# Hydrous Chondrites under Shock

Adrien Saurety, Razvan Caracas

► To cite this version:

Adrien Saurety, Razvan Caracas. Hydrous Chondrites under Shock. The Astrophysical Journal, 2025, 988 (2), pp.226. 10.3847/1538-4357/ade87f. hal-05377422

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# Hydrous Chondrites under Shock

Adrien Saurety<fnref n="1" />, and Razvan Caracas<fnref n="1" />,<fnref n="2" />

Received 2025 April 25; revised 2025 June 23; accepted 2025 June 24; published 2025 July 28

## Abstract

We examine the shock response of a chondrule-like multicomponent silicate melt enriched with 2 wt% H₂O, representative of hydrous chondrites, using ab initio molecular dynamics. We calculate Hugoniot equations of state (HEOS) and evaluate how hydration affects transport, structural, and thermodynamic features under shock compression. Under the same initial conditions, our results show that water has a minimal direct effect on HEOS. However, the corresponding decrease in initial density significantly shifts the pressure-temperature trajectory. At constant shock pressures, hydration raises peak temperatures, altering volatile loss and melting behavior. The enhanced heating and melting caused by the presence of water implies that hydrated materials could have played a role in shaping the evolution of planetesimals. This challenges previous assumptions constructed on dry silicate models and suggests that volatile-rich bodies may have differentiated more efficiently. In shocked melts, the fast diffusion of hydrogen, compared to the cations, indicates its weak integration into the silicate network. Accordingly, we find that Si-H forms only transiently. Furthermore, analysis of the electron localization function supports the presence of bonded Si-H and Fe-H species along the HEOS, identified from a geometrical approach. The proportions of hydrides depend on the shock conditions and could affect the redox state of the melt, even when they are rare. Our results suggest that even a small amount of water in silicates influences the thermodynamics and chemical behavior during planetesimal impacts. These transformations should be considered in models of core formation and volatile depletion of early planetary bodies.

Unified Astronomy Thesaurus concepts: Impact phenomena (779); Mineral physics (2230); Planet formation (1241); Planetesimals (1259)

## 1. Introduction

Impact events play a fundamental role in shaping the evolution of terrestrial planets. All major models of planet formation require an impact-dominated phase. In the pebble accretion model, impacts are concentrated in the final stages of accretion (A. Johansen et al. 2021). In planetesimal accretion models, collisions are the central mechanism for mass accumulation and planetary growth (E. Kokubo & S. Ida 2000; S. N. Raymond et al. 2009; A. Morbidelli et al. 2012). Regardless of the accretion pathway, rocky planets undergo a series of high-energy collisions, culminating in giant impacts such as the Moon-forming event in the Earth's history (R. M. Canup & E. Asphaug 2001; M. Ćuk & S. T. Stewart 2012; M. Nakajima & D. J. Stevenson 2014).

The behavior of materials under such supersonic impacts is best described using shock physics via Hugoniot equations of state (HEOS). Because of their importance, many studies have focused on the determination of HEOS for a wide range of planetary materials (T. J. Ahrens et al. 1969), from simple oxides such as MgO (T. S. Duffy & T. J. Ahrens 1995; C. A. McCoy et al. 2019) or silica (H. J. Melosh 2007), to multicomponent silicate minerals and rocks such as forsterite (B. Militzer 2013; C. W. Thomas & P. D. Asimow 2013; S. Root et al. 2018), enstatite (D. K. Spaulding et al. 2012), dunite (G. S. Collins & H. J. Melosh 2014), bulk rock compositions such as granite (J. L. Shang et al. 2000), liquid silicates (P. D. Asimow & T. J. Ahrens 2010), or metallic

alloys (W. W. Anderson & T. J. Ahrens 1996). These studies have shown that giant impacts between silicate-rich bodies can induce partial vaporization of silicate materials (R. G. Kraus et al. 2015; E. J. Davies et al. 2020; J. Li et al. 2021; A. Saurety et al. 2025) or lead to the formation of supercritical fluids (R. Caracas & S. T. Stewart 2023). The vaporization of planetary materials during catastrophic impacts may drive the loss of volatile and moderately volatile elements, such as rubidium (E. A. Pringle & F. Moynier 2017), magnesium (R. C. Hin et al. 2017), or zinc (F. Moynier et al. 2010; Z.-Y. Long et al. 2024).

