# Origin of moderately volatile element depletion on differentiated bodies: Insights from the evaporation of indium from silicate melts

Deze Liu, Frédéric Moynier, Julien Siebert, Paolo Sossi, Yan Hu, Edith Kubik

► To cite this version:

Deze Liu, Frédéric Moynier, Julien Siebert, Paolo Sossi, Yan Hu, et al.. Origin of moderately volatile element depletion on differentiated bodies: Insights from the evaporation of indium from silicate melts. Geochimica et Cosmochimica Acta, 2022, 339, pp.46-57. 10.1016/j.gca.2022.09.043. hal-03936002

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1 **Origin of moderately volatile element depletion on differentiated bodies: insights**

2 **from the evaporation of indium from silicate melts**

3 Deze Liu¹*, Frédéric Moynier¹, Julien Siebert¹,², Paolo A. Sossi¹,³, Yan Hu¹, Edith

4 Kubik¹

5 1. Université Paris Cité, Institut de Physique du Globe de Paris, 1 Rue Jussieu,
6 75005 Paris, France

7 2. Institut Universitaire de France, Paris, France.

8 3. Institute of Geochemistry and Petrology, ETH Zürich, Sonneggstrasse 5, CH-8092

9 Zürich, Switzerland

10 Abstract: 303 words

11 Text: 11218 words

12 Figures: 7

13 Tables: 1

14 Supplementary Figures: 5

15 Supplementary Tables: 6

16
17 Submitted to GCA

18
(September, 2022)

19
20
*Corresponding author:

21 Email: liudeze@ipgp.fr

22
23 **Abstract**

24 In comparison with the Sun and CI chondrites, moderately volatile elements
25 (MVEs) are depleted in terrestrial planets and other small, rocky differentiated bodies
26 in the inner solar system. The abundances of most MVEs in the bulk silicate Earth
27 (BSE) fall on a trend that defines a near log-linear decrease with their 50% nebular
28 condensation temperature ($T_c^{50}$). This temperature scale has traditionally been used to
29 infer elemental volatility during planetary formation and accretion, however, indium
30 (In) deviates from this correlation. Despite being a siderophile element that could
31 have been depleted by core formation, In is overabundant for its calculated $T_c^{50}$ in
32 the BSE, as well as in the silicate portions of other small bodies (e.g., Moon and
33 Vesta). This overabundance of In indicates that $T_c^{50}$, calculated under nebular
34 conditions, may not be applicable to planetary evaporation that occurs at much higher
35 oxygen fugacity ($fO_2$) and pressure than nominal nebular conditions. Here, we
36 conduct a series of evaporation experiments for basaltic melts to quantify the
37 volatility of In under conditions relevant to planetary evaporation. Our results show
38 that, when using the evaporation temperature ($T_e^1$, refers to the temperature at which
39 1% of element *i* has evaporated from liquid to gas phase under equilibrium) as the
40 volatility scale, the abundances of volatile elements, including In, of the Moon and
41 Vesta display a progressive depletion with increasing volatility (decreasing $T_e^1$). This
42 smooth depletion pattern contrasts with the overabundance of In shown on the $T_c^{50}$
43 scale, suggesting that volatile depletion on small bodies occurred under non-nebular
44 environment instead of during nebular condensation. On the other hand, the volatile
45 element composition of the BSE (including In) could be explained by integrating *i*)
46 early accreted precursor materials of the proto-Earth that underwent volatile loss
47 under conditions more oxidizing than those of the solar nebula with *ii*) late added
48 volatile-rich materials.
49

49 **Keywords:** Indium; Evaporation experiment; Silicate melt; Volatile depletion
## 1. Introduction

Moderately volatile elements (MVEs) are the elements with volatility between S and the major components (Si, Mg and Fe) (Palme and O'Neill, 2014). The abundances of these MVEs in CI chondrites are similar to that in the solar photosphere. In contrast, they are variably depleted in the silicate portions of differentiated asteroids and planets, notably Earth and the Moon (e.g., Palme et al., 1988; O'Neill and Palme, 2008; Sossi and Fegley, 2018). These depletions can occur during nebular processes (e.g., incomplete condensation from the gas, Albarede, 2009; Morbidelli et al., 2020; Vollstaedt et al., 2020) and/or planetary (i.e., post-nebular) processes, for example, evaporative loss during accretion or differentiation on their bodies or precursor materials (Pringle et al., 2014; Hin et al., 2017; Norris and Wood, 2017; Ivanov et al., 2022). The volatility of a MVE changes in response to different physical and chemical conditions associated with nebular versus post-nebular processes.

The 50% condensation temperature ($T_c^{50}$) is a widely used volatility scale applicable to solar nebular conditions, and it refers to the temperature at which half the mass of an element is condensed from a gas of solar composition at equilibrium (Larimer, 1967). Differentiated telluric bodies display coherent elemental abundance patterns with $T_c^{50}$ as shown in Fig. 1. Specifically, refractory lithophile elements with high $T_c^{50}$ have near-chondritic relative abundances, therefore displaying a flat relative abundance pattern with $T_c^{50}$. By contrast, lithophile MVEs with $T_c^{50}$ between 1250 and 650 K show concomitant decreases in relative abundance with $T_c^{50}$, which is referred to as a volatility trend. In contrast to lithophile elements, siderophile elements are further depleted by core-formation and thus their relative abundances are lower than those defined by the volatility trend.

Indium (In) is a moderately to highly volatile element as characterized by its low $T_c^{50}$ (536 K in Lodders, 2003 or 492 K in Wood et al., 2019), and does not follow the volatility trend defined by lithophile MVEs in the BSE. Given that In is a siderophile element, a greater depletion of In in the BSE is expected due to its sequestration into
Earth's core. Contrary to this expectation, however, In lies above the volatility trend (cf. Witt-Eickschen et al. 2009). When compared to Zn, which has a higher $T_c^{50}$ (704 K, Wood et al., 2019) and is less siderophile and chalcophile (Wood et al., 2014), In has a similar or even higher CI-normalized abundance in both terrestrial planets such as Earth (Palme and O'Neill, 2014), Mars (Taylor, 2013) and smaller telluric bodies like the Moon (Hauri et al., 2015) and Vesta (Steenstra et al., 2019, Sossi et al., 2022). This ubiquitous overabundance of In observed across a range of planetary bodies provides strong grounds to reject a single nebular process as the origin of the volatile depletion in inner solar system planets. Therefore, post-nebular processes must have occurred, which include late added material to the planetary mantle, evaporation on precursor parent bodies, or collisional erosion (Norris and Wood, 2017; O'Neill and Palme, 2008; Wang and Becker, 2013; Wang et al., 2016; Allibert et al., 2021).

Post-nebular processes take place after the nebular gas has dispersed. As such, evaporation and condensation are expected to have occurred at higher total pressures and more oxidized conditions (O'Neill and Palme, 2008; Visscher and Fegley Jr., 2013) than under nebular conditions (an H₂-rich atmosphere at nominal pressures of ~10⁻⁴ bar). Given the substantial change in thermodynamic conditions and consequently elemental volatility, $T_c^{50}$ may not be a suitable volatility scale to describe the totality of planetary accretion processes. This contention is supported by previous evaporation experiments of Norris and Wood (2017) that conducted in the vapor-silicate melt system at fixed temperature and pressure (1300°C, 1 bar) but variable oxygen fugacity from 2.3 logarithmic units below Fe-FeO buffer (iron-wüstite, ΔIW-2.3) to Ni-NiO buffer (ΔNNO). They found that In evaporated at a rate comparable to that of Zn, which differs from their relative volatilities inferred from $T_c^{50}$, where In is much more volatile than Zn. Furthermore, In was found to be much less volatile than Tl and Cd, despite their similar $T_c^{50}$. Norris and Wood (2017) explained the relatively more volatile nature of In by the high partial pressures of H₂S and H₂O in the nebula gas, which stabilize In-bearing species in the gas phase (InS, In₂S and InOH) and hence increase its volatility under nebular conditions with respect to Zn.
The differing volatility of In under nebular versus post-nebular conditions provides
motivation for the development of a mechanism that predicts element volatility under
non-nebular conditions. Sossi et al. (2019) derived a theoretical framework to
quantify elemental volatility during evaporation of silicate melt based on
Hertz-Knudsen-Langmuir (HKL) theory (Hertz, 1882; Knudsen, 1909; Langmuir,
1916; Richter et al., 2002) and proposed a new volatility scale calibrated by the
evaporation temperature of elements in a vapor-melt system. Sossi et al. (2019)
performed evaporation experiments on a range of MVEs to determine elemental
volatility at 1 bar and variable temperature and oxygen fugacity ($fO_2$) conditions in
the absence of $H_2$. However, In was not investigated in their study, which hinders our
understanding of its overabundance on the $T_c^{50}$ volatility scale and volatile loss
during planetary processes.

To assess the volatility of In in a vapor-melt system, we conduct evaporation
experiments on $In_2O_3$ and ZnO-doped basaltic melt composition in $CO-CO_2$ gas
mixing furnace at 1 bar. We quantify the amount of In remaining in the quenched
glasses as a function of temperature and $fO_2$. This allows us to infer the speciation of
In in the gas phase and to determine its evaporation temperature based on the
empirically theoretical framework described in Sossi et al. (2019). Our new results
along with published elemental volatility data provide critical insights into the origin
of volatile depletion of the Earth and smaller differentiated bodies.

## 2. Method

### 2.1 Sample preparation and evaporation experiments

Basaltic glasses are used as starting materials for the experiments, including a
natural mid-ocean ridge basalt (MORB) glass and a synthetic glass in the
$FeO \cdot T$-CaO-MgO-Al$_2$O$_3$-SiO$_2$ (FCMAS) system (detailed compositions are listed in
Table S1). Fresh MORB chips were selected carefully to avoid any alteration product.
The synthetic FCMAS mixture was made by mixing reagent-grade oxide powders,
except that Ca was added as carbonate ($CaCO_3$). These powders were preserved in a
137 laboratory oven (set to 140°C) to avoid the influence of adsorbed water on weighing.
138 The mixed powders were ground with pestle and mortar under ethanol to make them
139 as homogenous as possible, then the ethanol was dried down on a hotplate at 100°C.
140 This step was repeated three times. Then this mixture was decarbonated at 950°C for
141 16 h with a box furnace in air condition. Reagent-grade indium oxide (In₂O₃, ~1 wt.%)
142 was then added to the MORB and FCMAS powders. ZnO powder (~ 1 wt.%) was
143 also added to allow a direct comparison with previous studies.

