# Potassium isotopic compositions and model exposure ages of lunar soils

Kun Wang, Zhen Tian, Megan Broussard, Mason Neuman, Piers Koefoed, Olga Pravdivtseva, Guillaume Avice, Richard V. Morris, Kees C. Welten, Randy L. Korotev, et al.

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► To cite this version:

Kun Wang, Zhen Tian, Megan Broussard, Mason Neuman, Piers Koefoed, et al. Potassium isotopic compositions and model exposure ages of lunar soils. Geochimica et Cosmochimica Acta, 2025, 396, pp.28-41. 10.1016/j.gca.2025.01.043. insu-05080895

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# Potassium isotopic compositions and model exposure ages of lunar soils

Kun Wang (王昆)<sup>a,b,*</sup>, Zhen Tian<sup>a,b</sup>, Megan Broussard<sup>a,b</sup>, Mason Neuman<sup>a,b</sup>, Piers Koefoed<sup>a,b</sup>, Olga Pravdivtseva<sup>a,c</sup>, Guillaume Avice<sup>d</sup>, Richard V. Morris<sup>e</sup>, Kees C. Welten<sup>f</sup>, Randy L. Korotev<sup>a,b</sup>, Bradley L. Jolliff<sup>a,b</sup>

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

## ARTICLE INFO

Associate editor: Liping Qin

### Keywords:

Space weathering

K isotopes

Maturity

Lunar soils

Lunar regolith

Exposure Age

## ABSTRACT

Space weathering has long been known to alter the chemical and physical properties of the surfaces of airless bodies such as the Moon. The isotopic compositions of moderately volatile elements in lunar regolith samples could serve as sensitive tracers for assessing the intensity and duration of space weathering. In this study, we develop a new quantitative tool to study space weathering and constrain surface exposure ages based on potassium isotopic compositions of lunar soils. We first report the K isotopic compositions of 13 bulk lunar soils and 20 interval soil samples from the Apollo 15 deep drill core (15004 – 15006). We observe significant K isotope fractionation in these lunar soil samples, ranging from 0.00 ‰ to + 11.77 ‰, compared to the bulk silicate Moon (–0.07 ± 0.09 ‰). Additionally, a strong correlation between soil maturity (I<sub>s</sub>/FeO) and K isotope fractionation is identified for the first time, consistent with other isotope systems of moderately volatile elements such as S, Cu, Zn, Se, Rb, and Cd. Subsequently, we conduct numerical modeling to better constrain the processes of volatile element depletion and isotope fractionation on the Moon and calculate a new K Isotope Model Exposure Age (KIMEA) through this model. We demonstrate that this KIMEA is most sensitive to samples with an exposure age lower than 1,000 Ma and becomes less effective for older samples. This novel K isotope tool can be utilized to evaluate the surface exposure ages of regolith samples on the Moon and potentially on other airless bodies if calibrated using other methods (e.g., cosmogenic noble gases) or experimental data.

## 1. Introduction

Space weathering describes the processes which alter the surface materials of airless planetary bodies, like the Moon and asteroids, including micrometeorite impacts, solar wind spallation, and cosmic ray irradiation (e.g., Pieters and Noble, 2016). These processes lead to gradual changes in physical and chemical properties, including reflectance spectra, thermomagnetic properties, grain morphology, and elemental and isotopic compositions (e.g., Adams and McCord, 1970; Blanford et al., 1974; Clayton et al., 1974; Morris et al., 1975). Understanding space weathering is crucial for accurate interpretation of remote sensing data on airless bodies in the solar system, as well as for providing insights into the long-term evolution of the surfaces and space environments of these airless bodies.

Lunar regolith and its < 1 mm grain-size fraction, referred to as lunar soil, are the most studied samples for space weathering (Lucey, 2006) and could serve as a basis for examining how space weathering impacts other airless bodies, particularly in relation to recent near-Earth asteroids sample return missions, such as Hayabusa, Hayabusa2, and OSIRIS-REx (Lauretta et al., 2017; Watanabe et al., 2017). The knowledge gained from studying lunar samples could help to reconstruct the original, “pristine” compositions of surface materials from other bodies visited by sample return missions, which are also likely altered to various degrees by space weathering fractionation effects (Chapman, 2004; Hiroi et al., 2006; Rubino et al., 2020; Noguchi, 2022; Clark et al., 2023).

Extensive studies since the Apollo program have revealed that lunar soils have experienced significant volatile element loss and isotopic

<footnote><sup>a</sup> McDonnell Center for the Space Sciences, Washington University in St. Louis, One Brookings Drive, St. Louis, MO 63130, USA</footnote>

<footnote><sup>b</sup> Department of Earth, Environmental, and Planetary Sciences, Washington University in St. Louis, One Brookings Drive, St. Louis, MO 63130, USA</footnote>

<footnote><sup>c</sup> Department of Physics, Washington University in St. Louis, One Brookings Drive, St. Louis, MO 63130, USA</footnote>

<footnote><sup>d</sup> Université Paris Cité, Institut de physique du globe de Paris, CNRS, F-75005 Paris, France</footnote>

<footnote><sup>e</sup> ARES NASA Johnson Space Center, Houston, TX 77058, USA</footnote>

<footnote><sup>f</sup> Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA</footnote>

<footnote>* Corresponding author.
E-mail address: wangkun@wustl.edu (K. Wang).</footnote>
fractionation during space weathering, for example, Si and O (Epstein and Taylor, 1972), S and K (Clayton et al., 1974). However, in relation to volatile element variation, common soil source materials such as ferroan anorthosite (FAN), mare basalt, and KREEP (K + Rare Earth Elements + P) components exhibit significant differences in elemental compositions, meaning that the starting composition of non-space-weathered lunar soils is difficult to establish. Consequently, differentiating between the effects from source material mixing and space weathering in chemical variations measured in soils is challenging. In contrast, the starting isotopic compositions of these source materials are relatively similar to each other meaning that variations can easily be attributed to space weathering effects. It has previously been shown that the isotopic compositions of S, Fe, Cu and Zn in lunar soils are typically correlated with their ferromagnetic resonance (FMR) maturity index, $I_s$/FeO (see Fig. 1) (Kaplan and Petrowski, 1971; Rees and Thode, 1972, 1974; Kerridge et al., 1975; Morris, 1976, 1978; Thode and Rees, 1976; Wiesli et al., 2003; Moynier et al., 2006; Herzog et al., 2009). Thus isotopic compositions can serve as ideal tracers of space weathering effects on chemical alteration.

In this study, we utilize the high-precision K isotope tracer to reexamine the isotopic fractionation effects resulting from space weathering on the Moon's surface. We begin by reporting a systematic investigation on the K isotopic compositions in both bulk lunar soils and interval samples from a deep drill regolith core. Subsequently, we conduct numerical modeling aimed at better constraining the processes of volatile element depletion and isotope fractionation on the Moon's surface.

## 2. Samples and Methods

Thirteen bulk lunar soils from Apollo 12, 15, 16, and 17, as well as 20 interval samples from the Apollo 15 deep drill core 15004 to 15006 (from the surface to 100.4 cm below the surface) were analyzed in this study (see Table 1 and 2). Their maturity index, as represented by $I_s$/FeO (ferromagnetic resonance normalized to the total iron concentration), vary from an immature value of 4.6 to a mature value of 94 (Morris, 1978). Between 4.2 to 85.0 mg of material per sample were dissolved in this study using concentrated HF-HNO₃ (~28.9 M and 15.7 M, respectively) on a hot plate, where the mass selected for each sample was based on previously reported K concentration data (see Table 1). Following the procedures described in Wang and Jacobsen (2016a) and Chen et al. (2019), the fully dissolved samples were passed through AG50W-X8 (100–200 mesh) cation-exchange chromatography columns twice to purify K. Pre-cuts and post-cuts were also collected for all samples at

each column stage and analyzed with a Thermo Scientific iCAP Q quadrupole ICP-MS (Inductively Coupled Plasma-Mass Spectrometry) to monitor column recovery rates. A recovery rate > 99 % was achieved to ensure no isotopic fractionation occurred during column chemistry. The total-procedure K blank of this method is ~13 ng K (Liu et al., 2020), which is negligible for all samples in this study.