Despite these advances, the response to shock of volatile-rich materials, especially hydrated silicate melts, remains poorly constrained. A few experimental and theoretical studies have investigated the behavior of carbon- and water-rich planetary materials under shock, including serpentine (M. B. Boslough et al. 1980; M. A. Lange et al. 1985), calcite (S. Ohno et al. 2008), phlogopite (X. Zhu et al. 2025), the Murchison meteorite (J. A. Tyburczy et al. 2001), or metal-carbon assemblages (N. Pineau et al. 2015). However, to the best of our knowledge, there are no studies on the role of volatiles in the shock behavior of complex natural bulk rock compositions relevant to planetesimals and planetary embryos. Such data are critical for understanding the partitioning and behavior of volatile elements during the high-energy impacts that dominated accretion.

Atomistic simulations, like ab initio molecular dynamics (AIMD), have been successfully applied to investigate the HEOS for a variety of planetary materials, including feldspars (A. Kobsch & R. Caracas 2020), forsterite (B. Militzer 2013; S. Root et al. 2018), chondrule melts (A. Saurety et al. 2025), silica (Y. Laudernet et al. 2004; R. Renou et al. 2017;

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹Institut de Physique du Globe de Paris, 1 rue Jussieu, Paris, 75005, France</footnote>

<footnote n="2">²The Center for Planetary Habitability (PHAB), University of Oslo, Oslo, 0371, Norway</footnote>
<table><caption>**Table 1**
Chemical Composition of the Two Materials Described in This Study</caption><thead><tr><th rowspan="2">Material</th><th colspan="7">Oxide (wt %)</th></tr><tr><th>FeO</th><th>SiO<sub>2</sub></th><th>MgO</th><th>Al<sub>2</sub>O<sub>3</sub></th><th>CaO</th><th>Na<sub>2</sub>O</th><th>H<sub>2</sub>O</th></tr></thead><tbody><tr><td>Dry chondrule</td><td>6.98</td><td>46.57</td><td>41.13</td><td>2.91</td><td>2.17</td><td>1.05</td><td>...</td></tr><tr><td>Chondrule + H<sub>2</sub>O</td><td>6.84</td><td>45.61</td><td>40.29</td><td>2.34</td><td>2.12</td><td>1.02</td><td>2.05</td></tr></tbody></table>

Y.-F. Xie et al. 2021), calcium silicate hydrate (W. Lin et al. 2018), and pyrolite (S. Stewart et al. 2020; R. Caracas & S. T. Stewart 2023). AIMD also effectively simulates volatile-bearing silicate melts (B. B. Karki et al. 2010; R. Vuilleumier et al. 2015; N. V. Solomatova et al. 2019; S. K. Bajgain & M. Mookherjee 2021). Here, we employ AIMD to compute the HEOS of a chondrule-like silicate melt enriched with 2.05 wt% H₂O, a realistic amount of water in chondrites (C. Allègre et al. 2001; L. Piani et al. 2020). We examine the effect of water on the properties of the fluid and the position of the HEOS.

## 2. Methods

### 2.1. Materials

We modeled a multicomponent silicate melt with the composition of a chondrule, as in A. Saurety et al. (2025), using the data of P. Friend et al. (2018). We added six molecules of H₂O to this initial simulation cell to obtain a hydrated silicate melt. Table 1 shows the composition of the simulated material in oxide wt%. The addition of H₂O does not significantly modify the proportion of SiO₂ and MgO. Thus, our hydrated chondrule is still close to the composition measured by P. Friend et al. (2018).

### 2.2. The Equation of State

Shocks are processes in which materials are compressed and heated extremely fast by impact. These processes are out of equilibrium and cannot be treated by Vinet or Birch–Murnaghan-type equations of state, which are derived for static, equilibrated processes using Taylor expansions of the energy with respect to static strain.

However, by applying the conservation of mass and momentum to the material before and after the shock wave passes (B. Y. Zel'dovich & Y. P. Raizer 2002; W. M. Isbell 2005; J. W. Forbes 2012), we can obtain the following equation:

$$E - E_0 + \frac{1}{2}(P - P_0)\left(\frac{1}{\rho} - \frac{1}{\rho_0}\right) = 0, \quad (1)$$

where E, P, and ρ (respectively, E₀, P₀, and ρ₀) stand for the internal energy, pressure, and density of the material during (respectively, before) the shock wave passes. This equation is known as the Hugoniot–Rankine equation. We call the ensemble of points that verify the Hugoniot–Rankine equation the HEOS.

