An Empirical Model for Predicting Diffusion Coefficients in Silicate Minerals

Fortier, Steven M.; Giletti, Bruno J.

doi:10.1126/science.245.4925.1481

Cited by 173 publications

(72 citation statements)

References 21 publications

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“…3) The transpression was a single event that occurred at 2.00 Ga. Two hornblendes give a peak age in agreement with the ages from the Triangle shear zone, the sphene and three hornblendes give is expected since the flexibility of the amphibole structure in accomodating diverse compositions translates into variance in overall metal-oxygen bond length/strength (Hawthorne 1983;Lee 1993) and probably in Ar volume-diffusion kinetics also (Dahl 1994(Dahl , 1995 (Dowty 1980;Fortier and Giletti 1989), defined as the percentage of unit cell not occupied by ions, is a first-order approximation for the overall length and strength of the ionic bonds in a crystal and is thus a good proxy for the resistance that a given lattice will exert on the diffusion of Ar. The quantitative diffusivity-porosity model of Fortier and Giletti (1989) has been extended by Dahl (1994Dahl ( , 1995 to predict diffusion parameters (E and Do) for Ar in hornblendes as simple functions of Z.…”

Section: Structural Geologysupporting

confidence: 50%

“…The quantitative diffusivity-porosity model of Fortier and Giletti (1989) has been extended by Dahl (1994Dahl ( , 1995 to predict diffusion parameters (E and Do) for Ar in hornblendes as simple functions of Z. According to Dahl, there should be an inverse correlation between porosity and closure temperature Tc such that each 1% (absolute) difference in Z among natural hornblendes translates into 37 ± 2 K and 37 ± 2 m.y.…”

Section: Structural Geologymentioning

confidence: 99%

“…Analyses were performed on aliquots of the same fractions used for dating. All ionic porosity values were calculated from compositional and (24°C) unit cell data according to the conventions of Fortier and Giletti (1989); see also Dahl (1994 and.…”

Section: Structural Geologymentioning

confidence: 99%

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Proterozoic Transpressive Deformation in the Northern Marginal Zone, Limpopo Belt, Zimbabwe

Kamber¹,

Blenkinsop²,

Villa³

et al. 1995

The Journal of Geology

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Section: Structural Geologysupporting

confidence: 50%

Section: Structural Geologymentioning

confidence: 99%

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Proterozoic Transpressive Deformation in the Northern Marginal Zone, Limpopo Belt, Zimbabwe

Kamber¹,

Blenkinsop²,

Villa³

et al. 1995

The Journal of Geology

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“…The experiments were run at 700° to 900°C and 100 MPa water The solid line represents a least squares linear regression fit to the diffusion coefficients for transport parallel to the c-axis , and yields Do = .1!1' x 10-8 m2/sec and Q = 254 ± 28 kJ/mol. The dashed line is calculated using an empirical relation from Fortier and Giletti (1989); see text for details.…”

Section: Resultsmentioning

confidence: 99%

Volume self-diffusion of oxygen in titanite.

1996

Self Cite

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Oxygen self-diffusion coefficients in natural titanite (sphene) single crystals were experimentally de termined under hydrothermal conditions at 700° to 900°C and 100 MPa water pressure using an ion microprobe (SIMS). Oxygen self-diffusion parallel to the c-axis is described by an Arrhenius relation with pre-exponential factor Do = 1±i x 10-8 m2/sec and activation energy Q = 254 ± 28 kJ/mol. Oxygen diffu sion is isotropic within the measurement reproducibility of approximately a factor of 2. The relatively low diffusion coefficients for oxygen yield closure temperatures of 450° to 750°C for small crystals of titanite at typical cooling rates, which suggests that useful data on cooling rates of igneous rocks, or of metamorphic episodes, can be obtained because the size of titanite crystals in rocks is normally small.

