# Theoretical Calculations on the Effect of Adsorbed Atom Coverage on the Sodium Exospheres of Airless Bodies

Liam S Morrissey, Jesse Lewis, Amanda Ricketts, Deborah Berhanu, Caixia Bu, Chuanfei Dong, Denton S Ebel, George E Harlow, Ziyu Huang, François Leblanc, et al.

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Liam S Morrissey, Jesse Lewis, Amanda Ricketts, Deborah Berhanu, Caixia Bu, et al. Theoretical Calculations on the Effect of Adsorbed Atom Coverage on the Sodium Exospheres of Airless Bodies. The Astrophysical Journal, 2025, 981 (1), pp.73. 10.3847/1538-4357/adad63. hal-04974965

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# Theoretical Calculations on the Effect of Adsorbed Atom Coverage on the Sodium Exospheres of Airless Bodies

Liam S. Morrissey<fnref n="1" />,<fnref n="2" /> ID, Jesse Lewis<fnref n="1" /> ID, Amanda Ricketts<fnref n="1" /> ID, Deborah Berhanu<fnref n="2" />,<fnref n="3" /> ID, Caixia Bu<fnref n="4" /> ID, Chuanfei Dong<fnref n="5" /> ID, Denton S. Ebel<fnref n="2" /> ID, George E. Harlow<fnref n="2" />, Ziyu Huang<fnref n="5" /> ID, Francois Leblanc<fnref n="6" /> ID, Menelaos Sarantos<fnref n="7" /> ID, and Sebastien Verkercke<fnref n="6" />

Received 2024 October 7; revised 2025 January 13; accepted 2025 January 14; published 2025 February 27

## Abstract

Our ability to understand the formation of the exospheres of airless bodies such as the Moon and Mercury has been hindered by uncertainties in how surface processes influence exospheric sources. Ejection processes important for exosphere formation rely on the notion that an emitted atom must first overcome an attractive energy with the surface to be ejected into the exosphere (the surface binding energy, SBE). Recent studies have shown that atoms from minerals are more tightly bound than commonly assumed, making it difficult to reconcile how such high volatile concentrations are being observed in the exospheres of airless bodies. Here, we used molecular dynamics modeling to explain the physics underlying the interaction of low-energy returning atoms, initially ejected below the escape energy of the body, with mineral surfaces. Global exosphere models make ill-informed assumptions for these interactions due to a lack of SBEs for adsorbed atoms. Results provide first-of-their-kind SBE distributions for adsorbed atoms and can be used by global models to better understand exosphere formation on airless bodies. We highlight the importance of adsorbate coverage and the atomic arrangement of a surface on the SBE. At low absorbate coverage sodium forms ionic bonds with oxygen, leading to tightly bound adsorbates (SBE ~6 eV). At 1 ML of coverage the free O is terminated and Na is unable to form strong ionic bonds, leading to loosely bound adsorbates (SBE 1-3 eV). Emission processes from covered surfaces will be far more efficient than those without adsorbates. These improvements will allow for better interpretation of mission data such as from MESSENGER, BepiColombo, LADEE, Europa Clipper, and Artemis.

*Unified Astronomy Thesaurus concepts: Solar wind (1534); Mercury (planet) (1024); The Moon (1692); Exosphere (499); Theoretical models (2107); Planetary surfaces (2113); Comet volatiles (2162); Lunar mineralogy (962); Lunar surface (974); Surface processes (2116)*

## 1. Introduction

Planetary science studies of the exospheres of the Moon, Mercury, and other airless bodies have been hindered because of uncertainties in our understanding of how surface processes influence exosphere formation: the surface-exosphere connection. When meteoroids, the solar wind (SW), or photons impinge onto the surfaces of airless bodies in the solar system, they can produce ejecta that contribute to a surface-bound exosphere. An accurate description of the ejecta's behavior in these cases is important because atoms and molecules experience no collisions after their release from the surface in the rarified environments surrounding the body. Global models have explored several processes thought to be responsible for the presence of surface-bound exospheres: thermal stimulated desorption, photon-stimulated desorption (PSD), micrometeoroid impact vaporization, and SW ion sputtering (D. E. Shemansky & T. H. Morgan 1991; F. Leblanc & R. E. Johnson 2003; R. M. Killen et al. 2004; P. Wurz et al. 2010; D. Gamborino et al. 2019; M. Sarantos & S. Tsavachidis 2021; J.-Y. Chaufray et al. 2022; A. Mura et al. 2023). Each of