A high-precision K isotope analysis method using a Thermo Scientific Neptune Plus Multi-Collector (MC)-ICP-MS and an Elemental Scientific APEX Omega desolvating nebulizer was applied here (Chen et al., 2019; Koefoed et al., 2023). The sample-standard bracketing protocol was used, with K isotopic compositions reported in the delta notation, where $\delta^{41}K = [(^{41}K/^{39}K)_{\text{sample}}/(^{41}K/^{39}K)_{\text{NIST SRM3141a}} - 1] \times 1000$. The within-run reproducibility is the two-standard error (2SE) of ~10 analyses in one analytical session for each sample and is evaluated as $\pm 0.05 \, \text{‰}$. The long-term reproducibility is evaluated by the two standard deviation (2SD) of the reference material BHVO-2 in different analytical sessions over ~20 months and is $\pm 0.11 \, \text{‰}$ (Chen et al., 2019). This reference material was also analyzed in each analytical session for quality control.

## 3. Results

The K isotopic compositions ($\delta^{41}K$) of bulk lunar soils and interval samples from the Apollo 15 deep drill core (15004–15006) from this study are shown in Table 1 and 2, respectively. The K isotopic compositions of bulk lunar soils vary from 0.00 ‰ $\pm$ 0.07 ‰ (61220, immature trench soil) to + 11.77 ‰ $\pm$ 0.06 ‰ (15041, surface trench soil), while those of interval samples from the deep drill core vary from 2.85 $\pm$ 0.11 ‰ (depth 84.9–85.2 cm) to 10.87 $\pm$ 0.11 ‰ (depth 0–0.7 cm). Nearly all lunar soils are significantly enriched in heavy K isotopes (i.e., $^{41}K$) compared to the K isotopic composition of the bulk silicate Moon (BSM) defined by mare basalts (–0.07 $\pm$ 0.09 ‰) (Tian et al., 2020). In contrast, mare basalts show a restricted range of K isotopic variation from –0.15 $\pm$ 0.04 ‰ to –0.04 $\pm$ 0.04 ‰ (Tian et al., 2020). The K isotopic compositions of the bulk lunar soils are well-correlated with their soil maturity index (Morris, 1976, 1978) (Fig. 2 and Supplementary Fig. S1). The K isotopic compositions of the interval samples from the Apollo 15 deep drill core generally decrease with increasing depth, broadly mirroring the variation in maturity (see Fig. 3). Both the K isotope and maturity profiles of the Apollo 15 deep drill core show an inflection point at ~45 cm depth. Above that depth, K isotopic composition and maturity index sharply decrease from the surface, while below that depth, they stabilize and fluctuate around the average value of the lower core (see Fig. 3). The K isotope profile here is consistent with the top 45

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Isotopic compositions of Zn, Cu, Fe, and S in lunar soils vs. maturities ($I_s$/FeO). All data is from literature: maturity (Morris, 1976, 1978), Zn (Moynier et al., 2006; Herzog et al., 2009), Cu (Moynier et al., 2006), Fe (Wiesli et al., 2003; Moynier et al., 2006), and S (Kaplan and Petrowski, 1971; Rees and Thode, 1972, 1974; Kerridge et al., 1975; Thode and Rees, 1976).</figcaption></figure>
<table><caption>**Table 1**
Potassium isotopic compositions of Apollo bulk lunar soils.</caption><thead><tr><th></th><th>Type</th><th>Mass [mg]</th><th>I<sub>s</sub>/FeO<sup>a</sup></th><th>K<sub>2</sub>O<sup>b</sup> (wt.%)</th><th>δ<sup>41</sup>K<sub>NIST</sub></th><th>2SE<sup>c</sup></th><th>n<sup>d</sup></th><th>Ca/K(mol/mol)<sup>b</sup></th></tr></thead><tbody><tr><td>12033,694</td><td>Trench soil</td><td>17.2</td><td>4.6</td><td>0.41</td><td>1.06</td><td>±</td><td>10</td><td>23</td></tr><tr><td>12070,923</td><td>Soil</td><td>28.6</td><td>47</td><td>0.23</td><td>7.94</td><td>±</td><td>10</td><td>39</td></tr><tr><td>15031,196</td><td>Trench soil (subsurface)</td><td>41.0</td><td>68</td><td>0.23</td><td>9.07</td><td>±</td><td>11</td><td>37</td></tr><tr><td>15041,256</td><td>Trench soil (surface)</td><td>24.1</td><td>94</td><td>0.20</td><td>11.77</td><td>±</td><td>11</td><td>43</td></tr><tr><td>60601,70</td><td>Soil</td><td>48.4</td><td>85</td><td>0.13</td><td>4.73</td><td>±</td><td>10</td><td>104</td></tr><tr><td>61220,40</td><td>Immature trench soil</td><td>60.7</td><td>9.2</td><td>0.09</td><td>0.00</td><td>±</td><td>10</td><td>151</td></tr><tr><td>64501,244</td><td>Soil</td><td>56.4</td><td>61</td><td>0.11</td><td>3.49</td><td>±</td><td>9</td><td>126</td></tr><tr><td>67461,166</td><td>Soil</td><td>85.0</td><td>25</td><td>0.046</td><td>1.38</td><td>±</td><td>9</td><td>309</td></tr><tr><td>71061,192</td><td>Partially shaded soil (subsurface)</td><td>65.0</td><td>14</td><td>0.08</td><td>0.61</td><td>±</td><td>9</td><td>111</td></tr><tr><td>71131,16</td><td>Soil</td><td>69.9</td><td>33</td><td>0.075</td><td>4.58</td><td>±</td><td>8</td><td></td></tr><tr><td>79221,164</td><td>Trench soil</td><td>64.8</td><td>81</td><td>0.09</td><td>3.60</td><td>±</td><td>9</td><td>104</td></tr><tr><td>79241,31</td><td>Trench soil</td><td>44.9</td><td>51</td><td>0.09</td><td>2.31</td><td>±</td><td>10</td><td>103</td></tr><tr><td>79261,102</td><td>Trench soil</td><td>45.1</td><td>43</td><td>0.11</td><td>1.60</td><td>±</td><td>10</td><td>88</td></tr></tbody></table>

<table><caption>**Table 2**
Potassium isotopic compositions of Apollo 15 deep drill core.</caption><thead><tr><th></th><th>Depth range [cm]</th><th>Mass [mg]</th><th>I<sub>s</sub>/FeO<sup>a</sup></th><th>K<sub>2</sub>O (wt.%)</th><th>δ<sup>41</sup>K<sub>NIST</sub></th><th>2SE<sup>b</sup></th><th>n<sup>c</sup></th></tr></thead><tbody><tr><td>15006,348</td><td>0–0.7</td><td>14.6</td><td>74</td><td>0.225<sup>d</sup></td><td>10.87</td><td>±</td><td>11</td></tr><tr><td>15006,347</td><td>4.7–5.2</td><td>9.3</td><td>83</td><td>0.211<sup>e</sup></td><td>9.36</td><td>±</td><td>11</td></tr><tr><td>15006,346</td><td>9.7–10.2</td><td>13.5</td><td>78</td><td>0.198<sup>e</sup></td><td>8.64</td><td>±</td><td>11</td></tr><tr><td>15006,354</td><td>14.7–15.2</td><td>8.9</td><td>79</td><td>0.162<sup>e</sup></td><td>8.38</td><td>±</td><td>11</td></tr><tr><td>15006,353</td><td>19.7–20.2</td><td>10.2</td><td>58</td><td>0.183<sup>e</sup></td><td>6.85</td><td>±</td><td>11</td></tr><tr><td>15006,351</td><td>24.7–25.2</td><td>17.1</td><td>58</td><td></td><td>6.35</td><td>±</td><td>11</td></tr><tr><td>15006,350</td><td>29.7–30.2</td><td>5.8</td><td>66</td><td>0.248<sup>d</sup></td><td>5.20</td><td>±</td><td>11</td></tr><tr><td>15006,349</td><td>34.7–35.2</td><td>7.5</td><td>55</td><td>0.196<sup>e</sup></td><td>5.97</td><td>±</td><td>11</td></tr><tr><td>15006,352</td><td>40.0–40.7</td><td>4.2</td><td>52</td><td></td><td>6.21</td><td>±</td><td>10</td></tr><tr><td>15005,818</td><td>44.5–45.1</td><td>12.3</td><td>40</td><td>0.292<sup>d</sup></td><td>4.05</td><td>±</td><td>9</td></tr><tr><td>15005,820</td><td>50.0–50.5</td><td>12.4</td><td>40</td><td>0.164<sup>e</sup></td><td>4.24</td><td>±</td><td>14</td></tr><tr><td>15005,819</td><td>55.0–55.5</td><td>10.4</td><td>37</td><td></td><td>4.49</td><td>±</td><td>14</td></tr><tr><td>15005,821</td><td>60.0–60.5</td><td>12.4</td><td>33</td><td></td><td>4.34</td><td>±</td><td>14</td></tr><tr><td>15005,822</td><td>65.0–65.5</td><td>6.3</td><td>33</td><td></td><td>3.44</td><td>±</td><td>14</td></tr><tr><td>15005,823</td><td>70.0–70.5</td><td>6.4</td><td>40</td><td>0.236<sup>d</sup></td><td>3.75</td><td>±</td><td>13</td></tr><tr><td>15005,824</td><td>79.5–80.1</td><td>6.4</td><td>37</td><td>0.077<sup>e</sup></td><td>3.02</td><td>±</td><td>13</td></tr><tr><td>15004,274</td><td>84.9–85.4</td><td>4.5</td><td>27</td><td></td><td>2.85</td><td>±</td><td>14</td></tr><tr><td>15004,275</td><td>89.9–90.4</td><td>9.5</td><td>22</td><td></td><td>3.80</td><td>±</td><td>13</td></tr><tr><td>15004,276</td><td>94.9–95.4</td><td>7.9</td><td>27</td><td>0.120<sup>e</sup></td><td>4.21</td><td>±</td><td>11</td></tr><tr><td>15004,277</td><td>99.9–100.4</td><td>4.9</td><td>39</td><td>0.192<sup>d</sup></td><td>3.20</td><td>±</td><td>11</td></tr></tbody></table>