144 The powder mixtures were then put in Pt crucibles and heated to be completely
145 molten at 1400°C for 30 min in air, and then quenched into water to form glass. This
146 step was designed to ensure that In₂O₃ and ZnO were fully dissolved in the silicate
147 melt to prevent unexpected evaporative loss of In₂O₃ or ZnO in pure oxide state
148 during the following evaporation experiments. The measured In concentrations of
149 synthetic mixtures~ 3% lower than the calculated initial concentration (Table. S1),
150 which may indicate a minor loss to Pt crucible/evaporation loss and/or uncertainty on
151 powder weighting or concentration analysis. The measured and calculated Zn
152 concentrations are nearly identical. The following calculations used the measured
153 concentration in synthetic MORB and FCMAS glasses as the initial compositions.
154 Then, the synthetic basaltic glass mixtures were ground to a fine-grained and
155 homogeneous powder in an agate mortar in preparation for further evaporation
156 experiments. For each experiment, ~50 mg of pulverized glass was mixed into a
157 slurry with polyethylene oxide (10,000 molecular weight) and then loaded onto a
158 metallic wire. Two types of wires (Pt and Re wire) were used for evaporation
159 experiments, of which Pt wire was used for the samples that performed at- or above
160 log(fO₂) > -6, while Re wire was used under more reducing conditions (log(fO₂) < -6).
161 This choice was dictated by the different solubilities of In into Pt and Re wire, where
162 In is observed to significantly alloy with the Pt wire as fO₂ decreases, while negligible
163 In was detected in the Re wire (see section 3.2 and Supplementary materials).
164 However, solid Re metal wire is unstable with respect to its gaseous oxides above
165 ~log(fO₂) > -6, restricting its use under these conditions. The total amounts of In in
166 the metallic wire were assessed by analyzing the solutions that produced by dissolving
whole wires after removal of the silicate part (results see Supplementary materials, Fig. S2).

The oxygen fugacity of each experiment was buffered by CO-CO₂ gas mixing in a GERO atmosphere-controlled furnace at IPGP (furnace tube size: 70-cm-long, diameter: 4.2 cm; Sossi et al. 2020), and the ratio of CO₂ and CO was adjusted using four MKS G-series mass flow controllers. The log(fO₂) investigated here ranged from -10 to -0.68 (air) at different temperatures (1300°C, 1400°C and 1500°C). The total gas flow rate of all the gas-mixing experiments was fixed to 200 standard cubic centimeters per minute (sccm, ca. 0.24 cm/s) to eliminate the effect of thermal diffusion on fluctuations in the ratio of CO/CO₂ (Darken and Gurry, 1945) and potential variations in evaporation rate induced by variable gas flow rates. Conditions (T, fO₂ and duration) of experiments are listed in Table S2. A type B thermocouple (Pt₉₄Rh₆/Pt₇₀Rh₃₀, measured uncertainty ± 0.5%) is located less than 1 cm above the sample beads, providing a precise measurement of the temperature within the ~4 cm-long hotspot in the furnace. Before sample introduction, CO and CO₂ gases were fluxed through the alumina tube furnace for 10 min to ensure a homogeneous and stable oxygen fugacity that prevents unwanted evaporative loss of In due to fluctuations in fO₂ to occur. The samples were held at the set temperature for a duration of either 30 or 60 minutes. The bottom of the furnace alumina tube was isolated from outside by a steel ball valve. This valve was closed during heating to prevent potential fluctuations of oxygen fugacity. Once the evaporation experiment was complete, the valve was quickly opened manually, and sample subsequently drop-quenched into Milli-Q (18.2 Ω) deionized water.

After performing the first experiment, In was observed to build up on the walls of the alumina tube due to condensation, which could lead to unexpected contamination of the samples during heating. To estimate this potential contamination, blank experiments were performed with In-undoped pure MORB powders (see section 3.1).
## 2.2 Chemical analyses of the samples

Trace element concentrations of the quenched run products were measured with a Quadrupole Inductively-Coupled Plasma Mass Spectrometer (Q-ICP-MS) at the Institut de Physique du Globe de Paris. The glass samples were removed from the metal wires carefully and ground into powders. The sample powders were dissolved in mixed acids by 1ml HNO₃ (16M) and 3ml HF (28M) in Savillex® standard PFA Teflon vials. The Teflon vials were closed and heated on a hotplate at 130°C for 2 days. The samples were dried at 100°C and re-dissolved in 2ml aqua regia at 130°C for 24h to remove insoluble fluorides. The samples were dried down again and redissolved in 6M HCl at 130°C for 18h. Samples were finally dissolved in 5ml 0.5M HNO₃ for 24h before ICP-MS measurements. The metal (Pt and Re) wires were also analyzed to quantify the amount of In loss by diffusion into the wire. They were dissolved in 3ml aqua regia for 24h, then dried and re-dissolved in 2ml 0.5N HNO₃ before measurements.

A set of ICP-MS standard solutions in 2 % v/v HNO₃ were used as calibration standards (0.01 to 20 ppm for major elements, 0.1 to 200 ppb for typical trace elements, and 0.01 to 200 ppb for In). Scandium and Re were used as internal standards to correct for matrix effects and mass bias of the instrument. For the Re wires, only Sc was used as an internal standard. A basalt geostandard BHVO-2 was analyzed to test the accuracy of the results, and giving an In concentration of 82 ppb (RSD = 1.5%), which is consistent with the reported values on ID-ICP-MS (82 to 87 ppb) from GEOREM (http://georem.mpch-mainz.gwdg.de/).

## 2.3 Electron probe micro-analysis for elemental zoning of In

Four samples that used the MORB mixture were run at 1300°C for 60 min at variable fO₂ (-10 to -0.68), to test for compositional heterogeneity. Samples were mounted in epoxy, polished to their largest cross sections and then analyzed with a CAMECA SX Five electron probe micro-analysis (EPMA) at CAMPARIS service (Sorbonne University). Operating conditions of the probe were set to a 20 KeV
accelerating voltage and 10 nA beam current for the analyses on Na, Mg, Si, Al, K, Ca, Fe and 20 KeV, 200 nA were set for the analyses on P, S, Mn, In and Ti. Standards used for In₂O₃ is an alloy of In and P; albite for Na₂O; diopside for MgO, SiO₂ and CaO; orthopyroxene for K₂O and Al₂O₃; pyrite for FeO and S; Mn-Ti oxide for MnO and TiO₂. Detection limit of In is ~ 160 ppm. Elemental zoning was assessed through profile mode analysis with a beam size of 30 µm and 15 to 20 analytical points were collected along the radius from the center to the rim of a glass bead. The final point was typically placed at < 30 µm from the edge of the bead. No crystalline phases were observed in our quenched glass beads.

## 3. Results

### 3.1 Evaluation of In contamination

To determine the extent of In and Zn contamination of the liquid silicate beads from the furnace, 16 blank experiments were conducted over the course of this study with temperature varying from 1300°C to 1500°C and fO₂ (log(fO₂)) ranging from -10 to -0.68) for 1 hour on undoped MORB powders. Each blank sample was generally performed following the experiments using doped samples and were performed under the same experimental conditions. The concentration of In in the blank samples is observed to correlate with temperature and fO₂. Higher temperature and more reduced conditions lead to an increased contamination ratio of In (see supplementary information Table. S3 and Fig. S1). For example, a blank run at 1500°C and log(fO₂) = -10 for 1 hour, is measured to contain ~ 3 ppm of In, while the doped sample (~ 1 wt.% of initial In) performed under the same conditions has ~7 ppm of In left in the residual glass. The ratio of blank/sample is therefore nearly 50%. Considering the higher contribution from contamination for the experiments performed at 1500°C and log(fO₂) = -10 ~ -8, these conditions were not included for the discussion, other than to show that In concentration in the glasses of these experiments is essentially nil with respect to the initial quantity (~ 1 wt. % In).
249 **3.2 In loss to metal wire**

250 Under the imposed oxygen fugacities and temperatures in the furnace (down to
251 log fO₂ = -10, ~ ΔIW+1 to -1 from 1300°C to 1500°C), In is assumed to exist as InO₁.₅
252 in the melt (see section 3.4), and its solubility in metal increases with decreasing fO₂
253 by a reaction of InO₁.₅ (silicate melt) = In (metal) + 3/4O₂ (gas) (e.g., Mann et al.
254 2009). After removal of the glass, the entirety of the remaining wire was dissolved to
255 quantify the amount of In dissolved in metal. The amount of In dissolved in Re wire
256 was found to be negligible (3 ~ 30 ng) compared to an initial doped amount of ~ 500
257 µg in the experiments. In comparison, Pt wires are observed to contain variably more
258 In (from 4 to 120 µg) depending on experimental temperature and fO₂ (see
259 supplementary information Table. S4 and Fig. S2). The solubility of In into Pt wire
260 increases significantly at higher temperature and lower fO₂ (see supplementary
261 information). For instance, an experiment performed under 1500°C and log(f(O₂)) =
262 -5.01 for 30 min, In dissolved into the Pt wire accounts for approximately 24% of that
263 in the initial doping amount. Given the excessive In loss (> 20%) to the Pt wire for
264 experiments conducted at 1500°C and log(f(O₂)) = -5 ~ -4, their run products are not
265 included in data fitting and relevant discussion.
266

266 **3.3 Elemental zoning**

267 The rate of In loss from the melt surface during evaporation is presumably affected
268 by the rate of In diffusion through the silicate. When diffusion is much slower than
269 evaporation, the extent of evaporative In loss is limited by the diffusion rate, resulting
270 in a radial zonation in In concentration in the glass bead. In contrast, should the
271 diffusion rate exceed the evaporation rate, then In is transported sufficiently quickly to
272 the melt surface to allow for continuous In loss by evaporation, and thus In should be
273 homogeneously distributed in the glass bead.
274

274 To examine the spatial distribution of In in the glasses, a few replicates of MORB
275 mixture were performed under the lowest temperature 1300°C, 60 min and variable
276 fO₂ (-10, -8, -3.44 and -0.68). The In concentrations of these replicates were measured
by EPMA. In Sossi et al. (2019), elemental zoning was observed only in their lowest
temperature (1300°C) and most reduced (log fO₂= -10) run products, whereas run
products performed under higher temperature (1400°C, 1500°C and 1550°C), all
MVEs were homogeneously distributed in the glass regardless of the oxygen fugacity
under which they were synthesized. This observation implies that the increase of
diffusion rate is faster than that of the evaporation rate with the increase of
temperature given the experimental oxygen fugacity (fO₂ = -10 to -0.68) and
ferrobasaltic melt composition. This suggests that elemental zoning is more likely to
be present in samples performed under the lowest temperature and therefore the
1300°C-series were chosen to test the potential zoning. Moreover, the samples with
the fastest evaporation rate (log fO₂= -8 to -10, 1400°C and 1500°C) were not used for
fitting, as discussed in section 3.1.