During the passage of the shock wave, the temperature and pressure state of the material are projected from the initial values to another point on this HEOS line. We can calculate the position of this point on the HEOS using the particle velocity in the material and the impactor velocity. The pressure

P is related to the particle velocity in the material $u_p$ as (B. Y. Zel'dovich & Y. P. Raizer 2002; J. W. Forbes 2012)

$$P = a \times u_p^2 + b \times u_p + c, \quad (2)$$

where a, b, and c are constant, and $u_p$ is the particle velocity. We can obtain $u_p$ out of the AIMD simulations using (W. M. Isbell 2005)

$$u_p = \sqrt{2(E - E_0)}, \quad (3)$$

which allows us to fit $P(u_p)$ and find the a, b, and c of Equation (2).

### 2.3. Ab Initio Simulations

To compute the internal energies and pressures as a function of density and temperature, we perform ab initio molecular dynamics simulations using the Vienna Ab initio Simulation Package software (G. Kresse & J. Hafner 1993; G. Kresse & J. Furthmüller 1996a, 1996b). We compute the interatomic forces using the projector-augmented wave (PAW) method (P. E. Blöchl 1994) of the density functional theory (DFT; P. Hohenberg & W. Kohn 1964; W. Kohn & L. J. Sham 1965) with the Perdew–Burke–Ernzerhof functional from the generalized gradient approximation formalism (J. P. Perdew et al. 1996). Atomic cores and core electrons are treated using pseudopotentials. The kinetic energy cutoff of the plane waves outside the PAW spheres is set to 550 eV; the cutoff for the Hänkel functions, which describe the augmented charge inside the PAW spheres, is set to 800 eV. The Brillouin zone is sampled at the gamma point. The electronic population of the energy states is treated using a Fermi distribution with smearing energy proportional to the temperature ($k_bT$) (N. D. Mermin 1965).

For the electronic minimization, we use the RMM-DIIS algorithm for the AIMD run (P. Pulay 1980; G. Kresse & J. Furthmüller 1996a, 1996b) and the blocked-Davidson algorithm for the single-point calculations (G. Kresse & J. Furthmüller 1996a, 1996b). On selected snapshots, we analyze the interatomic bonding using the electron localization function (A. D. Becke & K. E. Edgecombe 1990; B. Silvi & A. Savin 1994).

Simulations are performed at a constant number of particles, volume, and temperature within the canonical ensemble. A Nosé–Hoover thermostat (S. Nosé 1984; W. G. Hoover 1985) controls the temperature. The time steps are 1 fs long.

### 2.4. Postprocessing of Simulations

To determine the diffusivity of an atomic type from AIMD simulations, we compute the average mean square displacement (MSD) of this atomic type as a function of time. We obtain the self-diffusion coefficient, D, using the MSD and the Einstein relation:

$$D = \frac{\text{MSD}}{2nt}, \quad (4)$$

where *t* is the simulation time, and *n* is the degree of freedom. In our case, *n* = 3 as we work in three dimensions. The slope of the linear fit of the MSD as a function of time is then proportional to the diffusion coefficient.

We used the pair distribution function (PDF) to identify the first coordination sphere of Mg, Si, H, and C in the different
<figure><img src="image_4.png" /><figcaption>**Figure 1.** HEOS of hydrated (pink plus signs) and dry (green circles) chondrules with the same initial condition of $T_0$ = 10 K and $\rho_0$ = 3.5 g cm$^3$. The points are calculated, and the curves are fitted using spline interpolation. The fits are not physical and should be used to guide the eyes. The presence of H$_2$O induces a change in the HEOS, which tends to disappear with the temperature.</figcaption></figure>

melts along the HEOS. It measures the number of atoms A surrounding a central atom B as a function of the distance to B. This measure is averaged over all the atoms throughout the simulation. After an interatomic exclusion zone, where the PDFs lie at zero, the first maximum represents the most likely interatomic distance, oftentimes assigned as the average bond distance. The next minimum corresponds to the radius of the first coordination sphere. Accordingly, we consider all the atoms A in the coordination sphere of B to be bonded to B. We employ the term “bonded” to describe neighboring atoms geometrically. There are particular cases, like in the case of noble gases in silicate melts (A. Saurety et al. 2024), where a well-defined PDF and a sphere of coordination are purely geometric constructions without having any chemical bonding in the electronic sense. Nevertheless, this approach provides an excellent and intuitive insight into the proximity and physical interactions between atoms in a melt.

The MSD and the PDF are computed using the Magmatomix package (R. Caracas et al. 2021).

