| Abstract: | SUMMARIES. The rate at which chloride ions diffuse from archaeological iron into a treatment solution depends on how the chloride ions are initially distributed in the corrosion layer. This paper compares solutions of the diffusion equation for two limiting cases: (1) where the chloride ions are initially spread uniformly through the corrosion layer; and (2) where the chloride ions are initially concentrated at the interface between the iron and the corrosion layer. Although the first model has been used in the past to describe chloride ions diffusing from marine iron, the second is more appropriate in cases where corrosion has drawn chloride ions toward the iron surface. Because diffusion processes in archaeological iron are complicated, the limitations of both these models are discussed
CONCLUSION. A diffusion model will predict the behaviour of Cl¯ ions diffusing into treatment solutions from archae¬ological iron only if the conditions under which the diffusion model equations were derived remain valid. The two diffusion models discussed here are based on Cl¯ ions diffusing through a constant distance (e.g., the corrosion layer) and the solid matrix remaining unchanged. If the object undergoes a physical change during the course of a treatment, then the two diffusion models will no longer accurately reflect the diffusion behaviour of the Cl¯ ions. The diffusion distance will change if the outer corrosion layers fall off during treatment. The solid matrix will change if the physical properties of the solid are changed, for example by expansion, electrochemical processes or reduction. Expansion and possibly irreversible dimensional changes are caused by iron treatments involving heating, particularly boiling [I]. Rapid electrochemical processes cause cracking and an increased porosity of the corrosion products on iron treated in sodium hydroxide [16]. Electrolysis of iron in alkaline solutions causes reduction of the iron corrosion products (usually to magnetite) and an increase in their porosity [20]. Also, it may be inappropriate to use diffusion models to interpret the results when several objects are treated in a single treatment solution because the initial Cl¯ ion concentrations and corrosion thick nesses vary between objects. The uniform model, equation (15), could be used to interpret data at short times if one assumed all objects had the same C0 (a reasonable assumption if the objects come from very similar microenvironments) and A was calculated from the total surface area of all objects. If. during the washing treatment of archaeological iron, the Cl¯ ion concentration of the treatment solution is measured regularly, then a graph can be constructed of the total Cl¯ ion concentration released (vertical axis) versus the square root of the total treatment time (horizontal axis). This method of plotting the dala was first recommended by North and Pearson for monitoring treatment progress and for observing if the experimental data behaved in a manner predicted by their diffusion model (i.e. the 'uniform' model discussed above) [1], The predicted behaviour for the Cl¯ ion concentration plotted against t1/2 is a linear dependence during the early stages of treatment and the line passing through the origin. Approximately linear graphs have been observed in treatment solutions for marine iron [3, 4]. When such linear graphs have been observed, the behaviour has sometimes been referred to in the conservation literature as "diffusion controlled' [3, 21], where the uniform diffusion model, although not mentioned specifically, is implied by reference to the paper by North and Pearson [I] and refers to the Cl¯ ions behaving as predicted by the uniform model (given by equation (15) for objects in general, and by equation (13) if the diffusion is restricted to one dimension). Although the diffusion model no longer holds when there are physical changes to the corrosion layer, the behaviour of the Cl¯ ion data can still be qualitatively interpreted. For example, the changing diffusion behaviour for Cl¯ ions diffusing through iron undergoing electrolysis can be observed in the increase in slope of Cl¯ ion concentration plotted versus tl/2 for data collected during a treatment: after about 16 hours, the slope increased, presumably because the iron corrosion products had been reduced, the porosity increased, and the Cl¯ ions could diffuse out faster [20]. The uniform model is based on one simple extreme for the initial Cl¯ ion distribution; the assumption is that the Cl¯ ions are uniformly distributed through the solid. The experiments of North and Pearson [1] are a particularly good example of the uniform model, at least in part, because the corrosion layer had been removed from the metal surface, so that the Cl¯ ion in the corrosion layer could spread uniformly through the corrosion layer before treatment began. In cases where the Cl¯ ion is concentrated near the metal surface when treatment begins, particularly in terrestrial iron where the Cl¯ ions must diffuse through a thicker layer of corrosion products and extraneous material than in marine iron, the abrupt model should be closer to the truth. The abrupt model is based on another simple extreme for the initial Cl¯ ion distribution; here the assumption is that the initial Cl¯ ion distribution is abrupt, with all the Cl¯ ions located at the metal surface. As demonstrated by the curves in Figures 4-6, the abrupt model predicts a time delay between the beginning of treatment and the time when Cl¯ ions first enter the treatment solution. It also predicts a sigmoidal rather than linear shape to the curves in graphs of Cl¯ ion concentrations against t1/2, and qualitatively describes the S-shaped behaviour of the experimental data in Figure 2. The delay time in this model can be divided into two parts. One delay is caused by the time needed to passivate the metal surface by OH ions diffusing in from the treatment solution. The other delay is caused by the time needed for the Cl" ions to diffuse through the corrosion layer and enter the treatment solution. This sigmoidal behaviour is expected for objects of any shape if the chloride is initially concentrated deep inside the corrosion layer. But the specific quantitative details, such as the numerical coefficients in equations (16) or (20), apply only to the one-dimensional model discussed here. The abrupt model is more dependent than the uniform model on the geometry of the object because the abrupt model has no counterpart to equation (15), a formula that applies to objects of arbitrary shape. Because of this limitation, it would be difficult to apply abrupt models quantitatively to experimental data. The diffusion equation would have to be solved for the specific geometry of the artifact. A more accurate starting distribution for the C would be needed, and the passivation step would be more complicated than considered above, as OH ions diffuse in and displace Cl" ions before eventually passivating the iron surface. Nevertheless, the simple abrupt model described here does illustrate that diffusion models can describe delay times and sigmoidal shapes, such as in Figure 2. To summarize, we have argued that the uniform model is not the only possible solution of the diffusion model appropriate to the removal of Cl ions from archaeological artifacts. We have discussed the abrupt model as a useful counterpoint to the uniform model, to show how dramatically the starting distribution of chloride ions can influence the rate at which they are removed from the corrosion layer |
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