Our results on these samples do not exhibit significant concentration gradient from
center to rim, and suggest a near-homogeneous distribution of In (Fig. S3). Therefore,
it is reasonable to assume that the influence of diffusivity is negligible at all
conditions investigated in this study. However, there is still no available diffusion data
of In, the diffusion limit on other melt compositions such as rhyolitic or dacitic melts
would require further experimental tests.

## 3.4 In concentration and data fitting

The initial In concentration in both synthetic starting materials (mixtures of MORB
and FCMAS) is ~ 0.96 wt.% (concentration for elemental In). The In concentration in
fresh MORB is generally less than 0.1 ppm (Yi et al., 2000), which is negligible
compared to the doped amount of In (~ 1 wt.% In₂O₃). For the glassy run products,
the final In concentrations after evaporation vary from 12 ppm (DLF 04) to ~ 9700
ppm (DLF 02, see Table. S1) depending on different T and fO₂ conditions of
experiments.

The extent of In depletion is expressed by the molar fraction of In in the evaporated
residue, i.e., the sample glasses, relative to that in the starting materials. Here, we
make the approximation that the ratio of molar fraction of In between evaporated residue and initial value ($X_i^t/X_i^0$) is equal to their ratio of concentration ($C_i^t/C_i^0$) due to lack of other abundant volatile components. Hence, In depletion can be expressed as:

$$ \frac{X_i^t}{X_i^0} \approx \frac{C_i^t}{C_i^0} \quad (1) $$

where $X_i^t$ and $X_i^0$ refer to the fraction of element $i$ at time $t$ and the initial fraction of $i$, respectively, and $C_i^t$ and $C_i^0$ represent the concentration of $i$ at time $t$ and the initial concentration, respectively.

The extent of depletion of In is related to its volatility and the specific physical conditions during an evaporation process. The volatility of In increases with increasing temperature and decreasing $fO_2$, which is consistent with the behavior of most MVEs such as Zn, Ge, Pb and Cu reported in previous studies (Norris and Wood 2017, Sossi et al. 2019). Sossi et al. (2019) provided a framework to assess elemental volatility based on the empirical application of the HKL equation for the evaporation on silicate melt. For a congruent dissociative evaporation reaction with single oxidation in liquid and multiple in gas, the volatility of an element, $i$, can be described by the following equation:

$$ \frac{X_i^t}{X_i^0} = \exp \left( - \left( 1 - \frac{P_i}{P_{i,sat}} \right) \left( \frac{K_a^*}{f(O_2)^{\frac{n_a}{4}}} + \frac{K_b^*}{f(O_2)^{\frac{n_b}{4}}} \right) \frac{3M}{r\rho} \sqrt{\frac{1}{2\pi M_i R T}} (t - t_0) \right) \quad (2) $$

In this equation, $K^*$ the modified equilibrium constant of a vaporization reaction, is defined as $K^* = \alpha_e \gamma_e^\infty K$. $a$ and $b$ refer to the different vaporization reactions (see below). $\alpha_e$ refers to the evaporation coefficient, representing the fraction of molecules that strike the vapor-liquid interface and change phases from their initial liquid state with respect to that expected for an ideal, Maxwell-Boltzmann gas. For an evaporation process occurring under ideal conditions, $\alpha_e$ can be taken as unity, i.e., $\alpha_e = 1$. However, the value of $\alpha_e$ in an experimental and/or natural evaporation system could deviate from unity due to the influences from many factors, for example, temperature discrepancy between liquid and vapor interface, surface properties of
melt, impurities at interface (Persad and Ward, 2016; Sossi and Fegley, 2018), which makes $\alpha_e$ difficult to determine *a priori*. The factor $\gamma_e^\infty$ refers to activity coefficient of an element *e* in a given silicate melt at infinite dilution, and the studies on $\gamma_e^\infty$ of indium in ferrobasaltic melt are still scarce to date. Given the uncertainties of both $\alpha_e$ and $\gamma_e^\infty$, Sossi et al. (2019) and Zhang et al. (2021) used the product of $\alpha_e$ and $\gamma_e^\infty$ as unknown and fit the value of $K^*$ without assuming an individual value of $\alpha_e$ or $\gamma_e^\infty$. Based on their experimental results, Sossi et al. (2019) suggested that the $\alpha_e$ values among different MVEs were all close to unity under their experimental conditions (1573K to 1823K, 1 bar; the same conditions are applied in this study); Zhang et al. (2021) calculated the values of $\alpha_e\gamma_e^\infty$ of evaporation experiments on basaltic and chondrule-like compositions, and observed a good consistency of $\alpha_e\gamma_e^\infty$ in the literature. The apparent discrepancy of a factor ~1000 to the experiments of Sossi et al. (2019) derives from the fact that Zhang et al. (2021) neglected to include the factor $1-P_i/P_{i,sat}$ (taken to be 0.001 in Sossi et al. 2019) when comparing their experiments performed under vacuum (and hence $1-P_i/P_{i,sat} \sim 1$) to those performed at 1 bar (Sossi et al. 2019). When this correction is included, the agreement is consistent among these studies.

In this study, the same approach was followed to fit $K^*$. The symbols $P_i$ and $P_{i,sat}$ represent the partial pressure and equilibrium pressure, respectively, of the gas species of In presented in the experiments. Sossi et al. (2019) assumed a value of $P_i/P_{i,sat} = 0.999$ for fitting the value of $K^*$ and calculating the elemental evaporation temperature. The subsequent experimental calibration by Sossi et al. (2020) suggested that $P_i/P_{i,sat} =0.996$ is a more appropriate value. To compare with the results in this study, $K^*$ and evaporation temperature of elements reported in Sossi et al. (2019) are re-calculated with $P_i/P_{i,sat} =0.996$. The $fO_2$ is the oxygen fugacity in bar; $r$ is the radius of sample glass bead, which is typically ~1.6-1.7 mm, and is set be ~0.00165 m; $\rho$ is the density of basaltic glass (2750 kg/m³); $n$, is the electron number in reaction; $M$ and $M_i$ are the molar masses (kg/mol) of the basaltic glass bead and evaporated stable gas species, respectively. $R$ is the gas constant (8.3145 J/K⁻¹·mol⁻¹); $T$ is the experimental temperature in Kelvin. The symbol $t_0$ marks the time at which volatiles start to
362 evaporate, an empirically-determined quantity that approximately relates to the
363 thermal equilibrium time since insertion, recorded once temperature reached 99% of
364 the set temperature (typically < 4 min), and t indicates experiment duration (in
365 seconds) from insertion to quenching. The value of t-t₀ was maintained at either 30
366 min or 60 min in this study.

367 The number of electrons exchanged, n, in a given vaporization reaction depends on
368 the dominant melt species and that in the gas produced during evaporation. Here we
369 assume In occurring as trivalent cation (In³⁺) in melt over the fO₂ imposed in this
370 study (air to ΔIW-2). This assumption is based on the estimated valence state of In in
371 metal-silicate segregation experiments (e.g., Righter et al., 2017; Steenstra et al.,
372 2020), which performed mostly under more reducing conditions than in this study
373 (~ΔIW-1 to -5). The generated stable gas species of In are not known a priori, and
374 there are three possible species including In (g), InO (g) and In₂O (g) (Lamoreaux et
375 al., 1987). Assuming these species to be the vaporization products of In from the melt,
376 the vaporization reactions can be written as following:

$$
377 \qquad \mathrm{InO}_{1.5}(\mathrm{l}) = \mathrm{In}(\mathrm{g}) + 0.75\mathrm{O}_2(\mathrm{g}) \quad (3.1)
$$

$$
378 \qquad \mathrm{InO}_{1.5}(\mathrm{l}) = \mathrm{InO}(\mathrm{g}) + 0.25\mathrm{O}_2(\mathrm{g}) \quad (3.2)
$$

$$
379 \qquad 2\mathrm{InO}_{1.5}(\mathrm{l}) = \mathrm{In}_2\mathrm{O}(\mathrm{g}) + \mathrm{O}_2(\mathrm{g}) \quad (3.3)
$$

380 The equilibrium constants (K) of these equations can be expressed as:

$$
381 \qquad K(3.1) = \frac{p_{\mathrm{In}f\mathrm{O}_2}^{3/4}}{a_{\mathrm{InO}_{1.5}}}
$$

$$
382 \qquad K(3.2) = \frac{p_{\mathrm{In}of\mathrm{O}_2}^{1/4}}{a_{\mathrm{InO}_{1.5}}}
$$

$$
383 \qquad K(3.3) = \frac{p_{\mathrm{In}_2\mathrm{O}f\mathrm{O}_2}}{a_{\mathrm{InO}_{1.5}}^2}
$$

384 Where *p* refers to partial pressure of corresponding gas species; *a*<sub>InO<sub>1.5</sub></sub> refers to the
385 activity of InO<sub>1.5</sub> in the silicate melt. Thermodynamic data taken from Lamoreaux et
386 al. (1987) to calculate the relative stabilities of the three gas species at fixed *T*
387 (1400 °C) and *P* (1 bar) with variable *fO*<sub>2</sub>. Among these three gas species, In (g) is
388 observed to be dominant under most of our experimental conditions (Fig.2). The ratio
pIn/pInO is proportional to 1/f(O₂)¹/², suggesting that In (g) should be more stable at low f(O₂) (Fig.2a); pIn/pIn₂O is proportional to f(O₂)¹/²/ aInO₁.₅, indicating that In₂O (g) can be more stable at reducing conditions (Fig.2a) provided aInO₁.₅ is high. However, if aInO₁.₅ is diluted (e.g., from 0.01 to 0.001), pIn/pIn₂O can exceed 1, resulting in In (g) remaining as the dominant gas species within the range of experimental fO₂ (Fig.2b). In addition, when taking into account the equilibrium reactions between gas species as following:

$$396 \qquad \text{InO (g)} = \text{In (g)} + 0.5 \text{ O}_2 \text{ (g)} \quad (3.4)$$

$$397 \qquad \text{In}_2\text{O (g)} = 2\text{In (g)} + 0.5 \text{ O}_2 \text{ (g)} \quad (3.5)$$

the ratio of partial pressure of gas species can be expressed as:

$$399 \qquad \frac{p_{\text{In}}}{p_{\text{InO}}} = \frac{K(3.4)}{p_{O_2}^{\frac{1}{2}}} \quad (3.6)$$

$$400 \qquad \frac{p_{\text{In}}^2}{p_{\text{In}_2\text{O}}} = \frac{K(3.5)}{p_{O_2}^{\frac{1}{2}}} \quad (3.7)$$

The relative stability of each gas species is shown in Fig.2c and d, where In (g) is still the dominant gas species at the experimental conditions. We find that InO (g) is only stable under very oxidizing conditions (near- or above the fO₂ of air at 1400 °C) and hence is assumed to be negligible in our experiments. In₂O (g) can be stable at the most reducing experiments. However, due to the low concentration of In in nature (~ usually below 200 ppb), aInO₁.₅ is several orders of magnitude lower than in the experimental system, hence pIn₂O is likely negligible during natural evaporation processes and only In (g) is likely to be present.

