Accretion and Core Formation of Earth-like Planets: Insights from Metal–Silicate Partitioning of Siderophile and Volatile Elements

Abstract

The origin of volatile elements, the timing of their accretion and their distribution during Earth’s differentiation are fundamental aspects of Earth’s early evolution. Here, we present the result of a newly developed accretion and core formation model, which features the results of high P–T metal–silicate partitioning experiments. The model includes well-studied reference elements (Fe, Ni, Ca, Al, Mg, Si) as well as trace elements (V, Ga, Ag, Au, S) covering a wide range from refractory to volatile behavior. The accretion model simulates the different steps of planet formation, such as the effects of continuous, heterogenous core formation at high P–T, the effect of the Moon-forming giant impact and the addition of matter after the core formation was completed, the so-called “late veneer”. To explore the “core formation signature” of the volatile depletion patterns and the quantitative influence of a late veneer, we modeled planets that would have formed from known materials, such as CI, CM, CV, CO, EH and EL meteorites, and from a hypothetical volatile depleted material, CI*. Some of the resulting planets are Earth-like in key properties, such as overall core size, major element composition, oxygen fugacity and trace element composition. The model predicts the chemical signatures of the main planetary reservoirs, the metallic core and bulk silicate planet (BSP) of the modeled planets, which we compare with the chemical signature of Earth derived previously from core formation models and mass balance-based approaches. We show that planets accreted from volatile depleted carbonaceous chondrites (CM, CV, CO and CI*) are closest in terms of major element (Si, Mg, Fe, Ca, Al, Ni) and also siderophile volatile element (Ge, Ga, Au) concentrations to the components from which Earth accreted. Chalcophile volatile elements (S, Ag), instead, require an additional process to lower their concentrations in the BSP to Earth-like concentrations, perhaps the late segregation of a sulfide melt.

1. Introduction

The differentiation of Earth into a metal core and a silicate mantle, perhaps the most prominent process in the history of our planet, has been dated back to the first ~30 million years of our solar system [1,2,3]. Understanding the process of core-metal differentiation leads to a better understanding of the accretion history of Earth, since it is directly linked to the nature of the accreted material. Constraints on terrestrial core formation are largely based on the comparison between the composition of the bulk silicate Earth (BSE) and chondritic meteorites (e.g., [4,5,6,7]). A longstanding question is whether planet Earth was built from known material represented by samples in the international meteorite collection or whether hitherto unknown building blocks are necessary. This debate is ongoing and concerns major elements [5,8,9,10], volatile elements (e.g., [11,12,13,14]) and stable isotopes and their nucleosynthetic anomalies (e.g., [15,16,17,18]). We advance this debate by comparing the chemical and physical characteristics of model planets that accrete from known meteorites and the chemical and physical characteristics of Earth.

Previous accretion simulations indicate that impacts of planetesimals and embryos dominate the terrestrial planets’ final gain of mass [19,20,21]. These high-energy impacts, the most recent and largest of which was the Moon-forming giant impact [21,22,23,24,25], likely led to extensive melting on the growing Earth and to the formation of a global magma ocean [26,27]. In this context, an extended experimental dataset for metal–silicate partition coefficients for higher pressure up to 100 GPa provides evidence that core–mantle equilibration occurred under high-pressure (P > 30 GPa) and high-temperature (T) conditions that represent the bottom of a deep global magma ocean (e.g., [28,29,30,31,32,33,34,35,36,37,38]). These studies have demonstrated the P–T dependence of partition coefficients (D-values) and imply that a one-step core formation model is unable to reproduce the BSE element concentrations relative to CI. Wade and Wood [35] developed a continuous core formation model that assumes metal–silicate equilibrium at the bottom of a deep magma ocean, with P, T and oxygen fugacity (${fO}_2$) conditions changing as the planet grows. In their model, the increasing average pressure of equilibration is the main driving force for the other parameters. They also stressed the fact that bulk ${fO}_2$ should have evolved from initial strongly reducing to more oxidizing conditions at the end of accretion, which mitigates the problem of excess siderophiles [39,40,41,42] and explains the concentrations of Fe, Cr, V and Mn in the BSE [9,10,35,43,44].

Most accretion models assume chondritic material arrived on Earth at a time when core formation was already complete, an addition known as the “late veneer” event (e.g., [4,5,11,42,45,46,47,48,49,50]). Originally, a chondritic late veneer was considered because highly siderophile elements (HSE) were found to be overabundant in the BSE compared to the concentrations expected from metal–silicate partitioning experiments. In addition, HSE were found to be present in chondritic relative proportions, which is not consistent with their respective metal melt–silicate melt partition coefficients (D^{(metal/silicate)}). The amount of presumed volatile-rich late veneer [11] has been estimated to be between 0.3% and 0.7% of Earth’s mass (%M_E) based on HSE abundances (e.g., [6,51]). However, the abundances of volatile elements and their isotopic systematics (H, C, Ne, Ar, Ag) require a much higher proportion of chondritic material added after core formation finished, between 2.0% M_E and 10% M_E [46,47,49,52].

Element abundances in the BSE normalized to CI chondrite are commonly interpreted as a function of their 50% condensation temperature (T_C50; Figure 1), which is used as a proxy for the volatility of elements under solar nebular conditions [52,53]. Except for CI chondrites, all chondrite groups and differentiated objects, including Earth and small telluric bodies such as Mars, the Moon and the non-primitive achondrite parent body, are depleted of elements with a T_C50 below that of Mg (1343 K). Moderately volatile and lithophile elements (e.g., Li, Na, K, Rb, Zn, In) form a nearly linear trend of continuous depletion relative to CI chondrite as a function of decreasing T_C50 on a logarithmic scale. This trend is commonly referred to as the volatility trend of Earth [7,50,54,55,56]. It is hypothesized that the volatility trend is not influenced by evaporation processes but caused by pre-existing depletion of Earth’s building blocks, as similar trends are also observed in all chondrites except CI (e.g., [7]). Elements depleted in the BSE relative to the volatility trend are volatile and siderophile and, thus, were sequestered into the core during core–mantle differentiation [57,58,59]. Compared to refractory siderophile elements (e.g., HSE, Fe, Ni, Co), which have been intensively studied to constrain core formation models, siderophile volatile elements (SVE) have received much less attention in recent decades. Furthermore, the abundances in the BSE for some of these elements are not well constrained, e.g., Ag ± 50%, Cd ± 20%, Cu ± 30% and Ge ± 20% [60]. The experimental database regarding the partitioning of SVE, especially at high P and T, is rather small, leading to large uncertainties when parameterized and extrapolated to the conditions in a deep magma ocean.

