Measurement of corrosion content of archaeological lead artifacts by their Meissner response in the superconducting state; a new dating method

Meissner fraction in the superconducting state of lead archaeological artifacts is used to evaluate the mass of the uncorroded metal in the sample. Knowing the total mass of the sample, the mass of all corrosion products is established. It is shown that this mass correlates with the archaeological age of the lead artifacts over a time span of ∼2500 years. Well-dated untreated lead samples from Tel-Dor, the Persian period, Caesarea, the Byzantine and the Crusader periods as well as contemporary data were used to establish the dating correlation. This new chemical dating method is apparently applicable to lead artifacts buried in soils with pH > 6.5. In such soils the corrosion process is very slow and the corrosion products, mainly PbO and PbCO3, accumulate over hundreds of years. The method presented is in principle non-destructive.

. SEM image of a corroded lead disc punched out from an archaeological artifact from the Persian period. PbCO 3 crystallites are present on the surface.

Introduction
Dating of metal artifacts is in most cases an unsolved problem. We propose a new chemical dating method for lead which is found quite frequently in archaeological excavations. In our method the corrosion extent on the surface of lead, used in antiquity for weights, pipes, claddings etc, is correlated with the burial time of the archaeological artifact. Conceptually our method is similar to the obsidian dating developed in 1960 by Friedman and Smith [1]; see also [2] for a review on chemical methods.
Lead metal at room temperature exhibits diamagnetic susceptibility of the same order of magnitude as its salts and oxide. However, when cooled below 7.2 K it enters into the superconducting state in which it exhibits the ideal diamagnetic susceptibility. The value of this susceptibility is 10 4 -10 5 higher than that of its oxide and salts which are not superconductors (s.c.). The value of the volume susceptibility (χ v ) of lead in the Meissner state (see [3]), i.e. a state in which there is a total expulsion of the magnetic field from the volume of the lead sample, is −1/4π = −0.0796. This value translates to a molar susceptibility (χ M ) of χ M = −1.453 cgs. The molar susceptibility of lead oxide and lead salts is of the order of −10 −5 to −10 −4 cgs at room temperature [4] and down to cryogenic temperatures. Thus the contribution to the diamagnetic signal of these compounds at cryogenic temperatures is negligible in comparison to the diamagnetic signal of lead.
The volume magnetic susceptibility measured in the s.c. state of a corroded lead sample is where M is the magnetic moment in emu; ρ = 11.34 g cm −3 the density of lead, m Pb is the mass of the lead metal in the sample and η is the demagnetizing factor. η is shape dependent and its Experimentally we find that this procedure has an accuracy of ∼1% in samples of ∼100 mg. By measuring the transition temperature to the s.c. state we can distinguish between the relatively pure lead metal phase, T c = 7.2 K, and homogeneous lead alloy phases which exhibit different values of T c . Inclusions of a diamagnetic non-superconducting phase in the lead phase will not affect the T c value.
Lead's corrosion resistance accounts for its successful use in many environments when exposed to the atmosphere, soil, fresh water and sea water (see [5]). Its good resistance in contact with many corrodents is due to the formation of relatively insoluble films of corrosion products deposited on the metal in the initial stages of exposure, which then protect it from further attack. The resistance to corrosion of lead in soils is usually good and it varies with the acidity of the soil. In a controlled corrosion experiment of lead pipes in a number of soils for periods up to 10 years (see [6]) it has been found that for soils with pH above 6.5 the rate of corrosion was between 4 × 10 −5 and 6 × 10 −5 cm year −1 . In acidic soils pH 4-5 the rate was about 50 times higher. Thus we may assume that lead buried in sites with similar low value of acidity will  have a comparable rate of corrosion over very long time periods. Also it is assumed that the geological conditions such as soil conductivity and water table must have remained relatively constant throughout the archaeological time.
The corrosion products of lead in soil are mainly lead oxide, PbO, and lead carbonate, PbCO 3 . The solubility of these compounds in water at room temperature is very low, 2.3 × 10 −3 and 1.1 × 10 −4 g/100 ml respectively, thus the accumulation of these products on the surface of archaeological artifacts in soil over hundreds of years could be expected.

Experimental details and results
In our study the sampling of lead artifacts is done by punching out discs in a corroded untreated lead sheet or ribbon. These discs are 0.5-2.5 mm in thickness and are 4.0 mm in diameter. The punching procedure is performed with a hard steel shearing cylindrical knife.
Before the disc is cut, the corroded lead sheet is sandwiched between two paraffin films, which keep the brittle corrosion encapsulated on the sample. After the punching procedure the mass of the disc is measured. A SEM image of the surface of a sample from the Persian period is presented in figure 1 Magnetization versus field and versus temperature for the disc samples is measured in a SQUID MPMS 2 magnetometer. Magnetization versus field at 5 K and versus temperature in a field of H 0 = 10 Oe for lead artifacts ∼2500 year old, Persian period, excavated in Tel Dor are shown in figure 3. The critical field H c and the critical temperature, T c , are the same as those measured in contemporary samples. To calculate the demagnetizing factor, η, the magnetization in small enough fields, O ≤ H 0 ≤ 30 Oe, is measured in two configurations: discs parallel and perpendicular to H 0 . Figure 4 presents data for 14 discs cut out from seven artifacts.
It can be shown that for thin enough discs (see [7]) where The m c cm −2 values for these discs as calculated from equations (3) and (2) are shown in table 1. The archaeological site, the pH of the soil (see [8]) at the site, the archaeological dating of the 99.8 sampled objects (see [9]) and an estimated corrosion time are presented for samples from the Persian, the Byzantine and the Crusader periods. Contemporary samples are detailed in table 1 as well.
In figure 5 we present the corrosion extent for the above samples as a function of the estimated corrosion time. The power law curve y(t) =m c (t)/cm 2 = K t (1/(α+1)) , α = 0.07, K = 0.12, is the best fit to the experimental points.

Discussion
A power law dependence of y on t is reasonable (see [10]). In a very general way the act of corrosion is based on the local existence of an electrochemical cell, which comprises a junction of a metallic oxide to a metal surface on the one hand and to oxygen and water on the other. This cell is characterized by certain potential difference, ε, that drives a current, I , through the cell: assuming R(y) ∼ y α we get The power law fit is close to a rectilinear line. Such a behaviour is characteristic for a corrosion process in which the continuity of a thin protective layer of oxide on the surface of the metal is controlled by stress. When the layer reaches a certain thickness it breaks down and the metal surface is re-exposed to the environment. More oxide is then formed in contact with the metal, and, after a similar time interval, the thin film of corrosion is again disrupted, and then the process is repeated. The net result of such behaviour is the production of an oxidation curve, which is virtually a straight line (see [10]). This curve may serve for the approximate dating of lead archaeological artifacts buried in soils of relatively high pH, such as carbonate buffered soils, where the corrosion rate is comparable and relatively slow so that time averaging of external condition does occur. As the relevant corrosion signal grows in time the relative dating accuracy should improve with the age of the sample. Thus the 2500 year span, dictated by the availability of samples, is not an upper limit of our method.
The new method presented here for the determination of lead metal content in a nonmagnetic artifact is in principle non-destructive as it does not require any chemical or mechanical separation of the corrosion products from the lead metal. Thus, for example, lead inclusions in copper, silver and gold ancient coins can also be studied.