Therefore, we assume that both In (g) and In₂O (g) are stable under our experimental conditions. Considering pIn₂O and pIn are dependent variables (Eq. 3.10), the modified equilibrium constant (K*(3.3)) of reaction (3.3) is calculated by combining reaction (3.1) and (3.7). Reaction (3.5) is assumed to be ideal gas reaction under our experimental conditions (1573 K to 1773 K), substituting thermodynamic data of the gas species from Lamoreaux et al. (1987). Therefore, K*(3.3) is determined by K*(3.1) and K (3.5), can be expressed as:
$$K_{3.3}^* = \frac{(K_{3.1}^*)^2}{K_{3.5}} \quad (3.8)$$

Using Eq. 2 to fit the data, the correlation of $X_i^t/X_i^0$ and $fO_2$ is consistent with the 3 and 4-electrons reactions (Fig. 3). For the evaporation experiment of Zn, Sossi et al. (2019) suggested that Zn remains as divalent cation ($Zn^{2+}$) in melt, and only has one stable gas species Zn (g), and hence corresponding to a 2-electrons reaction ($n = 2$). Our experimental results of Zn evaporation are similar to those reported in Sossi et al. (2019), exhibiting good reproducibility on evaporation experiments. The fitted results are shown in Fig. 3.

## 4. Discussion

The experiments presented here were performed under controlled physical conditions ($T, P, fO_2$) on basaltic silicate melts that were derived from both natural and synthetic rocks. The activity coefficients of trace elements, such as In, may change at varying silicate melt compositions (Holzheid et al. 1997, O'Neill and Eggins. 2002), which may lead to different volatility behavior than that inferred here using a basaltic composition (Wood and Wade 2013). Here, we assume that the basaltic melts (FCMAS and MORB) used in the experiments are representative of natural magmatic liquids, and we discuss elemental volatilities with respect to these compositions. Our experiments, performed in the absence of $H_2$ (g) and at atmospheric total pressure, are relevant to the assessment of elemental volatility during post-nebular processes that occurred at much higher $fO_2$ and total pressure than the $H_2$-dominant solar nebular environment ($10^{-4}$ bar).

### 4.1 Elemental volatility and evaporation temperature

Volatile loss during evaporation is constrained by the physical conditions ($T, P, fO_2$ and silicate composition) of the system. Sossi et al. (2019) provided a new volatility scale based on elemental evaporation temperature, which can be used to quantify the elemental volatility in this study. For a congruent dissociative evaporation, the evaporation temperature ($T_{e,i}^f$) can be expressed as following:
443

$$T_{e,i}^{f} = \frac{-\Delta A_{i}^{*}}{\left(R\left(\frac{n}{4} \ln f_{O_2} + \ln P_{T} + \ln \frac{f_{i}^{vap}}{f_{i}^{lid}}\right) - \Delta B_{i}^{*}\right)} \quad (4.1)$$

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

The symbols $f_i^{vap}$ and $f_i^{lid}$ represent the fractions of element i in the gas and in the liquid respectively and sum up to 1. $P_T$ is the total pressure of experiment, and is equal to 1 bar in this study. The quantity n refers to the electron number in vaporization reaction (e.g., Eq 3.1), given the low abundance of In in nature (~ 0.1 ppm), In (g) is considered as the dominant gas species during evaporation (see section 3.4), corresponding to n = 3. The derivation of Eq. 4.1 can be found in Sossi et al. (2019). To compare our data with published data directly, the evaporation temperature is also set to 1% evaporation temperature that refers to the temperature at which 1% of element i has evaporated from liquid to gas phase under equilibrium, and calculated at $log(fO_2)$= -10 and -5, respectively (noted as $T_{e,i}^{1,-10}$ and $T_{e,i}^{1,-5}$) corresponding to values near the ΔIW buffer ($logfO_2$ = -10 at 1650 K) and near ΔFMQ (Fayalite-Magnetite-Quartz) buffer ($logfO_2$ = -5 at 1750 K) for representative MVEs like Na, K, Zn, Cu, Rb and In. $\Delta A_i^*$ and $\Delta B_i^*$ refer to the enthalpy and entropy of experimental vapor-melt reaction, calculated from the modified equilibrium constant $K^*$ by converting to Gibbs free energies:

459

$$\Delta G^* = -RT\ln K^* \quad (4.2)$$

460

461

462

463

464

465

466

Combining with the value of $K^*$ defined in section 3.4 (which is different from that calculated in the pure oxide system), $\Delta G^*$ is calculated to describe the Gibbs free energy for the non-ideality of trace element dissolution in silicate melt (i.e., $\gamma_e^\infty$) and the deviation of the evaporation coefficient, which may vary with temperature (Sossi et al., 2019). Therefore, the estimation of $\Delta G^*$ in this study is constrained by melt composition and experimental P-T conditions (1 bar, 1573K to 1773K). Then, $\Delta A_i^*$ and $\Delta B_i^*$ can be calculated by the Gibbs-Helmholtz equation:

467

$$\Delta G^* = \Delta A^* - T\Delta B^* \quad (4.3)$$

468

469

where, $\Delta G^*$ is a linear function of absolute temperature, T. $\Delta A_i^*$ is the intercept of the line, $-\Delta B_i^*$ is its slope on an Ellingham diagram (Fig. 4).
The $T_c^{50}$ of a given element is estimated for condensation of a gas of solar composition from thermodynamic data combined with their solution properties in condensing phases. In comparison, $T_{e,i}^f$ is assessed from the thermodynamic properties (e.g., enthalpy and entropy) of the relevant vaporization reaction in a two-phase (liquid, vapor) system determined from the results of evaporation experiments. Therefore, $T_{e,i}^f$ can be seen as a direct approach to quantify elemental volatility during evaporation. For most volatile elements such as Na, K, Rb and Zn, $T_{e,i}^f$ from a ferrobasaltic melt correlates with $T_c^{50}$, because these elements tend to condense into silicate minerals (Sossi et al., 2019). However, $T_{e,i}^f$ of In is not consistent with the correlation defined by other elements (Fig. 5), which shows that In is relatively less volatile compared to that which would be expected from its nebular condensation temperature. This observation confirms that the relative volatility of In in the vapor-melt system, an analogue of molten silicate mantles, is significantly lower than its volatility at nebular conditions, as also proposed by Norris and Wood (2017). These authors argued that the predominant gas species of In in the solar nebula is InCl⁰, given the CI chondritic abundances of Clay et al. (2017), allowing it to remain in the gas phase until Cl condenses ($T_c^{50} \sim 470$ K). This destabilizes InCl⁰, promoting its condensation into troilite as InS at the same temperature. Sossi and Fegley (2018), using the CI chondrite abundances of Lodders (2003), determine In⁰ as the prevailing gas species, but also obtain similar condensation temperatures. Nevertheless, the fact that In condenses into sulfide from the solar nebula, as opposed to silicate melt for planetary evaporation, leads to the large discrepancy between $T_c^{50}$ and $T_e$ (see also Sossi et al. (2019)).

In contrast to other highly volatile elements, whose $T_c^{50} < 500$ K, the evaporation temperature of In ($T_{e,In}^{1,-10} = 1578 \pm 15$ K; $T_{e,In}^{1,-5} = 1841 \pm 29$ K) is higher than Zn ($T_{e,Zn}^{1,-10} = 1466 \pm 8$ K; $T_{e,Zn}^{1,-5} = 1679 \pm 2$ K) whose $T_c^{50} = 704$ K (Wood et al., 2019). Therefore, the CI-, Mg-normalized abundance of In in the BSE may be expected to approach that of Zn, should planetary evaporation have been the
predominant cause of volatile depletion. Indeed, their CI-, Mg-normalized abundances in the BSE are observed to be similar, where ~ 0.070 for Zn, ~ 0.066 or 0.1 for In, depending on different estimations (Witt-Eickschen et al., 2009; Palme and O'Neill, 2014; Wang et al., 2016). Nevertheless, as In is a siderophile element, core formation on differentiated bodies should be considered when calculating the In budget in bulk planetary bodies (i.e., core + mantle). The influence of core-formation on the compositions of both the Earth and small differentiated planetary bodies (Moon and Vesta) is discussed below.

## 4.2 The origin of overabundance of In in the BSE

The overabundance of In in the BSE was attributed to a heterogeneous accretion model of the Earth (e.g., Braukmüller et al., 2019). This model proposes that the Earth was accreted primarily from volatile depleted materials, followed by the delivery of volatile-rich materials whose MVEs are present in CI-chondritic relative abundances during the last 10-20 % accretion of Earth's mass before core formation ceased (e.g., Wänke et al., 1984; Rubie et al. 2011). This hypothesis finds support in previous studies on MVEs and their isotopes, including Ag (Schönbächler et al., 2010), Cu (Savage et al., 2015; Mahan et al., 2018a), S (Suer et al., 2017), Zn (Mahan et al., 2018b), and Sn (Kubik et al., 2021). However, whether these late-added volatile-rich materials are the sufficient sources to explain the whole Earth's In budget, or in other words, whether the early accreted materials still carry a considerable amount of In, require further discussion.