We analyzed the electronic properties of our melts using the electron localization function (ELF; A. D. Becke & K. E. Edgecombe 1990; B. Silvi & A. Savin 1994). As the name suggests, the ELF measures the localization of electrons when forming chemical bonds. The ELF is a tool for identifying the presence of covalent bonds between pairs of atoms (Á. Martín Pendás & J. Contreras-García 2023). Together with the Bader charge analysis (R. F. W. Bader 1990), which provides indications about the ionic character of a bond, they enable us to complete a topological analysis of the electronic density distribution in the melt and, from there, obtain information about the chemical bonding between atoms.

### 3. HEOS of Dry and Wet Chondritic Material

Chondrules are former droplets of multicomponent silicate melt (R. H. Hewins & P. M. Radomsky 1990; Y. Amelin et al. 2002; R. Hewins et al. 2005; C. M. O. Alexander et al. 2008; M. A. Morris et al. 2012; B. C. Johnson et al. 2015; A. Johansen & M. Lambrechts 2017; S. T. Stewart et al. 2025).

Their spherical shape suggests they crystallized, most probably in a vacuum. During cooling, they transformed into an aggregate of crystals, the form we find them in today, which are nearly impossible to place on an HEOS as such. Consequently, to describe the initial state, we start with a quenched silicate melt with the composition of a chondrule at different initial temperatures ($T$) and densities ($\rho$). To this

silicate, we incorporate H$_2$O to assess its influence on the HEOS.

Figures 1(a) and (b) illustrate the HEOS for pure chondrule and chondrule + H$_2$O systems, with an initial temperature $T_0$ = 10 K and density $\rho_0$ = 3.5 g cm$^3$ in a temperature–pressure and density–pressure diagram. At moderate peak temperatures, the influence of H is visible, with a difference of about 10 GPa between the two curves at 2000 K. At higher temperatures, the HEOS trajectories overlap. These findings suggest that adding H$_2$O has a weak effect on the HEOS of silicate glasses under comparable initial conditions. This observation aligns well with previous studies, such as P. D. Asimow & T. J. Ahrens (2010) and A. Saurety et al. (2025), which showed similar tendencies. Silicates with varying compositions but similar starting densities tend to fall on similar HEOS.

We derive a second set of HEOS for the hydrated melt starting from an initial pressure of 0 GPa. To establish the reference state, we first perform a relaxation at constant number of particle, pressure, and temperature (NPT) of a silicate glass until it equilibrates at 0 GPa. Using the resulting relaxed density, we quench a well-thermalized hydrated melt from 2000 to 0 K over 2 ps (with a cooling rate of 1 K fs$^{-1}$). The resulting glass, at 0 K and 0 GPa, has a density of 2.76 g cm$^{-3}$, consistent with previous theoretical predictions (S. Bajgain et al. 2015; L. Yuan et al. 2020) and experimental measurements (P. Richet et al. 2000; P. Kiefer et al. 2019). Applying the same procedure at an initial temperature of 1000 K yields a relaxed density of 2.70 g cm$^{-3}$ for the hydrous chondrule.

The observed reduction in initial density due to volatile incorporation directly affects the HEOS. As shown in Figure 2, in the pressure–temperature space (panel (a)), the HEOS are shifted upward in temperature for higher initial temperatures. Thus, for a peak pressure of 100 GPa, an increase in the initial temperature of 1000 K results in an upward shift of the HEOS, which remains roughly constant by about 1000 K. In terms of pressure, for a peak temperature of 4000 K, the peak pressure along the HEOS for the dry chondrule system is 25 GPa higher than for the chondrule + H$_2$O. Beyond about 70 GPa, HEOS become roughly linear, 600 K higher than the HEOS of the wet chondrule with $T_0$ = 10 K. This difference between the dry and wet HEOS is also clear in the density–pressure diagram (see Figure 2(b)). We note that, in this representation, the wet HEOS with $T_0$ = 10 K and $T_0$ = 1000 K are less separated.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** HEOS of a dry (orange circles) chondrule with the same initial condition of $T_0 = 10$ K and $\rho_0 = 3.5 \text{ g cm}^{-3}$ and a hydrated chondrule with an initial density of 2.76 g cm$^{-3}$ and initial temperatures of 10 K (blue plus signs) and 1000 K (green squares). HEOS are plotted in a temperature–pressure diagram (panel (a)) and a density–pressure diagram (panel (b)). The points are calculated, and the curves are fitted using spline interpolation. The fits are not physical and should be used as a guide for the eyes. The modification of the initial density due to water induces a major change in the HEOS of the silicate. This effect is even more critical if the initial temperature is also modified. Panel (c) presents the conditions marked as letters that correspond to the pressure-temperature conditions along the HEOS of wet (A, B, C) and dry (A', B', C') chondrules. These notations are used throughout the paper to illustrate the properties of the melt along the HEOS.</figcaption></figure>

These results demonstrate the nuanced effects of volatiles on the HEOS of silicate glasses. Although compositional changes alone appear to exert a minimal influence under analogous initial conditions, the reductions in initial density resulting from the presence of volatiles significantly modify the pressure–temperature trajectory along the HEOS.