cm of the core being an in-situ reworking/gardening zone, while deeper parts remain undisturbed (McKay et al., 1991).

Three bulk lunar soil samples measured in this study (12033, 12070, and 15041) were also measured previously using thermal ionization mass spectrometry (TIMS) and secondary ion mass spectrometry (SIMS) (TIMS: Barnes et al., 1973; Garner et al., 1975; SIMS: Humayun and Clayton, 1995). Despite the different analytical methods used, the new values measured here agree well with the previous values within analytical uncertainties (1.06 ± 0.06 ‰ vs. 0.09 ± 1.96 ‰; 7.94 ± 0.10 ‰ vs. 8.35 ± 1.97 ‰; 11.77 ± 0.06 ‰ vs. 12.0 ± 0.7 ‰) (Fig. 4). One bulk lunar soil sample (12033) was also analyzed using a different type of MC-ICP-MS (IsoProbe) equipped with a collision cell (Wang and Jacobsen, 2016b) and the results also agree well (1.06 ± 0.06 ‰ vs. 1.00 ± 0.04 ‰) (Fig. 4).

# 4. Discussion

## 4.1. Controlling factors for K isotopic fractionation in lunar soils

### 4.1.1. Soil maturity

The FMR maturity index $I_s$/FeO is a measure of the intensity of the characteristic resonance ($I_s$) normalized to the FeO content of the sample and has been a useful tool to evaluate the degree of space weathering for lunar soils (Morris, 1976, 1978). The FMR maturity index has previously been demonstrated to broadly correlate with intensity of isotopic fractionation for moderately volatile elements such as S, Cu, and Zn, and, on a smaller scale, for the less volatile element Fe (see Fig. 1). Previous K isotope data also show a similar correlation trend between K isotopic composition and soil maturity (Barnes et al., 1973; Garner et al., 1975; Church et al., 1976; Humayun and Clayton, 1995; Wang and Jacobsen,

<footnote>a Literature values are from (Morris, 1978).</footnote>

<footnote>b From literature (see Supplementary Table S2 for references).</footnote>

<footnote>c Standard errors (SE = standard deviation divided by the square root of the total number of measurements).</footnote>

<footnote>d Number of measurements.</footnote>

<footnote>a Literature values from (Morris, 1978). Not from the exact depth. The closest depth was chosen.</footnote>

<footnote>b Standard errors (SE = standard deviation divided by the square root of the total number of measurements).</footnote>

<footnote>c Number of measurements.</footnote>

<footnote>d Literature values from (Nishiizumi et al., 1984). Not from the exact depth. The closest depth was chosen.</footnote>

<footnote>e Literature values from (Fruchter et al., 1975). Not from the exact depth. The closest depth was chosen.</footnote>
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** K isotopic compositions of lunar soil samples vs. maturities ($I_s$/FeO). Color coded according to Apollo missions. Maturity index values are from Morris (1976; 1978) and K isotope data are from this study and literature (Barnes et al., 1973; Garner et al., 1975; Church et al., 1976; Humayun and Clayton, 1995; Wang and Jacobsen, 2016b; Tian et al., 2020).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** K isotopic compositions of samples from Apollo 15 deep drill core vs. maturities ($I_s$/FeO) and depth from the surface (cm). Note that the K isotope and maturity analyses were not conducted on the same sample nor at the same exact depth. Maturity index values are from Morris (1978).</figcaption></figure>

2016b; Tian et al., 2020). However, the new K isotope data in this study fill in the gaps (e.g., $I_s$/FeO between 10 and 40) and firmly establish this relationship (see Fig. 2 and Supplementary Fig. S1). The correlation

coefficient for the new K isotope data alone is 0.60 (R²), while the overall correlation, including both this study and literature data, is 0.55 (R²). Furthermore, when considering only samples from the same location (i.e., Apollo 15 deep drill core), the correlation greatly improves (R² = 0.81; see Fig. 3). This improved correlation is possibly due to two factors: 1) all these data are measured using the same method in the same laboratory, avoiding any possible discrepancies between laboratories; 2) Apollo 15 deep drill core interval samples have a small mass per sample, thus exhibiting less heterogeneity in terms of maturity between different subsamples of the same interval (see discussion in Section 4.1.3).

Overall, the new K isotope results and the correlation with soil maturities are consistent with previous studies of other isotope systems such as S (Kaplan and Petrowski, 1971; Rees and Thode, 1972, 1974; Kerridge et al., 1975; Thode and Rees, 1976), Fe (Wiesli et al., 2003; Moynier et al., 2006), Cu (Moynier et al., 2006), Zn (Moynier et al., 2006; Herzog et al., 2009), Se (Vollstaedt et al., 2020), Rb (Nie et al., 2024), Cd (Sands et al., 2001; Wombacher et al., 2008; Abouchami et al., 2025), which strongly supports thermal volatilization by micrometeorite impacts as responsible for the volatile element loss and heavy isotope enrichment in lunar soils. During micrometeorite bombardment, lunar soils preferentially lose lighter isotopes relative to the lunar soil source materials, thus resulting in the remaining soil becoming increasingly heavy isotope-enriched with increasing maturity. This isotopic fractionation mechanism is discussed in detail in Section 4.2 where a quantitative model is presented.

### 4.1.2. Soil composition

While soil maturity appears to correlate well with the K isotope fractionation observed in lunar soils, there is also considerable scattering (see Fig. 2). This scattering cannot be solely explained by interlaboratory discrepancies, except for one outlier (14163; see Fig. 4), the K isotope data from different literature sources agree with each other within analytical uncertainties. Therefore, other factors, in addition to soil maturity, must also be considered in relation to this observed K isotopic fractionation on the Moon. As previously mentioned in Section 4.1.1, the correlation between K isotope systematics and soil maturity is relatively poor when considering all bulk lunar soil data combined (R² = 0.55) but is significantly stronger when considering only the Apollo 15 deep drill core intervals (R² = 0.81), samples from the same location with less compositional variation. Thus, we consider soil composition variations as another possible factor influencing the observed K isotopic compositions.