The late added volatile-rich materials are suggested to have a CI-like constant-abundance plateau for elements with $T_c^{50} < 750$ K such as In, Zn and Cd (Braukmüller et al., 2019). In this case, assuming the entire budget for these 'plateau-abundance' elements in the Earth brought by these late-accreted materials, given the on-going core-formation process, their relative abundance in the BSE should follow the order of their partition coefficients (D) between core and mantle. The partition coefficients between core-forming metal and the overlying molten
silicate mantle are primarily affected by P-T, fO₂, and abundances of light elements in the metallic phase. Metal-silicate equilibration experiments reveal that In generally has a higher tendency to partition into the metallic phase than do Zn and Cd (DIn > DCd >DZn) regardless of temperature and pressure conditions (Mann et al., 2009; Ballhaus et al., 2013; Wood et al., 2014; Wang et al., 2016; Righter et al., 2017; Righter et al., 2018). However, this observation is inconsistent with the CI, -Mg normalized abundances of In, Zn and Cd in BSE, where In is present at levels similar to Zn, and higher than Cd (e.g., Palme and O'Neill., 2014). Although the presence of light elements like S and Si can play a role on the partitioning coefficient, they should not result in In becoming less siderophile than Cd and Zn, given the current estimation of the S content of Earth's core (~2 wt.%, Dreibus and Palme, 1996; Suer et al., 2017) and Si (~2 to 10 wt.%, Malavergne et al., 2004; Siebert et al., 2013; Badro et al., 2015; Rubie et al., 2015; for further discussion see Supplementary materials, Fig. S4 and S5). In order to accommodate these observations, the precursor materials of the proto-Earth are required to have higher CI-, Mg normalized abundance of In than Cd, thereby counteracting the greater depletion of In expected during core formation. To achieve this, In must have behaved in less volatile manner than Cd, as observed in our evaporation experiments on silicate melt.

Here, and in the previous study of Norris and Wood. (2017), we find that In is less volatile than Zn (see Fig. 3 and Fig. 5) and Cd during silicate melt evaporation. However, Cd was observed to be too volatile to have measurable content in most of the samples in Sossi et al. (2019), making it impossible to assess its 1% evaporation temperature from their experiments alone. This contrasts with the higher volatility of In than Zn and Cd during nebular condensation (e.g., Wood et al., 2019). Using the Te¹ volatility scale calibrated in our study, the BSE abundance of In now falls below the volatility trend defined by other MVEs (Fig. 6), meaning it is no longer overabundant in the BSE. This observation permits the additional loss of In to the core during its formation, and suggests In depletion occurred on building blocks of the Earth (i.e., precursor materials of proto-Earth) were set by silicate melt evaporation rather than nebular condensation. Additionally, enrichments in the heavier isotopes of
Si (Pringle et al., 2014; Moynier et al., 2020), Fe (Sossi et al. 2016) and Mg (Hin et al., 2017) in the Earth relative to chondrites are also taken as evidence for evaporation-induced volatile loss on the precursor materials of the Earth. Therefore, the In budget in the Earth would be suggested as a mixture of i) late added volatile-rich materials and ii) precursor materials of the proto-Earth with considerable quantities of In owing to its limited volatile depletion under non-nebular conditions.

The In isotopic compositions of Earth and chondrites will be a useful test to the various scenarios as discussed above. If Earth's In budget is derived from late-added chondritic materials or non-vaporized precursors, the In isotopic composition of the Earth should be similar to those of chondrites. Alternatively, if the precursor materials experienced partial evaporation, the In isotope composition of the Earth would be expected to record these event(s). However, the isotopic fractionation reflects the physical-chemical conditions under which evaporation occurred, namely, the total pressure, gas composition/density and species of evaporated gas, which can suppress the extent of fractionation, and possibly result in insignificant isotopic fractionation (e.g., Young et al., 2019; Sossi et al., 2020). Furthermore, given the siderophile behavior of In, isotope fractionation during metal-silicate segregation also requires consideration when estimating the isotopic composition of In of the bulk Earth. Future studies of In isotopic compositions of terrestrial samples and chondrites, and isotope fractionation during metal-silicate partitioning are required.

## 4.3 Moon and Vesta: implications for smaller differentiated bodies

Atmospheric loss is most likely to occur during the early stages of accretion of the proto-Earth, after which Earth's gravity field is sufficiently large to prevent the effective loss of volatile components. These chemical and isotopic signatures of evaporation during early-stage accretion could be entirely or partially overprinted by late-added volatile-rich materials. By contrast, partial evaporation is more likely to generate volatile depletion among smaller telluric bodies with lower masses and escape velocities (cf. Pringle et al. 2014; Hin et al. 2017; Young et al. 2019; Benedikt
et al. 2020, Sossi et al., 2022). In support of this assertion, smaller bodies show evidence of post-nebular volatile depletion. Most notably, the Mn/Na ratios of Mars, the Moon, Vesta and angrite parent bodies are higher than chondritic values (O'Neill and Palme, 2008; Siebert et al., 2018). Isotopic evidence from MVEs also supports that planetary volatilization is the dominant mechanism for volatile depletion. Moderately volatile elements in lunar samples, like Zn (Kato et al., 2015; Paniello et al., 2012a; Van Kooten et al., 2020), Ga (Kato and Moynier, 2017, Wimpenny et al., 2022), Rb (Pringle and Moynier, 2017; Nie and Dauphas, 2019), and K (Wang and Jacobsen, 2016; Tian et al., 2020) are enriched in the heavier isotopes, which indicate volatile loss by an evaporation process. A similar trend of heavy isotope enrichment is found for other volatile depleted bodies (e.g., Vesta and the angrite parent body) (Paniello et al., 2012b; Wang et al., 2012; Pringle et al., 2014; Pringle and Moynier, 2017).

Evaporation that caused the depletion in MVEs of small bodies likely occurred under a vapor-liquid environment, because mass transport in the solid-state is too slow relative to atmospheric cooling timescales to cause wholescale depletion of rocky bodies (e.g., Bower et al. 2019). In these settings, the evaporation temperature is likely a more relevant scale of element volatilities than is the $T_c^{50}$. The abundances of lithophile elements in the Moon correlate well ($R^2 = 0.94$) with their respective evaporation temperatures (Fig. 7). Furthermore, assuming the Moon was formed from a BSE-like precursor (e.g., Ringwood, 1986), the BSE-Mg normalized abundance of In in the bulk silicate Moon (BSM) falls slightly below the volatile depletion trend defined by other lithophile MVEs, which implies limited In partitioning into the small lunar core. This conclusion is in agreement with the volatilities of MVEs calculated by Gibbs Free Energy minimization incorporating activity coefficients of metal oxide species into a BSE-like silicate melt in *FactSage* (Ivanov et al. 2022). These authors argue that the chemical signature of the Moon may have been inherited from two distinct stages of condensation at both high (~4000 K) and low (~2000 K), each time at pressures higher (>0.1 bar) and oxygen fugacities (~near the Fayalite-Magnetite-Quartz buffer) significantly higher than those in the solar nebula.
Although these authors did not consider In in their calculations, this scenario is
broadly consistent with the physicochemical conditions proposed here.

The amount of In that resides in the lunar core can be estimated from published
metal-silicate experiment data. Righter et al. (2017) estimated 1 ppb In in the lunar
mantle and 4.5 ppb In in the bulk Moon using a remarkably high D<sub>ln</sub> of ~ 200
determined in their experiments. This D value is more than an order of magnitude
higher than other reported values under similar P-T-fO<sub>2</sub> conditions (e.g., Mann et al.,
2009; Wood et al., 2014; Ballhaus et al., 2013). Mann et al. (2009) obtained D<sub>ln</sub> of 11
to 15 under 2 GPa and ~ 2000 K, ΔIW -1.5, similar to the D<sub>ln</sub> of 3~12 reported by
Ballhaus et al. (2013) under 1.5 GPa, 1800 ~ 2100 K and ΔIW -1.5 ~ -2.1. These P-T
conditions are comparable to those estimated for lunar core formation (~ 5 GPa, 2200
K and ΔIW-2; Rai and van Westrenen, 2014), and the median value of reported D<sub>ln</sub> of
~12 (Mann et al., 2009; Ballhaus et al. 2013) is used here to estimate In concentration
in lunar core. An earlier estimate by O'Neill (1991) suggests that the bulk Moon
contains 0.4 ppb In, based on the assumption of a volatile-free proto-Moon acquired
its volatile inventory by ~ 4 wt.% H-chondrite late veneer. This estimate is slightly
lower than the In concentration of 1.6 ppb estimated from lunar volcanic glass (Hauri
et al., 2015). Assuming that the BSM with 1.6 ppb In (Hauri et al., 2015) is
homogeneously and fully equilibrated with the lunar core that accounts for 1.5% of
the Moon's mass (Weber et al., 2011), the In abundance of the bulk Moon is
calculated to be 1.9 ppb. This means that BSM is the dominant reservoir of In.

The mantle of Vesta is known to be depleted in MVEs (Mittlefehldt, 2015;
Steenstra et al., 2019), yet the origin of this depletion is still poorly understood. The
super-chondritic Mn/Na ratio of HED meteorites implies that evaporative loss may
have occurred under non-nebular conditions. The isotopically light Cr in eucrites also
suggests evaporation of Cr under relatively high fO₂, possibly during a magma ocean
(Zhu et al., 2019). The CI-Mg normalized abundances of MVEs, particularly of In and
Zn, in the Vestan mantle also correlate well with the evaporation temperature (Fig. 7).
The smooth decrease in MVE abundance with evaporation temperature observed for
the Moon and Vesta strongly supports an evaporation-induced volatile depletion, and
suggests that $T_e^1$ is a more suitable volatility scale for thermodynamic processes occurring in a post-nebular environment.

The significantly different volatility of In under nebular and non-nebular conditions makes the In/Zn ratio an useful indicator of the conditions under which MVE depletion of a planetary body occurred. Under nebular conditions, In is more volatile than Zn ($T_c^{50}$ of In < $T_c^{50}$ of Zn), and thus volatile-depleted materials would be characterized by In/Zn < 1. Under non-nebular conditions, In becomes less volatile than Zn ($T_e^1$ of In > $T_e^1$ of Zn), and planetary evaporation should give rise to residues with In/Zn ≥ 1. Therefore, the observed higher relative abundance of In than Zn in the lunar and Vestan mantle indicates a non-nebular origin of their MVEs (Fig.7). The isotopic composition of In in differentiated and undifferentiated meteorites should also shed light on whether partial evaporation or condensation was associated with volatile loss, and if so, under what conditions. Hence, future studies of the In isotope composition of achondritic meteorites is required.

