Читать книгу Isotopic Constraints on Earth System Processes - Группа авторов - Страница 58

The Zhang (1993) model deviates significantly from the EBD model when the component of interest diffuses significantly faster than SiO₂. In this situation, which is common in silicate liquids, the component of interest will not reach homogeneity quickly, but rather, will partition along the compositional continuum between the high‐ and low‐silica liquids and reach compositional homogeneity only as fast as SiO₂ diffuses.

The behavior of the model is shown in Fig. 2.6 for an infinite diffusion couple where the initial concentration gradient is small and = 8. If C_f is negative (Fig. 2.6a), the element partitions into the high‐silica liquid and the hypothetical C_e gradient opposes the concentration gradient. In this case, mass diffuses from the high concentration to the low concentration side at a higher rate than if C_f=0, resulting in a pair of bumps in the concentration profile. If C_f is positive (Fig. 2.6b), the activity gradient is opposite the concentration gradient and uphill diffusion occurs. Note that in both cases, the C_e profile evolves at a rate given by D_b (equation 2.6) and is thus less evolved than the concentration profiles exhibiting uphill diffusion.

Figure 2.6 Model behavior showing concentration, activity, and transient equilibrium concentration profiles for C₋ = 6 wt%, C₊ = 8 wt%, /D_b = 8, and variable C_f. The top panel is identical to Fig. 2c in Zhang (1993) to validate the Matlab code used in calculations herein. For an element with small initial concentration contrast, the sign and magnitude of uphill diffusion depends on the sign and magnitude of C_f, which describes how the element partitions between high silica versus low silica liquids.