As shown in Fig. 5, the lunar soil K isotopic compositions show no obvious correlation with K₂O, Sm, FeO, TiO₂, MgO, and CaO abundances, all of which are elements that vary among the different soil source materials. For example, in the [K₂O] versus K isotope plot, the data show two clusters: Apollo 12 and 14 samples with high K (>0.4 % [K₂O]), and all other samples having low K (0.1–0.2 % [K₂O]). This difference in K concentration between the Apollo 12 and 14 samples and samples from the other missions (see Supplementary Fig. S2) can be explained by the different amounts of KREEP components incorporated (Haskin and Warren, 1991) (see Supplementary Fig. S3). There is no overall correlation between K concentration and K isotopic compositions between high- and low-K samples. Within each K-group cluster, the K isotopic composition are mostly defined by their maturities (see Fig. 5). The same observation can be made on the [Sm] versus K isotope plot where KREEP element Sm is well correlated with K (see Supplementary Fig. S3). Therefore, the [Sm] versus K isotope plot mimics the [K₂O] versus K isotope plot, with no correlation observed between Sm abundance and K isotopic compositions. Within either the high-Sm group (Apollo 12 and 14 samples) or low-Sm group (other mission samples), the K isotopic compositions plot nearly vertically and are mostly related to sample maturity (see Supplementary Fig. S2). This lack of correlation between K isotopic composition and [K₂O] and [Sm] suggests that the abundance of the KREEP component in the soils has no control on
<figure><img src="image_8.png" /><figcaption>Fig. 4. Inter-laboratory comparison of K isotopic compositions of lunar soils. All values are normalized to NIST SRM 3141a, even though various standards were employed in the literature (Barnes et al., 1973; Garner et al., 1975; Church et al., 1976; Humayun and Clayton, 1995; Wang and Jacobsen, 2016b; Tian et al., 2020). The error bars of recent studies (Wang and Jacobsen, 2016b; Tian et al., 2020; this study) are smaller than the symbol sizes.</figcaption></figure>

the observed K isotopic fractionation.

At first glance, this lack of KREEP control seems to be inconsistent with the prediction by Tian et al. (2020) who suggested that the KREEP component should have heavier K isotopic compositions as inferred from KREEP-rich lunar meteorites (average + 0.31 ± 0.27 ‰ compared to average -0.07 ± 0.09 ‰ for mare basalts). However, such small enrichment induced by incorporation of a KREEP component would be overwhelmed by the large kinetic isotopic fractionation caused by space weathering. Indeed, most soil samples, even those with low maturity, have K isotopic compositions much heavier than that of the KREEP component (e.g., see Table 1). Thus, varying proportions of the KREEP component would not have any noticeable effect on the K isotopic composition of these lunar soils.

The FeO and MgO contents of lunar soils serve as indicators of mafic mare basalt components, while CaO and Al₂O₃ abundances act as tracers of feldspathic highland components. The FeO and MgO abundances are negatively correlated with CaO and Al₂O₃ abundances among lunar soils (Haskin and Warren, 1991). As shown in Fig. 5, neither FeO, MgO, nor CaO exhibit any correlations with the K isotopic compositions, suggesting that different mixing proportions of basaltic and feldspathic components do not affect the K isotopic composition of these lunar soils.

The TiO₂ abundances of lunar soils are primarily influenced by the proportions of high- and low-Ti basalt components (Haskin and Warren, 1991), yet other minor components can have some effect (e.g., orange glass; Korotev and Kremser, 1992). This distinction can be clearly seen on Fig. 5, as two clusters of data can be identified. However, much like
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Potassium isotopic compositions vs. K₂O, Sm, FeO, TiO₂, MgO, CaO, K₂O/CaO, and CaO/FeO of lunar soils. The K isotopic values are from this study and literatures (Barnes et al., 1973; Garner et al., 1975; Church et al., 1976; Humayun and Clayton, 1995; Wang and Jacobsen, 2016b; Tian et al., 2020). All elemental compositions are from literature (Wänke et al., 1971, 1972, 1973; Keith et al., 1972; Laul and Schmitt, 1973a,b; Haskin et al., 1973; LSPET, 1973; Gibson and Moore, 1973; Compston et al., 1973; Rhodes et al., 1974; Rose Jr. et al., 1974; Eldridge et al., 1974; Gold et al., 1977; Laul and Papike, 1980; Korotev, 1987, 1991; Korotev and Kremser, 1992; Korotev and Gillis, 2001; Meyer, 2009). Note not all elemental data are available for every sample.</figcaption></figure>
the other elements discussed in this section, TiO₂ compositions are also not correlated with K isotopic compositions, with high- and low-Ti soils showing both heavier and lighter K isotopic compositions. Within each Ti-group cluster, the K isotopic compositions also vary vertically and seem to be only related to their maturities (see Fig. 5).

The chemical compositions of soils from different locations are mostly influenced by the local bedrock types (McKay et al., 1991) and the proportions of mixed components such as highland feldspathic, mare basaltic, and KREEP components (along with meteoritic input, although less significant for the lithophile element K). Since there are no systematic K isotopic differences between mare basalts and highland rocks, and between high- and low-Ti basalts (Wang and Jacobsen, 2016b; Tian et al., 2020), the soil chemical compositions would not have a major effect on the K isotopic compositions of lunar soils. Even certain components, such as KREEP, which could have unique K isotopic compositions, and might have influenced the source compositions of the soils, show variation orders of magnitude less than space weathering effects (i. e., tenths of a per mil vs. several per mil). Thus, we conclude that the chemical compositions of the initial components that make up the soils are not a controlling factor for the observed K isotopic fractionation in these lunar soils.

### 4.1.3. Sample heterogeneity

After excluding chemical composition variability as the source of the data scattering for the K isotope versus maturity plot (Fig. 2), the most likely explanation left is sample heterogeneity among different subsamples of the bulk soil samples. The K isotope and maturity measurements on lunar soils were all conducted on different subsamples. Lunar soils are not well homogenized, so different subsamples of the same lunar samples may have different soil maturities and K isotopic compositions since both are very sensitive to surface exposure. Thus, as seen in Fig. 2, when plotting K isotopic composition and soil maturity from different subsamples a large degree of scatter is observed. For samples where both K isotopic composition and maturity measurements were conducted on the exact same subsamples, we would expect that the correlation would be much tighter. This is what has been observed in preliminary work by Broussard et al. (2024), where they studied the K isotopic compositions and soil maturities of Apollo 17 double drive tube samples (73001/2) from the exact same subsamples and found a correlation coefficient $R^2 = 0.93$ (Broussard et al., 2024). The same conclusion can also be inferred from the Apollo 15 deep drill core samples in this study, where the samples from each dissection interval (0.5 cm) are quite small (typically 1–2 g per interval; Allton et al., 1981) and less variable in terms of maturity within each interval subsample. Thus, we observe a better correlation ($R^2 = 0.81$) between K isotopic compositions and soil maturities for the Apollo 15 deep drill core samples even though the K isotopic compositions and maturities were still conducted on different subsamples (i.e., small sample, less variable between subsamples). In contrast, bulk lunar soil samples that have been measured for K isotopic compositions usually have much more weight per sample (up to several kg), thus it is reasonable to expect large heterogeneity among different subsamples of the same samples in term of maturity. Thus it is no surprise that the only outlier, 14163, where different studies reported significantly different K isotopic compositions (see Fig. 4), is the soil with the largest mass (7,776 g) among all samples having K isotope analyzed. Therefore, we conclude that the data scattering on the K isotope versus maturity plot (Fig. 2) is caused by the sample heterogeneity of different subsamples of large bulk lunar samples. If both K isotopic compositions and soil maturities were done on the same subsamples, the correlation between K isotopic compositions and maturities would likely be much stronger (e.g., $R^2 = 0.93$; Broussard et al., 2024).

We also note that the correlation between K isotopic compositions and maturities for Apollo 17 double drive tube samples (73001/2) is slightly better than that for Apollo 15 deep drill core in this study ($R^2 = 0.93$ vs. 0.81). This is likely because that in the maturity calculation ($I_s$/

FeO) of Apollo 15 deep drill core, the FeO value was estimated and a single FeO value was used for the whole core (Morris, 1976). This was not the case for 73001/2 where the FeO values were measured for each interval (Broussard et al., 2024). This could cause a larger uncertainty for the maturity of the Apollo 15 deep drill core and a greater scatter compared to 73001/2.

Alternatively, the better correlation between maturity and K isotope compositions in the core samples, compared to the bulk samples, might result from simple binary mixing between surface mature (more K isotope fractionated) and deeper immature (less K isotope fractionated) samples. The current dataset does not allow us to distinguish between these two explanations. Future work should focus on analyzing the maturity index and K isotopic compositions, as well as other MVE isotopes, on the exact subsamples of bulk soils.