Our new partitioning data for SVE with T_C50 between 1343 K (Mg) and 700 K (Ag) in metal melt–silicate melt and sulfide melt–silicate melt systems fill some of these data gaps [62]. We use the data for V, Ga, Ge, Ag and Au to incorporate these variably volatile elements into a quantitative model of accretion and core formation. Because our models include episodes of linear mass addition and continuous core formation, a giant impact of a Mars-sized planetary embryo and the addition of a late veneer, we can quantify the contributions of these individual processes to the BSP element abundances. The combination of these accretion episodes allows for us to model the concentrations of Fe, Ni, V, Ga, Ge, Ag, Au and S in the BSP and in the planet’s core after differentiation. A comparison of the modelling results with the observed BSE element concentrations enables us to identify the “core formation signature” of the volatile depletion pattern.

Simulations were performed for seven different compositions, six of which represent averages of known meteorite groups from the carbonaceous and non-carbonaceous reservoirs (CI, CM, CV, CO, EH and EL chondrites) and one composition (CI*) designed to be a volatile-depleted CI composition, modified from [27].

2. Materials and Methods

This study is based on the experimental dataset by Loroch et al. [62], which includes the systematic evaluation of experimentally determined metal–silicate D-values with increasing S content for a large suite of elements (Li, Mg, Al, Si, S, Ca, V, Cr, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Rb, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, Te, Cs, Hf, Ta, W, Au, Pb, Bi), covering a wide range of temperatures (1673 K ≤ T ≤ 2573 K) and pressures (1 GPa ≤ P ≤ 20 GPa; Supplementary Materials).

This new experimental dataset was combined with a multitude of literature data for the aforementioned elements to increase the data density for better regression results. The final database used for the calculations in this study consists of ~650 individual experiments, including 38 different elements and a total of 9618 concentration measurements based on ~30 different studies. For the course of this study, the literature data had to be fitted into the overall question; therefore, we had to exclude some literature data based on the following criteria: (1) experiments using starting material composition containing water or carbon, including experiments utilizing carbon capsules; (2) experiments in systems where “trace elements” were added in wt% levels; (3) 2σ uncertainties on concentration measurements larger than 100% and (4) extremely reducing conditions below ∆IW − 4.

Since this study employs only a slice of the Loroch et al. [62] dataset, all further explanations of data treatment are only valid for this reduced dataset of Fe, Ni, S, V, Ga, Ge, Ag and Au. The dataset presented by the elements in use contains the results of 393 individual samples (see Supplementary Table S1 for references).

The selection of these elements from the extensive available dataset was made to showcase a broad range of geochemical characteristics among volatile elements. Additionally, these elements were chosen due to the abundance of studies that describe their behavior across various scenarios, providing a robust foundation for comparison and analysis. Steenstra et al. [63] discovered a significant matrix effect for the volatile elements measured in metal by laser ablation, which increases with element volatility. Therefore, we corrected all metal concentrations in the dataset that were analyzed by LA-ICP-MS techniques, according to the method of Steenstra et al. [63] (for details and examples, see also [62] and Supplementary Text). This correction of the LA-ICP-MS data drastically reduces the previously existing analytical scatter between different studies, especially in experimental studies at low pressure. In addition, the corrected concentrations obtained with LA-ICP-MS are now in much better agreement with the results derived by other analytical methods, such as EMPA, SIMS and conventional ICP-MS.

Since different studies used different definitions for the partition coefficient (D-values) and other parameters, such as oxygen fugacity (${fO}_2$), we recalculated all parameters using the corrected concentration data from the literature to unify the database (see Supplementary Materials and [62] for data table and references).

Element Partitioning The elemental partitioning between metal, silicate and sulfide melts can be described by the Nernst partition coefficient, which is defined as the ratio between the concentrations of a trace element in the two phases of interest [64]:

$$D_i^{met/sil}={\displaystyle \frac{C_i^{met}}{C_i^{sil}}}$$

(1)

C is the concentration in wt.% for the element of interest (i) in the respective phases (sil = silicate melt, met = metal to sulfide melts). Using Equation (1) and the refined dataset, we calculated the corresponding D-values for each element and run product. As an example, the D-values for Fe and Ni are summarized in Figure 2 together with the available literature data. The experimental scatter is predominantly due to the simultaneous variation in T, ${fO}_2$ and chemical composition, such as S and Si content, in the metal phase. Nevertheless, Fe and Ni fit well within the range of experimental data from previous studies for the entire pressure range. We use the known concentrations of these elements in the BSE and, later, in Earth’s core as reference points in our core formation simulations. We assume that experiments capable of reproducing literature values for major elements and well-characterized elements, such as Fe, Co and Ni, will also provide reliable partition coefficients for the less intensively studied elements V, Ga, Ge, Ag, Au and S. The complete set of D-values, including all elements not shown in Figure 2, is compiled in the Supplementary Figure S1.

Pressure, T, S content and ${fO}_2$ significantly affect the distribution behavior of trace elements in metal–silicate and sulfide–silicate melts. To provide a mathematical description for the distribution of trace elements in these systems, it is essential to consider these dominant variables. When the distribution behavior of an element is expressed by an exchange reaction via the exchange coefficient K_D (Equation (2)), the distribution becomes independent of the ${fO}_2$, which allows for a better comparison between different experimental conditions [44,55,65]:

$$K_D^i=D_i·D_{Fe}^{-{\displaystyle \frac{v_i}{2}}}$$

(2)

The expression normalizes the D-value of a respective element i (D_i) to the D-value of Fe (D_Fe), considering the influence of the valence v_i of the element [64].

Figure 2. Experimentally derived D-values of this study (blue squares = metal/silicate, red triangles = sulfide/silicate) in comparison to literature values (grey circles). Errors are given as two times standard deviation. If error bars are not visible, they are smaller than the symbol size (compilation of data taken from [30,31,36,37,44,55,56,66,67,68,69,70,71,72,73,74,75]).

Figure 2. Experimentally derived D-values of this study (blue squares = metal/silicate, red triangles = sulfide/silicate) in comparison to literature values (grey circles). Errors are given as two times standard deviation. If error bars are not visible, they are smaller than the symbol size (compilation of data taken from [30,31,36,37,44,55,56,66,67,68,69,70,71,72,73,74,75]).

