theory that will explain all the forms of localised attack that occur with the variety of metal/environment systems encountered in practice, e.g. the mechanism of the pitting of stainless steels in Cl -containing solutions is quite different from the dezincification of brass in a fresh natural water. Nevertheless, many of the following factors play an important part in most forms of localised attack ... 

The development of acidity within an occluded cell is by no means a new concept, and it was used by Hoar s as early as 1947 in his Acid Theory of Pitting to explain the pitting of passive metals in solutions containing Cl ions. According to Hoar the Cl ions migrate to the anodic sites and the metal ions at these sites hydrolyse with the formation of HCl, a strong acid that inhibits the formation of a protective film of oxide or hydroxide. Edeleanu and Evans followed the pH changes when aluminium was made anodic in Cl solutions and found that the pH decreased from 8-8 to 5-3. 

Vermilyea" has adopted a thermodynamic approach to pitting, and considers that the critical pitting potential is the potential at which the metal salt of the aggressive ion (e.g. AICI3) is in equilibrium with metal oxide (e.g. AljOj). On the basis of this theory the critical pitting potential should decrease by 0-059V per decade increase in chloride ion concentration. Vermilyea s theory successfully predicts the values of the critical potentials for Al, Mg, Fe and Ni, but in the case of Zr, Ti and Ta there are large discrepancies. 

The principal cathodic reaction on the upper surface of the membrane is the reduction of Cu " that is formed by the reaction of Cu with dissolved oxygen in the water these Cu ions are provided partly from the diffusion through the pores in the oxide membrane from within the pit and partly from those produced by cathodic reduction (equation 1.154). Lucey s theory thus rejects the conventional large cathode small anode relationship that is invoked to explain localised attack, and this concept of an electronically conducting membrane has also been used by Evans to explain localised attack on steel due to a discontinuous film of magnetite. 

Schwenk, W., Theory of Stainless Steel Pitting , Corrosion, 20, 129 (1964)... 

Inside a pit in electrolytic solution, anodic dissolution (the critical dissolution current density, and diffusion of dissolved metal hydrates to the bulk solution outside the pit take place simultaneously, so that the mass transfer is kept in a steady state. According to the theory of mass transport at an electrode surface for anodic dissolution of a metal electrode,32 the total increase of the hydrates inside a pit, AC(0) = AZC,<0),is given by the following equation33,34 ... 

In the potential region where nonequilibrium fluctuations are kept stable, subsequent pitting dissolution of the metal is kept to a minimum. In this case, the passive metal apparently can be treated as an ideally polarized electrode. Then, the passive film is thought to repeat more or less stochastically, rupturing and repairing all over the surface. So it can be assumed that the passive film itself (at least at the initial stage of dissolution) behaves just like an adsorption film dynamically formed by adsorbants. This assumption allows us to employ the usual double-layer theory including a diffuse layer and a Helmholtz layer. 

Figure 38. Classification of nonequilibrium fluctuations. (Reprinted from M. Asanuma and R. Aogaki, Non-equilibrium fluctuation theory on pitting dissolution. I. Derivation of dissolution current equations." J. Chem. Phys. 106,9938,1997. Copyright 1997, American Institute of Physics.)...

Figure 40. Plot of the fluctuation-diffusion current J vs. iwr.91 id is the slope of the fluctuation-diffusion current given by Eq. (115). Solid and dotted lines correspond to the theoretical and experimental results, respectively. (NiCljJ = 0.1 mol nT3. [NsCl] = 7 mol m 3. V = 0.1 V, T= 300 K. (Reprinted from M. Asanuma and R. Aogaki, Nonequilibrium fluctuation theory on pitting dissolution, n. Determination of surface coverage of nickel passive film, J. Chem. Phys. 106, 9938, 1997, Fig. 8. Copyright 1997, American Institute of Physics.)...

Flade potential, 247 Flame-annealed gold surfaces and the work of Kolb, 81 Flat band potential, 483 Fluctuations asymmetrical and unstable systems, 255 controlling progress in pitting, 299 in pitting dissolution, 251 and corrosion processes, 217 during dissolution, 252 at electrodes, theory, 281 during film breakdown, 233 and mathematical expressions thereof, 276... 

Several refinements of our experiments could test these theories further. By measuring etch pit densities as well as pit dimensions on sequentially-etched crystals, nucleation rate data and pit growth data could be collected, yielding information about the rate-limiting steps and mechanisms of dissolution. In addition, since the critical concentration is extremely dependent on surface energy of the crystal-water interface (Equation 4), careful measurement of Ccrit yields a precise measurement of Y. Our data indicates an interfacial energy of 280 + 90 mjm- for Arkansas quartz at 300°C, which compares well with Parks value of 360 mJm for 25°C (10). Similar experiments on other minerals could provide essential surface energy data. 

Shinoda K, Kunieda FI (1983) Phase Properties of Emulsions PIT and HLB. In Becher P (ed) Encyclopedia of Emulsion Technology, vol 1 Basic Theory, Chap. 5. Marcel Dekker, NY, pp 337-367... 

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