these processes produces ejecta with different characteristic energies and yields, all of which depend, in part, on the characteristics of the exposed surface such as the type of mineral and its degree of crystallinity. Despite the availability of numerous measurements, the relative contribution of each process to a body's exosphere remains an open question due in part to a lack of understanding of how surface characteristics alter their behavior. For example, the variable sodium observed in the exosphere of Mercury suggests a temperature range most characteristic for PSD (1000-1500 K). However, these observations are observed mainly at regions confined to regions with SW ion precipitation, suggesting some interplay with SW ion sputtering (B. Teolis et al. 2023). M. Sarantos et al. (2008, 2010) have suggested that this observation is explained by diffusion enhanced by ion sputtering that leads to a more efficient desorption mechanism. This highlights the need to better understand the combined effects of ejection and surface processes to truly understand the exosphere of an airless body.

When an atom is ejected from the surface it must overcome an attractive energy with the surface, termed the surface binding energy (SBE). This SBE is often poorly constrained for surfaces representative of planetary bodies because for many of the relevant exospheric species, laboratory experiments are either not available or are too complex to interpret when

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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">¹Engineering and Applied Science, Memorial University, St. John's, NL, A1B2W4, Canada; lsm088@mun.ca</footnote>

<footnote n="2">²American Museum of Natural History, New York, NY 10024, USA</footnote>

<footnote n="3">³State University of New York-Fashion Institute of Technology, New York, NY 10001, USA</footnote>

<footnote n="4">⁴Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA</footnote>

<footnote n="5">⁵Center for Space Physics, Boston University, Boston, MA 02215, USA</footnote>

<footnote n="6">⁶LATMOS/CNRS, Sorbonne Université, Paris, 75252, France</footnote>

<footnote n="7">⁷NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA</footnote>
performed with lunar/simulant powders. Several recent studies have highlighted the need for more careful consideration of realistic SBEs representing the surfaces we can expect on airless bodies (P. Wurz et al. 2022; N. Jäggi et al. 2023; B. Teolis et al. 2023; P. S. Szabo et al. 2024). These studies all agree that our ability to predict exosphere sources relies on an accurate SBE input. More recently, molecular dynamics (MD) simulations, conducted on the atomic scale, have been used to better constrain the SBE for different elemental species from mineral surfaces. For instance, in previous studies of SW sputtering on the Moon and Mercury, it was demonstrated that discrepancies in the SBE can have a significant effect on the predicted sputtering yield, the energy distribution of the ejecta, and the resulting exosphere composition (R. M. Killen et al. 2022; L. S. Morrissey et al. 2022b, 2023). Furthermore, SBEs used in exosphere models are often derived from monoelemental substrates, not representative of the mineral surfaces found on moons and planets (B. V. Yakshinskiy et al. 2000). When complex minerals like albite and anorthite, the end-members of plagioclase feldspar-type minerals, were used to study the SBEs of all elemental species, MD-derived values proved to be significantly higher than the monoelemental substrate values commonly used (L. S. Morrissey et al. 2024). For example, the SBE of sodium (Na) from albite ranged from 4.1 to 10.7 eV, more tightly bound than a commonly assumed value of 0.27 eV (F. Leblanc & R. E. Johnson 2003). These findings affect the resulting yields and energy distributions. In conclusion, results suggested a need for careful consideration of realistic surfaces when modeling the surface-exosphere connection.

These recent studies on the SBE have shown that atoms from minerals are more tightly bound than commonly assumed. Once an atom is ejected from the surface of an airless body, it can either escape the body's gravity field or it can follow a ballistic trajectory ruled by radiative pressure and gravity, until it eventually returns on the surface. Upon return it can then either reflect off the surface, stick through adsorption, or diffuse into the bulk of the substrate. Limited experimental data for Na adsorbed onto SiO₂ suggests that those atoms that stick to the surface may form metallic bonds, different than the ionic bonds found in silicates (T. E. Madey et al. 1998; B. V. Yakshinskiy et al. 2000; B. V. Yakshinskiy & T. E. Madey 2005). Despite this, theoretical exosphere models typically equate the behavior of ejecta from the mineral surface to that from the thin layer of atoms adsorbed to the surface. It is unknown how the SBE of an adsorbed atom changes from its mineral-bound value. In response to the need for more realistic and applicable SBEs, in this study we use MD modeling to study the physics underlying the adsorption of Na onto silicates and discuss the effects on ejection processes. We report first-of-their-kind MD-derived SBEs of Na atoms adsorbed onto minerals at different extremes of surface coverage, which can be used to improve global exosphere models. These improvements are timely and will allow for better interpretation of future mission data such as from MESSENGER, BepiColombo, LADEE, Europa Clipper, or the Artemis missions, which can observe the exosphere but not differentiate the different sources.

