Models of diffusion-limited uptake of trace elements in fossils and ...

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Trace element uptake in fossils? 3767 The radius of (hydrated) mono- and divalent cations is comparable to (hydrated) LREE (+3) and U (+4) cations (Sandström et al., 2001), so D for REE and U in enamel is expected to be comparable, i.e., 10 8 cm 2 /s. The phosphate-fluid partition coefficient (K d ) is believed to be at least 5 10 5 for U (Millard and Hedges, 1996) and 1 10 6 for REE (Koeppenkastrop and De Carlo, 1992), with uncertainties of about one order of magnitude. Thus D eff is 62 10 14 cm 2 /s for U and 61 10 14 cm 2 /s for REE in modern enamel, with uncertainties of about 1 1 2 orders of magnitude. These values are 2–4 times lower than some rates derived from fossil fish dentine (Toyoda and Tokonami, 1990), and the estimated rate for U diffusion in bone (Millard and Hedges, 1996). Possibly calculated values for D eff in enamel reflect an adsorption rather than bulk equilibrium distribution coefficient, and both K d and inferred minimum t should be higher. Because the purpose of the inversion is to provide a minimum limit on t, however, use of the larger coefficients (2 10 14 cm 2 /s for U and 1 10 14 cm 2 /s for REE) is warranted. Substituting these values of D eff yields minimum estimates of about a decade to produce the U profiles, and about a century for the REE profiles (Fig. 5 and Table 2). While these values may not realistically estimate total durations, they assuredly provide a lower limit. Fossilization of dentine and bone is expected to be many times faster because they have much higher porosity (Millard and Hedges, 1996), i.e., minimum limits are on the order of years to decades. Large differences in fossilization rates among samples might be expected from different physical and microbial environments attending fossilization and trace element uptake in different materials. Yet all samples yield rather similar results for either REE or U profiles, irrespective of age. If trace element uptake in these samples was governed by some common process, then the fact that the diffusion profiles in the 630 ka samples are no shorter than older samples implies that the older samples probably developed their diffusion profiles in 630 kyr, and that fossilization of dentine and bone occurred at least as quickly. This result supports other types of studies that assume relatively rapid (6100 kyr) alteration/uptake in bone and dentine (e.g., Staudigel et al., 1985; Elderfield and Pagett, 1986; Martin and Haley, 2000; Trueman and Tuross, 2002; Kohn and Law, 2006; MacFadden et al., 2007; Zanazzi et al., 2007). Uncertainties in partition coefficients and hence D eff could reconcile the REE- and U-derived estimates. Generally shorter penetration distances for U compared to REE suggest lower D eff for U than for REE, in contrast to published K d ’s that suggest the opposite. Calculated durations are strict minima for two reasons. First, as described previously, K d may be underestimated, resulting in too large an assumed D eff . Second, preservation of the diffusion profiles requires some mechanism for retarding D eff to values lower than measured in pristine enamel, otherwise fossils older than 1 Ma would never preserve diffusion profiles. Occlusion of pore space via clays, metal oxides, and oxyhydroxides (Kohn et al., 1999) must ultimately shut down diffusive exchange of the enamel interior with its margins. Therefore, the age of the youngest fossils, 22–33 kyr, limits the maximum duration. The inferred rates (>10–100 yr, but
3768 M.J. Kohn / Geochimica et Cosmochimica Acta 72 (2008) 3758–3770 The U-series ages were then converted to reduced apparent age ðt 0 app Þ using a preferred value of D eff of 4 10 14 cm 2 /s (Millard and Hedges, 1996), and plotted vs. 1 X 02 for direct comparison to DA predictions in Fig. 3. This value of D eff implies t 0 Dep 0.8, which balances DA model misfit between the U concentration data (Fig. 3A) and the chronologic data (Fig. 3B). Increasing D eff to P5 10 14 cm 2 /s maximizes the quality of fit for the U concentration data, but shifts the regression line in Fig. 3B upward and further steepens its slope, increasing misfit with the DA model. Conversely, decreasing D eff to 61 10 14 cm 2 /s maximizes the quality of fit for the chronologic data (Fig. 3B), but the resulting t 0 Dep 60.1 cannot possibly be reconciled with the U concentration data (Fig. 3A). That is, a DA model cannot simultaneously account for the homogeneity of U, yet strong age gradients and young ages. In contrast, a DR model can explain these data and other samples with uniform U because it automatically produces a homogeneous U profile irrespective of t 0 