Open Access Kent State (OAKS)

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 (T_c) vs. Z in the clinoamphiboles. The Ar model yields a ΔT_C/ΔZ of −38 ±3°C/Z %, which translates into: (1) a ∼120°C increase in T_C from synthetic ferro-actinolite to edenite and (2) a ∼70°C range in T_c for natural hornblendes amenable to ⁴⁰Ar/³⁹Ar dating. Model T_C-X effects isolated from available amphibole data include increases in T_C 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 T_C-Z-X relationship is more applicable for determining relative (rather than absolute) T_C 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-T_C-Z-Xresults promote physical understanding of the diffusional closure process, as shown at both unit-cell and grain scales.