## 2. Methodology

We have used MD to study the adsorption of Na atoms onto the surface of an SiO₂ substrate. Na was chosen as an adsorbate as it is easily detectable in the exospheres of the Moon and

Mercury, despite being only a trace element on their surfaces (M. A. McGrath et al. 1986; A. E. Potter & T. H. Morgan 1988; R. M. Killen & W. Ip 1999; A. Mura et al. 2009; P. N. Peplowski et al. 2014; A. Colaprete et al. 2016; H. Y. Song et al. 2016; C. A. Schmidt et al. 2012, 2020; R. M. Killen et al. 2019, 2021; M. Sarantos & S. Tsavachidis 2021). An SiO₂ substrate was chosen as it is a fundamental building block of silicates, the dominant species of lunar regolith (D. S. McKay et al. 1991), and is commonly used in experimental and theoretical studies (D. G. Cahill & T. H. Allen 1994; B. V. Yakshinskiy et al. 2000; M. J. Loeffler et al. 2016; Z. Huang et al. 2022; L. S. Morrissey et al. 2022a; F. Leblanc et al. 2023; S. Verkercke et al. 2023).

The role of thermal desorption in populating exospheric Na is not well defined due to uncertainties in the SBE of both adsorbed and bound Na and to whether it moves deeper into regolith (T. A. Cassidy et al. 2016; M. Sarantos & S. Tsavachidis 2021), and the present work directly addresses this knowledge gap. Here, we initially considered two coverage cases: 0% and 100% coverage. For 0% coverage, we studied how Na adsorbs onto a pure SiO₂ surface. For 100% coverage, we assumed several monolayers (MLs) of Na had been deposited (approximating the extended fluence times found in a laboratory) and instead studied Na atoms interacting with an Na surface. While it is likely that neither the Moon or Mercury are completely covered by several MLs of Na, these extreme cases can be used to study the effects of coverage on SBE, can be readily compared to experiment, and can potentially guide the intermediate cases.

### 2.1. Developing a Silicate Substrate

To capture the 0% Na coverage case, we developed crystalline and amorphous SiO₂ substrates for adsorption. Crystalline SiO₂ was chosen to represent an unweathered, freshly exposed surface that is also commonly used in experimental studies. Amorphous SiO₂ was selected to represent the weathered rims found in mature lunar regolith (L. P. Keller & D. S. McKay 1997; A. R. Poppe et al. 2018; L. C. Chaves et al. 2023). To model crystalline SiO₂, we replicated the conventional unit cell from the Materials Project database: eight times in the x-direction (40.1 Å wide), eight times in the y-direction (34.8 Å wide), and four times in the z-direction (22.0 Å thick) to create a slab containing ~2200 atoms. The final density of the sample, ~2.7 g cm⁻³, agreed with experiment, 2.7 g cm⁻³ (W. M. Haynes 2014), thus validating the method and interatomic potential chosen. For the amorphous substrate, we followed a melting and cooling procedure as described in L. S. Morrissey et al. (2022a) to create an amorphous sample with a density, 2.1 g cm⁻³, that again agreed well with experiment, 2.2 g cm⁻³ (W. M. Haynes 2014). The final amorphous substrate contained ~12,000 atoms. Each substrate then underwent a charge equilibration using the electron equilibration method (W. J. Mortier et al. 1986) as implemented in the Large-scale Atomic/Molecular Massively Parallel Simulation (LAMMPS; S. J. Plimpton 1995) code and described by A. C. T. van Duin et al. (2001). The equilibration minimized the electrostatic energy by adjusting partial charges on individual atoms based on neighbor interactions.