We consider three conditions on the wet and dry HEOS and name them, respectively, A, B, and C and A', B', and C' in Figure 2(c). For the rest of this work, we compared the properties of the two melts under these conditions.

## 4. Hydride Formation

Figure 3 shows the PDF of several selected pairs of atoms in the hydrated and dry chondrule melts at 2000, 4000, and 6000 K. Most of the bond distances are nearly constant at the three points along the HEOS. This is the coupled result of increasing both temperature and pressure. In addition, Figures 3(b) and (d) show that the hydrated and dry melts exhibit the same Si–O bond length, 1.62 Å at 2000 K, which is consistent with previous values from the literature (B. B. Karki et al. 2007, 2010; N. Solomatova & R. Caracas 2019; A. H. Davis et al. 2022). This suggests that volatiles do not significantly affect the Si–O bond length, at least not at the thermodynamic conditions studied here. We observe similar results for the Mg–O bond. The bond length values for H–O bonds (see Figure 3(a)) align well with the literature (M. Pöhlmann et al. 2004; M. Mookherjee et al. 2008; B. B. Karki et al. 2010; S. K. Bajgain et al. 2019; J. W. E. Drewitt et al. 2022).

Molecular water is very rare in our simulations, as the water molecules are immediately dissociated. But we can monitor the H symmetrization between O atoms as observed in various hydrous silicates (J. Tsuchiya et al. 2008; R. Caracas & W. R. Panero 2017; A. Sano-Furukawa et al. 2018) and ices (M. Benoit et al. 2002; A. F. Goncharov et al. 2005; R. Caracas 2008). To do so, we study the cluster of H and O, with H as the central atom. Table 2 shows that the proportion of single HO decreases when the shock peak temperature increases. The proportion of HO$_3$ follows the opposite tendency, and the proportion of HO$_2$ stays constant. This indicates that hydrogen clusters are mainly pressure sensitive, and their coordination increases due to compression.

At 2000 K, the PDF of Si–H presents a small, but distinct, first peak at 1.53 Å in Figure 3(e). This suggests a Si–H direct bonding, and its position is consistent with previous experimental measurements of M. Betrencourt et al. (1986). The second peak on the PDF corresponds to the second coordination sphere, with a sequence of bonds like Si–O–H. The distance between H and Si in the Si–O–H species is around 2.36 Å. We can use simple trigonometry to calculate that the bond angle Si–O–H should be around 122°. In this case, H is in the second coordination sphere of Si. This measure is consistent with the data of M. Pöhlmann et al. (2004), W. R. Panero et al. (2013), and R. Caracas & W. R. Panero (2017). The first peak of the Si–H PDF disappears at higher temperatures when thermal agitation smooths out the second peak and merges it into the first peak. Note that the PDF is just a statistical geometric measure, and the absence of a distinct
<figure><img src="image_6.png" /><figcaption>**Figure 3.** PDF of HO (a) and SiH (c) along the hydrated HEOS, SiO along both dry (d) and hydrated (b) HEOS, and FeH (e). The conditions A, B, and C are along the wet chondrule HEOS, and A', B', and C' are along the dry chondrule HEOS (see Figure 2). The “ch” stands for chondrule composition.</figcaption></figure>

<table><caption>**Table 2**
Proportion of HOₓ Clusters in Simulations along the HEOS</caption><thead><tr><th>Peak Temperature</th><th>2000 K</th><th>4000 K</th><th>6000 K</th></tr></thead><tbody><tr><td>HO</td><td>33%</td><td>27%</td><td>19%</td></tr><tr><td>HO₂</td><td>50%</td><td>50%</td><td>46%</td></tr><tr><td>HO₃</td><td>16%</td><td>22%</td><td>31%</td></tr></tbody></table>

**Note.** This table shows that the average number of oxygen atoms surrounding hydrogen increases when the pressure increases.

peak does not mean there is no Si-H bonding at all. After the first peak, at 2000 K, the first minimum of the PDF corresponds to the maximum Si-H bond length. We measure a maximum bond length of 1.73 Å. The low height of this peak indicates that this bonding is very rare. We use the maximum bond length of SiH measured at 2000 K as a criterion for identifying Si-H bonding at several points along the HEOS. The results are presented in Figure 4.

