Argon enters the retentive zone: Reassessment of diffusion parameters for K-feldspar
Marnie Forster and Gordon Lister
Research School of Earth Sciences, Australian
National University, Canberra, ACT 0200, Australia
Figure 1. Arrhenius plots where (a) activation is calculated at 46.5 kcal/mol (Baldwin & Lister 1998). The fundamental asymmetry principle (FAP) has not been followed in this calculation and the activation energy incorrect; (b) when the FAP is applied to this same plot the calculated activation energy is much higher, 60.2 kcal/mol; (c) mathemical calculation using the fractual cube and Menger sponge (d) (http://members.cox.net/fathauerrecent/FractalCrystal.html) (http://en.wikipedia.org/wiki/Menger_sponge) used in the mathematical representation of the Arrhenius plot; (e) A Temperature / Time plot show the region where the shear zone is at rest and where the shear zone operated, temperature calculated from mineral paragenesis.
40Ar/39Ar apparent age spectra have been measured for unusually retentive potassium feldspars from the South Cyclades Shear Zone, Ios, Greece. The data obtained helped constrain the age and duration of the operation of this crustal-scale shear zone. We investigated traditional methods used to analyse Arrhenius plots by simulating the effect of step-heating experiments on argon loss. Fractals were used to define theoretical distributions of diffusion domain size and volume, allowing recognition of a Fundamental Asymmetry Principle (FAP) which is required if line fitting is to be consistent with the multi-domain diffusion hypothesis. The FAP means that a fitted line must divide the population by rank order. Points from data obtained earlier in the sequence of step heating experiments must lie on the fitted line, or to the right of it. Points from data obtained later in the sequence must lie on the fitted line, or to the left of it. Applying the FAP has lead to the estimation of higher activation energies.
To understand whether these results are limited, for example, to the K-feldspars from this study, data from previously published papers was examined (Fig. 1a), including data from the UCLA archive. The results obtained, using multi-domain diffusion modelling (Lovera et al. 1997) led us to an in depth look at the method and the fundamentals behind these methods. Analysis of Arrhenius data should take account of the Fundamental Asymmetry Principle since this is an inherent part of any multi-domain diffusion model. Results showed that if the Fundamental Asymmetry Principle is not applied (Fig. 1a b), numerical analysis will invariably underestimate the value of activation energy used in simulating the effect of step-heating experiments on fractal volume-size distributions (Fig. 1c d).
It was found that the application of the Fundamental Asymmetry Principle, determined from modeling using eAr software makes a considerable difference in respect to the magnitude of the activation energies estimated. The average of activation energy for K-feldspar is significantly higher than previously reported. These results imply that the Argon Partial Retention Zone for the most retentive domains in K-feldspar can expand into the ductile regime (i.e. with temperatures ~400-450°C), as recorded for the South Cyclades Shear Zone (Fig 1e). This means that K-feldspar can routinely be used as a geochronometer to estimate the timing and duration of events in complexly deformed terranes.
Baldwin SL, Lister GS, (1998) Thermochronology of the South Cyclades shear zone, Ios, Greece: effects of ductile shear in the argon partial retention zone. JGR, 103, 7315-7336.
Lovera OM, Grove M, et al (1997) Systematic analysis of K-feldspar 40Ar/39Ar step heating results: I. Significance of activation energy determinations. Geo Cosmochimica Acta, 61: 3171-3192.
Forster MA, Lister GS (2008) Argon enters the retentive zone: reassessment of diffusion parameters for K-feldspar in the South Cyclades Shear Zone, Ios, Greece. Lithos, in press.