### 2.2. Developing a Sodium Substrate

To capture the 100% coverage case, we also created a pure Na crystalline substrate for adsorption. A single-crystal body-centered cubic Na substrate was formed from 12 × 12 × 6 unit
<table><caption>**Table 1**
Simulated SBEs for Na Adsorbed to Different Surfaces as a Function of Surface Temperature and Impact Energy</caption><thead><tr><th>Surface</th><th>Atomic Arrangement</th><th>Temperature (K)</th><th>Impact Energy (eV)</th><th>Median</th><th>Mean</th><th>Std. Dev.</th><th>Count</th></tr></thead><tbody><tr><td rowspan="10">SiO<sub>2</sub></td><td>Amorphous</td><td>1</td><td>0.1</td><td>7.0</td><td>7.2</td><td>1.3</td><td>670</td></tr><tr><td>Amorphous</td><td>1</td><td>2.0</td><td>7.0</td><td>7.2</td><td>1.5</td><td>360</td></tr><tr><td>Amorphous</td><td>100</td><td>0.1</td><td>7.0</td><td>7.3</td><td>1.7</td><td>490</td></tr><tr><td>Amorphous</td><td>100</td><td>2.0</td><td>7.0</td><td>7.2</td><td>1.4</td><td>330</td></tr><tr><td>Amorphous</td><td>700</td><td>0.1</td><td>6.4</td><td>6.5</td><td>1.6</td><td>650</td></tr><tr><td>Amorphous</td><td>700</td><td>2.0</td><td>6.4</td><td>6.4</td><td>1.6</td><td>305</td></tr><tr><td>Crystalline</td><td>1</td><td>0.1</td><td>5.4</td><td>5.7</td><td>0.5</td><td>305</td></tr><tr><td>Crystalline</td><td>1</td><td>2.0</td><td>5.4</td><td>5.7</td><td>0.5</td><td>498</td></tr><tr><td>Crystalline</td><td>100</td><td>0.1</td><td>5.8</td><td>5.8</td><td>0.6</td><td>477</td></tr><tr><td>Crystalline</td><td>100</td><td>2.0</td><td>5.4</td><td>5.6</td><td>0.6</td><td>523</td></tr><tr><td>Crystalline</td><td>700</td><td>0.1</td><td>5.0</td><td>5.0</td><td>0.4</td><td>499</td></tr><tr><td>Crystalline</td><td>700</td><td>2.0</td><td>5.0</td><td>5.1</td><td>0.4</td><td>528</td></tr><tr><td rowspan="2">Na</td><td>Crystalline</td><td>1</td><td>0.1</td><td>1.2</td><td>1.2</td><td>0.1</td><td>115</td></tr><tr><td>Crystalline</td><td>100</td><td>0.1</td><td>1.2</td><td>1.2</td><td>0.2</td><td>197</td></tr></tbody></table>

cells in the x-, y-, and z-axes, respectively, with a lattice unit of 4.29 Å. This surface was oriented, using Miller indices, with the [100], [010], and [001] directions along the x-, y-, and z-axes, respectively.

## 2.3. Simulating the SBE of Adsorbed Na

For each of the substrates described, the simulation domain was then extended 100 Å in the z-direction, creating a free surface. The surface was constructed such that the perfect (001) cleavage plane was exposed along the z-direction. Boundary conditions were fixed in the direction of the exposed surface (z) and periodic along the lateral directions (x and y), representing an infinite slab with a free surface. We then equilibrated each slab using a Berendsen barostat algorithm and then a Berendsen thermostat (H. J. C. Berendsen et al. 1984) to the desired temperature and zero pressure. Temperatures were selected to represent the athermal case (1 K), along with the minimum and maximum temperatures on Mercury, 100 K and 700 K, respectively (S. C. Chase Jr. et al. 1976).

An Na atom was then created 5 Å above the surface with a random lateral x- and y-position and given a velocity in the normal direction toward the surface. Na velocities corresponding to 0.1 and 2 eV were simulated, a range of values below the escape energy for Na on both the Moon (~0.7 eV) and Mercury (~2.2 eV). The Na atom's position was tracked until its energy on the surface was less than 0.1 eV and a minimum of 3000 steps were completed, which we defined as adsorption. We then used an iterative approach to calculate the SBE of the adsorbed Na atom (L. S. Morrissey et al. 2022b). The SBE was defined as the minimum energy in the normal direction needed to separate the adsorbed atom from the surface such that it experienced no attractive or repulsive forces and the energy remained constant. If the adsorbing Na atom did not stick to the surface, it was not counted in the simulation. After the adsorbed SBE was calculated, the simulation was reset to a new surface with the same initial conditions for the next Na atom. This approach was repeated for different random initial Na x- and y-positions to obtain statistical power. The total number of simulations for each case was between ~200 and 700 Na atoms, depending on the width of the distribution for statistics.

