Читать книгу Isotopic Constraints on Earth System Processes - Группа авторов - Страница 27

The type of piston cylinder assembly used by Richter et al. (2003) to determine the isotopic fractionation of calcium and lithium in rhyolite‐basalt diffusion couples is shown schematically in Fig. 1.2.

Fig. 1.3 shows the weight percent of major oxide components measured along five parallel lines along the long dimension of the glass recovered from experiment RB‐2. The data from all five lines fall along common smooth curves that are not symmetric with respect to the original interface between the rhyolite and basalt because the rate of diffusion is much faster in the lower SiO₂ content of the basalt side of the couple. The Al₂O₃ profile is a classic example of uphill diffusion in that the low concentration side of the couple became lower than the initial concentration. This uphill diffusion is an indication that the flux of Al₂O₃ is dominated by off‐diagonal terms in the diffusion matrix. Except for Al₂O₃, an effective binary diffusion coefficient D ^E can be derived from fits to the concentration data of all the other major oxides. Experiment RB‐2 was one of two that were run to determine whether calcium isotopes would become measurably fractionated as calcium diffused from the basalt into the rhyolite.

Figure 1.2 A schematic of the piston cylinder assembly used by Richter et al. (2003) to study isotope fractionation by diffusion between molten rhyolite and basalt.

Fig. 1.4 shows the ⁴⁴Ca/⁴⁰Ca fractionation measured by thermal ionization mass spectrometry of purified solutions derived by dissolving thin (~ 0.5 mm) slabs cut perpendicular to the long axis of the recovered glass from experiment RB‐2 run for 15.7 hours at 1450°C and 1.3 GPa, and from a second diffusion couple, RB‐3, run for 12 hours at 1450°C and 1.2 GPa. The calcium isotopic fractionation is reported in the usual per mil notation with the ⁴⁴Ca/⁴⁰Ca of a purified CaCO₃ salt used as the standard. The calcium isotopic composition of the rhyolite is within error (± 0.2), the same as that of the basalt, and therefore the initial δ⁴⁴Ca across the couple was effectively uniform. The locally negative δ⁴⁴Ca in that part of the couple where calcium diffused from the basalt into the rhyolite is evidence of ⁴⁰Ca having diffused measurably faster than ⁴⁴Ca.

The model calculation for the evolution of the major oxide components and the calcium isotopes was formulated using effective binary diffusion coefficients. The conservation equations for total CaO, SiO₂, ⁴⁰CaO, and ⁴⁴CaO with effective 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.