## 5. Conclusion

Indium is both a siderophile and a volatile element in a cosmochemical context. However, when considering its $T_c^{50}$, it is overabundant in the BSE compared to other MVEs. Here we show that the $T_c^{50}$ is not suitable for assessing elemental volatility for evaporation processes that occurred under oxidizing planetary conditions and that a new scale is required. In this study, we have performed a series of evaporation experiments and calculated the evaporation temperature of In ($T_{e,l}^{1,-10}$ =1578 ± 15 K) using the empirically theoretical framework developed in Sossi et al. (2019). This evaporation temperature indicates a significantly lower relative volatility of In with respect to other MVEs compared to the 50% condensation temperature scale. Our results suggest that the volatile depletion of small bodies, like the Moon and Vesta, were controlled by volatilization processes under more oxidizing conditions than the solar nebula. Combining published partitioning data (with the limitation that all experiments were performed at pressure
conditions lower than that relevant to Earth's core formation), we suggest that the present Earth's In budget consists of two components, the considerable amount of In carried by the early precursor materials and the subsequent complement from CI-like materials during late-accretion stage.

## Acknowledgements

D. L. thanks the China Scholarship Council (CSC) for a PhD fellowship. D.L appreciate Pierre Burckel for the analysis on ICP-MS at IPGP. D.L and J.S thank

Daniel R. Neuville for the synthesis of starting materials at IPGP. D.L thanks Nicolas Wehr for the technique assistance on evaporation experiments.

## References

Albarede, F. (2009). "Volatile accretion history of the terrestrial planets and dynamic implications." *Nature* **461**(7268): 1227-1233.

Allibert, L., Charnoz, S., Siebert, J., Jacobson, S.A. and Raymond, S.N. (2021) Quantitative estimates of impact induced crustal erosion during accretion and its influence on the Sm/Nd ratio of the Earth. *Icarus* 363, 114412.

Armytage, R., Georg, R., Williams, H. and Halliday, A. (2012) Silicon isotopes in lunar rocks: Implications for the Moon's formation and the early history of the Earth. *Geochimica et Cosmochimica Acta* 77, 504-514.

Badro, J., Brodholt, J.P., Piet, H., Siebert, J. and Ryerson, F.J. (2015) Core formation and core composition from coupled geochemical and geophysical constraints. *Proceedings of the National Academy of Sciences* 112, 12310-12314.

Ballhaus, C., Laurenz, V., Münker, C., Fonseca, R.O.C., Albarède, F., Rohrbach, A., Lagos, M., Schmidt, M.W., Jochum, K.-P., Stoll, B., Weis, U. and Helmy, H.M. (2013) The U/Pb ratio of the Earth's mantle—A signature of late volatile addition. *Earth and Planetary Science Letters* 362, 237-245.

Barin, I. and Platzki, G. (1989) Thermochemical data of pure substances. *Wiley Online Library*.

Benedikt, M., Scherf, M., Lammer, H., Marcq, E., Odert, P., Leitzinger, M. and Erkaev, N.V. (2020) Escape of rock-forming volatile elements and noble gases from planetary embryos. *Icarus* 347, 113772.
702 Bower, D.J., Kitzmann, D., Wolf, A.S., Sanan, P., Dorn, C. and Oza, A.V. (2019)
703 Linking the evolution of terrestrial interiors and an early outgassed atmosphere to
704 astrophysical observations. Astronomy & Astrophysics 631, A103.

705 Braukmüller, N., Wombacher, F., Funk, C. and Münker, C. (2019) Earth's volatile
706 element depletion pattern inherited from a carbonaceous chondrite-like source.
707 Nature Geoscience 12, 564-568.

708 Canup, R.M., Visscher, C., Salmon, J. and Fegley Jr, B. (2015) Lunar volatile
709 depletion due to incomplete accretion within an impact-generated disk. Nature
710 geoscience 8, 918-921.

711 Chakraborty, S. (2018) Diffusion in silicate melts. Structure, Dynamics, and
712 Properties of Silicate Melts, 411-504.

713 Clay, P.L., Burgess, R., Busemann, H., Ruzié-Hamilton, L., Joachim, B., Day, J.M.
714 and Ballentine, C.J. (2017) Halogens in chondritic meteorites and terrestrial
715 accretion. Nature 551, 614-618.

716 Corgne, A., Keshav, S., Wood, B.J., McDonough, W.F. and Fei, Y. (2008) Metal-
717 silicate partitioning and constraints on core composition and oxygen fugacity
718 during Earth accretion. Geochimica et Cosmochimica Acta 72, 574-589.

719 Darken, L.S. and Gurry, R. (1945) The system iron-oxygen. I. The wüstite field and
720 related equilibria. Journal of the American Chemical Society 67, 1398-1412.

721 Day, J.M. and Moynier, F. (2014) Evaporative fractionation of volatile stable isotopes
722 and their bearing on the origin of the Moon. Philosophical Transactions of the
723 Royal Society of London A: Mathematical, Physical and Engineering Sciences
724 372, 20130259.

725 Dreibus, G. and Palme, H. (1996) Cosmochemical constraints on the sulfur content in
726 the Earth's core. Geochimica et Cosmochimica Acta 60, 1125-1130.

727 Gaillard, F. and Scaillet, B. (2014) A theoretical framework for volcanic degassing
728 chemistry in a comparative planetology perspective and implications for planetary
729 atmospheres. Earth and Planetary Science Letters 403, 307-316.

730 Grundy, A.N., Jung, I.-H., Pelton, A.D. and Decterov, S.A. (2008) A model to
731 calculate the viscosity of silicate melts. International Journal of Materials
732 Research 99, 1195-1209.

733 Hauri, E.H., Saal, A.E., Rutherford, M.J. and Van Orman, J.A. (2015) Water in the
734 Moon's interior: Truth and consequences. Earth and Planetary Science Letters 409,
735 252-264.

736 Hertz, H. (1882) Ueber die Verdunstung der Flüssigkeiten, insbesondere des
737 Quecksilbers, im luftleeren Raume. Annalen der Physik 253, 177-193.

738 Hin, R.C., Coath, C.D., Carter, P.J., Nimmo, F., Lai, Y.-J., Pogge von Strandmann,
739 P.A.E., Willbold, M., Leinhardt, Z.M., Walter, M.J. and Elliott, T. (2017)
740 Magnesium isotope evidence that accretional vapour loss shapes planetary
741 compositions. Nature 549, 511-515.

742 Holzheid, A., H. Palme and S. Chakraborty (1997). "The activities of NiO, CoO and
743 FeO in silicate melts." *Chemical Geology* **139**(1-4): 21-38.

744 Ivanov, D., Fitoussi, C. and Bourdon, B. (2022) Trace element volatility and the
745 conditions of liquid-vapor separation in the proto-lunar disk. *Icarus* 386, 115143.

746 Kato, C. and Moynier, F. (2017) Gallium isotopic evidence for extensive volatile loss
747 from the Moon during its formation. *Science advances* 3, e1700571.

748 Kato, C., Moynier, F., Valdes, M.C., Dhaliwal, J.K. and Day, J.M.D. (2015) Extensive
749 volatile loss during formation and differentiation of the Moon. *Nature*
750 Communications 6, 7617.

751 Kilburn, M. and Wood, B. (1997) Metal-silicate partitioning and the incompatibility
752 of S and Si during core formation. *Earth and Planetary Science Letters* 152,
753 139-148.

754 Knudsen, M. (1909) Die Gesetze der Molekularströmung und der inneren
755 Reibungsströmung der Gase durch Röhren. *Annalen der Physik* 333, 75-130.

756 Kubik, E., Siebert, J., Mahan, B., Creech, J., Blanchard, I., Agranier, A., Shcheka, S.
757 and Moynier, F. (2021) Tracing Earth's Volatile Delivery With Tin. *Journal of
758 Geophysical Research: Solid Earth* 126, e2021JB022026.

759 Labidi, J., Cartigny, P. and Moreira, M. (2013) Non-chondritic sulphur isotope
760 composition of the terrestrial mantle. *Nature* 501, 208.

761 Lamoreaux, R.H., Hildenbrand, D.L. and Brewer, L. (1987) High-Temperature
762 Vaporization Behavior of Oxides II. Oxides of Be, Mg, Ca, Sr, Ba, B, Al, Ga, In,
763 Tl, Si, Ge, Sn, Pb, Zn, Cd, and Hg. *Journal of Physical and Chemical Reference
764 Data* 16, 419-443.

765 Langmuir, I. (1916) The Evaporation, Condensation and Reflection of Molecules and
766 the Mechanism of Adsorption. *Physical Review* 8, 149-176.

767 Larimer, J.W. (1967) Chemical fractionations in meteorites—I. Condensation of the
768 elements. *Geochimica et Cosmochimica Acta* 31, 1215-1238.

769 Lodders, K. (2003) Solar system abundances and condensation temperatures of the
770 elements. *The Astrophysical Journal* 591, 1220.

771 Mann, U., Frost, D.J. and Rubie, D.C. (2009) Evidence for high-pressure core-mantle
772 differentiation from the metal-silicate partitioning of lithophile and
773 weakly-siderophile elements. *Geochimica Et Cosmochimica Acta* 73, 7360-7386.

774 Mahan, B., Siebert, J., Blanchard, I., Badro, J., Kubik, E., Sossi, P. and Moynier, F.
775 (2018a) Investigating Earth's Formation History Through Copper and Sulfur
776 Metal-Silicate Partitioning During Core-Mantle Differentiation. *Journal of
777 Geophysical Research-Solid Earth* 123, 8349-8363.

778 Mahan, B., Siebert, J., Blanchard, I., Borensztajn, S., Badro, J. and Moynier, F.
779 (2018b) Constraining compositional proxies for Earth's accretion and core
780 formation through high pressure and high temperature Zn and S metal-silicate
781 partitioning. Geochimica et Cosmochimica Acta 235, 21-40.

782 Malavergne, V., Siebert, J., Guyot, F., Gautron, L., Combes, R., Hammouda, T.,
783 Borensztajn, S., Frost, D. and Martinez, I. (2004) Si in the core? New
784 high-pressure and high-temperature experimental data. Geochimica et
785 Cosmochimica Acta 68, 4201-4211.

786 Mittlefehldt, David W. "Asteroid (4) Vesta: I. The howardite-eucrite-diogenite (HED) 787 clan of meteorites." Geochemistry 75.2 (2015): 155-183.

788 Morbidelli, A., Libourel, G., Palme, H., Jacobson, S.A. and Rubie, D.C. (2020)
789 Subsolar Al/Si and Mg/Si ratios of non-carbonaceous chondrites reveal
790 planetesimal formation during early condensation in the protoplanetary disk. Earth
791 and Planetary Science Letters 538, 116220.

792 Moynier, F., Deng, Z., Lanteri, A., Martins, R., Chaussidon, M., Savage, P. and
793 Siebert, J. (2020) Metal-silicate silicon isotopic fractionation and the composition
794 of the bulk Earth. Earth and Planetary Science Letters 549, 116468.