## 2.4. Interatomic Potential

All MD simulations were performed using the LAMMPS package (S. J. Plimpton 1995; A. P. Thompson et al. 2022). Interactions between atoms were simulated using a reactive force field (ReaxFF) empirical potential that allows for the dynamic simulation of bond breaking and reformation in a multielemental substrate (A. C. T. van Duin et al. 2001). ReaxFF is uniquely able to simulate both bonded and nonbonded interactions. Connectivity-dependent reactions (valence and torsion energy) are modeled so that when bonds are broken their contribution to the total energy is zero. Nonbonded, van der Waals, and long-range Coulomb interactions are calculated irrespective of the connections between all atom pairs in the simulation. As a result, ReaxFF potentials do not require the use of long-range interaction methods such as P. P. Ewald (1921) or D. Wolf et al. (1999). Coulomb interactions are cut off at a standard distance of 10 Å. More details are given in A. C. T. van Duin et al. (2001). We selected a ReaxFF potential developed originally by M. C. Pitman & A. C. T. van Duin (2012) and modified by G. A. Lyngdoh et al. (2019) for structures composed of Na, Ca, Al, Si, and O. Bulk and surface properties agreed well with the limited available experimental data. This potential has been used to study a range of silicate structures, including those containing Na, and has demonstrated accurate descriptions of both bulk and surface properties of albite and anorthite (G. A. Lyngdoh et al. 2019; L. S. Morrissey et al. 2022b).

# 3. Results and Discussion

## 3.1. 0% Coverage: Adsorbed Na SBE on SiO<sub>2</sub>

### 3.1.1. Crystalline SiO<sub>2</sub> Surface

Table 1 shows the simulated SBE's for Na adsorbed onto SiO₂ as a function of impact energy and substrate temperature. For crystalline SiO₂, the mean SBE in all cases was between 5.0 and 5.8 eV with a standard deviation of ~0.5 eV. For all temperatures simulated there was also no significant difference in the mean SBE with the incoming energy of the Na atom. While an increased incidence energy would likely increase the proportion of atoms that are deposited below the surface, these atoms were not considered to be adsorbed and were not
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<figure><img src="image_9.png" /><figcaption>**Figure 1.** Probability distributions of the SBE of Na adsorbed onto crystalline SiO₂ as a function of substrate temperature and incidence energy.</figcaption></figure>

included in the SBE calculation, ensuring that only the SBE of adsorbed atoms is being studied. In contrast, temperature had less of an effect on the SBE of the adsorbed atoms. When the surface temperature was increased from 1 K to 700 K, the mean SBE decreased from 5.4 to 5.0 eV.

Figure 1 shows the distribution of SBEs for each simulated case on crystalline SiO₂. At 1 and 100 K surface temperatures the SBE has three distinct peaks, at ~5.4 eV, 6.0 eV, and 6.8 eV, with decreasing intensity. At 100 K there was a slight increase in the intensity of the third peak, potentially due to increased surface diffusion away from the lower-energy peak at the higher temperature (e.g., M. Sarantos & S. Tsavachidis 2021). If that interpretation is correct, this implies much lower surface diffusion barriers than the measured SBEs. In contrast, at 700 K surface temperature the distribution of SBEs shifts to only one peak centered at ~5.0 eV. We suggest that the difference in these distributions is due to the atomic rearrangement of the surface at higher temperatures. Figure 2 shows a top view of each surface at the different simulated temperatures, and Figure 3 shows an example of Na adsorbed on the SiO₂ surface at the different regular SBEs. At low temperatures there are

different regular repeating sites that can be occupied. The low Na SBE peak (~5.2 eV) at 1 K occurs along a single row of surface O atoms without interaction with adjacent O atoms (Figure 3(A)). Higher SBEs occur when the adsorbed Na atom sits between two rows of surface O atoms and is thus interacting with more O atoms and becoming more tightly bound (Figure 3(B)). At 700 K the increased temperature causes a clear rearrangement of the surface O to higher positions relative to 1 and 100 K. This results in Na no longer bonding with O atoms across the two rows (Figure 3(C)) and a distribution with a single peak at ~5 eV (with similar SBE to that in Figure 3(A)).

