The ionic porosity model of Fortier and Giletti (1989), which parameterizes variations in diffusion coefficients among different mineral structures, has been extended to estimate the variation in diffusivities in a single mineral structure as a function of composition (X). Applied to Ar and O diffusion in hornblende and related K-rich amphiboles, the extended model predicts that diffusivity, D, increases one-hundredfold as ionic porosity (Z, a monitor of atomic packing density) increases from 36.5% (edenite) to 39.7% (ferro-actinolite). Partitioning this trend into its separate activation energy (E) and frequency factor (D0) components leads to new E-Z and D0-Z expressions that predict antipathetic trends of closure temperature (Tc) vs. Z in the clinoamphiboles. The Ar model yields a ΔTC/ΔZ of −38 ±3°C/Z %, which translates into: (1) a ∼120°C increase in TC from synthetic ferro-actinolite to edenite and (2) a ∼70°C range in Tc for natural hornblendes amenable to 40Ar/39Ar dating. Model TC-X effects isolated from available amphibole data include increases in TC of up to: (1) 60 ± 10°C as Mg# ranges from 0–100; (2) 40 ± 15°C as A-sites progress from empty to full; (3) ∼38°C as Al-Tschermak's substitution progresses from zero to full; and (4) ∼17°C as Fe3+/(Fe2+ + Fe3+) varies from 0.2–0.5. Comparable results are obtained for O. The Ar diffusion model also predicts a 38 ± 3 Ma difference in 40Ar/39Ar cooling age between adjacent, slowly-cooled (1°C/Ma) hornblendes differing in Zby 1% (absolute)—all other age-determining factors equal. At a cooling rate of 10°C/Ma, however, the model age discordance reduces to 3.8 ± 0.3 Ma, such that any compositional effects become lost within analytical uncertainty. As calibrated, the TC-Z-X relationship is more applicable for determining relative (rather than absolute) TC values among hornblendes. Preliminary evidence supportive of the model (in its relative form) is provided by antipathetic age-Z trends preserved in two lower crustal terranes. Finally, the model D-TC-Z-Xresults promote physical understanding of the diffusional closure process, as shown at both unit-cell and grain scales.
Geochimica et Cosmochimica Acta
Copyright 1996 Meteocritical Society.
Dahl, Peter (1996). The Effects of Composition on Retentivity of Argon and Oxygen in Hornblende and Related Amphiboles: A Field-Tested Empirical Model. Geochimica et Cosmochimica Acta 60(19) 3687-3700. doi: 10.1016/0016-7037(96)00170-6. Retrieved from https://oaks.kent.edu/geolpubs/15