The dependencies of the element distribution on P, T and S content are parameterized as follows: assuming chemical equilibrium between the phases or melts, the exchange reaction is expressed as an exchange coefficient and its relation to the Gibbs free energy in the standard state. The latter is translated into the relationship between enthalpy, entropy and volume change:

$${\lg K}_D^i=a_i+{\displaystyle \frac{b_i}{T}}+{\displaystyle \frac{c_{i}P}{T}}+d_i{\displaystyle \frac{\mathrm{l}\mathrm{n}(1-C_S)}{ln10}}$$

(3)

This approach has been described and evaluated in previous studies by Righter et al. [76,77] as well as Rubie et al. [9] but without the sulfur term. The parameters a, b and c result from the expansion of the free energy terms:

$${∆G}^0={∆H}^0+{∆S}^0+P{∆V}^0$$

The effects of the non-ideal behavior of elements in the metal phase are summarized in an additional term $\mathrm{l}\mathrm{n}(1-C_S)/ln10$, also considering the sulfur concentration in the metal. The distribution of sulfur between metal melts and silicate melts is described in our model by the following expression:

$$\lg K_D^S=2.32-T^{-1}\left(1088-276.5P\right)$$

This parameterization (Equation (3)) allows for us to mathematically describe the main effect on the distribution behavior for the respective elements. We chose a nonlinear curve-fitting method to fit all four parameters (a_i, b_i, c_i, d_i) simultaneously, which minimizes the number of assumptions required for the individual parameter. The calculations were performed using the SciPy.optimize package version 1.3.1 (see official package documentation for details). This method uses a least squares approach to find a local minimum of the correlated quadratic loss function, which includes an error value not only for the dependent variable but also for the independent ones.

In addition to this approach, we used the modified unified Wagner ε-formalism [78]. This model describes the interaction between trace elements and their solvent—in our case Fe—and major components. This formalism has to be solved for all trace elements at the same time, which we performed for S, V, Co, Ni, Ga, Ge, Ag and Au. The first-order interaction parameters used for these calculations are based on the values given in the Steelmaking data sourcebook [79] and additional data from A. Norris’ online calculator (http://www.earth.ox.ac.uk/~expet/metalact/ (accessed on 21 October 2024)).

Unfortunately, the interaction parameters for most of the elements studied here are either unknown or poorly constrained; previous studies (e.g., [55,65]) and the online calculator consider them to be negligible and set their activity value to zero. This hinders the usability of the formalism significantly. After a direct comparison of the results of the two methods, their statistical significance and accuracy, we decided to use the parameterization approach (Equation (3)), which more precisely describes the experimental data and the influence of each parameter.

We converted the experimental partition coefficients into the corresponding exchange coefficients according to Equation (2) and then fitted them with the parameterization Equation (3). This data treatment was applied in the same way to all elements of interest: S, V, Fe, Co, Ni, Ga, Ge, Ag and Au. Figure 3 shows the experimentally determined lg K_D-values of our study and the literature data compared to the calculated lg K_D-values. There is some scatter around the 1:1 correlation lines, but our parameterization approach reproduces the experimentally determined values within an uncertainty of 2σ, which is consistent with the uncertainty ranges of previous models [9,27,35,55].

In addition to Equation (3), we employed a formalism derived from Mann et al. [55] to address silicon partitioning into the metal phase. This approach was necessitated by the absence of silicon in the metal phase in our experiments, which may be attributed to the relatively low P–T conditions compared to previous ultra-high P–T experiments conducted in diamond anvil cells (e.g., [75,80]); for a more comprehensive view on this topic, see Blanchard et al. [80]. This consideration helps to bridge the gap in our findings and provides a more comprehensive understanding of silicon behavior under varying conditions.

Modeling Planetary Accretion and Core Formation. The accretion of matter was modeled in a total of 1000 steps (n). The starting point was a proto-planet having 5% (m_p) of the present Earth’s mass (M_E). The first 998 steps of mass influx follow a linear relationship:

$$M_{\left(t\right)}=\left\{\begin{array}{c}\begin{array}{cc}{M}_E{m}_p& for t=0\\ M_E\left(m_p+{\displaystyle \frac{1-m_p-m_{GI}-m_{LV}}{n-2}}t\right)& for 1\le t\le 998\end{array}\\ \begin{array}{cc}{M}_E\left(m_p+m_{GI}+{\displaystyle \frac{1-m_p-m_{GI}-m_{LV}}{n-2}}\right)\left(t-1\right)& for t=999 \\ M_E\left(m_p+m_{GI}+m_{LV}+{\displaystyle \frac{1-m_p-m_{GI}-m_{LV}}{n-2}}\right)\left(t-2\right)& for t=1000\end{array}\end{array}\right.$$

(4)

Step 999 represents the giant impact (GI), which adds 10% M_E and triggers another episode of core formation, while step 1000 is the addition of a late chondritic veneer (LV) of 0.5% M_E at a point where core formation had ceased (Figure 4). We have modeled core formation as a multi-stage process that, apart from the late veneer, occurs throughout the accretionary history of the planet. The core is fed by infalling material that equilibrates and differentiates into molten metal and silicate in a deep magma ocean (e.g., [35]). The core–mantle mass ratio was initially set at 1/3 (core) to 2/3 (bulk silicate planet; BSP) of the proto-planet and may evolve during accretion. The depth of the magma ocean is kept static at 2/3 of the core–mantle boundary, while the average pressure at the bottom of the magma ocean is calculated as a function of the total accreted mass and the maximum final pressure after Badro et al. [81]:

$$P_{\left(t\right)}=P_{final}{\left({\displaystyle \frac{M_{\left(t\right)}}{M_E}}\right)}^{2/3}$$

(5)

This pressure, P_(t), is assumed to be the average equilibration pressure within the magma ocean, as equilibration of sinking material occurs over a range of pressures. This implies that this pressure is not a true estimate of the depth of the magma ocean but rather the average pressure at which the main equilibration occurs. As the magma ocean is in equilibrium with the underlying solid silicate portion of the mantle, the temperature in the contact region must be above the solidus and below the liquidus temperatures of peridotite [81]. We adopted the geotherm of Rubie et al. [27], which uses the solidus/liquidus temperatures of Herzberg and Zhang [82] and Tronnes and Frost [83] for pressures below 24 GPa and the FeO-corrected liquidus of Liebske and Frost [84] for higher pressures (uncertainty ~100 K):

$$T_{\left(t\right)}=\left\{\begin{array}{cc}1874+55.43P_{\left(t\right)}-1.74P_{\left(t\right)}^2+0.0193P_{\left(t\right)}^3& for P\le 24 \mathrm{G}\mathrm{P}\mathrm{a}\\ 1249+55.28P_{\left(t\right)}-0.395P_{\left(t\right)}^2+0.00011P_{\left(t\right)}^3& for P>24 \mathrm{G}\mathrm{P}\mathrm{a}\end{array}\right.$$

(6)

Meteorite Composition. Using the fitting parameters from

Table 1. Fitting parameters for studied elements as derived from least minimum square curve regression. The errors are reported as two times regression standard errors.