### 3.1.2. Amorphous SiO₂ Surface

For amorphous SiO₂, there was an increase in the mean SBE relative to the crystalline case for all temperatures simulated, with a mean SBE between 6.4 and 7.0 eV. The standard deviation and range of SBEs were also both significantly larger than the crystalline case. As in the previous case, temperature and incident energy had only minor effects on the mean SBE (<0.5 eV). Figure 4 shows the distribution of Na SBEs on
<figure><img src="image_10.png" /><figcaption>**Figure 2.** Side view of an $SiO_2$ surface slab at 1 K (A), 100 K (B), and 700 K (C). Oxygen atoms are shown in red and silicon atoms in blue.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 3.** Na adsorption onto an $SiO_2$ surface at 1 K and an SBE of 5.2 eV (A), 1 K and an SBE of 6.8 eV (B), and 700 K and an SBE of 5.0 eV. Oxygen atoms are shown in red, silicon atoms in blue, and sodium atoms in yellow.</figcaption></figure>

amorphous $SiO_2$ for each temperature. Unlike the crystalline case, which showed distinct peaks, there are more fluctuations in the distribution for the amorphous case, all with higher-energy tails. Amorphous samples are atomically rough, presenting sites for Na to adsorb deeper onto the surface relative to the crystalline case and to interact with more undercoordinated O. This randomly rough surface creates a wider distribution of SBEs and an increase in the mean due to the presence of higher-energy SBE peaks. Taken together, these atomic arrangements of the substrate have a significant effect on both the mean and the distribution of the SBE.

## 3.2. 100% Coverage: Na on an Na Surface

We also simulated the SBE of Na adsorbed onto a crystalline Na surface, approximating the case where several MLs of Na have adsorbed onto a surface. For Na, we considered 1 and 100 K surface temperatures, as 700 K is above the melting point of Na. For Na adsorbed onto Na, the mean SBE decreased by a factor of ~6 to 1.2 eV, with a standard deviation of only 0.1 eV. This value is in strong agreement with the commonly suggested SBE for Na from pure Na, 1.1 eV, based on the Na sublimation energy (A. Mutzke et al. 2019). This agreement between the SBE of adsorbed Na on Na and the Na sublimation energy further validates the simulation methodology and the interatomic potential. Figure 5 shows the distribution of Na SBEs for each simulated case. For both temperatures there is a distinct peak at 1–1.4 eV, followed by a second smaller peak at ~1.8 eV. This suggests that only low-energy binding sites are available for Na on Na.

## 3.3. Planetary Science Implications and Coverage Considerations

The present results have demonstrated the clear importance of coverage on the SBE, but we have considered only pure

surfaces or Na on Na (approximating several MLs of Na coverage). However, several MLs of Na coverage are unlikely to be present on the surface of either the Moon or Mercury. Therefore, we also conducted MD simulations of Na adsorbed onto an amorphous $SiO_2$ surface that was first covered by 1 ML of adsorbed Na atoms as shown in Table 2. We defined 1 ML of Na as the case when all exposed surface O was terminated by at least 1 adsorbed Na atom. As with previous simulations, Na atoms were then deposited at 0.1 eV at normal incidence on a 1 K, 100 K, and 700 K $SiO_2$ surface. Figure 6 shows the distribution of adsorbed Na SBE on the covered surface. Unlike the case of several Na MLs, where no Na–O interactions were observed, we observed a large range (1–4.2 eV) in the SBE with several distinct peaks. The first peak and most probable peak occurred at ~1.6 eV, close to the SBE found for Na adsorbed onto pure Na, suggesting the presence of Na–Na bonds that are not influenced by the underlying O in the substrate. The next highest peak was observed at ~3.4 eV, below the range found for Na onto crystalline and amorphous $SiO_2$. Therefore, only 1 ML of Na significantly reduced both the mean SBE and the highest values in the distribution. The most common SBEs occurred at energies of 2.8–3.5 eV. These SBE values were not observed when Na was adsorbed onto either pure Na or pure $SiO_2$. This suggests that, despite the O being terminated by Na, there are still long-range Na–O attractive forces beyond 1 ML that increase the SBE from the Na on pure Na case. It is important to note that we do not see any peaks as high as 7.0 eV, what was most common for Na on pure $SiO_2$. In addition, unlike the clean surface case, we do not see a significant difference in the distributions with temperature. This suggests that the effects of the surface rearrangement are limited once the surface is covered in Na. Therefore, 1 ML of coverage significantly affects the SBE of adsorbates relative to a clean pure surface. Depending on the location, the exposed weathered surfaces on airless bodies may also be
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<figure><img src="image_17.png" /><figcaption>**Figure 4.** Probability distributions of SBE of Na adsorbed onto amorphous SiO₂ as a function of substrate temperature and incidence energy.</figcaption></figure>

depleted in near-surface O relative to perfect unweathered samples (D. J. Burke et al. 2011; L. C. Chaves & M. S. Thompson 2022; L. C. Chaves et al. 2023). As shown for Na on a covered surface, when no ionic bonds are available the longer-range bonds with O are comparatively weaker. We expect that adsorbates on O-depleted surfaces would again have comparatively lower SBEs than a stoichiometric surface. It is also important to note that in this study we have considered only crystalline and amorphous SiO₂. In a future study we will model the SBE of other relevant adsorbates and silicate types (such as albite and anorthite) on perfect and O-depleted substrates.

