Loss and Isotopic Fractionation of Alkali Elements during Diffusion-Limited Evaporation from Molten Silicate: Theory and Experiments

Abstract

Moderately volatile elements (MVEs) are variably depleted in planetary bodies, reflecting the imprints of nebular and planetary processes. Among MVEs, Na, K, and Rb are excellent tracers for unraveling the history of MVE depletion in planetary bodies because they have similar geochemical behaviors but can be chemically fractionated by evaporation and condensation processes. Furthermore, K and Rb are amenable to high-precision isotopic analyses, which can help constrain the conditions of evaporation and condensation. To quantitatively understand why Na, K, and Rb are depleted in planetary bodies, we have carried out vacuum evaporation experiments from basaltic melt at 1200 and 1400 °C to study their evaporation kinetics and isotopic fractionations. We chose this composition because it is relevant to evaporation from small differentiated planetesimals. The Rb isotopic compositions of the evaporation residues were measured by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS), and the K isotopic compositions were measured along profiles across the residues by secondary ion mass spectrometry (SIMS). In the 1400 °C run products, we found that the concentrations of both K and Rb in the run products decreased from core to rim, which was accompanied by a heavy K isotope enrichment near the surface. This indicates that, in this run, evaporation was limited by diffusion. To use those data quantitatively, we derive analytical equations that describe the evaporation rate and isotopic fractionation associated with diffusion-limited evaporation from a sphere, slab, and cylinder in transient and quasi-steady state regimes. This model is used to tease out the roles that diffusive transport in the melt and evaporation at the melt/gas interface play in setting the elemental depletion and isotopic composition of the residue. Under our experimental conditions, volatility decreases in the order of Na, Rb, and K. Using our experimental results in a thermodynamic model, we have estimated the product γΓ of activity coefficients × evaporation coefficients of Na, Rb, and K. The measured isotopic compositions of the residues are well explained using Rayleigh distillations, whereby the relative volatilities of K and Rb isotopes are given by the square root of their masses. We use our results and previously published data to predict how K and Rb could have been lost as a function of temperature, melt composition, oxygen fugacity, and saturation degree relevant to Vesta's building blocks. We find that the K and Rb depletions, K/Rb elemental fractionation, and δ 41 K and δ 87 Rb isotopic fractionations of Vesta (as sampled by howardite-eucrite-diogenite (HED) meteorites) are best explained by evaporation of submillimeter size objects for 0.1−10 years at moderate temperatures (∼1050 °C) in a medium ∼98.8% saturated.

The Extent, Nature, and Origin of K and Rb Depletions and Isotopic Fractionations in Earth, the Moon, and Other Planetary Bodies

“…The oxygen fugacity is buffered by BSE liquid (Visscher & Fegley 2013;Canup et al 2015;Equation (30)), the same assumption that was made by Charnoz et al (2021). The blue solid curves are from this study, using the parameterization for γΓ from Zhang et al (2021, Equations (31) ), S = 0.99, and evaporation coefficients γ of 0.1 (Alexander 2002;Fedkin et al 2006;Richter et al 2011;Zhang et al 2021). The dashed red lines were calculated by using the thermodynamic data provided by Charnoz et al (2021) and assuming S = 0.99 and γ = 0.1.…”

“…The only way that we have found to decrease the evaporation timescales to values comparable to the lifetime of the exposed LMO is by taking S = 0.8 and γ = 1 and using the digitized K and Na equilibrium vapor pressures from Figure 14 of Charnoz et al (2021). However, isotopic data call for evaporation in a near-saturated medium (S = 0.99; this study; Nie & Dauphas 2019;Charnoz et al 2021), free evaporation experiments support an evaporation coefficient of γ = 0.1 (Alexander 2002;Fedkin et al 2006;Richter et al 2011;Zhang et al 2021), and the K and Na equilibrium vapor pressures plotted in Figure 14 of Charnoz et al (2021) are inconsistent with the thermodynamic data that accompany this figure.…”

“…(ii) The evaporation timescale is inversely proportional to the evaporation coefficient (γ i in Equation ( 29)). For Na in silicate melts, the evaporation coefficients reported in the literature are 0.12 (Alexander 2002), 0.26 (Fedkin et al 2006), 0.06-0.22 (Richter et al 2011), 0.078 and 0.14 (Zhang et al 2021). Charnoz et al (2021) do not discuss the value of the evaporation coefficient of Na, but judging from their writing of the Hertz-Knudsen equation (their Equation (D13)), it is likely that they adopted a value of 1 for γ.…”

“…No experiment has been performed to document the value of b during condensation from highly supersaturated vapor, but unless the condensation coefficients depend strongly on isotopic mass, one would expect b ; 0.5. Experiments of evaporation from silicate melts give b ; 0.5 for both K (Yu et al 2003;Richter et al 2011;Zhang et al 2021) and Rb (Zhang et al 2021). We are unaware of vacuum evaporation experiments for Cu, Zn, Ga, and Sn from silicate melt.…”

Imprint of chondrule formation on the K and Rb isotopic compositions of carbonaceous meteorites

“…S2). Here, we focus on K and Rb isotopes because (i) K and Rb are less volatile than Zn and Te, and the temperature range at which they condense into chondrules corresponds to the main stage of chondrule melt crystallization (49), meaning that the cooling rate estimated based on K and Rb isotopic fractionation should be comparable to the cooling rate based on chondrule textures; (ii) the thermodynamic parameters (Gibbs free energies and activity coefficients) and kinetic parameters (evaporation/ condensation coefficients and kinetic isotopic fractionation factors) of Rb and K are better constrained than for Zn and Te at the temperatures relevant to chondrule formation (54,(59)(60)(61)(62); and (iii) K and Rb are both lithophile elements, meaning that they condense and reside in silicate melt, while Zn and Te are siderophile/chalcophile and their abundances and isotopic fractionations are more easily affected by the presence of metal and sulfide.…”