Along the HEOS, from 2000 to 4000 K (Figure 7(b)), the average lifetime of the Si-H pairs decreases from 18.0 to 5.6 fs. This result is expected as the thermal agitation increases. The number of clusters also decreases, as the effect of temperature is more important than that of pressure, which tends to pack atoms together. From 4000 to 6000 K, the average lifetime increases from 5.6 to 6.5 fs, suggesting an increase of the importance of packing under pressure. However, especially at higher temperatures, the average lifetime of the Si-H clusters is polluted by ultrashort clusters that last only a few femtoseconds. These clusters are likely the result of ballistic effects due to the fast diffusion of hydrogen that passes close to a Si atom. Most of these hydrogen atoms bounce around a given Si atom, come close enough to it to blur the limit of the first coordination sphere of SiH and, consequently, are counted as a SiH pair. However, they do not stay long enough to bond with Si. Instead, they generate a large number of short-lived clusters, as we see in Figure 4.

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Analysis of the number and the lifetime of the Si-H pairs recorded in our simulation along HEOS. Each bar of the histogram corresponds to one Si-H pair, and the height of the bar corresponds to the lifetime of this pair.</figcaption></figure>

This behavior, where H comes close to Si due to its fast diffusion, may cause the smoothing and merging of the peaks on the PDF.

Therefore, we can count the number of clusters with a lifetime greater than a chosen cutoff time. The frequency of the stretching vibration of the Si-H bond is 2000–2100 cm⁻¹ (G. Lucovsky 1992), corresponding to a 16 fs period. Then we can choose a cutoff time of 32 fs to account for only the Si-H pairs that undergo more than two vibrations. With this approach, at 2000 K, the slow kinetics results in a large number of long-lived Si-H pairs. At 4000 K, the increase in temperature reduces the number of Si-H clusters. We observe only 13 Si-H pairs that live more than 32 fs. By the time the HEOS reaches 6000 K, the increase in pressure is sufficient to promote the bonding between Si and H despite the high temperature, which increases the number of long-lived clusters. This interplay of temperature and pressure is the reason why the number of long-lived clusters changes from 45 at 2000 K down to 13 at 4000 K and then back up to 43 at 6000 K.

To further distinguish between the ballistic effects and the actual electronic bonding, we can analyze the electronic properties, such as the ELF, for the Si-H and O-H pairs of
<figure><img src="image_8.png" /><figcaption>**Figure 5.** ELF of our melt around a hydrogen atom in a SiH bonding case (a) and an OH bonding case (b). The color scale indicates the probability of finding an electron close to another electron at every point of the simulation. The red color indicates high probability, while blue indicates low probability. Therefore, the red zone highlights the presence of an electron pair near the hydrogen atom. Only the local environment of the atoms of interest is displayed, for clarity.</figcaption></figure>

atoms. For this, we identify a snapshot in the simulation at 4000 K in which hydrogen is close to silicon (1.5 Å or less) but far from the surrounding oxygen (more than 2 Å). We also identify a snapshot in the same simulation where the same hydrogen is far from the silicon but at 1 Å distance from an oxygen atom. Thus, we can analyze the difference in Si–H and O–H bonding. For this, we run single-point DFT calculations with high electronic precision to compute the ELF on both snapshots. For the rest of this work, we refer to the first snapshot as the SiH snapshot and the second snapshot as the OH snapshot; they are represented, respectively, in Figures 5(a) and (b).

The ELF is particularly useful in analyzing covalent bonds. When investigating the ELF, we search for regions of high values that correspond to the localization of electrons, typically found in covalent bonds or lone pairs. These are called basins. The basins are separated by regions of low ELF values, which suggest a lack of a covalent bond. In DFT studies, the pseudopotentials create an exclusion zone around the nuclei where the ELF is typically low. Thus, the basins are concentrated in the surrounding regions where covalent bonds exist. The only exception is hydrogen, as its pseudopotential does not include core electrons and does not present such an exclusion zone.

In the SiH snapshot (Figure 5(a)), there are large ELF basins around the O atoms and on the H atom. They are all separated from each other by large zones of low ELF values, suggesting that there is no O–H bonding. But the Si atom and its exclusion zone, due to the existence of a pseudopotential, are in contact with the ELF basin of H. An integral of the charge density over the geometrical space occupied by the H basin indicates 2.1 electrons in this basin (A. Otero-de-la Roza et al. 2014). This suggests that H is covalently bonded to the Si atom, which shares electrons. This interpretation is consistent with the number of charges in the basin. Indeed, Si has an electronegativity of 1.9 and H of 2.2 (J. Mullay 1987). Moreover, the shape of the protonated disynaptic basins, i.e., a shared electron pair involving H, is consistent with other ELF studies (V. G. Avakyan et al. 2006; K. Koumpouras & J. A. Larsson 2020).

