vary depending on the element as well as liquid composition, and that large diffusive isotope effects can arise even in the absence of a large initial concentration gradient. The retrieved β factor for Ca (0.10 ± 0.02) is typical of Ca in natural silicate liquids, whereas the β factor for K (0.25 ± 0.03) is the highest value yet reported, suggesting that large diffusive K isotope effects may yet be found in high‐T environments.
2.1. INTRODUCTION
Igneous and metamorphic rocks exhibit stable isotope variations in excess of what can reasonably be attributed to mixing processes or equilibrium partitioning during partial melting and (re)crystallization. Experimental studies have shown that diffusion is capable of generating measurable (sub‐permil) to large (tens of permil) kinetic isotopic fractionations that can account for some of this variability, and detailed knowledge of these effects can yield unique insights into the molecular level controls on diffusive transport and the role of kinetics in the formation of minerals in high temperature settings (Antonelli et al., 2019b; Barrat et al., 2005; Beck et al., 2006; Chen et al., 2018; Chopra et al., 2012; Dauphas, 2007; Dauphas et al., 2010; Gallagher & Elliott, 2009; Gao et al., 2011; Jeffcoate et al., 2007; Kil et al., 2016; Lundstrom et al., 2005; Marschall et al., 2007; Mueller et al., 2014; Oeser et al., 2015; Parkinson et al., 2007; Richter et al., 2009, 2014, 2016, 2017; Roskosz et al., 2006; Rudnick & Ionov, 2007; Sio et al., 2013; Su et al., 2016; Teng et al., 2006, 2011; Wu et al., 2018; Zhao et al., 2017).
Current knowledge of diffusive isotopic fractionations in molten silicates is based on a few elements (Ca, Fe, Mg, Li, and Si) and silicate melt compositions (cf. Watkins et al., 2017, for a review). The mass dependence on diffusion coefficients varies between cations and with liquid composition. In basalt‐rhyolite diffusion couples, for example, the stable isotopes of major elements (Ca, Fe, Mg) exhibit less mass discrimination ( β < 0.075) than the stable isotopes of trace element Li ( β ≈ 0.215) (Richter et al., 2003, 2009; Watkins et al., 2009). In simplified silicate liquids, it has been found that the β factor for Ca and Mg varies between 0.05 and 0.21, depending on liquid composition, and is correlated with the “solvent‐normalized” diffusivity (e.g., DCa/DSi), suggesting that faster diffusing elements exhibit greater mass discrimination because they move as single atoms or small moities whose diffusion is decoupled from that of the major melt structures/components (Goel et al., 2012; Watkins et al., 2009, 2011). This simple relationship provides a useful framework for choosing an appropriate value for β in diffusion models and for predicting where there might be large diffusive isotope effects in nature.
In this contribution, we present results from new diffusion couple experiments with two motivating factors in mind. First, the solvent‐normalized diffusivity can only be defined in situations where there is a large initial concentration gradient for the component of interest and an effective binary diffusion model is applicable. And yet, we are aware that large diffusive isotope effects can arise even in the absence of large initial concentration gradients. One such example is in ugandite‐rhyolite diffusion couple experiments where Ca isotopes were fractionated by ∼2‰ due to diffusive coupling of CaO with Al2O3 (Watkins et al., 2009). Such strong multicomponent diffusion effects warrant further investigation because they may contribute to isotope variations within and among minerals formed in high‐T settings. Second, the ratio Di/DSi tends to be lower and approach unity for elements that are present in major quantities because the net flux of a major element requires cooperative motion of the other major components of the liquid. The β factor for Li can be high because it diffuses fast, and it can diffuse fast because it is present in trace quantities. The same may be true for Ca; the β factor for Ca approaches that of Li in experiments where Ca is present in minor quantities (∼2 wt%; Watkins et al., 2011). These observations raise the question of whether the (typically) fast‐diffusing K2O component will behave like Li and have a high β factor or whether it will behave like other major elements and have a β factor closer to zero.
2.2. METHODS
2.2.1. Experiments
Two rock compositions used for the diffusion couple experiments were chosen on the basis of being as different from each other as possible while having similar CaO but different K2O. The compositions that best matched these criteria are a high‐CaO rhyolite with 70 wt% SiO2 and a phonolite with 55 wt% SiO2 (Table 2.1). The rhyolite was supplied by Shaun Brown and comes from Chuginadak Island in the Aleutians (Sample ID FMI‐6; Yogodzinski et al., 2010) and the phonolite was collected in 2002 by JMW from the northern Black Hills tertiary magmatic province. The two compositions have nearly identical CaO (2.9 wt% versus 3.0 wt%) and the large difference in SiO2 is balanced mostly by the extremely high K2O (10.4 wt%) and high Al2O3 (19 wt%) of the phonolite (Figure 2.1).
Approximately 0.055 grams of rock powder from each sample were tamped into a graphite capsule, with the higher density phonolite on the bottom to ensure gravitational stability. The capsule was capped with a graphite plug and graphite lid and loaded into a standard 3/4‐inch piston‐cylinder assembly (Fig. 2.2). The assembly was cold‐pressurized to 12.8 kbar and then brought to 1450°C at a ramp rate of 150°C/min. During the ramp, pressure increased initially due to thermal expansion but ultimately decreased to nearly the target pressure of 10 kbar and was brought to the target pressure through manual adjustments. Once the target temperature was reached, it was held at constant temperature (± 2°C) and pressure (± 0.2 kbar) for the dwell time. To end a run, the power was turned off and the sample cooled to below the glass transition within a few seconds and to 130°C in about 30 seconds.
Table 2.1 Major element composition of starting materials (fused glasses) measured by electron microprobe.
| Oxide | Rhyolite (n=13 spots) | Phonolite (n=14 spots) |
|---|---|---|
| SiO2 | 70.06 | 54.88 |
| Al2O3 | 14.75 | 19.10 |
| CaO | 2.88 | 3.01 |
| FeO | 3.93 | 4.93 |
| MgO | 0.89 | 1.38 |
| K2O | 2.86 | 10.43 |
| Na2O | 5.39 | 5.47 |
| TiO2 | 0.59 | 0.90 |
| P2O5 | 0.10 | 0.35 |
| MnO | 0.08 | 0.10 |
| Total | 101.09 | 100.27 |