The SBE is an important input into global-scale models used to predict the relative contributions of different Na sources to the exospheres of the Moon and Mercury. According to Thompson theory (M. W. Thompson 1968), decreasing the Na SBE from 7.0 eV (Na on amorphous SiO₂) to 1.2 eV (Na on Na) would decrease the peak in the energy distribution of the ejected Na from 3.5 to 0.6 eV, a factor of ~5.8. The energy distribution of the ejecta is a key parameter dictating the

proportion of the ejecta that escapes the body relative to that which contributes to its exosphere. For the sputtering yield, we previously showed that increasing the Na SBE from ~1.5 to ~7 eV decreased the Na sputtering yield by almost an order of magnitude (L. S. Morrissey et al. 2022b). Therefore, accurately predicting the relative contributions of different emission sources to a body's exosphere relies on first understanding the characteristics of the exposed local surface. If the surface is already partially covered, for example if adsorbates have accumulated over long timescales, then adsorbed atoms will bond weakly and would lead to more efficient sputtering at low emission energies, contributing significantly to the exosphere. It is unknown how adsorbed atoms would bond to weathered surfaces, where exposed undercoordinated O has been removed first. Future research is also needed on intermediate coverage values beyond the three cases considered here, along with a better understanding of how the surface coverage of different volatiles might be expected to change at different locations on bodies such as the Moon and Mercury. It is unknown if Na
<figure><img src="image_18.png" /><figcaption>**Figure 5.** Probability distributions of SBE of Na adsorbed onto Na as a function of substrate temperature.</figcaption></figure>

<table><caption>**Table 2**
Simulated SBEs for Na Adsorbed onto Amorphous SiO₂ Surfaces with 1 ML of Adsorbed Na</caption><thead><tr><th>Surface</th><th>Temperature (K)</th><th>Impact Energy (eV)</th><th>Median</th><th>SBE (eV) Mean</th><th>Std. Dev.</th><th>Count</th></tr></thead><tbody><tr><td>Amorphous SiO2 w/1 ML of Na</td><td>1</td><td>0.1</td><td>2.8</td><td>2.8</td><td>0.9</td><td>300</td></tr></tbody></table>

adsorbing onto sub-ML cases will be influenced by other Na atoms or if the clean and 1 ML cases can be scaled linearly.

### 3.4. Comparison with Previous Simulations and Experiments

These MD-derived SBEs can also be used to better explain and quantify previous simulation and experimental results. Previous MD simulations of SBEs from silicates have suggested that the SBE of a bound atom in the lattice is dependent on the local surface position that the atom occupies along with the cleavage plane exposed (L. S. Morrissey et al. 2024). For Na in crystalline albite, our previous simulations found SBEs ranging from 4.1 to 10.7 eV, all of which contained Na–O bonds. The differences in SBEs were attributed to the coordination of the Na atom and the location of the O bonds formed. Here, we show that even when Na is adsorbed onto a pure crystalline surface, instead of being a part

of the mineral, the mean SBE is still within this range. Hence, whether the Na is contained within the lattice or adsorbed to the surface it is forming a strong ionic bond with O (Na–O single bonds have dissociation energy of ~2.8 eV J. A. Dean 1999). We note that our values are discrepant from dissociation energies as we form more than just a single bond. When O is no longer available on the surface, the Na instead forms comparatively weaker Na–Na covalent bonds (the Na–Na single bond dissociation energy is ~0.8 eV; J. A. Dean 1999). These findings suggest that the presence of undercoordinated O on the surface has a significant effect on the SBE of the adsorbed Na. Surfaces with low coverage have exposed undercoordinated O and can form significantly stronger bonds with Na than those where the O has been covered and is no longer available for bonding (W. M. Farrell et al. 2016; X. Wang et al. 2018).
<figure><img src="image_19.png" /><figcaption>**Figure 6.** Probability distributions of the SBE of Na adsorbed onto an SiO₂ surface with 1 ML of adsorbed Na at different surface temperatures.</figcaption></figure>