	Val.	ai	bi	ci	di
S	−2	2.32	−1088	226.5
V	3	−2.03 ± 0.20	−882 ± 393	−11.6 ± 9.7	−2.53 ± 0.24
Ni	2	−0.90 ± 0.12	5670 ± 220	−61.3 ± 6.4	2.44 ± 0.15
Ga	3	−0.03 ± 0.43	298 ± 813	−87.0 ± 19.7	10.9 ± 0.40
Ge	3	0.17 ± 0.45	3132 ± 878	−23.8 ± 24.2	13.6 ± 0.48
Ag	1	−0.87 ± 0.47	1315 ± 866	−36.7 ± 30.3	−3.49 ± 0.40
Au	4	2.00 ± 0.82	−1812 ± 1634	−112 ± 49.8	4.09 ± 0.76

, we modeled accretion and core formation for seven different compositions representing carbonaceous chondrite (CC: CI, CM, CV, CO) and non-carbonaceous chondrite (NC: EH, EL) meteorite groups [7,61,85]. These meteorites may represent building block analogs for Earth and, therefore, can also set the compositional boundary conditions for Earth. We also included a synthetic composition from Rubie et al. [27] that represents a modified CI composition (CI*) enriched in Al, Ca, Nb, Ta and W by 22% and in V by 11% relative to CI. To simulate a volatile depleted component, CI* has 50% lower concentrations of the most volatile elements S and Ag than CI (

Table 2. Starting compositions of the proto-Earth and the impactor material. CI from Palme and O’Neill [7], CI* (see text), others are taken from Lodders and Fegley [61].

	Unit	Cl	Cl*	CM	CV	CO	EH	EL
O	wt.%	45.9	47.0	43.2	37.0	28.0	31.0
Mg	wt.%	9.50	9.80	11.5	14.3	14.5	10.7	13.8
Al	wt.%	0.84	1.02	1.13	1.68	1.40	0.82	1.00
Si	wt.%	10.7	11.0	12.7	15.7	15.8	16.6	18.8
S	wt.%	5.35	2.68	2.70	2.20	5.60	3.10
Ca	wt.%	0.91	1.11	1.29	1.84	1.58	0.85	1.02
V	μg/g	54.6	60.6	75.0	97.0	95.0	56.0	64.0
Cr	μg/g	2623	2686	3050	3480	3520	3300	3030
Mn	μg/g	1916	1962	1650	1520	1620	2120	1580
Fe	wt.%	18.7	19.1	21.3	23.5	25.0	30.5	24.8
Co	μg/g	513	525	560	640	680	870	720
Ni	wt.%	1.09	1.12	1.23	1.32	1.42	1.84	1.47
Ga	μg/g	9.62	9.85	7.60	6.10	7.10	16.7	11.0
Ge	μg/g	32.6	33.4	26.0	16.0	20.0	38.0	30.0
Ag	ng/g	20.1	10.1	16.0	10.0	28.0	8.50
Au	ng/g	14.8	15.2	15.0	15.3	19.0	33.0	24.0

).

Figure 5 gives an overview of the concentrations of refractory, moderately volatile and volatile elements of various meteoritic groups (CI, CI*, CV, CO, CM, EH and EL) normalized to CI chondrites (Mg = 1), plotted against T_C50. Refractory elements (e.g., Ni, Si, Fe) exhibit enrichment relative to CI for the enstatite chondrites, while moderately volatile to volatile elements (e.g., Ge, Ag) tend to be depleted in all carbonaceous chondrites relative to CI. Each meteoritic group represents material from a different parent body in the early solar system, and these parent bodies formed in different regions of the protoplanetary disk. The distance from the Sun influenced the temperature and availability of volatile materials during their formation. Volatile elements, which condense at lower temperatures, tend to be lost from bodies that form in high-temperature regions, while refractory elements, which condense at higher temperatures, are retained. This fractionation is one of the major reasons for the differences in composition across the meteorite groups.

The calculated models represent end-member scenarios, i.e., the entire planet consists of a single (meteorite) composition. However, since the Fe⁰–FeO ratio of the impactors may vary depending on the ${fO}_2$ path and the atmophile element content may vary (see below), our models do not represent a homogeneous accretion in the strict sense but rather a heterogeneous model evolving from a homogenous composition. This is especially clear for Enstatite chondrites; this group, in general, is too low in refractory elements to build up Earth-like planets. Nevertheless, the main driving parameter in our model was to fulfill the oxygen fugacity path as closely as possible. This means our model is able to change the impactors Fe⁰–FeO, similar to Rubie et al. [9], but in a far more dynamical way. This shift will also affect other refractory elements due to the assumption that a reducing process on the impactor is not only limited to FeO if we reduce the O and H content drastically, within the limitation, that the impactor still needs to have enough oxygen to build up its silicate fraction. Therefore, an impactor will never be a pure lump of Fe and other elements in metallic form.

Equilibration of Material in the Magma Ocean. Impacting material is taken up into the magma ocean and remains there until it is fully equilibrated under the P–T–fO₂ conditions calculated for the bottom of the magma ocean. Wade and Wood [35] argued that the metal–silicate equilibrium depth is only 30% to 40% of the pressure at the core–mantle boundary, and thus, the lower mantle must be largely solid or at least in a crystalline state during metal segregation. The metal droplets that form during equilibration in the magma ocean accumulate and segregate in larger diapirs down to the core [43]. Therefore, and in lack of solid–melt partitioning data at very high pressures, we assume that the solid portion of the BSP is not involved in any chemical process relevant to the partitioning, equilibration or segregation of the metal. After the metal portion of the infalling material has segregated through the entire mantle, the metal is confined to the continuously growing core. After its formation, the core is considered a closed reservoir that does not react with the surrounding mantle due to the large density contrast between liquid metal and solid silicate [35]. Subsequently, the magma ocean and the underlying partially solid silicate return to an equilibrium stage, maintaining a constant mass ratio.

There is debate about how large and presumably differentiated impactors equilibrate with the target planet. Whether the impactor core emulsifies and fully equilibrates or whether it merges with the target planet’s core without a chemical reaction depends on a variety of parameters, such as impact angle, impact location and target planet rotational velocity (e.g., [9,27]). For the sake of simplicity and in the absence of detailed information about the giant impact, we assume in our models that an impactor fully emulsifies and equilibrates with the pre-existing magma ocean. The advantage of not using this tuning parameter is that the model results are based directly on measured partition coefficients.

Conditions of Core Formation. A boundary condition for each model was to reproduce the well-established Fe–Ni ratios of Earth’s mantle and core [7,27,86,87,88]. While all other parameters were held constant, equilibrium P and T were varied to obtain the correct Fe–Ni ratios in the core and the BSP. The maximum equilibrium pressure had to be adjusted within a narrow range overall (56 to 75 GPa) for each composition. The boundary conditions for the models are summearized in

Table 3. Boundary conditions of the different models. Pressure and composition are free parameters, temperature depends on Equation (4). For compositional details see Table 2.