### 4.1.4. Possible decoupling between K isotopic composition and FMR maturity index

As discussed in previous sections, the K isotopic composition and FMR maturity index in lunar soil are generally correlated (Fig. 2), with deviations largely attributed to sample heterogeneity (Section 4.1.3). However, some of the imperfect correlation or scattering may also arise from a potential decoupling between the K isotopic composition and the maturity index. While both the FMR maturity index and K isotopic composition are influenced by space weathering and should exhibit a strong correlation, the distinct physical and chemical properties of the two systems could lead to some degrees of decoupling.

The FMR maturity index is defined as the ferromagnetic resonance intensity ($I_s$) normalized by the total iron content (FeO) in the sample (Morris, 1976; 1978). The ferromagnetic resonance intensity measures the “amount” of single-domain (~<30 nm) metallic iron (i.e., nano-phase Fe⁰) present in the sample. Thompson et al. (2016) demonstrated that nano-phase Fe⁰ becomes increasingly reoxidized with maturity due to the diffusion of oxygen atoms from the surrounding minerals/phases. This reoxidation of metallic iron may influence the FMR maturity index without affecting the K isotopic composition, potentially leading to decoupling between the two systems.

Another possible mechanism involves the recondensation of vaporized K (enriched in lighter isotopes) during micrometeorite impacts. Tian et al. (2020) observed that some low-K lunar rocks (e.g., anorthosites) are significantly enriched in lighter K isotopes. They hypothesized that this enrichment results from the recondensation of lighter K isotopes, with low-K lunar rocks being more sensitive to such effects due to mass-balance considerations. This recondensation process could influence the K isotopic composition of lunar soils without impacting the FMR maturity index, further contributing to decoupling between the two systems. Additionally, the recondensation of lighter K isotopes would primarily affect low-K lunar soils by shifting their isotopic values lower, whereas high-K samples would experience negligible effects. This phenomenon might partially explain the apparent positive trend between K abundance and K isotopic composition observed for the low-K soil samples in Fig. 5.

## 4.2. Mechanism for K isotopic fractionation in lunar soils

### 4.2.1. Micrometeorite impact vaporization

As shown in the previous section, the K isotopic composition of lunar soils is highly correlated with the soil maturity index (as high as $R^2 = 0.81$ for Apollo 15 deep drill core in this study and $R^2 = 0.93$ for Apollo 17 double drive tube; Broussard et al., 2024). We attribute the extreme K isotopic fractionation and correlation with maturity to the kinetic isotopic effect caused by space weathering, specifically micrometeorite impact and vaporization. This interpretation is in agreement with many other isotopic systems, such as O, Si, S, Cl, Fe, K, Cu, Zn, Se, Rb, and Cd. These systems also exhibit significant isotopic fractionations between lunar regolith and lunar rocks (Kaplan and Petrowski, 1971; Rees and Thode, 1972, 1974; Clayton et al., 1974; Kerridge et al., 1975; Thode
<table><caption>**Table 3**
Terms, parameters, and values used in the model.</caption><thead><tr><th>Term</th><th>Unit</th><th>Definition</th><th>Value</th><th>Reference</th></tr></thead><tbody><tr><td>N</td><td>atom/cm<sup>3</sup></td><td>The concentration of an isotope</td><td>computed</td><td>—</td></tr><tr><td>t</td><td>Ma</td><td>Exposure age</td><td>variable</td><td>—</td></tr><tr><td>A</td><td>atom<br>cm<sup>-2</sup><br>Ma<sup>-1</sup></td><td>Input from<br>micrometeorites</td><td>computed</td><td>—</td></tr><tr><td>φ</td><td>g cm<sup>-2</sup><br>Ma<sup>-1</sup></td><td>Micrometeorite mass<br>flux</td><td>3 × 10<sup>-3</sup></td><td>(Gault et al., 1972;<br>Zook, 1975;<br>Halliday et al.,<br>1989; Peucker-<br>Ehrenbrink and<br>Ravizza, 2000;<br>Taylor et al., 2000)</td></tr><tr><td>C<sub>meteor</sub></td><td>g/g</td><td>K concentration in<br>ordinary chondrites</td><td>900 × 10<sup>-6</sup></td><td>(Lodders and<br>Fegley, 1998)</td></tr><tr><td>C<sub>moon</sub></td><td>g/g</td><td>K concentration in<br>lunar soil</td><td>500-4000 ×<br>10<sup>-6</sup></td><td>(Lucey, 2006)</td></tr><tr><td>N<sub>Avo</sub></td><td>atom/mol</td><td>Avogadro's number</td><td>6.02214076<br>× 10<sup>23</sup></td><td>constant</td></tr><tr><td>M</td><td>g/mol</td><td>Molar mass of<br>element</td><td>39.0983</td><td>constant</td></tr><tr><td>I</td><td>atom/<br>atom</td><td>Abundance of<br>isotopes in ordinary<br>chondrites and mare<br>basalts</td><td>-0.76 ‰;<br>-0.07 ‰</td><td>(Tian et al., 2020;<br>Koefoed et al.,<br>2023)</td></tr><tr><td>f</td><td>atom/<br>atom</td><td>Fraction of isotope<br><sup>39</sup>K retained</td><td>0.7</td><td>free parameter</td></tr><tr><td>B</td><td>cm/Ma</td><td>Stripping rate due to<br>impact volatilization</td><td>computed</td><td>—</td></tr><tr><td>F</td><td>g/g</td><td>Lunar mass<br>volatilized per unit<br>mass of<br>micrometeorite input</td><td>10</td><td>(Pierazzo et al.,<br>1997)</td></tr><tr><td>ρ</td><td>g/cm<sup>3</sup></td><td>Density of lunar soil</td><td>1.5</td><td>(McKay et al., 1991)</td></tr><tr><td>G(t)</td><td>cm</td><td>Thickness of mixed<br>layer</td><td>computed</td><td>—</td></tr><tr><td>γ</td><td>cm</td><td>Thickness of surficial<br>disturbed layer</td><td>4</td><td>assumption in<br>Moynier et al.<br>(2006)</td></tr><tr><td>β</td><td>cm/Ma</td><td>Gardening/mixing<br>rate</td><td>0.005</td><td>best fit from<br>Moynier et al.<br>(2006) for S and Zn</td></tr><tr><td>D</td><td>atom/<br>cm<sup>3</sup></td><td>Initial isotope <sup>39</sup>K or<br><sup>41</sup>K concentration in<br>lunar soils</td><td>computed</td><td>—</td></tr></tbody></table>

and Rees, 1976; Humayun and Clayton, 1995; Sands et al., 2001; Wiesli et al., 2003; Moynier et al., 2006; Wombacher et al., 2008; Herzog et al., 2009; Sharp et al., 2010; Wang et al., 2012; Tian et al., 2019; Vollstaedt et al., 2020; Okabayashi et al., 2020; Nie et al., 2024; Abouchami et al., 2025). To demonstrate the validity of this interpretation, we can model K isotope fractionation through micrometeorite impact vaporization. We note that in this study, we focus solely on micrometeorite impact as the primary mechanism of isotopic fractionation. Other mechanisms, such as ion sputtering, are not considered in our simplified model below. This simplification is justified by the recent work of Nie et al. (2024), which provides a detailed analysis of various mechanisms of K and Rb isotopic fractionation in lunar soils and concludes that micrometeorite impact vaporization is the dominant process.

As early as the 1970s, models with various degrees of complexity have been developed in order to explain the isotopic fractionation initially observed in “traditional” light element isotope systems such as O, Si, and S (Clayton et al., 1974; Haff et al., 1977; Switkowski et al., 1977); however, these earlier models cannot explain and predict the new observations in “non-traditional” heavy element isotope systems, such as Fe, Cu, and Zn, in recent years (Wiesli et al., 2003; Moynier et al., 2006; Herzog et al., 2009; Wang et al., 2012; Okabayashi et al., 2020). Thus, Moynier et al. (2006) proposed a new model, which successfully explained the observed isotopic fractionations in both the “traditional”

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** The model schematics after Moynier et al. (2006). The isotopic compositions of the top lunar soil column are the results of three processes: micrometeorite addition, vaporization loss, and gardening addition of “fresh” lunar soils from below (or surroundings).</figcaption></figure>

light element and “non-traditional” heavy element isotope systems (e.g., S and Zn).

In this study, we have followed Moynier et al. (2006) and applied their model to K isotopes. Here we illustrate the main assumptions and the equations used in this modeling. Definitions of all terms and values used are provided in Table 3. An illustrative figure explaining all the processes involved is presented as Fig. 6.

