# Grain Boundary Diffusion of Ferropericlase: Implications for the Core-Mantle Interaction

Yihang Peng, Pierre Hirel, Philippe Carrez, Jie Deng

► To cite this version:

Yihang Peng, Pierre Hirel, Philippe Carrez, Jie Deng. Grain Boundary Diffusion of Ferropericlase: Implications for the Core-Mantle Interaction. Geophysical Research Letters, 2025, Geophysical Research Letters, 52 (8), 10.1029/2024gl112669. hal-05051012

HAL Id: hal-05051012

https://lilloa.hal.science/hal-05051012v1

Submitted on 29 Apr 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2024GL112669

**Key Points:**

* The grain boundary diffusivities of Mg, Fe, and O in ferropericlase are calculated from molecular dynamics simulations

* The grain boundary diffusivity first increases and then converges to a constant with increasing vacancy concentration

* Grain boundary diffusion alone is unlikely to be efficient enough for iron transport across the core-mantle boundary

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

Y. Peng and J. Deng,
yhpeng@princeton.edu;
jie.deng@princeton.edu

**Citation:**

Peng, Y., Hirel, P., Carrez, P., & Deng, J. (2025). Grain boundary diffusion of ferropericlase: Implications for the core-mantle interaction. *Geophysical Research Letters*, *52*, e2024GL112669.
https://doi.org/10.1029/2024GL112669

Received 20 SEP 2024
Accepted 4 APR 2025

**Author Contributions:**

**Conceptualization:** Jie Deng
**Data curation:** Yihang Peng
**Formal analysis:** Yihang Peng, Pierre Hirel, Philippe Carrez, Jie Deng

**Funding acquisition:** Jie Deng

**Investigation:** Yihang Peng, Jie Deng

**Methodology:** Yihang Peng, Pierre Hirel, Philippe Carrez

**Project administration:** Jie Deng

**Software:** Yihang Peng

**Supervision:** Jie Deng

**Visualization:** Yihang Peng

**Writing – original draft:** Yihang Peng

**Writing – review & editing:**

Yihang Peng, Pierre Hirel,
Philippe Carrez, Jie Deng

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

<figure><img src="image_2.png" /></figure>

# Grain Boundary Diffusion of Ferropericlase: Implications for the Core-Mantle Interaction

Yihang Peng¹, Pierre Hirel², Philippe Carrez², and Jie Deng¹

¹Department of Geosciences, Princeton University, Princeton, NJ, USA, ²University of Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité Matériaux et Transformations, Lille, France

**Abstract** Geophysical observations indicate that iron enrichment of various spatial scales may be present in the lowermost mantle. Various mechanisms have been proposed to explain the process of iron infiltration from the core to the mantle, each with its own inherent limitations. Grain boundary (GB) diffusion significantly outpaces bulk diffusion within crystal interiors, and may facilitate iron transport across the core-mantle boundary (CMB). In this study, we investigate diffusion in two symmetric tilt GBs of ferropericlase and ferropericlase single crystals using large-scale molecular dynamics simulations. The GB diffusivities in pure periclase and their temperature dependence agree well with previous studies. In addition, we study the GB diffusion of Fe in (Mg, Fe)O GBs for the first time. The results suggest that GB diffusion of Fe is likely to be sluggish near the CMB, and thus may not be an effective mechanism for transporting iron from the core to the mantle.

**Plain Language Summary** Seismic observations suggest the existence of regions rich in iron of scales from a few hundred meters to thousands of kilometers above the Earth's core-mantle boundary. The Earth's core, composed primarily of liquid iron, may interact with the mantle rocks and transport iron into the mantle. The diffusion of atoms along the boundaries of different grains of mantle rocks has been proposed as a possible mechanism for the core-mantle interaction. We performed atomistic simulations of one of the dominant mineral phases at the core-mantle boundary, (Mg, Fe)O ferropericlase to calculate the diffusion rates of magnesium, iron, and oxygen within grain boundary regions. The results suggest that, on the time scale of the Earth's history, the distance of the grain boundary diffusion of iron is likely to be very limited and insufficient to explain any iron enrichment phenomena at the bottom of the lower mantle.