Model	Pressure		Temperature		Composition
	Min	Max	Min	Max
	[GPa]	[GPa]	[K]	[K]
Cl 56	7.6	56	2203	3467	Cl
Cl* 64	8.7	64	2237	3649	Cl*
CM 65	8.8	65	2241	3670	CM
CO 69	9.4	69	2256	3751	CO
CV 75	10.2	75	2278	3862	CV
EH 58	7.9	58	2212	3515	EH
EL 71	9.6	71	2264	3789	EL

. The models started with a proto-planet of 5% M_E, differentiated into a core (85.5 wt.% Fe [60]) and a mantle by a one-step core formation event. The adopted oxygen fugacity was ∆IW −4, while the pressure and temperature ranged from 7.3 GPa to 8.6 GPa and 2194 K to 2237 K, respectively. Thus, the models never reached conditions where core formation was active at lower pressure. The oxygen fugacity of the system was set to evolve from ∆IW −4 to ∆IW −2 at the end of accretion [9,27,35,89], the latter representing equilibrium between an Fe-rich core and mantle olivine with a Mg# of 0.9. The accreting material affects the evolution of the proto-planet in several ways. The ${fO}_2$ of the impactors is not preset, but they adopt the ${fO}_2$ of the preexisting magma ocean, which is determined by the ${fO}_2$ pathway. This assumed ${fO}_2$ determines the Fe⁰–FeO ratio of the infalling material and, thus, the amount of metal available for core building. The Fe concentration is, therefore, a semi-fixed but crucial parameter in the model since the underlying parameterization is tied to lg K_D-values and, thus, requires D_Fe to calculate the partition coefficients of the other elements.

Core mass (~33.3% M_E), core composition (~85.5 wt.% Fe) and magma ocean depth (2/3 of the core–mantle boundary) are parameters that are free to evolve during the simulations. However, they vary only slightly as long as the total iron content of the impactors is approximately equal to the Fe⁰ content required to build the core.

3. Results

Several compositional models for the formation of Earth have been proposed in recent decades based on either mass balance calculations [5,7,60] or on the results of core formation simulations [9,27,35,71,90]. The novelty of our approach is that our core formation model considers a variety of elements ranging from refractory to volatile, from lithophile to chalcophile/siderophile. Moreover, our model includes S, one of the most abundant volatile elements and the importance of which is still controversially debated despite the increasing number of experimental data [13,30,31,33,56,73,91,92,93,94]. Our study did not aim to achieve perfect agreement between model BSP and BSE element concentrations using fictitious impactor compositions. Our approach was to evaluate end-member scenarios employing compositions of known meteorite groups (except for CI*) to decipher the effects of varying composition on major and (volatile) trace element concentrations in the model planets. The quantitative model presented here is based on a comprehensive experimental dataset as well as on geophysical and geochemical constraints regarding the conditions of core formation on Earth. The model allows for us to trace the geochemical signature of the individual accretion and core formation processes in terms of major and trace elements.

3.1. Major Element Concentrations in Planetary Reservoirs

The results of our simulations for the major elements Fe, Ni, Ca, Al, Mg and Si are compared in

Table 4. Bulk Earth/Planet composition for all simulations and for previous models.

Bulk Earth/Planet	Core/Earth	Fe	Ni	Ca	Al	Mg	Si	S
	%	wt.%	wt.%	wt.%	wt.%	wt.%	wt.%	wt.%
McDonough [60]	32.3	32.0	1.82	1.71	1.59	15.4	16.1	0.64
Moynier and Fegley [95] a	32.5	29.5	1.74	1.76	1.61	15.0	16.2	0.01
Kargel and Lewis [96]		32.0	1.72	1.66	1.43	14.9	14.6	0.89
Morgan and Anders [97]		32.1	1.82	1.54	1.41	13.9	15.1	2.92
Lodders and Fegley [98] (EH)		30.4	1.84	0.85	0.82	10.7	16.6	5.60
Rubie et al. [9] *	30.7	30.1	1.80	1.85	1.69	15.7	17.4
Rubie et al. [27] **	31.1	29.9	1.70	1.78	1.64	15.3	17.2
CI_56	39.7	31.6	1.79	1.40	1.29	14.7	17.4	8.60
CI*_64	34.6	31.9	1.87	1.84	1.40	15.9	17.8	3.42
CM_65	35.1	31.9	1.88	1.86	1.64	16.6	18.4	3.92
CO_69	33.7	32.1	1.85	1.99	1.76	18.2	19.9	2.53
CV_75	33.7	32.0	1.82	2.33	2.13	18.1	19.9	2.60
EH_58	37.2	31.8	1.70	0.85	0.82	10.7	16.9	6.02
EL_71	34.8	32.0	1.98	1.21	1.19	16.3	22.0	3.48

^a Moynier and Fegley [96] using Palme and O’Neill [7] BSE abundances recalculated to 0.675 (BSE/Earth), core model by Badro et al. [90] (3.7 wt.% O, 1.9 wt.% Si, 94.4 wt.% Fe₉₄Ni₆) and a solar Co/Fe ratio of 0.0029l. * HET-2 Model by Rubie et al. [9] ** Planet#57 “Earth” by Rubie et al. [27].

and

Table 5. Core and BSE/BSP element abundances for all simulations and for previous models.

	Fe [wt.%]	Ni [wt.%]	Ca [wt.%]	Al [wt.%]	Mg [wt.%]	Si wt.%	S wt.%
BSE/BSP: Palme and O’Neill [7]	6.30	0.186	2.61	2.38	22.2	21.2	0.020
	±1%	±5%	±8%	±8%	±1%	±1%	±40%
Rubie et al. [9]	6.30	0.177	2.67	2.43	22.6	21.4
Rubie et al. [27]	6.29	0.170	2.59	2.39	22.2	21.4
CI_56	6.65	0.184	2.32	2.14	24.3	25.7	0.350
CI*_64	6.65	0.179	2.82	2.14	24.3	25.6	0.100
CM_65	6.65	0.186	2.87	2.52	25.6	26.7	0.120
CO_69	6.65	0.185	3.00	2.66	27.5	28.3	0.080
CV_75	6.65	0.184	3.52	3.21	27.3	28.2	0.070
EH_58	6.65	0.186	1.35	1.30	17.1	24.9	0.240
EL_71	6.65	0.184	1.86	1.82	25.0	32.1	0.110
Core: McDonough [60]	85.5	5.20	−	−	−	6.00	1.90
Rubie et al. [9]	83.7	5.30	−	−	−	8.30	−
Rubie et al. [27]	82.3	5.23	−	−	−	7.73	−
CI_56	69.5	4.41				2.59	21.1
CI*_64	79.8	5.08				3.06	9.69
CM_65	78.8	4.93				3.15	11.0
CO_69	82.0	5.05				3.50	7.35
CV_75	81.9	4.70				3.73	7.59
EH_58	74.3	4.99				2.79	15.8
EL_71	79.4	4.85				4.08	9.80

with previous compositional models for bulk Earth, BSE and Earth’s core compositions [60,95,96,97,98]. Generally, the accretion of impactors containing large amounts of siderophile major elements inevitably leads to a planet with a core larger than that of Earth because the metal portion of the planet is accreted more rapidly than the silicate portion of the planet if the ${fO}_2$ constraints are met (e.g., EH_58). Conversely, the accretion of bodies with low contents of siderophile major element leads to core masses that are too small. To increase the Fe content while meeting the mass balance between core, BSP and impactor reservoirs, the latter compositions were increasingly depleted of the atmophile elements H, N and O.