The concentrations of <sup>39</sup>K and <sup>41</sup>K after exposure time, t, are defined as N<sup>39</sup>(t) and N<sup>41</sup>(t), respectively, in units of atom/cm<sup>3</sup>. The total numbers of <sup>39</sup>K and <sup>41</sup>K atoms in the topmost mixed layer would be N<sup>39</sup>(t)G(t) and N<sup>39</sup>(t)G(t), respectively, where G(t) is the thickness (cm) of the mixed layer. We assume that three processes, micrometeorite addition, vaporization loss, and gardening addition of “fresh” lunar materials, affect the concentrations of <sup>39</sup>K and <sup>41</sup>K in lunar soils (as Fig. 6), therefore:

$$ \frac{d}{dt} \{N(t)G(t)\} = \text{micrometeorite addition} - \text{vaporization loss} + \text{gardening addition} \quad (1) $$

$$ \frac{d}{dt} \{N(t)G(t)\} = A - BN(t) + \frac{dG(t)}{dt} D \quad (2) $$

where

$$ A = \phi(C_{\text{meteor}}N_{\text{Avo}}/M)If \quad (3) $$

$$ B = \phi(F/\rho)(1-f) \quad (4) $$

$$ D = C_{\text{moon}}(\rho N_{\text{Avo}}/M) \quad (5) $$

All other terms, parameters, and values used in the model are listed in Table 3.

For example, φ is the micrometeorite mass flux in g cm<sup>-2</sup> Ma<sup>-1</sup>. We use the same value (3 × 10<sup>-3</sup>) as Moynier et al. (2006), which is based on the literature (Gault et al., 1972; Zook, 1975; Halliday et al., 1989; Peucker-Ehrenbrink and Ravizza, 2000; Taylor et al., 2000), and assumes the meteorite flux has remained constant within at least the last 1,000 Ma.

The solution for the differential Eq. (2) was given by Moynier et al. (2006) as:

$$ N(t) = \frac{A + D\beta}{B + \beta} \times \left( 1 - \left[ \frac{\gamma + \beta t}{\gamma} \right]^{-\frac{B+\beta}{\beta}} \right) + D \times \left[ \frac{\gamma + \beta t}{\gamma} \right]^{-\frac{B+\beta}{\beta}} \quad (6) $$

In the model of Moynier et al. (2006), isotopic fractionation during
evaporation is controlled by the free parameter *f*, the fraction of a given isotope (e.g., ³⁹K and ⁴¹K) remaining after evaporation. This *f* is a free parameter and cannot be directly constrained. Moynier et al. (2006) selected *f* = 0.7 for Zn in order to match the model result to the observed Zn isotope fractionation. We also use *f* = 0.7 for ³⁹K in this study because, although K is less volatile than Zn (Lodders, 2003), it has a smaller mass.

Due to the kinetic fractionation effect, the lighter isotopes of K is preferably lost to space due to micrometoroite impacts, thus the *f* of the lighter isotope is smaller than that of the heavier isotope, such that:

$$ \mathrm{Ln}(f^{41}) = \sqrt{\frac{m^{39}}{m^{41}}} \mathrm{Ln}(f^{39}) \qquad (7) $$

For the micrometeorites added to the top of the lunar soils, we use ordinary chondrites as they are the most common class of meteorite delivered to the Moon (Lucey, 2006). We also explored other types of meteorites (e.g., CI carbonaceous chondrites; see Supplementary Fig. S4) and found that meteorite type has an insignificant effect on the model result. The lunar soil starting compositions *C*<sub>moon</sub> could also have a small effect on the model result. We picked two end-member values, 500 and 4000 ppm, to cover the range of K abundances in typical lunar soils (Lucey, 2006).

The final modeling result is shown in Fig. 7 and Supplementary Fig. S4 (the MATLAB code is also provided in the supplementary materials).

As expected, with increasing exposure time (*t*), the K isotopic compositions increase from the bulk silicate Moon value (−0.07 ± 0.09 ‰; Tian et al., 2020) to ~ 12 ‰ at 1,000 Ma, which can explain the entire range of the K isotopic compositions measured in lunar soils in both this study and in the literature (Barnes et al., 1973; Garner et al., 1975; Church et al., 1976; Humayun and Clayton, 1995; Wang and Jacobsen, 2016b; Tian et al., 2020). The exposure ages from 0 to 1,000 Ma also cover the whole range of exposure ages measured among lunar soils (e.g., see compilation in Curran et al., 2020).

According to the model, isotopic fractionation is mostly due to the preferential loss of ³⁹K during micrometeorite impact vaporization loss. The other two processes, micrometeorite addition and gardening addition, cannot generate the large K isotopic fractionation observed. They would only lower the isotopic fractionation effect by diluting the signal with added K from “fresh” micrometeorite and “fresh” lunar soils. Among the two lunar soil starting composition scenarios (500 and 4000 ppm), the higher K in the starting composition, the less K isotopic fractionation in the mixing layer (see Fig. 7), which is also due to more dilution by the added “fresh” lunar K from gardening.

The concentration of K in the soils also varies with exposure time (see Fig. 7). Among the three processes (micrometeorite addition, vaporization loss, and gardening addition), vaporization loss is more significant than the other two processes because in the model, the lunar mass volatilized per unit mass of micrometeorite input is set as 10 (Pierazzo

<figure><img src="image_11.png" /><figcaption>Fig. 7. The model results of K isotope and concentration variation with varying exposure ages. Two lunar soil starting compositions (500 and 4,000 ppm) are used. The ²¹Ne exposure ages (average ± SD) from compilation are also plotted for comparison (Curran et al., 2020). The original exposure age data are from (Pepin et al., 1970; Funkhouser, 1971; Hintenberger et al., 1971, 1975; Kaiser, 1971; Yaniv and Heymann, 1972; Lakatos et al., 1973; Kirsten et al., 1973; Walton et al., 1973; Hintenberger and Weber, 1973; Jordan et al., 1974).</figcaption></figure>
et al., 1997). Thus, the overall change in the K concentration in the top lunar soil column is a net loss. Therefore, the model demonstrates a decrease in the concentration of K with increasing exposure time. For example, the K concentrations in lunar soils will decrease from 500 and 4000 ppm to 369 and 2282 ppm, respectively, over 1,000 Ma. When plotting the covariation of K isotope systematics and concentrations (see Fig. 7), a negative correlation between K isotopic compositions and concentrations is observed. It is important to note, however, that this negative correlation between K isotopic compositions and concentrations only applies to samples with the same starting compositions but varying exposure ages. We would not expect samples with different starting compositions and exposure ages to show this negative correlation between K isotopic compositions and concentrations. In other words, for the samples studied here, we would not necessarily expect this negative correlation in the [K₂O] versus K isotope plot (Fig. 5), as these samples have very different starting compositions and exposure history. We also note the decrease in K concentration is very insignificant for samples with low-K concentration and/or low exposure ages, which is another reason why we do not expect a negative correlation in Fig. 5.

There is no clear correlation, either negative or positive, between K isotopic compositions and concentrations in Fig. 5. However, for samples with [K₂O] below 0.3 %, there appears to be a subtle positive trend between K isotopic compositions and concentrations. While this trend is not predicted by the model of Moynier et al. (2006), it could result from additional processes not captured by the model, such as the redeposition of K vapor (enriched in lighter K isotopes) generated during micrometeorite impacts.

The current model does not account for complexities like the redeposition of K vapor. As mentioned earlier, Tian et al. (2020) proposed that the recondensation of lighter K isotopes could explain the lighter isotopic compositions observed in low-K lunar rocks. Similarly, the recondensation of lighter K isotopes would also affect low-K lunar soils, shifting their isotopic values lower. This mechanism could explain the apparent positive trend between K abundance and isotopic composition observed for the low-K soil samples in Fig. 5.

In summary, this numerical model for K isotopic fractionation during micrometeorite impact vaporization, following Moynier et al. (2006) with reasonable assumptions (see Table 3), can successfully explain the observed K isotopic fractionation for lunar soil samples in this study and in literatures. Since we adopted this model from Moynier et al. (2006) and used the same set of parameters during modeling, it is safe to say that the same model and parameters can simultaneously satisfy three independent isotope systems including S and Zn isotopes in Moynier et al. (2006) and K in this study. Therefore this model supports the notion that isotopic fractionations of K, S, and Zn, as well as other moderately volatile elements, can be attributed to the micrometeorite impact vaporization on the surface of the Moon.