In the OH snapshot (Figure 5(b)), clear ELF basins are again observed centered on the H and in contact with those around its neighboring O atoms (A. Otero-de-la Roza et al. 2014). We find 1.6 electrons inside the H basin. This value indicates that O shares a considerable fraction of an electron with H; the deviation from the nominal two is due to the electronegativity of O that drags charges from the OH bond (J. Mullay 1987).

This analysis shows that both Si–H and O–H are characterized by covalent bonding. Their formation contributes to the extension of the lifetime of the respective pairs, as seen in the several cases that last for beyond two vibrations.

The Fe–H PDF in Figure 3(e) indicates a well-defined first coordination sphere at 2000 K with a radius of the first coordination sphere of 1.8 Å and a first peak of 1.47 Å. These results are consistent with the bond distance measurement of J.-R. Hamon et al. (2002). The PDFs get blurry at 4000 and 6000 K, similar to what we observed with Si–H. Therefore, we apply the same method as for Si–H and compute the number of Fe–H clusters within a distance of 1.8 Å that last longer than 32 fs. We found 70 clusters at 2000 K, 75 at 4000 K, and 57 at 6000 K. These numbers suggest that the different effects of temperature and pressure are shifted upward along the HEOS for Fe–H compared to Si–H.

# 5. Other Properties of the Melt

## 5.1. Speciation of Mg and Si

Along with the speciation of H, we investigate the evolution of magnesium and silicon speciation with oxygen along the HEOS. Figure 6 shows the proportion of each MgOₓ ((c) and (d)) and SiOₓ ((a) and (b)) species as a function of condition on the HEOS in dry and wet melts. In both cases, the proportions of highly coordinated species increase with pressure and temperature. In parallel, the proportion of less coordinated species decreases.

These results were expected as the pressure increases with the temperature along the HEOS. Moreover, one can notice that, for the same temperature, the proportion of highly coordinated species is higher in the dry melt than in the melt with water, which was expected as the pressure is higher along the dry HEOS. This difference in species distribution at the
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Proportion of SiO<sub>7</sub> (a), SiO<sub>5</sub> (b), MgO<sub>9</sub> (c), and MgO<sub>6</sub> (d) in the melt along dry and hydrated chondrule HEOS with T<sub>0</sub> = 10 K.</figcaption></figure>

same temperature between the different HEOS is smaller at 6000 K than at 2000 K. This is observed in Figures 6(c) and (d), where the proportion of MgO<sub>6</sub> and MgO<sub>9</sub> converge to similar values for the dry and hydrated melts.

## 5.2. *Diffusivity*

We calculate the self-diffusion coefficients along the HEOS to analyze the transport properties of the melt and better understand the behavior of hydrogen under the shock.

From the MSD, we determine the self-diffusion coefficients of H, Si, and Mg at several pressure-temperature conditions along the HEOS. Figure 7 shows that H diffuses 1 order of magnitude faster than the other cations of the melt. This difference in diffusion highlights its different behavior in the melt structure. The hydrogen atoms bounce freely between the other atoms due to their small size and limited effect on the structure of the melt. The self-diffusion coefficients increase along the HEOS as the effect of temperature outweighs the limitations imposed by the denser packing at higher pressures.

# 6. Discussion and Conclusion

## 6.1. *The Redox State of the Melt*

Our analysis shows the existence of various hydrides at all conditions along the HEOS. If water dissociating into hydroxides is a common feature of hydrated melts, the Si-H and the Fe-H bonds have rarely been observed in complex silicate melts (M. Betrencourt et al. 1986; V. G. Avakyan et al. 2006; N. V. Solomatova & R. Caracas 2021). Their occurrences also vary along the HEOS, more likely to exist at 2000 and 6000 K than at 4000 K. This is the direct result of the interplay between temperature and pressure.

