Contributions to Mineralogy and Petrology

, Volume 161, Issue 5, pp 683–702 | Cite as

Uphill diffusion, zero-flux planes and transient chemical solitary waves in garnet

  • D. VielzeufEmail author
  • A. Saúl
Original Paper


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 \( \tilde{D}_{FeFe}^{Ca} \), \( \tilde{D}_{FeMg}^{Ca} \), \( \tilde{D}_{MgFe}^{Ca} \), \( \tilde{D}_{MgMg}^{Ca} \), 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.


Garnet Multicomponent diffusion Fe–Mg–Ca interdiffusion Uphill diffusion Chemical solitary wave Zero-flux plane 



This work was supported by the French Centre National de la Recherche Scientifique—Institut National des Sciences de l’Univers through grants DyETI 2005 to D. V. We performed the ATEM analyses at the French Earth Science TEM facility (Lille and Marseille). We thank A. Addad for his supervision during the analytical sessions at Lille. Part of this work was completed while D. V. was at Caltech as part of a CNRS/Caltech exchange; E. M. Stolper is gratefully acknowledged for his recurrent support. We are grateful to H. Kawabata and H. Raimbourg for providing the analytical data shown in Fig. 11. This paper benefited from discussions with A. Lupulescu, J. P. Monchoux and F. Costa, comments of an early version of the manuscript by J. Ganguly and P. Wynblatt, and careful reviews and constructive comments by J. E. Morral and S. Chakraborty. We thank F. Poitrasson for efficient editorial handling. Matlab scripts developed in this study are available upon request.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Centre Interdisciplinaire de Nanoscience de MarseilleCNRS, Aix-Marseille UniversityMarseilleFrance

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