The mass ratios between the core and the bulk model planets for most simulations are slightly larger than those suggested for Earth. Especially, the planets that are composed of EH and CI have much more massive cores than that of Earth (Table 4). However, considering that our calculation uses only an initial estimate for the core size of 5% M_E and can evolve thereafter without additional restrictions, it is remarkable that the simulations fall within a narrow range of 35.5 ± 2.17 wt.% core/total Earth mass, which fits well with the literature values of 32.3–32.5 % [60,95]. We expected larger differences in core sizes due to the large differences in Fe contents of the meteorites (18.66–30.5 wt.%; Table 2), but the adaptation of the atmophile elements and, thus, also the Fe⁰–FeO ratio of the impactors to the ${fO}_2$ pathway appears to largely compensate for these differences.

With respect to the major elements, the compositions of the bulk planets resulting from the simulations CI*_64, CM_65 and, with few exceptions, CO_69 and CV_75 are similar to Earth (Table 4). In detail, bulk Fe, Ni, Ca and Al concentrations are most similar to those of Earth in these simulations. Mg concentrations in CO_69 and CV_75 are 2.5 wt.% higher than in the literature models, whereas the Si (for CO, CV, EH) and, especially, the S contents (for CI, CM, EH; see Section 3.2 below) of the modeled planets are higher than those of Earth (Table 4). CI_56 gives reasonable concentrations for all refractory elements; however, the core/Earth proportion of almost 40 wt.% makes the model appear unrealistic. The planet resulting from simulation EH_58 delivers Ca, Al and Mg concentrations for the bulk planet that are ~50% lower than those of Earth because of its overly massive core. However, EH_58 agrees perfectly with the EH model calculated by Lodders and Fegley [98], which was derived from mass balance (Table 4). On the one hand, this means that EH chondrites with their averaged composition used here are most likely not the main building blocks of Earth; on the other hand, it emphasizes the reliability of our model and the element partitioning parameterization, since the results of two different methodological approaches are very similar.

Please note that all models are designed such that the Fe and Ni concentrations of the BSP are those of BSE. The observation that the simulations for the volatile depleted carbonaceous chondrites (CI*, CM and, with exceptions, CV and CO) result in Earth-like planets also holds when considering the modeled compositions of the BSP and core reservoirs separately (Table 5). The best-fitting models in terms of Ca, Al and Mg concentrations in the BSP compared to BSE are CI_56, CI*_64 and CM_65; however, note that, as for the bulk planet, all simulations except for EH_58 deliver higher Mg and Si concentrations in the BSP compared to BSE, particularly pronounced in the CO_69, CV_75 and EL_71 simulations. The discrepancy in Si concentration between the BSP and BSE could be mitigated by removing more Si into the core than predicted by our models [9,27].

3.2. Sulfur

The results of our simulations confirm previous results in that the S budget of planets accreted from all CC and NC meteorites is generally higher than that calculated for Earth (Table 4 and Table 5 [5,7,60]). Simulations CI_56 and EH_58 are most different to Earth regarding their sulfur budgets. Planets built from CI and EH meteorites yield 15 and 21 wt.% S in the core, respectively, which exceeds the geophysically plausible limit of light element concentrations in the core (e.g., [99]). The other simulations are consistent with the geophysical limits for the sulfur budget of the core (7 wt.% to 11 wt.% S). Li and Fei [99] calculated the abundances of Si and S in Earth’s core to be a maximum of 12 wt.%, assuming that each element is the sole cause of the density difference between the inner and outer cores. This estimate is consistent with the values predicted by our models CI*_64 (9.69 wt.%), CM_65 (11.0 wt.%), CO_69 (7.35 wt.%), CV_75 (7.59 wt.%) and EL_71 (9.80 wt.%). When combined with the predicted amounts of Si in the core, the average value for all models is 12.6 ± 1.47 wt.% (S + Si). A caveat at this point is that our model does not account for the potential contributions of carbon, oxygen and hydrogen to the light element budget in Earth’s core.

Sulfur concentrations in the BSP resulting from the CI*, CM, CO, CV and EL compositions are between 800 μg/g and 1000 μg/g and, thus, higher than the cosmochemical estimate of the BSE of 200 μg/g to 250 μg/g [7,60], again reflecting the high S concentrations in all meteorites. One process that could deplete the BSP of S after the end of core formation would be the late segregation of a sulfide melt (“Hadean Matte” [5,27,56]). Combining the BSP S excesses of the model outputs with ~0.35 wt.% FeO yields a stoichiometric FeS layer around the core (isolated from the other reservoirs) with an average thickness of ~17–18 km for all simulations. This is within the range calculated by Savage et al. [100], who estimated 10–30 km. By adding this late sulfide segregation step, our models produce Earth-like planets in terms of all major elements, including S.

Although geophysically plausible, one argument against such high S contents in the bulk Earth is certainly the position of S relative to the volatility trend of the BSE (Figure 1). If the assumption is correct that sulfur was accreted at the same time and in the same relative concentrations as lithophile elements of the same T_C50 (e.g., Zn [50,56]), bulk Earth contains ~0.64 wt.% S, and Earth’s core should, thus, contain no more than ~2 wt.% S [7,27,60].

3.3. Moderately Volatile Elements

The trace elements V, Ga, Ge, Ag and Au were selected because of their different geochemical character and the wide range of their T_C50 values from refractory to volatile (Figure 1).

Vanadium has the highest T_C50 of the elements studied here (1370 K [53]) and is one of the intermediate group elements along with Fe, Ni and Co (Figure 1). In addition, V is a lithophile and shows little depletion relative to the BSE volatility trend.

The geochemical character of Ga (T_C50 = 1010 K [53]) is debated. The relative Ga concentration in the BSE is close to the volatility trend, which renders it a lithophile [60]. Our partition coefficients for Ga, however, agree well with the literature data [55,66,68] and confirm that Ga is a siderophile under conditions relevant to core formation (Supplementary Figure S1).

Gold is often treated analogously to the highly siderophile platinum group elements (PGE) because Au has a similarly low concentration in the BSE (Figure 1). However, Au is much more volatile than the PGE, with a T_C50 of 1060 K [85] or 967 K [53].

