Isotopic Constraints on Earth System Processes. Группа авторов

Figure 1.8 The panel on the left shows the steady state distribution of the mole fraction of MgO and SiO₂ as a function of temperature in glass recovered from two Soret experiments (SRT4 and SRT8) from Richter et al. (2008). Note that the mole fraction of SiO₂/2 is plotted, not SiO₂. The panel on the right shows the magnesium isotopic fractionation as function of temperature from the two experiments.

      Figure taken from Richter et al. (2008).

Figure 1.9 Thermal fractionation of isotopes of the listed elements in molten basalt in terms of the parameter Ω defined as per mil per one atomic mass unit difference of the isotopes per 100°C. In every case the heavy isotope migrated to the cold end of the sample.

The Soret experiments run by Richter et al. (2008; 2009b; 2014a) were to determine the degree to which a sustained temperature difference across molten basalt fractionates the isotopes of the major elements and alkali elements. Fig. 1.9 summarizes the results in terms of a thermal isotope fractionation parameter Ω defined as the per mil fractionation per unit atomic mass difference between the isotopes per 100°C temperature difference. The thermal isotope fractionation of calcium by Ω_Ca=1.5‰/amu per 100°C makes it likely that the “unexplained” positive fractionation of ⁴⁴Ca/⁴⁰Ca in the basalt side of experiment RB‐2 (see Fig. 1.4) resulted from the temperature at the basalt end of the diffusion couple having been several tens of degree colder than in the middle of the sample. A more explicit example of how thermal isotope fractionations associated with known temperature differences can account for the isotopic data measured in materials recovered from a piston cylinder diffusion experiment was shown in Fig. 1.6.

The degree of elemental and isotopic fractionation associated with a difference in temperature depends in part on how long the temperature difference is maintained. The fraction of the full steady state separation achieved as a function of time was given by Tyrell (1961) as 1 − e ^{−t/ θ} , where θ = L ²/Dπ ², D is the effective binary diffusion coefficient of the chemical specie, and L is a measure of the distance over which the temperature difference was maintained. In a piston cylinder experiment a steady state can be realized because the temperature difference is maintained for as long as necessary by the graphite heater surrounding the sample. The situation in natural settings is very different as Bowen (1921) recognized early on when he wrote “… when we realize that the diffusivity of mass is, according to our determinations, from 10,000 to 100,000 times smaller than the diffusivity of temperature in rocks, it is apparent that the temperature of any igneous body will fall too rapidly to allow sufficient time for the Soret phenomenon to manifest itself.” The only potential exception to Bowen’s assertion that I have been able to come up with involves effects across a double‐diffusive boundary in a layer magma chamber where a long‐time average temperature difference is maintained by the recurring stripping away and reforming of the thermal boundary layers. The interested reader will find model calculations and discussion of isotopic fractionation across a doubly diffusive boundary layer in Richter et al. (2009b).

1.5. ISOTOPE FRACTIONATION BY DIFFUSION IN SILICATE MINERALS

      The question addressed in this section is whether the measurably large kinetic isotopic fractionations that were found in silicate melts also arise during diffusion in igneous minerals. Many of the laboratory experiments and natural examples focused on lithium because of its special attributes of large isotopic mass ratio and extremely fast diffusion, which makes it a potentially unique constraint on thermal histories on geologically very short time scales. Experiments and field examples of isotope fractionation during Fe‐Mg interdiffusion in olivine are also discussed.

      1.5.1. Experiments documenting Lithium Isotopic Fractionation by Diffusion in Pyroxene

Richter et al. (2014b) carried out a number of experiments in which powdered spodumene (LiAlSi₂O₆), or Li₂SiO_3, was used as a source to diffuse lithium into Templeton augite or into Dekalb diopside at 900°C and oxygen fugacity ranging from log fO₂ = –17 to log fO₂ = –12. Fig. 1.10 shows the experimental design of these experiments. The major element composition of the pyroxene grains was sufficiently homogenous that the lithium measurements, which were made with a CAMECA 1270 ion microprobe at the Centre de Recherches Pétrographiques et Géochimiques in Nancy, France, did not require corrections for matrix effects.

The lithium concentration profiles and isotopic fractionations measured in the augite grains recovered from some of the Richter et al. (2014b) experiments were nothing like the smoothly varying profiles found in earlier experiments involving diffusion in silicate liquids (see Figs. 1.3 and 1.6). Fig. 1.11 shows the results from one such experiment, in which the lithium diffused into augite as a sharp step that propagated into the grain with time. The negative isotopic fractionation is extraordinarily large (~30‰) for only a factor of two difference in lithium concentration and it abruptly returns to the unfractionated value of the interior at the place where the lithium concentration abruptly drops down to the initial concentration in the grain. Dohmen et al. (2010) had previously reported similar step‐like profiles for lithium diffusing in olivine, which they explained in terms of lithium existing in two distinct sites, one as fast diffusing interstitial lithium and much slower diffusing lithium in octahedral metal sites. Exchange between these sites was mediated by vacancies. Richter et al. (2014b) adopted the Dohmen et al. (2010) two‐site model to generate model curves to fit of the lithium concentration and isotopic fractionation from experiments where lithium had diffused into augite. The interested reader will find a detailed description of the two‐site model for lithium diffusing in olivine in Dohmen et al. (2010) and its implementation for modeling both the concentration and isotopic fraction of lithium diffusing in pyroxene in Richter et al. (2014b). For present purposes the important result is that the isotopic fractionation shown in Fig. 1.11 was fit by a model calculation using a Dohmen‐type two‐site diffusion model with and β _Li=0.27 for the relative diffusion coefficients of the isotopes of the interstitial lithium.

Figure 1.10 Diagram showing the experimental design used to diffused lithium from a Li‐rich powder (spodumene in this figure)