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Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications

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Abstract

We present new experimental data on diffusion of divalent cations in almandine-spessartine diffusion couples in graphite capsules in the P-T range of 14–35 kb, 1100–1200° C. The tracer diffusion coefficients of the major divalent cations, viz. Fe, Mg and Mn, retrieved from the multicomponent diffusion profiles, have been combined with earlier data from our laboratory at 29–43 kb, 1300–1480° C (Loomis et al. 1985) to derive expressions of the P-T dependence of the diffusion coefficients at fO2 approximately corresponding to that defined by equilibrium in the system graphite-O2. We review the conditions, discussed earlier by Cooper, under which the flux of a component in a multicomponent system becomes proportional to its concentration gradient (Fickian diffusion), as if the entire solvent matrix behaves as a single component, and also suggest a method of incorporating the thermodynamic effect on diffusion in the same spirit. Regardless of the magnitude or sign of the off-diagonal terms of the D matrix, it is always possible to define an effective binary diffusion coefficient (EBDC) of a component in a semi-infinite multicomponent diffusion-couple experiment such that it has the property of the Fickian diffusion coefficient, provided that there is no inflection on the diffusion profiles. It is shown that the success of Elphick et al. in fitting the experimental diffusion profiles of all components over a limited concentration range by a single diffusion coefficient is due to fortuitous similarity of the EBDCs of the components (Fe, Mg, Mn and Ca) in their diffusion couple experiments. In common metapelitic garnets showing compositional zoning, the EBDCs of the divalent cations do not differ from each other by more than a factor of 2.5. However, the EBDC of a component changes from core to rim by a factor of 3 to 12, depending on the composition. We suggest a method of volume averaging of the EBDC which should prove useful in approximate calculations of diffusion flux during relaxation of compositional zoning. The EBDC of Mn is found to reduce essentially to D MnMn, the main diagonal term of the D matrix, and consequently can be calculated quite easily. Evaluation of EBDC of Fe, Mg and Mn in garnets from a prograde Barrovian sequence did not reveal any significant dependence on the extent of relaxation of garnet. The diffusion data have been applied to calculate the cooling rate of natural biotite-garnet diffusion couple from eastern Finland and diffusional modification of growth zoning in garnet in early Proterozoic Wopmay orogen, Canada. The results are in good agreement with geochronological and other independent constraints.

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Abbreviations

a :

Radius of a spherical garnet crystal

BSE :

Back-scattered electron imaging

C :

Column vector of (n-1) independent components

D :

Diffusion coefficient matrix

D ij :

An element of the diffusion matrix on the i th row and j th column

D i* :

Tracer diffusion coefficient of component i

D(i) :

Effective interdiffusion coefficient (EIC) of various components in a multicomponent solution rich in the component i

D(i-j) :

Interdiffusion coefficient of components i and j in a binary solution

D i (EB):

Effective binary diffusion coefficient of component i in a multicomponent solution

D i (EB:Ideal):

D i (EB) under condition of ideal thermodynamic mixing of the diffusing species

D i (EB:thermo):

Thermodynamic component of D i(EB)

D AO :

Interdiffusion coefficient at peak temperature T 0 in the phase A

D 0 :

Pre-exponential factor in an Arrhenius relation

EBDC :

Effective binary diffusion coefficient between a solute and a multicomponent solvent matrix

FEC :

Fixed edge composition model

EIC :

Effective interdiffusion coefficient

f i :

Fugacity of component i

HM :

Hematite-magnetite oxygen fugacity buffer

kb:

Kilobars

P :

Pressure

Q :

Activation energy (enthalpy) of diffusion

\(\mathbb{R}\) :

Extent of relaxation defined as the difference between core and rim compositions normalized to the same difference in the initial zoning profile

R :

Gas constant

s :

Cooling rate

T 0, T Ch :

Peak temperature and characteristic temperature, respectively

t :

Time

VEC :

Variable edge composition model

ΔV + :

Activation volume

W ij :

Simple mixture interaction parameter between i and j

W i(EB):

Effective simple mixture interaction parameter of a component i in a multicomponent solution

Ŵ ij :

Margules interaction parameter between i and j

X i :

Mole fraction of component i

τi :

Activity coefficient of component i

ϕ:

A dimensionless variable =πD t/a 2

δ ij :

Kronecker delta (i=j, δ ij =1; i≠j, δ ij =0)

Zi :

Charge on the ion i

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Authors and Affiliations

  1. Bayerisches Geoinstitut, Universität Bayreuth, Postfach 101251, W-8580, Bayreuth, Germany

    Sumit Chakraborty

  2. Department of Geosciences, University of Arizona, 85721, Tucson, AZ, USA

    Jibamitra Ganguly

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  1. Sumit Chakraborty
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  2. Jibamitra Ganguly
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Chakraborty, S., Ganguly, J. Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications. Contrib Mineral Petrol 111, 74–86 (1992). https://doi.org/10.1007/BF00296579

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