binary diffusion coefficients for CaO and SiO2 that depend on the local SiO2 content of the melt are
(1.7)
Figure 1.3 The panels show the concentration of major oxides measured along five parallel lines perpendicular to the interface between a natural basalt melt (SUNY MORB) and a natural rhyolite melt (Lake County obsidian) that were juxtaposed and annealed in a piston cylinder assembly. The data from each parallel line is plotted with a different symbol, but because the data measured along the five lines are effectively identical, they are not easily distinguished from each other. The fact that the data measured along the parallel lines are indistinguishable shows that diffusion in this couple was perfectly one‐dimensional.
The data plotted in this figure are from Richter et al. (2003).
The initial condition used for the model result shown in Fig. 1.4 was a step function with on the rhyolite side and on the basalt side. The units of ρ in equations 1.7 are weight percent. The initial 44C/40Ca was a constant –0.2‰ across the couple and no‐flux boundary conditions were imposed at both ends. A series of forward‐difference numerical solutions to the conservation equations CaO and SiO2 were calculated until the dependence of the effective diffusion coefficients on the evolving SiO2 content of the melt (i.e., ) was found that simultaneously fit the CaO and SiO2 profiles shown in Fig. 1.3. The isotopic fractionation of calcium was then calculated by repeating the calculation with separate conservation equations for 40Ca and 44Ca. The diffusion coefficient for 40CaO (40Ca is ~97 % of natural calcium) was taken to be the same as for the total CaO (i.e., ) while that for 44CaO was reduced by a factor with β determined by fitting the calcium isotopic fractionation data.
The solid black line in Fig. 1.4 shows the calcium isotopic fractionation calculated using solutions to equations 1.7 for 44CaO, and 40CaO, and with β = 0.075. The calculated calcium isotope fractionation is a reasonably good fit to the negatively fractionated portion of the data; however, it does not account for the increasingly positive isotope fractionation values towards left end of the couple, which is most noticeable in the RB‐2 data. This isotopic fractionation in the basaltic side of diffusion couple RB‐2 was very surprising, in that it occurs in a part of the couple that had lost very little of its original CaO and thus it would require that some unimaginably large negatively fractionated CaO had to have been removed in order to leave behind the observed positive values. The discrepancy between the isotopic fractionation profile in the basaltic side of couple RB‐2 calculated by Richter and the data measured by DePaolo became a serious point of contention, as each blamed the other for the discrepancy. Several years later it was realized that the positive isotopic fractionations might be due to thermal isotopic fractionation (i.e., Soret diffusion) associated with the typical temperature differences of several tens of degrees centigrade across samples run in piston cylinder assemblies. However, for this to be a viable explanation it would have to be shown that differences of a few tens of degrees across molten basalt can produce calcium isotopic fractionations of several per mil. Soret experiments designed to address this are discussed in Section 1.4.
Figure 1.4 Figure taken from Richter et al. (2003) showing the δ44Ca of slabs cut perpendicular to the long axis of glass recovered from rhyolite‐basalt diffusion couples RB‐2 and RB‐3. A normalized distance scale with units x/t 1/2 , where x is in microns and t is the run duration in hours is used in order that the data from the two experiments of different size and duration can be plotted along the same normalized distance axis. The thin horizontal line shows the initial 44C/40Ca of the rhyolite and basalt relative that of a CaCO3 salt standard. The thicker black line is the result of a model calculation with the mass‐dependence of the diffusion coefficient of calcium calculated as with β = 0.075.
1.3.2.