Germanium concentrations in the BSE (T_C50 = 830 K [53]) plot significantly below the volatility trend. This is consistent with the classification of Ge as a siderophile element by Palme and O’Neill [7] and McDonough and Sun [101], while Lee [102] considers Ge to be more a lithophile. Ge behaves as a siderophile in our experiments (see Supplementary Figure S1), and the partition coefficients agree well with the literature data [65,66,68,73,103].

Silver is, together with S, the most volatile element studied here (T_C50 = 699 K [53]). Ag is considered to behave as a siderophile [7,101] or chalcophile [7,102]. While the fit for Ag shows good agreement between predicted values and experimental values (Figure 3), we note that the data density could still be better at high pressures and that the fit—and hence the pressure extrapolation—is controlled by only a few experiments.

Modelling Results We draw the reader’s attention to the fact that a perfect match between our model planets and Earth in terms of volatile elements is not expected as the meteorites we start with contain higher concentrations of LVEs and SVEs than Earth (Figure 5). Nevertheless, the distribution of volatile elements among the planetary reservoirs (core and BSP) can be compared to models for Earth and provide information on whether the distribution behavior of the elements and its extrapolation to P–T conditions of core formation on Earth are well approximated and to assess the extent to which processes that additionally modify the volatile elements during the evolution of Earth are necessary.

Table 6. Trace element compositions for all simulations and various literature models for BSE/BSP, core and bulk planet.

	Ga [μg/g]	Ge [μg/g]	Ag [μg/g]	Au [μg/g]	V [μg/g]
BSE/BSP:
Palme and O’Neill [7]	4.40	1.20	0.006	0.002	86.0
	±5%	±20%	±50%	±30%	±5%
Rubie et al. [9]					81.0
Rubie et al. [27]					90.0
CI_56	13.0	6.85	0.153	0.003	53.9
CI*_64	6.41	0.94	0.120	0.002	75.1
CM_65	4.86	0.70	0.164	0.002	80.0
CO_69	2.95	0.30	0.097	0.002	90.6
CV_75	2.65	0.25	0.097	0.002	88.9
EH_58	9.83	2.06	0.166	0.004	38.9
EL_71	5.17	0.56	0.073	0.003	54.2
Core:
McDonough [60]	0.01	20.0	0.15	0.50	150
Rubie et al. [9]					137
Rubie et al. [27]					113
CI_56	19.5	130	0.61	0.64	145
CI*_64	35.3	160	0.27	0.73	155
CM_65	23.3	111	0.37	0.64	168
CO_69	21.2	76.0	0.19	0.72	181
CV_75	18.1	61.0	0.19	0.58	194
EH_58	30.5	106	0.51	0.95	91.0
EL_71	28.9	105	0.16	0.84	121
Bulk:
McDonough [60]	3.00	7.00	0.10	0.20	105
Rubie et al. [9]					98.3
Rubie et al. [27]					97.0
CI_56	15.6	55.7	0.33	0.26	90.0
CI*_64	16.4	56.0	0.17	0.25	103
CM_65	11.3	39.4	0.24	0.23	111
CO_69	9.1	25.8	0.13	0.24	121
CV_75	7.9	20.7	0.13	0.20	124
EH_58	17.5	40.7	0.29	0.36	58.0
EL_71	13.4	36.9	0.10	0.29	77.0

summarizes the simulation results for trace element concentrations in the various planetary reservoirs (BSP, core and bulk planet) and compares them to models for Earth based on mass balance calculations [7,60]. Stepwise results can be found in Supplementary Table S2. Figure 6 is the graphical representation of our modeling. It shows the concentrations of the elements V, Ga, Ge, Ag, Au and S in μg/g (wt.% for S) in the BSPs for which the different processes, core formation (steps 1–998), the giant impact (step 999) and the addition of a late veneer (step 1000), are responsible. The concentrations of the elements in the BSE, including their uncertainties (the grey band in Figure 6), are shown for comparison. The concentrations of these elements in the BSP normalized to concentrations in the BSE [7] are shown in Supplementary Figure S3. The modeled concentrations normalized to CI (Mg = 1) for a total of 24 elements are shown in Supplementary Figure S4.

The BSP concentrations of the moderately volatile and siderophile elements V, Ge and Ga, like those of Fe, Ni and Co, are substantially controlled by core formation during the main phase of accretion (including the giant impact), i.e., by metal–silicate partitioning at high pressure and temperature. As expected, the late veneer has little to no influence on their element concentrations due to the low mass increase and their comparatively low metal–silicate partition coefficients. Gold is the most siderophilic of the elements studied here, and its concentration in the BSP is consequently largely controlled by the late veneer. In contrast to the HSE, however, our model predicts that ~40–50% of the Au present in the BSP already accreted prior to the late veneer. The best-fitting models for major elements yield Au concentrations in the BSP between 0.0018 μg/g (CV_75) and 0.0023 μg/g (CO_69) and are slightly higher than the literature value of 0.0017 μg/g ± 30% [7].

As noted above for major elements (Table 5), not all planets modeled here are similar to Earth, and the same is true for the volatile trace elements. The CI_56 and EH_58 model planets show the largest discrepancies in comparison to the trace element abundances in the BSE. This is particularly evident for the most volatile elements S and Ag, but Au, Ge and Ga concentrations in the BSP are also significantly higher than in the BSE. The models for the volatile-depleted meteorites CM, CO and CV as well as for the synthetic composition CI* (Figure 5) that were most successful with respect to the major elements (Table 5) generally yield planets whose volatile contents in the BSP better match those of the BSE than CI_56 or EH_58 (Table 6, Figure 6). Therefore, in the following, we will focus on the results of these four simulations. In reality, the end-member scenarios are less likely than mixtures of these, which is why the range of concentrations can provide information about which compositions can be achieved by mixtures.

The modeled V_BSP concentrations for CI*_64, CM_65, CO_69 and CV_75 vary between 75.1 μg/g (CI*_64) and 90.6 μg/g (CO_69) and, thus, frame the literature value for the BSE of V_BSE = 86 ± 4.3 μg/g [7] and the results from previous models (V_BSE = 81 μg/g [9] and V_BSE = 90 ±2.8 μg/g [27]. The V concentrations for these models in the planetary cores vary between 155 μg/g and 194 μg/g and are slightly higher than previously published core compositions derived by mass balances (150 μg/g [60]) or by core formation models (113–137 μg/g [9,27]) (Table 6).

