Uphill diffusion,zero-flux planes and transient chemical solitary waves in garnet |
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Authors: | D Vielzeuf A Saúl |
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Institution: | (1) Centre Interdisciplinaire de Nanoscience de Marseille, CNRS, Aix-Marseille University, Campus de Luminy, 13288 Marseille, France |
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Abstract: | Diffusion profiles in minerals are increasingly used to determine the duration of geological events. For this purpose, the
distinction between growth and diffusion zoning is critical; it requires the understanding of complex features associated
with multicomponent diffusion. Seed-overgrowth interdiffusion experiments carried out in the range 1,050–1,250°C at 1.3 GPa
have been designed to quantify and better understand Fe–Mg–Ca interdiffusion in garnet. Some of the diffusion profiles measured
by analytical transmission electron microscope show characteristic features of multicomponent diffusion such as uphill diffusion,
chemical solitary waves, zero-flux planes and complex diffusion paths. We implemented three different methods to calculate
the interdiffusion coefficients of the D matrix from the experimental penetration curves and determined that with Ca as the dependent component, the crossed coefficients
of the D matrix are negative. Experiments and numerical simulations indicate that: (1) uphill diffusion in garnet can be observed
indifferently on the three components Fe, Mg and Ca, (2) it takes the form of complementary depletion/repletion waves and
(3) chemical waves occur preferentially on initially flat concentration profiles. Derived D matrices are used to simulate the fate of chemical waves in time, in finite crystals. These examples show that the flow of
atoms in multicomponent systems is not necessarily unidirectional for all components; it can change both in space along the
diffusion profile and in time. Moving zero-flux planes in finite crystals are transitory features that allow flux reversals
of atoms in the diffusion zone. Interdiffusion coefficients of the D matrices are also analyzed in terms of eigenvalues and eigenvectors. This analysis and the experimental results show that
depending on the composition of the diffusion couple, (1) the shape of chemical waves and diffusion paths changes; (2) the
width of the diffusion zone for each component may or may not be identical; and (3) the width of diffusion calculated at a
given D and duration may greatly vary. D matrices were retrieved from thirteen sets of diffusion profiles. Data were cast in Arrhenius relations. Linear regressions
of the data yield activation energies equal to 368, 148, 394, 152 kJ mol−1 at 1 bar and frequency factors Do equal to 2.37 × 10−6, −4.46 × 10−16, −1.31 × 10−5, 9.85 × 10−15 m2 s−1 for (D)\tilde]FeFeCa \tilde{D}_{FeFe}^{Ca} , (D)\tilde]FeMgCa \tilde{D}_{FeMg}^{Ca} , (D)\tilde]MgFeCa \tilde{D}_{MgFe}^{Ca} , (D)\tilde]MgMgCa \tilde{D}_{MgMg}^{Ca} , respectively. These values can be used to calculate interdiffusion coefficients in Fe–Mg–Ca garnets and determine the duration
of geological events in high temperature metamorphic or magmatic garnets. |
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