795 Nebel, O., Mezger, K. and van Westrenen, W. (2011) Rubidium isotopes in primitive
796 chondrites: Constraints on Earth's volatile element depletion and lead isotope
797 evolution. Earth and Planetary Science Letters 305, 309-316.

798 Nie, N.X. and Dauphas, N. (2019) Vapor Drainage in the Protolunar Disk as the
799 Cause for the Depletion in Volatile Elements of the Moon. The Astrophysical
800 Journal Letters 884, L48

801 Norris, C.A. and Wood, B.J. (2017) Earth's volatile contents established by melting
802 and vaporization. Nature 549, 507.

803 Okamoto, H. (1990) The Fe-In (Iron-Indium) system. Bulletin of Alloy Phase
804 Diagrams 11, 143-146.

805 O'Neill, H.S.C. (1991) The origin of the Moon and the early history of the Earth—A
806 chemical model. Part 2: The Earth. Geochimica et Cosmochimica Acta 55,
807 1159-1172.

808 O'Neill, H. S. C. and S. M. Eggins (2002). The effect of melt composition on trace
809 element partitioning: an experimental investigation of the activity coefficients of
810 FeO, NiO, CoO, MoO₂ and MoO₃ in silicate melts. Chemical Geology 186(1-2):
811 151-181.

812 O'Neill, H.S.C. and Palme, H. (2008) Collisional erosion and the non-chondritic
813 composition of the terrestrial planets. Philosophical Transactions of the Royal
814 Society A: Mathematical, Physical and Engineering Sciences 366, 4205-4238.

815 Palme, H., Larimer, J. and Lipschutz, M. (1988) Moderately volatile elements.
816 Meteorites and the early solar system, 436-461.

817 Palme, H. and O'Neill, H. (2014) Cosmochemical Estimates of Mantle Composition.
818 Planets, Asteriods, Comets and The Solar System, Volume 2 of Treatise on
819 Geochemistry. Edited by Andrew M. Davis. Elsevier.

820 Paniello, R.C., Day, J.M. and Moynier, F. (2012a) Zinc isotopic evidence for the
821 origin of the Moon. Nature 490, 376-379.

822 Paniello, R.C., Moynier, F., Beck, P., Barrat, J.-A., Podosek, F.A. and Pichat, S.
823 (2012b) Zinc isotopes in HEDs: Clues to the formation of 4-Vesta, and the unique
824 composition of Pecora Escarpment 82502. Geochimica et Cosmochimica Acta 86,
825 76-87.

826 Persad, A.H. and Ward, C.A. (2016) Expressions for the Evaporation and
827 Condensation Coefficients in the Hertz-Knudsen Relation. Chemical Reviews 116,
828 7727-7767.

829 Pringle, E.A. and Moynier, F. (2017) Rubidium isotopic composition of the Earth,
830 meteorites, and the Moon: Evidence for the origin of volatile loss during planetary
831 accretion. Earth and Planetary Science Letters 473, 62-70.

832 Pringle, E.A., Moynier, F., Savage, P.S., Badro, J. and Barrat, J.-A. (2014) Silicon
833 isotopes in angrites and volatile loss in planetesimals. Proceedings of the National
834 Academy of Sciences 111, 17029-17032.

835 Rai, N. and van Westrenen, W. (2014) Lunar core formation: New constraints from
836 metal-silicate partitioning of siderophile elements. Earth and Planetary Science
837 Letters 388, 343-352.

838 Reyes, R. and Gaskell, D. (1983) The thermodynamic activity of ZnO in silicate melts.
839 Metallurgical Transactions B 14, 725-731.

840 Richter, F.M., Davis, A.M., Ebel, D.S. and Hashimoto, A. (2002) Elemental and
841 isotopic fractionation of Type B calcium-, aluminum-rich inclusions: experiments,
842 theoretical considerations, and constraints on their thermal evolution. Geochimica
843 et Cosmochimica Acta 66, 521-540.

844 Ricolleau, A., Fei, Y.W., Corgne, A., Siebert, J. and Badro, J. (2011) Oxygen and
845 silicon contents of Earth's core from high pressure metal-silicate partitioning
846 experiments. Earth and Planetary Science Letters 310, 409-421.

847 Righter, K., Nickodem, K., Pando, K., Danielson, L., Boujibar, A., Righter, M. and
848 Lapen, T. (2017) Distribution of Sb, As, Ge, and In between metal and silicate
849 during accretion and core formation in the Earth. Geochimica et Cosmochimica
850 Acta 198, 1-16.

851 Righter, K., Pando, K., Marin, N., Ross, D., Righter, M., Danielson, L., Lapen, T. and
852 Lee, C. (2018) Volatile element signatures in the mantles of Earth, Moon, and
853 Mars: Core formation fingerprints from Bi, Cd, In, and Sn. Meteorit. Planet. Sci.
854 53, 284-305.

855 Ringwood, A. (1986) Terrestrial origin of the Moon. Nature 322, 323-328.

856 Rubie, D.C., Frost, D.J., Mann, U., Asahara, Y., Nimmo, F., Tsuno, K., Kegler, P.,
857 Holzheid, A. and Palme, H., (2011). Heterogeneous accretion, composition and
858 core-mantle differentiation of the Earth. Earth and Planetary Science Letters,
859 301(1-2), pp.31-42.

860 Rubie, D.C., Jacobson, S.A., Morbidelli, A., O'Brien, D.P., Young, E.D., de Vries, J.,
861 Nimmo, F., Palme, H. and Frost, D.J. (2015) Accretion and differentiation of the
862 terrestrial planets with implications for the compositions of early-formed Solar
863 System bodies and accretion of water. Icarus 248, 89-108.

864 Sarafian, A.R., John, T., Roszjar, J. and Whitehouse, M.J. (2017) Chlorine and
865 hydrogen degassing in Vesta's magma ocean. Earth and Planetary Science Letters
866 459, 311-319.

867 Savage, P.S., Moynier, F., Chen, H., Shofner, G., Siebert, J., Badro, J. and Puchtel, I.S.
868 (2015) Copper isotope evidence for large-scale sulphide fractionation during
869 Earth's differentiation. Geochem. Perspect. Lett. 1, 53-63.

870 Schönbächler, M., Carlson, R., Horan, M., Mock, T. and Hauri, E. (2010)
871 Heterogeneous accretion and the moderately volatile element budget of Earth.
872 Science 328, 884-887.

873 Siebert, J., Badro, J., Antonangeli, D. and Ryerson, F.J. (2013) Terrestrial accretion
874 under oxidizing conditions. Science, 1227923.

875 Siebert, J. and Shahar, A. (2015) An Experimental Geochemistry Perspective on
876 Earth's Core Formation. The Early Earth: Accretion and Differentiation 212,
877 103-121.

878 Siebert, J., Sossi, P.A., Blanchard, I., Mahan, B., Badro, J. and Moynier, F. (2018)
879 Chondritic Mn/Na ratio and limited post-nebular volatile loss of the Earth. Earth
880 and Planetary Science Letters 485, 130-139.

881 Sossi, P.A. and Fegley Jr, B. (2018) Thermodynamics of element volatility and its
882 application to planetary processes. Reviews in Mineralogy and Geochemistry 84,
883 393-459.

884 Sossi, P.A., Klemme, S., O'Neill, H.S.C., Berndt, J. and Moynier, F. (2019)
885 Evaporation of moderately volatile elements from silicate melts: Experiments and
886 theory. Geochimica et Cosmochimica Acta. 260, 204-231.

887 Sossi, P.A., Nebel, O. and Foden, J. (2016) Iron isotope systematics in planetary
888 reservoirs. Earth and Planetary Science Letters 452, 295-308.

889 Sossi, P.A., Nebel, O., O'Neill, H.S.C. and Moynier, F. (2018) Zinc isotope
890 composition of the Earth and its behaviour during planetary accretion. Chem.
891 Geol. 477, 73-84.

892 Sossi, P.A., Stotz, I.L., Jacobson, S.A., Morbidelli, A. and O'Neill, H.S.C. (2022)
893 Stochastic accretion of the Earth. Nature Astronomy, 1-10.

894 Steenstra, E., Rai, N., Knibbe, J., Lin, Y. and van Westrenen, W. (2016) New
895 geochemical models of core formation in the Moon from metal-silicate
896 partitioning of 15 siderophile elements. Earth and Planetary Science Letters 441,
897 1-9.

898 Steenstra, E.S., Dankers, D., Berndt, J., Klemme, S., Matveev, S. and van Westrenen, 899 W. (2019) Significant depletion of volatile elements in the mantle of asteroid 900 Vesta due to core formation. Icarus 317, 669-681.

901 Steenstra, E.S., Seegers, A.X., Putter, R., Berndt, J., Klemme, S., Matveev, S., 902 Bullock, E.S. and van Westrenen, W. (2020) Metal-silicate partitioning 903 systematics of siderophile elements at reducing conditions: A new experimental 904 database. Icarus 335, 113391.

905 Suer, T.-A., Siebert, J., Remusat, L., Menguy, N. and Fiquet, G. (2017) A sulfur-poor 906 terrestrial core inferred from metal-silicate partitioning experiments. Earth and 907 Planetary Science Letters 469, 84-97.

908 Taylor, G.J. (2013) The bulk composition of Mars. Geochemistry 73, 401-420.

909 Tartèse, R., Sossi, P.A. and Moynier, F. (2021) Conditions and extent of volatile loss 910 from the Moon during formation of the Procellarum basin. Proceedings of the 911 National Academy of Sciences 118.

912 Tian, Z., Jolliff, B.L., Korotev, R.L., Fegley Jr, B., Lodders, K., Day, J.M., Chen, H. 913 and Wang, K. (2020) Potassium isotopic composition of the Moon. Geochimica et 914 Cosmochimica Acta 280, 263-280.

915 Van Kooten, E.M., Moynier, F. and Day, J.M. (2020) Evidence for transient 916 atmospheres during eruptive outgassing on the Moon. The Planetary Science 917 Journal 1, 67.

918 Visscher, C. and Fegley Jr, B. (2013) Chemistry of impact-generated silicate 919 melt-vapor debris disks. The Astrophysical Journal Letters 767, L12.

920 Vollstaedt, H., Mezger, K. and Alibert, Y. (2020) Carbonaceous Chondrites and the 921 Condensation of Elements from the Solar Nebula. The Astrophysical Journal 897, 922 82.

923 Wade, J. and Wood, B. (2005) Core formation and the oxidation state of the Earth. 924 Earth and Planetary Science Letters 236, 78-95.

