FLUX-COUPLING AND THE IDENTIFICATION OF RATE-CONTROLLING OXIDE- OR EXCHANGE- COMPONENTS FOR DIFFUSION-CONTROLLED MINERAL GROWTH IN MULTICOMPONENT SYSTEMS

Retrieval of diffusion coefficients from measured progress of diffusion-controlled processes in solid aggregates, such as deformation, coarsening, or reaction rim growth, requires the arbitrary specification of the identity of the "rate-controlling species" to which the derived coefficient applies. Reaction rim growth in simple oxide and silicate systems analyzed by solution of system of mass balance, flux ratio and conservation equations, provides a simple and testable means of identifying the rate-controlling component(s). For example, while diffusion-controlled growth of enstatite (EN, Mg₂Si₂O₆) by reaction between quartz (Q, SiO₂) and forsterite (FO, Mg₂SiO₄), Q|EN|FO may be described in terms of the elemental fluxes J_Mg, J_Si, and J_O, charge balance (J_O=J_Mg + 2J_Si) requires that they couple in the proportions described by the components MgO, SiO₂, and Mg₂Si_-1, either singly, or in the combinations MgO + Mg₂Si_-1 or SiO₂ + Mg₂Si_-1, but not as MgO + SiO₂. Diffusion-controlled growth of EN is illustrated on a diagram showing variation of oxide and exchange component fluxes J_MgO, J_SiO2, and J_Mg2Si-1, as a function of elemental diffusion coefficient ratios, D_Mg/D_Si, and D_O/D_Si. The plot is dominated by a central "Y"-shaped field in which the fluxes, J_Mg, J_Si, and J_O, are all non-zero and in which flux-coupling allows description of transport by two components, MgO + Mg₂Si_-1 for D_Mg/D_Si > 2, and SiO₂ + Mg₂Si_-1 for D_Mg/D_Si < 2. This relatively narrow region is bounded by three fields in which diffusion is described by a single component, MgO, SiO₂, or Mg₂Si_-1, for which the diffusion coefficient is readily extracted from rim growth experiments.

• Where D_O/D_Si > 100 and D_Mg/D_Si > 100, J_Si=0, and diffusion is described by D_MgO, and the inert marker lies at lies at fractional distance of 0.5 from the Q|EN contact.
• Where D_O/D_Si < 0.01 and D_Mg/D_Si > 1, J_O=0, and diffusion is described by D_Mg2Si-1, and the inert marker lies at lies at fractional distance of 0.333 from the Q|EN contact.
• Where D_O/D_Si > 1 and D_Mg/D_Si < 0.01, J_Mg=0, and diffusion is described by D_SiO2, and the inert marker is at the Q|EN contact.

Marker location between 0 and 0.333 lie in the SiO₂+Mg₂Si_-1 field, and between 0.333 and 0.5 in the Mg₂Si_-1+MgO field. This type of diagram describes behavior of all simple oxide systems examined.