### 4.2.2. Cosmic-ray irradiation effect

Alternative to kinetic isotopic fractionation due to micrometeorite impact vaporization and preferential loss of lighter isotopes (see Section 4.2.1), the enrichments of heavy K isotopes ($^{41}$K) in lunar soils could be also attributed to the cosmic-ray irradiation effect. In this process, $^{41}$Ca can be produced via the low-energy neutron capture reaction: $^{40}$Ca(n, γ)$^{41}$Ca. The short-lived radionuclide $^{41}$Ca (half-life: 9.94 ± 0.15 × 10⁴ yr; Jörg et al., 2012) subsequently decays to $^{41}$K. However, this cosmic-ray irradiation effect is unlikely to account for the observed K isotope fractionation, for the following reasons:

Firstly, cosmogenic live $^{41}$Ca has been measured in the Apollo 15 deep drill core and other lunar soil samples (Nishiizumi et al., 1997); however, no correlation between $^{41}$Ca and $^{δ^{41}}$K in the Apollo 15 deep drill core is observed (see Supplementary Fig. S5). The $^{δ^{41}}$K profile of the Apollo 15 deep drill core shows that $^{δ^{41}}$K sharply decreases with depth; while in contrast, its $^{41}$Ca profile shows $^{41}$Ca production increases with depth, peaking at approximately 100 cm depth, then decreasing

below 100 cm. This observed $^{41}$Ca profile is due to $^{41}$Ca being produced by the capture of low-energy thermal neutrons instead of high-energy spallation reactions (Nishiizumi et al., 1997), thus the highest $^{41}$Ca production is not near the surface but at the depth where secondary neutron production was highest. This contrast and offset between $^{δ^{41}}$K and $^{41}$Ca profiles suggest that cosmogenic $^{41}$K via neutron capture reactions is not the reason why we observe high $^{δ^{41}}$K values on the surface of the Moon. Although the peak neutron fluence on the lunar surface occurs at a depth of 60–120 cm, the Sm and Gd isotopic compositions of Apollo 15 soils show that even the near-surface samples have received a large neutron fluence of ~ 4 x 10¹⁶n/cm² over the past few Ga (note: neutron fluence is the total neutron flux integrated over time) (Russ et al., 1972; Hidaka et al., 2000). These large isotopic shifts indicate that due to regolith mixing most soil samples have spent a significant amount of time at 0.5–2 m depth. This neutron fluence corresponds to a total exposure of ~ 500 Ma at the peak of the neutron depth profile or of ~ 1 Ga at a depth corresponding to half the peak production rate. Based on the peak $^{41}$Ca production rate of ~ 1 atom/min/g Ca, a bulk Ca content of ~ 8 wt% and a total CRE age of 0.5 Ga, we calculate that ~ 2.1 x 10¹³ atoms of $^{41}$K were produced by decay of $^{41}$Ca during exposure of the surface samples in the top few meters of the lunar regolith. Based on an average K content of 0.2 wt% for Apollo 15 samples, this cosmogenic $^{41}$K production would have increased the $^{41}$K/$^{39}$K ratio by ~ 10 ppm, or 0.01 ‰, which is well within the measurement uncertainty, so we conclude that cosmogenic $^{41}$K is negligible for the Apollo 15 samples.

Fig. 8 shows the expected cosmic-ray-induced enrichments in $^{41}$K as a function of neutron fluence and Ca/K ratio. Although in anorthosite-rich samples with Ca/K ratios > 1000 and high neutron fluences, the cosmogenic $^{41}$K contribution may have to be taken into account, in most lunar samples with Ca/K ratios of < 200 (see Table 1) and a neutron fluence of < 4x10¹⁶ n/cm², these contributions of cosmogenic $^{41}$K are negligible (<0.05 ‰). In this study, we expect the highest cosmogenic $^{41}$K contribution in Apollo 16 soil 67461, which has a Ca/K ratio of ~ 309 (Wänke et al., 1973). Although the neutron fluence for this sample is not known, we estimate an isotopic shift of $^{δ^{41}}$K of ~ 0.12 ‰ assuming this sample had a similar neutron fluence (~6x10¹⁶ n/cm²) as other Apollo 16 surface samples (Russ, 1973). This is less than 10 ‰ of the measured $^{δ^{41}}$K shift of 1.38 ± 0.07 ‰ (see Table 1), so it principally may require a small correction, but this correction will not affect the conclusions of this study significantly.

Secondly, many other moderately volatile elements also show large isotopic fractionations on the surface of the Moon, with all showing enrichments in heavier isotopes, such as Cu (Moynier et al., 2006), Zn (Moynier et al., 2006; Herzog et al., 2009), Se (Vollstaedt et al., 2020), Rb (Nie et al., 2024), and Cd (Sands et al., 2001; Wombacher et al., 2008; Abouchami et al., 2025). As such, even if cosmogenic $^{41}$K could account for the heavy K isotope enrichments in lunar soils, there are no cosmic-ray reactions which could explain the heavy isotope enrichments seen in all the other moderately volatile elements.

Thirdly, cosmic-ray irradiation effects would not produce mass-dependent fractionation. Although K has only two stable isotopes ($^{39}$K and $^{41}$K), making it difficult to determine whether mass-dependent fractionation has occurred, other moderately volatile elements have three or more stable isotopes. For example, four isotopes of zinc ($^{64}$Zn, $^{66}$Zn, $^{67}$Zn, and $^{68}$Zn) show only mass-dependent fractionation in lunar soils (Moynier et al., 2006; Herzog et al., 2009). Similar mass-dependent fractionations have also been observed for Fe and Cd isotopes in lunar soils (Sands et al., 2001; Wiesli et al., 2003; Moynier et al., 2006; Wombacher et al., 2008; Herzog et al., 2009; Wang et al., 2012; Oka-bayashi et al., 2020; Abouchami et al., 2025). Thus, cosmic-ray irradiation effects are unlikely to be the cause of the isotopic fractionation on the surface of the Moon.

Lastly, the observed isotopic compositions in lunar soils can be successfully explained using the model in Section 4.2.1, where only three processes were involved: micrometeorite addition, vaporization loss, and gardening addition. As such, there is no need to include any
<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Expected ⁴¹K enrichment from decay of neutron-capture produced ⁴¹Ca in lunar samples with Ca/K ratios ranging from 20 to 2000 and thermal neutron fluences ranging from 5 x 10¹⁵ n/cm² (roughly corresponding to surface exposure ages of ~ 50 Ma) to 2 x 10¹⁷ n/cm² (~2 Ga). As an example, the expected ⁴¹K enrichments are shown for samples from the Apollo 15 drill core, which have a Ca/K ratio of ~ 40 and have experienced neutron fluences of 3.5 to 5.5 x 10¹⁶ n/cm² (Russ et al., 1972).</figcaption></figure>

cosmic-ray irradiation effect, and the cosmogenic ⁴¹K accumulated over time is usually insignificant to influence the K isotopic compositions of lunar soils (see Fig. 8). Moreover, the same model has also been successfully applied to S and Zn isotope fractionations in lunar soils (Moynier et al., 2006). Thus, we conclude that cosmic-ray irradiation effects are not a major control on the isotopic compositions of moderately volatile elements on the Moon.

### 4.3. K Isotope Model Exposure Age (KIMEA) and comparison to noble gas Cosmic Ray Exposure (CRE) Age

The numerical model here suggests that exposure age is the dominant controlling factor for the observed isotopic fractionation of K on the surface of the Moon. Thus, we aim to apply this model to constrain the exposure ages of lunar soils. To avoid confusion with exposure ages derived from other tools (e.g., cosmogenic noble gases), we define these new exposure ages as the K Isotope Model Exposure Age (KIMEA). We have back-calculated the KIMEA using their K isotopic compositions and K concentrations for the samples measured in this study (Supplementary Table S1). They vary from 2 Ma (61220, Immature trench soil) to 1,074 Ma (15041, surface trench soil). To the best of our knowledge, both samples have never been analyzed for noble gas CRE ages (e.g., see compilation by Curran et al., 2020). Their new KIMEA values could provide new independent surface exposure ages constraint on samples lacking CRE age information.