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Diffusivity of Si (square), Mg (circle), and H (cross) along the HEOS of dry and hydrated chondrules with an initial T<sub>0</sub> = 10 K.</figcaption></figure>

The formation of Si-H and Fe-H changes the redox state of the surrounding environment (E. Grinenval et al. 2014) and is generally associated with more reduced silicates (B. B. Karki et al. 2020). As a result of the hydride formation, the hydrogen atoms replace oxygen atoms in the coordination sphere of the silicon. This released oxygen is then free to interact with other atoms in the melt and oxidize them. As the occurrence of bonding changes along the HEOS, we propose that the shock modifies the redox state of the silicate melt. Figure 8 shows a cartoon representation of the phase space, as suggested by our results. The phase space is separated into two regions, based on the likelihood of forming the SiH bond. High pressures and low temperatures increase the Si-H abundance. The melt is
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Sketch representation of the pressure-temperature phase space with the HEOS of the hydrated chondrule represented as a dotted line. The black zone represents the part where the Si-H bonding is unlikely, and the melt is not oxidizing. The Si-H bond forms more easily in the white part, and the melt may oxidize the surrounding environment. The gradient represents the in-between zone where the bond is more or less likely to form, giving the melt a different oxidation state.</figcaption></figure>

more oxidizing under those conditions. On the other hand, low pressure and high temperature inhibit the formation of the SiH bonds, making the melt less oxidizing. The passage between those two regions is gradual, and most likely the HEOS cross this intermediate zone.

This change in oxidizing conditions might affect the evolution of planets and planetary embryos due to impacts. It has been demonstrated (R. B. Georg & A. Shahar 2015) that silicon partitioning in the core depends on the redox condition during core formation. When core segregation takes place or starts during shocks (B. Tonks et al. 1992), the oxidizing state of the hydrated silicate may have an essential role in planetary differentiation.

The FeH formation is less dependent on the shock conditions as the number of clusters stays in the same order of magnitude throughout the conditions investigated here. Therefore, the energy of the impact may not affect the redox condition of the silicate through the FeH formation. Nevertheless, its presence could still be geologically relevant as it may affect the amount of hydrogen trapped in the core (T. Okuchi 1997; L. Yuan & G. Steinle-Neumann 2020; K. Hirose et al. 2021; E. R. Stoutenburg et al. 2024).

Nevertheless, our simulations are too short to draw precise conclusions about the chemical speciation of the hydrides. We only count a few dozen hydride clusters over 20 ps of simulation. While we demonstrate their existence under shock conditions, only longer simulations with better statistics can inform us precisely about the real effects of hydride formation on the redox states of planetary melts during shocks.

## 6.2. Influence of Water on Impacts

Our results suggest that the behavior of silicate melt under shock is affected by the presence of water. When exposed to an impact with a peak pressure of 100 GPa, a hydrated silicate at low temperature is projected to reach a temperature peak of 3800 K. In contrast, a dry silicate reaches only 2700 K. The shift in temperature is roughly constant along the HEOS. This variation could alter the melting and vaporization events of silicate bodies. These effects are observable with as little as 2 wt% of water content, which is close to estimations for

enstatite chondrites (L. Piani et al. 2020). Consequently, impacts between planetesimals in the inner solar system might adhere to HEOS similar to our hydrated scenario. However, mineral grain adsorption inside inner solar system bodies can increase the amount of water, as seen in CI or CH chondrites (M. D'Angelo et al. 2019). With potential water contents of up to 10 wt% (L. Piani et al. 2020), these bodies could undergo massive melting even during small impacts.

Moreover, as the presence of water also decreases the melting point of the silicate, the melting events following impacts might be more frequent than previously estimated when assuming dry silicates (L. T. Elkins-Tanton 2012). These have far-reaching consequences in terms of planetesimal and planetary differentiation (O. Šrámek et al. 2010), core formation (G. J. Golabek et al. 2009), and volatile loss (A. Saurety et al. 2025).

As planetary impacts are the main contributors to accretion, the presence of water in the initial silicate materials may aid in melt production, potentially leading to the creation of chondrules as silicate melt droplets ejected into space. The presence of water can increase entropy under certain peak pressure-temperature conditions, resulting in a greater loss of volatiles from these melt droplets. This might account for the generally dry nature of chondrules, even if they originated from water-rich silicate materials.

## Acknowledgments

A.S. thanks Flavio Siro Brigiano, Thomas Thévenet, and Julia Contreras-García for discussions about the electron localization function and for their help with the Critic2 software. R.C. acknowledges support from the UPC Labex UnivEarthS (project VADIS), the Research Council of Norway, project numbers 332523 (PHAB) and 325567 (HIDDEN), the Research Institute of the University of Bucharest (ICUB), and access to supercomputing facilities via eDARI stl2816 and Uninet2 NN9697K grants.

## ORCID iDs

Adrien Saurety https://orcid.org/0000-0001-6967-9718

Razvan Caracas https://orcid.org/0000-0003-4586-776X

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