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“…Variables chosen to express the transition from ''normal'' garnet to higher-pressure, majoritic garnet are the stoichiometric values of silicon and aluminum per 12-oxygen formula unit; with increasing majorite content, Si increases from the canonical 3.0 atoms per formula unit (apfu) typical of lower pressure, pyropic garnets, while Al decreases from the canonical 2.0 apfu. These changes reflect the enhanced solubility with increasing pressure of a pyroxene component, R (Xirouchakis et al 2002;Draper et al 2003 (Mysen 1983), and ionic porosity, a measure of the ''empty space'' in a silicate melt (Dowty 1980;Fortier and Giletti 1989;Carroll and Draper 1994). Although the data set (Table 1) contains several garnethydrous melt partitioning experiments, H 2 O was not included as a parameter in our statistical assessments.…”

Section: Choosing Variables For Statistical Evaluationsmentioning

confidence: 99%

Quantifying garnet-melt trace element partitioning using lattice-strain theory: assessment of statistically significant controls and a new predictive model

Draper

Westrenen

2007

Contrib Mineral Petrol

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As a complement to our efforts to update and revise the thermodynamic basis for predicting garnet-melt trace element partitioning using lattice-strain theory (van Westrenen and Draper in Contrib Mineral Petrol, this issue), we have performed detailed statistical evaluations of possible correlations between intensive and extensive variables and experimentally determined garnet-melt partitioning values for trivalent cations (rare earth elements, Y, and Sc) entering the dodecahedral garnet X-site. We applied these evaluations to a database containing over 300 partition coefficient determinations, compiled both from literature values and from our own work designed in part to expand that database. Available data include partitioning measurements in ultramafic to basaltic to intermediate bulk compositions, and recent studies in Fe-rich systems relevant to extraterrestrial petrogenesis, at pressures sufficiently high such that a significant component of majorite, the high-pressure form of garnet, is present. Through the application of lattice-strain theory, we obtained best-fit values for the ideal ionic radius of the dodecahedral garnet X-site, r 0 (3+), its apparent Young's modulus E(3+), and the strain-free partition coefficient D 0 (3+) for a fictive REE element J of ionic radius r 0 (3+). Resulting values of E, D 0 , and r 0 were used in multiple linear regressions involving sixteen variables that reflect the possible influence of garnet composition and stoichiometry, melt composition and structure, major-element partitioning, pressure, and temperature. We find no statistically significant correlations between fitted r 0 and E values and any combination of variables. However, a highly robust correlation between fitted D 0 and garnet-melt Fe-Mg exchange and D Mg is identified. The identification of more explicit melt-compositional influence is a first for this type of predictive modeling. We combine this statistically-derived expression for predicting D 0 with the new expressions for predicting E and r 0 outlined in the first of our pair of companion papers into an updated set of formulae that use easy-to-measure quantities (e.g. garnet composition, pressure, temperature) to predict variations in E, r 0 , and D 0 . These values are used in turn to calculate D values for those garnets. The updated model substantially improves upon a previous model (van Westrenen et al. in Contrib Mineral Petrol 142:219-234, 2001), and accounts well for trivalent cation partitioning in nominally anhydrous systems up to at least 15 GPa, including for eclogitic bulk compositions and for Fe-rich systems appropriate to magmagenesis on the Moon and Mars. The new model is slightly less successful in predicting partitioning with strongly majoritic garnets, although the mismatch is much less than with the original 2001 model. Although it also improves upon the 2001 model in predicting partitioning in hydrous systems, the mismatch between model and observation is still unacceptably large. The same statistical tools were applied in a...

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An Empirical Model for Predicting Diffusion Coefficients in Silicate Minerals

Cited by 173 publications

References 21 publications

Proterozoic Transpressive Deformation in the Northern Marginal Zone, Limpopo Belt, Zimbabwe

Proterozoic Transpressive Deformation in the Northern Marginal Zone, Limpopo Belt, Zimbabwe

Volume self-diffusion of oxygen in titanite.

Quantifying garnet-melt trace element partitioning using lattice-strain theory: assessment of statistically significant controls and a new predictive model

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