Dep . This conclusion presumes that t 0 Dep is sufficiently high to allow complete recrystallization of the bone, which is already implied by the presence of U in the center of the bone fragment analyzed. X-ray crystallographic data (Ayliffe et al., 1994) and trace element partitioning between enamel and dentine (Eggins et al., 2003; this study) are consistent with recrystallization of fine crystallites in bone and dentine during fossilization. Regardless of which diffusion model is assumed, the linearity of the data in Fig. 3 demonstrates the success of diffusion in explaining U uptake during fossilization (Millard and Hedges, 1996) and strongly supports previous age interpretations based on DA modeling (Pike et al., 2005). These observations and theoretical models have important implications for the use of trace elements and isotopes in geology, paleoclimatology, paleoceanography and archeology. For example, paleoclimate studies assume fossilization rates of tens of kyr or less for interpretation of geologic processes on timescales of hundreds of kyr to Myr (Staudigel et al., 1985; Elderfield and Pagett, 1986; Martin and Haley, 2000; Kohn and Law, 2006; MacFadden et al., 2007; Zanazzi et al., 2007). The data presented here conclusively support such assumptions, although instances of late-stage uptake do occur (e.g., see Peppe and Reiners, 2007). In contrast, many archeological applications focus on shorter timescales, and attempt to date initial uptake, i.e., determine the extrapolated age at the edge of a fossil based on direct geochronology across the sample. Reconsideration of diffusive models of trace element uptake indicates that these applications, which previously have relied on parabolic fitting of the DA model, can be more generally interpreted independent of a specific diffusion model, provided ages are regressed vs. (reduced) distance squared. 7. CONCLUSIONS Key conclusions of this study include: (1) Diffusion–adsorption models may not explain well the age distributions and physical changes documented in fossil bone, but may be applicable to trace element uptake in fossil enamel. (2) Age distributions in fossil bone can be readily interpreted in terms of diffusion-limited uptake, regardless of diffusion model, if measured ages are plotted with respect to (reduced) distance squared, rather than distance. Such plots are recommended because they allow straightforward regression diagnostics and interpretation of timing of initial uptake from the regression intercept. (3) Trace element zoning in fossil tooth enamel for a range of environments and ages is generally consistent with a double-medium diffusion model. Modeling profiles suggests that complete fossilization and trace element uptake could occur relatively rapidly, with a minimum bound on durations of about one century. This result does not rule out later stage alteration and trace element uptake, particularly on exposed surfaces. (4) Trace element uptake in bone and dentin is probably closely linked to degradation of interstitial proteins that otherwise protect biogenic crystallites from recrystallization and chemical alteration. Rates of trace element uptake may be controlled more by the diffusion-controlled export of degraded proteins and exposure of crystallite surfaces than diffusioncontrolled import of trace elements. ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. ATM 0400532. The author gratefully acknowledges reviews from Bruce MacFadden, Peter Reiners, Bernard Boudreau, and AE James McManus, which helped improve the presentation and discussion. Charles Knaack is thanked for help with LA–ICP–MS analysis. APPENDIX. DERIVATION OF DIFFUSION RELATIONS FOR THE DIFFUSION-REACTION (DR) MODEL Combined diffusion plus recrystallization is described in Crank (1975) under conditions of an immobilizing reaction (section 13.3, p. 298), which in turn is a special case of ‘‘Diffusion coefficients having a discontinuity at one concentration” (section 13.2.2 of Crank, 1975). In all such models, the following relation holds: X ¼ k t 1=2 ðA:1Þ where X is distance, k is a constant, and t is time. Eq. (A.1) already demonstrates the key relationship necessary for treatment of U-series dating of Quaternary materials (i.e., that t is proportional to X 2 ). The following derivation for DR shows that k is proportional to D 1/2 , yielding linearity between X 2 and Dt, as in all other diffusion solutions considered. In the endmember DR model, a sharp front moves through the original material, converting pristine material with negligible trace element content to recrystallized material with high trace element content. This model is consistent with the following considerations.
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