Nevertheless, some samples included here have been analyzed for both K isotopic compositions and noble gas CRE ages derived from the cosmogenic ²¹Ne and ³⁸Ar concentrations (T₂₁; T₃₈). The T₂₁ and T₃₈ ages are in a good agreement; however T₃₈ ages are probably better because Ar does not diffuse as fast as Ne and suffers less from diffusive loss (e.g., Bogard and Hirsch, 1975). On the other hand, the T₂₁ database is more extensive than the one for T₃₈, so we compare the KIMEA established here with the T₂₁ CRE ages for these samples (Curran et al., 2020) in Fig. 7 (comparison with T₃₈ can be seen in Supplementary Fig. S6). The KIMEA and CRE ages broadly agree but exhibit significant scattering. This is not entirely surprising as the T₂₁ ages are also not well correlated with the soil maturity index, Iₛ/FeO (see Supplementary Fig. S7). The CRE ages derived from noble gases are model-dependent and

inherently uncertain for two main reasons: shielding information is not always available (Wieler, 2002) and previous studies demonstrated that exposure ages are often biased toward low values due to diffusive loss of light noble gases such as helium and neon (Bogard and Hirsch, 1975). Lunar regolith is constantly stirred by meteorite impacts. So samples, especially soils, usually do not acquire all cosmogenic nuclides at the same depth. Because of that, the CRE ages are usually calculated using a surface production rate or the maximum production rate, which is located slightly below the surface, often leading to underestimation of the exposure ages. Cosmogenic nuclides are produced by galactic cosmic radiation (GCR) and solar cosmic radiation (SCR). However, the SCR contribution has usually been neglected during the CRE age calculation although it dominates over GCR component in the first 1 ~ 2 cm of the sample. Considering constant “gardening” of regolith, it is considered unlikely that the samples resided at the surface long enough during the relevant exposure period to make SCR contribution significant (Wieler, 2002). But if they did, neglecting the SCR contribution would result in overestimation of the exposure age. In any case, independent of the model used by the authors for calculation of the CRE ages in the compilation by Curran et al. (2020), these ages vary significantly for each sample, probably due to the sample heterogeneity, as discussed in detail in Section 4.1.3 or to diffusive loss of cosmogenic neon from the samples (e.g., Bogard and Hirsch, 1975). Finally, the KIMEA and CRE ages do not date the exactly same processes. Potassium isotope fractionation is due to micrometeorite impact vaporization, while the cosmogenic noble gases are produced by cosmic-ray irradiation, with a mean penetration depth in rock of about 50 cm for the galactic cosmic radiation (GCR). Hence, it is logical that the KIMEA and CRE ages show similar albeit different trends with depth.

We also note that the main outlier on the Fig. 7 is 15426 (green glass clods). The earlier reported ²¹Ne exposure ages for the bulk 15426 green spherule samples are 300–400 Ma (Lakatos et al., 1973) and 200 Ma (Megrue, 1973) which are quite different from the KIMEA. Recent noble gas study of individual Apollo 15426 green spherules (Füri et al., 2018), demonstrated the 105 ± 21—347 ± 73 Ma range of T₂₁ cosmic ray exposure ages, similar to the T₂₁ ages reported earlier for the bulk 15426 green glasses. However, the solar track exposure age of 15426 is 0.5 Ma (Fleischer and Hart, 1973). The authors attributed the difference in
noble gas and solar track exposure ages to a long previous existence (perhaps as a soil) prior to being assembled to form a soil clod. In any case, the direct comparison between KIMEA and $^{21}$Ne exposure ages for this sample is not justified since samples used in this work were a mixture of green glass and soil, while in the noble gas studies green spherules were hand-picked from the disaggregated clod and cleaned from the fine dust adhering to their surfaces.

This new KIMEA has the potential to become a useful tool for constraining the surface exposure ages of lunar soils in addition to the traditional noble gas CRE ages. While more work and calibration of this new tool needs to be done, for now, we provide a preliminary simple-fit equation (see Supplementary Fig. S8) to estimate the KIMEA without running the full model:

$$ \text{KIMEA (Ma)} = -13.32 + 58.43 \times \delta^{41}\text{K} - 8.932 \times (\delta^{41}\text{K})^2 + 0.9872 \times (\delta^{41}\text{K})^3 \quad (8) $$

As depicted in Fig. 7 and Supplementary Fig. S8, KIMEA is most sensitive for the samples with an exposure age younger than 1,000 Ma. However, its effectiveness decreases for samples older than this due to the curvature of the model. Further verification and calibration of KIMEA are necessary through measuring noble gas exposure ages and K isotopic compositions on the exact same samples.

## 5. Conclusions

In this study, we analyzed the K isotopic compositions of 13 bulk lunar soils and 20 interval samples from the Apollo 15 deep drill core. We also conducted numerical modeling to explain the observed K isotopic fractionation and calculated K Isotope Model Exposure Age (KIMEA). The following conclusions are drawn:

1) Lunar soils exhibit significant fractionation in K isotopes (up to + 11.77 ‰ in this study), and the degree of fractionation is primarily correlated with soil maturity.

2) The isotopic fractionation of K and other moderately volatile elements (such as S, Cu, Zn, Se, Rb, and Cd) show a correlation and are most likely caused by micrometeorite-impact-generated vaporization and preferential loss of lighter isotopes.

3) A numerical model previously proposed for S and Zn isotopic fractionation in lunar soils can be successfully applied to the observed K isotopic fractionation. Based on this model, K isotopic compositions of lunar soils can be used to determine the K Isotope Model Exposure Age (KIMEA) of lunar soils. The KIMEA ages have advantages over noble gas exposure ages which suffers from diffusive loss.

4) Further verification and calibration of KIMEA are needed and could be conducted through measuring noble gas exposure ages, FMR maturity index, K and other MVE (e.g., Cu and Zn) isotopes on the exact same samples.

### CRediT authorship contribution statement

**Kun Wang:** Writing – original draft, Supervision, Methodology, Funding acquisition, Conceptualization. **Zhen Tian:** Writing – original draft, Investigation. **Megan Broussard:** Writing – original draft. **Mason Neuman:** Writing – review & editing. **Piers Koefoed:** Writing – review & editing. **Olga Pravdivtseva:** Writing – original draft. **Guillaume Avice:** Writing – original draft. **Richard V. Morris:** Writing – review & editing. **Kees C. Welten:** Writing – original draft. **Randy L. Korotev:** Writing – review & editing. **Bradley L. Jolliff:** Writing – review & editing.

### Data availability

Data are available through ASTROMAT-Astromaterials Data System

repository at https://doi.org/10.60520/IEDA/113350.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

We thank NASA JSC curation team and Astromaterials Allocation Review Board (AARB) for kindly providing the Apollo samples. K.W. thanks financial support from McDonnell Center for the Space Sciences and NASA (Emerging Worlds Program grant #80NSSC21K0379 and OSIRIS-REx Sample Analysis Participating Scientist Program grant #80NSSC22K1689). K.W. also thanks Rita Parai for helpful discussion. We thank Dr. Frank Wombacher and two anonymous reviewers for their thorough reviews. We also thank Associate Editor Liping Qin for handling this manuscript.

## Appendix A. Supplementary material

The supplementary material include eight figures: (Fig. S1) K isotopic compositions of lunar soil samples vs. maturities, (Fig. S2) Potassium isotopic compositions vs. K$_2$O, (Fig. S3) K$_2$O vs. Sm in lunar soils, (Fig. S4) Modeling results with varying starting compositions (500 and 4,000 ppm) of lunar soils and different types of micrometeorites (ordinary chondrites and CI carbonaceous chondrites), (Fig. S5) K isotopic compositions of samples from Apollo 15 deep drill core vs. measured $^{41}$Ca activities (dpm/kg) and depth from the surface, (Fig. S6) The model results of K isotope variation with varying $^{38}$Ar exposure ages, (Fig. S7) CRE ages derived from $^{21}$Ne vs. soil maturity (Is/FeO), and (Fig. S8) A simple relationship between K isotopic composition and K Isotope Model Exposure Age (KIMEA). The supplementary material include two tables: (Table S1) K Isotope Model Exposure Age (KIMEA) calculated for samples analyzed in this study, and (Table S2) Potassium and Ca concentrations of Apollo bulk lunar soils from literature. Supplementary material to this article can be found online at https://doi.org/10.1016/j.gca.2025.01.043.

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