925 Wang, K., Moynier, F., Dauphas, N., Barrat, J.-A., Craddock, P. and Sio, C.K. (2012) 926 Iron isotope fractionation in planetary crusts. Geochimica et Cosmochimica Acta 927 89, 31-45.

928 Wang, K. and Jacobsen, S.B. (2016) Potassium isotopic evidence for a high-energy 929 giant impact origin of the Moon. Nature 538, 487-490.

930 Wang, Z. and Becker, H. (2013) Ratios of S, Se and Te in the silicate Earth require a 931 volatile-rich late veneer. Nature 499, 328.

932 Wang, Z., Laurenz, V., Petitgirard, S. and Becker, H. (2016) Earth's moderately 933 volatile element composition may not be chondritic: Evidence from In, Cd and Zn. 934 Earth and Planetary Science Letters 435, 136-146.

935 Wänke, H., G. Dreibus, and E. Jagoutz. "Mantle chemistry and accretion history of
936 the Earth." In Archaean geochemistry, pp. 1-24. Springer, Berlin, Heidelberg,
937 1984.

938 Weber, R.C., Lin, P.-Y., Garnero, E.J., Williams, Q. and Lognonné, P. (2011) Seismic
939 detection of the lunar core. science 331, 309-312.

940 Wood, B.J., Kiseeva, E.S. and Mirolo, F.J. (2014) Accretion and core formation: The
941 effects of sulfur on metal-silicate partition coefficients. Geochimica et
942 Cosmochimica Acta 145, 248-267.

943 Wimpenny, J., Borg, L. and Sio, C.K.I. (2022) The gallium isotopic composition of
944 the Moon. Earth and Planetary Science Letters 578, 117318.

945 Witt-Eickschen, G., Palme, H., O'neill, H.S.C. and Allen, C.M. (2009) The
946 geochemistry of the volatile trace elements As, Cd, Ga, In and Sn in the Earth's
947 mantle: new evidence from in situ analyses of mantle xenoliths. Geochimica et
948 Cosmochimica Acta 73, 1755-1778.

949 Wood, B.J. and Wade, J. (2013) Activities and volatilities of trace components in
950 silicate melts: a novel use of metal-silicate partitioning data. Contributions to
951 Mineralogy and Petrology 166, 911-921.

952 Wood, B.J., Smythe, D.J. and Harrison, T. (2019) The condensation temperatures of
953 the elements: A reappraisal. American Mineralogist 104, 844-856.

954 Yi, W., Halliday, A.N., Alt, J.C., Lee, D.C., Rehkämper, M., Garcia, M.O., Langmuir,
955 C. and Su, Y. (2000) Cadmium, indium, tin, tellurium, and sulfur in oceanic
956 basalts: Implications for chalcophile element fractionation in the Earth. Journal of
957 Geophysical Research: Solid Earth 105, 18927-18948.

958 Young, E., Shahar, A., Nimmo, F., Schlichting, H., Schauble, E., Tang, H. and Labidi,
959 J. (2019) Near-equilibrium isotope fractionation during planetesimal evaporation.
960 Icarus 323, 1-15.

961 Zhang, Z.J., Nie, N.X., Mendybaev, R.A., Liu, M.-C., Hu, J.J., Hopp, T., Alp, E.E.,
962 Lavina, B., Bullock, E.S. and McKeegan, K.D. (2021) Loss and isotopic
963 fractionation of alkali elements during diffusion-limited evaporation from molten
964 silicate: Theory and experiments. ACS Earth and Space Chemistry 5, 755-784.

965 Zhu, K., Sossi, P.A., Siebert, J. and Moynier, F. (2019) Tracking the volatile and
966 magmatic history of Vesta from chromium stable isotope variations in eucrite and
967 diogenite meteorites. Geochimica et Cosmochimica Acta 266, 598-610.

968 Zhu, K., Moynier, F., Alexander, C.M.D., Davidson, J., Schrader, D.L., Zhu, J.-M.,
969 Wu, G.-L., Schiller, M., Bizzarro, M. and Becker, H. (2021) Chromium Stable
970 Isotope Panorama of Chondrites and Implications for Earth Early Accretion. The
971 Astrophysical Journal 923, 94.

972
<table><caption>**Table. 1** 50% condensation temperature and evaporation temperature of MVEs at variable fO₂.</caption><thead><tr><th>Element</th><th>T<sup>50</sup><sub>c</sub> (K)</th><th>T<sup>1,-10</sup><sub>e,i</sub> (K)</th><th>SD</th><th>T<sup>1,-5</sup><sub>e,i</sub> (K)</th><th>SD</th></tr></thead><tbody><tr><td>Ge</td><td>830</td><td>1469</td><td>12</td><td>1664</td><td>3</td></tr><tr><td>Zn</td><td>704</td><td>1466</td><td>8</td><td>1679</td><td>2</td></tr><tr><td>Rb</td><td>752</td><td>1594</td><td>15</td><td>1762</td><td>7</td></tr><tr><td>Cu</td><td>1034</td><td>1619</td><td>10</td><td>1892</td><td>22</td></tr><tr><td>K</td><td>993</td><td>1688</td><td></td><td>2091</td><td></td></tr><tr><td>Ga</td><td>1010</td><td>1741</td><td>1</td><td>2044</td><td>5</td></tr><tr><td>Na</td><td>1035</td><td>1752</td><td></td><td>2096</td><td></td></tr><tr><td>Li</td><td>1148</td><td>1888</td><td></td><td>2120</td><td></td></tr><tr><td>Cr*</td><td>1291</td><td>2155</td><td></td><td>2096</td><td></td></tr><tr><td>Mg*</td><td>1343</td><td>2090</td><td></td><td>2138</td><td></td></tr><tr><td>Mn*</td><td>1123</td><td>1974</td><td></td><td>2339</td><td></td></tr><tr><td>Fe*</td><td>1338</td><td>2033</td><td></td><td>2394</td><td></td></tr><tr><td>In</td><td>492</td><td>1578</td><td>15</td><td>1841</td><td>29</td></tr></tbody></table>

50% condensation temperature is taken from Wood et al. (2019).

Elements with '*' symbols, their evaporation temperature are calculated with the thermodynamic properties of pure oxide system. The evaporation temperature and uncertainties of the other elements is re-calculated from the thermodynamic data in

Sossi et al. (2019) with the assumption that $\frac{P_i}{P_i^{sat}} = 0.996$.
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Abundances of representative volatile and refractory elements in the BSE normalized to CI chondrites and Mg vs. $T_c^{50}$. Elemental abundance of BSE and CI chondrite from Palme and O'Neill. (2014) and references therein; The abundance of In is taken from the current estimate of Wang et al. (2016); $T_c^{50}$ from Wood et al. (2019). The refractory lithophile elements such as Ca, Ti, Sc, Zr and rare earth elements (REE) have higher $T_c^{50}$ than Mg, and exhibit a flat pattern. The lithophile volatile elements display a near log-linear depletion along with $T_c^{50}$. As both volatile and siderophile element, the abundance of In in the BSE is similar as Zn, which is lithophile element and $T_c^{50}$ is markedly higher than In (~200 K).</figcaption></figure>
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Fig.2** The relative stability of gas species InO (g) and In₂O (g) and In (g) are displayed as a function of log(fO₂) at 1673K and a) a(InO1.5) = 0.01; b) a(InO1.5) = 0.001; The thermodynamic data are taken from Lamoreaux et al. (1987). InO (g) is only stable at the most oxidizing condition (air condition). In₂O (g) is negligible at oxidizing conditions and can become more stable as decrease of fO₂. Moreover, In₂O (g) is proportional to a(InO1.5)² (Eq. 3.3), thus lower a(InO1.5) can decrease the relative stability of In₂O (g) significantly. Fig.2 c and d further take into account the equilibrium between gas phases (see discussion in section 3.4)</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 3** The fraction of In and Zn remaining in the sample gas is displayed as a function of $logf(O_2)$. Figures show the experiments performed for 30 min and 60 min at variable temperature (1300°C to 1500°C), respectively. Both In-series are fit by non-linear least squares approach according to the reactions: $InO1.5(l) = In(g) + 3/4O_2$ and $2InO1.5(l) = In_2O(g) + O_2$. Zn-series are fit according to reaction: $ZnO(l) = Zn(g) + 1/2 O_2$ (g). The modified equilibrium constants ($log(K^*)$) are marked in figures. The circle symbols represent the experiments performed on synthetic MORB mixture; the diamond symbols represent the experiments on synthetic FCMAS mixture. The square symbols in Zn-series are the data points from Sossi et al. (2019), plotted as an comparison, where 60 min points are directly taken from their dataset, 30 min points are calculated from their 15min data points with Eq.2.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 4** $\Delta G^*$ is plotted as a function of temperature. $\Delta A^*$ and $\Delta B^*$ can be calculated with Eq. 4.3, the regressed $\Delta A^* = 791 \pm 87$ kJ/mol; $\Delta B^* = 319 \pm 52$ J/mol. Substitute $\Delta A^*$ and $\Delta B^*$ into Eq. 4.1, the evaporation temperature can be estimated, $T_{e,In}^{-10} = 1578 \pm 15$ K; $T_{e,In}^{-5} = 1841 \pm 29$ K.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Fig. 5** The 1% evaporation temperature is plotted against 50% condensation temperature from Wood et al, (2019). The error bars are within the symbol size. The yellow cycles data is recalculated from Sossi et al. (2019), and provide in Table.1; In and Zn in this study is shown as green symbols. The results of Zn in this study have good consistency with previous Zn data in Sossi et al. (2019). The evaporation temperature and condensation temperature show a clear correlation for most of MVEs, while In is significantly higher than the trend which regressed by the other MVEs, which indicate In less volatile during evaporation of vapor-melt system.</figcaption></figure>
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 6.** The CI-Mg normalized elemental abundances in the BSE plot as a function of evaporation temperature and 50% condensation temperature, respectively. When using the new evaporation temperature scale, In falls below the volatility trend defined by other lithophile volatile elements due to core formation process and does not show overabundance in the BSE.</figcaption></figure>
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 7** The BSE, -Mg normalized abundances of bulk silicate Moon (BSM) and CI, -Mg normalized Vesta (BSV) are plotted against 1% evaporation temperature at $logf(O_2) = -10$ and 50% condensation temperature. The abundance of BSM is from Hauri et al. (2015) and BSE from Palme and O'Neill. (2014). Vesta data from Sossi et al., 2022 and references therein. These elemental abundances are provided in supplementary materials. Both normalized elemental abundances in the BSM and BSV show a near log-linear with the new evaporation temperature scale.</figcaption></figure>