The behavior of Ga during core formation is rather difficult to understand. All models except CI_56 and EH_58 predict Ga_BSP concentrations ranging between 2.65 μg/g (CV_75) and 6.41 μg/g (CI*_64), again framing the literature BSE value (Table 6; Ga_BSE = 4.4 ± 0.02 μg/g [7]). In contrast, Ga concentrations in the cores of our modeled planets are significantly higher than those predicted by mass balance approaches. McDonough [60] points out that Ga does not appear depleted in Earth’s mantle but that its relative concentration is close to Earth’s volatility trend (see also Figure 1). Consequently, there should be little to no Ga in Earth’s core, which is difficult to reconcile with the results of the partitioning experiments (see above and Supplementary Figure S1) and our related modeling. Provided that the partitioning data are correct, the problem of Ga being more siderophilic than predicted by Earth’s volatility trend could be circumvented by either the T_C50 value for Ga being higher than calculated (1010 K [53]; 968 K [85]) or Ga being delivered at higher concentrations than predicted by the volatility trend. The total abundance of Ga in the planets would have to be approximately 60% to 80% above the value defined by its position on the volatility trend (~3 μg/g [60]) to match both its distribution and its BSE concentration. Ga becomes more lithophilic at high pressures and high S contents (Supplementary Figure S1; see also [55]), but it is unlikely that such an S-rich metal near the Fe–S eutectic forms Earth’s core (~20 wt.% S) during the main phases of accretion [5].

Modeling results for Ge concentrations in the BSP are variable, but the range is between 0.25 μg/g (CV_75) and 0.94 μg/g (CI*_64) Ge for the best-fitting models for major elements, CI*_64, CM_65, CO_69 and CV_75, and is systematically lower than the literature Ge_BSE value of 1.2 ± 0.24 μg/g [7]. Surprisingly, the concentrations of Ge in the cores of our modeled planets are 3–8 times higher than predicted by mass balance approaches (Table 6 [60]). Similar to Ga, Ge is too siderophilic to deliver both BSP values similar to BSE and at the same time concentrations in the core matching concentrations of Earth’s core (Table 6). This excess of Ge in the system would result in Ge concentrations ranging from 25.8 to 55.8 μg/g in the bulk planet (Table 6), which, at its maximum, is approximately eight times higher than the concentration in bulk Earth of 7 μg/g. The Ge partitioning data defining the extrapolation to higher pressures and temperatures are quite heterogeneous, with D_met/sil at 10–11 GPa and similar T ranging from 100 to ~800 in S-free systems (Supplementary Figure S1). Additional partitioning data at pressures > 20 GPa could help to reduce this source of uncertainty.

A striking feature is that all simulations predict large Ag overabundances in the BSP compared to its BSE concentration. The uncertainty of the BSE estimate for Ag is ~50% (Ag_PM = 0.006 ± 0.003 μg/g), yet even the best-fitting CO_69 and CV_75 simulations predict BSP concentrations at least an order of magnitude higher than in the BSE.

4. Concluding Remarks

A straightforward model of accretion and core formation in 1000 steps produces Earth-like planets from known meteorite compositions. Even though the goal was to determine where the meteorite compositions, mainly affected by element partitioning due to core formation, would end up, it is surprising that this process brings us already close to Earth. The modeled planets so far are different from Earth, but they offer the possibility of expanding the number of processes included in the model in order to get as close as possible to the result instead of adapting the model to a previously expected result.

The model considers the most important processes (core formation, giant impact and late veneer) and provides concentrations for the planetary cores and the bulk silicate planets for a total of 15 elements. The model planets are close to Earth in many properties, which may indicate that the most relevant processes are covered and well approximated (except maybe for the simplistic late sulfide segregation). The new experimental dataset of partition coefficients for volatile elements that specifically accounts for higher pressures and higher S contents allows for, in combination with literature data, a robust parameterization of the partitioning behavior of the SVE. Nevertheless, additional data, especially for Ge and Ag at pressures above 20 GPa, would help to make the P–T extrapolation even more reliable. Differences between individual partitioning studies can be greatly reduced when volatile element contents in metal melts measured by LA-ICP-MS are corrected using the method of Steenstra et al. [63]. Our modeling is consistent with previous calculations in that core formation on Earth occurred predominantly under high pressure, i.e., in a deep magma ocean. The pressure dependence of the very well characterized Fe, Ni and Co metal–silicate melt partitioning indicates average equilibrium pressures between 56 and 75 GPa. This observation agrees well with the conclusions of Mann et al. [55] and Rubie et al. [9], who calculated core formation pressures of >50 GPa. The volatile depleted carbonaceous chondrite meteorites CO, CV and CM as well as the volatile depleted CI composition CI* are (at similar ${fO}_2)$ similar in composition. The planets modeled from these compositions vary accordingly within rather narrow limits. Especially, the planets built from CI* and CM are similar to Earth in terms of core size, major and minor element contents of the bulk planet and the distribution of these elements among the core and BSP. Conversely, planets built up solely from EH and CI chondrites are quite different; they have too large cores that additionally contain unrealistically high amounts of S. A similar problem arises for the planet composed of EL chondrites. Although this planet performs well when compared to the planets made from carbonaceous chondrites in core size, refractory major element content and SVE contents, the Si content is clearly higher than models with 22 wt.% in the bulk planet and 32 wt.% in the BSP. In general, EH and EL meteorites of the NC reservoir seem less suitable for building up Earth than compositions originating from the CC reservoir.

Nominally, CO, CV, CM and CI* compositions are more volatile-rich than Earth (e.g., [13]; Figure 5). Nevertheless, the planets built from these compositions span (with the exception of Ge) a compositional range for V, Ga and Au in the BSP, framing the SVE content of the BSE. This may imply that a mixture of these components represents the composition of the BSE even better for these elements. This is true at least for volatile elements, including Au, which has a T_C50 of 967 K [53]. We interpret this as an indication that volatile elements with T_C50 higher than Au were available throughout the accretion and, as depicted in our core formation model, were continuously involved in core formation. The situation for the more volatile elements Ag and S (T_C50 = 699 K and 672 K [53]) is quite different. Although CO, CV, CM and CI* compositions are depleted in Ag and S relative to CI, Ag and S are strongly overabundant in the respective BSP (factor 3–5 for S; factors 13 to 27 for Ag; Supplementary Figure S3) in contrast to the moderately volatile elements. Two processes could be responsible for this effect. First, the highly volatile elements, like Ag and S, and correspondingly all other elements with comparable or even lower condensation temperatures might not have been available from the beginning of accretion and might have been delivered at a relatively late time in planetary evolution [47,56,104]. Another possibility, as mentioned above, would be the late segregation of a sulfide melt that determines both the S content and the concentrations of all other chalcophile elements in the BSE [5,17,50,56,105]. A detailed evaluation of these scenarios, however, is the subject of future work.

Finally, it should be noted that numerous isotope systems show that neither meteorites of the NC nor those of the CC reservoir can be directly considered as building blocks of Earth (e.g., [15,16,18,106]). However, our modeling implies that the building blocks of Earth resemble carbonaceous chondrites in many chemical characteristics, such as major element composition or depletion systematics of volatile elements, suggesting that their formation history was likely very similar.