Yakshinskiy and Madey (B. V. Yakshinskiy et al. 2000; B. V. Yakshinskiy & T. E. Madey 2005) conducted a series of experiments to study the thermal desorption of Na onto amorphous SiO₂ films. Their results showed a distinct change in desorption behavior with Na adsorbate coverage as temperature was increased, despite not being able to directly measure the SBE of the adsorbate. Because our MD simulations adsorbed and then immediately removed the Na atoms, we did not allow for the long durations (on the order of seconds; F. Leblanc & R. E. Johnson 2003) needed to observe subsequent desorption with temperature. However, our study expands on this work by quantifying the SBE distributions at the different coverage scenarios, something which could only be inferred based on intensity with increasing temperature. At coverage below 1 ML, B. V. Yakshinskiy et al. (2000) observed a high-temperature Na desorption peak, suggesting tightly bound Na. As coverage in the experiment increased to 1.1 MLs of Na, a higher-intensity low-temperature peak was observed (in addition to the presence of the smaller high-temperature peak), suggesting the presence of lower-energy bonds. Finally, at 1.9 and 2.2 ML of coverage the experimental low-energy peak was significantly larger, and the two cases overlapped. This suggests that at ~2 ML of coverage the comparatively weaker Na–Na bonds are dominant and are unaffected by the underlying substrate. Our MD simulations support and quantify these observations. We show that at zero coverage Na forms high-SBE ionic bonds with O, which could be observed as a high-temperature peak. At 1 ML of Na coverage, the Na in our simulation can form lower-energy covalent bonds with Na but is still influenced by the underlying O, leading to both low- and high-energy SBEs as suggested by the experiment. Finally, at significant coverage (approximated by Na on Na in our simulation) we see only a low-energy peak, agreeing with experimental results at ~2 ML.

B. V. Yakshinskiy et al. (2000) also conclude that the presence of a wide desorption peak in the data at sub-ML coverage suggests that these sites are populated simultaneously and thus the effect of diffusion is limited. Our simulations also demonstrate a large range in SBEs for the different adsorption cases, agreeing with the finding that adsorbates will randomly sample the different binding energies on the surface, producing a range of values. This agreement in the behavior of the binding energy with coverage also helps to validate the simulation methodology. It is important to note that B. V. Yakshinskiy & T. E. Madey (2005) also observed similar

behavior for the adsorption of potassium onto a similar SiO₂ surface, suggesting that other adsorbates can occupy surface O. It is unknown how other adsorbates, in particular hydrogen from the environment, can terminate free surface O and potentially reduce the SBE of subsequently adsorbed atoms.

## 4. Conclusions

We have used MD simulations to probe the underlying physics of adsorption onto silicates for planetary science and quantify the first-of-their-kind SBEs. This study is the first to consider SBEs for cases more relevant to planetary science and astrophysics. We highlight the importance of accounting for adsorbate coverage and the atomic arrangement of a substrate surface when trying to model different ejection processes on airless bodies. At low coverage there is little difference between the SBEs of adsorbed Na and Na in the mineral. However, those surfaces where free O is terminated by previously adsorbed atoms are unable to form strong ionic bonds and will thus contain loosely bound Na adsorbates. Emission processes from these covered surfaces will be far more efficient than from surfaces that are “clean” and without adsorbates. Future exosphere models must better incorporate our new understanding of coverage-dependent SBEs to better predict different exospheric sources on the Moon and Mercury.

## Acknowledgments

L.M. and A.R. were supported in part by the NSERC Discovery Grant and the CSA Research Opportunities in Space Sciences program awards. C.B, D.S.E, and G.E.H. were supported, in part, by NASA Solar System Workings Program Award grant No. 80NSSC18K0521. Z.H. and C.D. were supported, in part, by NASA grant 80NSSC23K0894. We thank Daniel Savin for stimulating discussions on the work.

## ORCID iDs

Liam S. Morrissey https://orcid.org/0000-0001-7860-9957

Jesse Lewis https://orcid.org/0009-0005-7639-6472

Amanda Ricketts https://orcid.org/0009-0001-6399-6226

Deborah Berhanu https://orcid.org/0009-0004-4349-030X

Caixia Bu https://orcid.org/0000-0002-4426-4425

Chuanfei Dong https://orcid.org/0000-0002-8990-094X

Denton S. Ebel https://orcid.org/0000-0003-2219-4902
Ziyu Huang https://orcid.org/0000-0002-8624-1264

François Leblanc https://orcid.org/0000-0002-5548-3519

Menelaos Sarantos https://orcid.org/0000-0003-0728-2971

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