Interface reaction rate

The interface reaction rate depends on temperature and on the degree of saturation. Right at saturation, the interface reaction rate is zero. If the melt (or... 

The above is for isothermal crystal growth. In nature, crystallization occurs in a continuously cooled magma. The cooling rate plays a main role in controlling crystallization, and the nucleation and interface-reaction rates shown in Figure 1-14 are instructive in understanding crystallization under various cooling rates. 

Geochemical kinetics is stiU in its infancy, and much research is necessary. One task is the accumulation of kinetic data, such as experimental determination of reaction rate laws and rate coefficients for homogeneous reactions, diffusion coefficients of various components in various phases under various conditions (temperature, pressure, fluid compositions, and phase compositions), interface reaction rates as a function of supersaturation, crystal growth and dissolution rates, and bubble growth and dissolution rates. These data are critical to geological applications of kinetics. Data collection requires increasingly more sophisticated experimental apparatus and analytical instruments, and often new progresses arise from new instrumentation or methods. 

Nucleation is necessary for the new phase to form, and is often the most difficult step. Because the new phase and old phase have the same composition, mass transport is not necessary. However, for very rapid interface reaction rate, heat transport may play a role. The growth rate may be controlled either by interface reaction or heat transport. Because diffusivity of heat is much greater than chemical diffusivity, crystal growth controlled by heat transport is expected to be much more rapid than crystal growth controlled by mass transport. For vaporization of liquid (e.g., water vapor) in air, because the gas phase is already present (air), nucleation is not necessary except for vaporization (bubbling) beginning in the interior. Similarly, for ice melting (ice water) in nature, nucleation does not seem to be difficult. 

Figure 4-6 Interface reaction rate as a function of temperature, pressure, and composition. The vertical dashed line indicates the equilibrium condition (growth rate is zero), (a) Diopside growth and melting in its own melt as a function of temperature with the following parameters Te= 1664K at 0.1 MPa, A5m-c = 82.76J mol K , E/R —30000 K, 4 = 12.8 ms K, and AV c l. l x 10 m /mol. The dots are experimental data on diopside melting (Kuo and Kirkpatrick, 1985). (b) Diopside growth and melting in its own melt as a function of pressure at 1810 K (Tg = 1810 K at 1 GPa from the equilibrium temperature at 0.1 MPa and the Clapeyron slope for diopside). (c) Calcite growth and dissolution rate in water at 25 °C as a function of Ca " and CO concentrations.

Examination of Figure 1-12 provides some clue to qualitatively gauge the interface reaction rate for reactions in water. Figure 1-12 shows that, for mineral with low solubility and high bond strength (characterized by (z+z )max, where z+ and z are valences of ions to be dissociated), the overall dissolution rate is controlled by interface reaction otherwise, it is controlled by mass transport. Because diffusivities of common cations and anions in water do not differ much (by less than a factor of 10 Table l-3a), when the overall reaction rate is controlled by interface reaction, it means that interface reaction is slow when the overall reaction rate is controlled by mass transport, the interface reaction rate is rapid. Therefore, from Figure 1-12, we may conclude that the interface reaction rate increases with mineral solubility and decreases with bond strength (z+z )max to be dissociated. 

If the interface reaction rate is extremely small so that mass/heat transfer is rapid enough to transport nutrients to the interface, then interface reaction rate (Equation 4-33) is the overall heterogeneous reaction rate (Figure 1-lla). If the interface reaction is relatively rapid and if the crystal composition is different from the melt composition, the heterogeneous reaction rate may be limited or slowed down by the mass transfer rate because nutrients must be transported to the interface and extra junk must be transported away from the interface (Figures 1-llb and 1-llc). If the crystal composition is the same as the melt composition, then mass transfer is not necessary. When interface reaction rate and mass transfer rate are comparable, both interface reaction and mass transfer would control the overall heterogeneous reaction (Figure 1-lld). 

Zhang et al. (1989) treated the interplay between diffusion and interface reaction during the initial and transient stages of crystal dissolution in a silicate melt. Using the interface reaction rate of diopside, they found that the period for... 

Experimental results on crystal growth might be affected by dendritic growth and the effect is difficult to evaluate. Hence, experimental data on the melting rate of a pure crystal in its own melt are expected to be a more reliable indication of interface reaction rate than those on crystal growth rate. 

That is, Topt is proportional to As the average crystal size increases, the interface reaction rate becomes smaller because the degree of oversaturation becomes smaller. Hence, the coarsening rate dtopt/df for mean crystal size of 1 mm is 10 times slower than that for mean crystal size of 1 fim coarsening timescale for a rock to grow from a mean crystal size of 1 to 2 mm is lO times that for a rock to grow from a mean crystal size of 1 to 2 /im. 

Crystal dissolution/melting/growth may be controlled by interface reaction rate (Figure 1-lla), meaning that mass/heat transfer rate is very high and interface reaction rate is low. Examples include dissolution of minerals with low... 

Diffusive crystal dissolution means that crystal dissolution is controlled by diffusion, which requires high interface reaction rate and absence of convection. In nature, diffusive crystal dissolution is rarely encountered, because there is almost always fluid flow, or crystal falling or rising in the fluid. That is, crystal dissolution in nature is often convective dissolution, which is discussed in the next section. One possible case of diffusive crystal dissolution is for crystals on the roof or floor of a magma chamber if melt produced by dissolution does not sink or rise. For these... 

Convective crystal dissolution means that crystal dissolution is controlled by convection, which requires (i) a high interface reaction rate so that crystal dissolution is controlled by mass transport (see previous section), and (ii) that mass transport be controlled by convection. In nature, convective crystal dissolution is common. In aqueous solutions, the dissolution of a falling crystal with high solubility (Figure 1-12) is convective. In a basaltic melt, the dissolution of most minerals is likely convection-controlled. 

If the melting is controlled by diffusion in the melt (which means extremely rapid interface reaction rate), the melt composition at the titanite-melt interface would be A, and that at the anorthite-melt interface would be B (Figure 4-35b). Treat the diffusion as binary diffusion. The diffusive flux across the melt at steady state is... 

Suppose there are many calcite grains and quartz grains in a rock. At each surface, there is interface reaction. For metamorphic reactions that take many years, mass transport in the fluid phase may be assumed to be rapid and the reaction rate is controlled by the interface reaction rate. The fluid composition may be regarded as uniform. At the surface of phase A (such as calcite), the interface reaction rate may be written as (Equation 4-34)... 

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