## 1. Introduction

As the sharpest compositional discontinuity in the Earth's interior, the core-mantle boundary (CMB) at a depth of 2,889 km exhibits strong complexity and has a significant impact on the chemical evolution of the Earth (Young & Lay, 1987). The interaction between the solid silicate mantle and the liquid iron core may cause extensive enrichment of iron at the lowermost mantle, which is supported by multiple geophysical observations. First, two continent-sized large low shear velocity provinces (LLSVPs) extend up to 1,200 km above the CMB (Garnero et al., 2016) and can be explained by iron-enriched materials (Vilella et al., 2021; Yuan et al., 2023). They exhibit electrical conductivity anomalies (Nagao et al., 2003; Ohta et al., 2010) which may also be associated with iron. Second, the 5–40 km thick patches right above the core with unusually low seismic velocities, known as ultralow-velocity zones (ULVZs) (Williams & Garnero, 1996), may be attributed to local iron enrichment (Wicks et al., 2010). Third, a thin (100–1,000 m) layer with high conductance above the core has been inferred from Earth's nutations (Buffett, 1992, 2015; Buffett et al., 2002) and may comprise metallic FeO (Knittle & Jean-loz, 1986; Sherman, 1989).

Various hypotheses have been proposed to explain this putative iron enrichment above the CMB. The thickness of the iron-enriched layer caused by capillary rise is only <20 m (Poirier et al., 1998). Alternative hypotheses suggest that pressure gradients caused by the dynamic topography at the CMB may drive iron upwards into the lower mantle (Kanda & Stevenson, 2006). Additionally, iron infiltration can be caused by the sedimentation of the liquid outer core (Buffett et al., 2000). However, both mechanisms are sensitive to the viscosity of the lowermost mantle, which is subject to considerable uncertainty (Rudolph et al., 2015). K. K. Otsuka and Karato (2012) proposed that the penetration of iron into the mantle can be caused by a morphological instability, a mechanism independent of
viscosity, but the effective diffusivity used to calculate iron infiltration thickness is extrapolated from low-pressure experimental data and remains controversial (J. Deng et al., 2019; Yoshino, 2019).

Grain boundaries (GBs) are regions that separate different grains in a polycrystalline material. Due to the more disordered atomistic structure at the interface compared to the crystalline lattice, atomic diffusion along GBs is typically orders of magnitude faster than its lattice counterpart (Dohmen & Milke, 2010; Joesten, 1991). Therefore, GB diffusion strongly affects physical properties in the Earth's materials, including the viscosity (Mantisi et al., 2017), electrical conductivity (ten Grotenhuis et al., 2004), and seismic attenuation (Jackson et al., 2002). It is suggested that GB diffusion provides an efficient mechanism to exchange carbon and siderophile elements between the mantle and the core (Hayden & Watson, 2007, 2008), and may effectively modify the tungsten and helium isotopic compositions of the plume-source mantle (Ferrick & Korenaga, 2023; Kaare-Rasmussen et al., 2023; Yoshino et al., 2020). The diffusion of iron along GBs may be another potential mechanism for iron infiltration from the outer core to the lower mantle.

Previous experimental and theoretical studies have explored the GB diffusion in MgO periclase (Karki et al., 2015; Landuzzi et al., 2015; McKenzie et al., 1971; Riet et al., 2021; Van Orman et al., 2003). However, most of these results do not account explicitly for pressure and temperature conditions near the CMB, and the GB diffusion in (Mg,Fe)O, one of the most abundant phases at the CMB (X. Deng et al., 2023), remains poorly understood. In addition, recent results have shown that the structure of a GB is far from unique, and is not simply determined by the misorientation between the grains. In particular, GB structures evolve when interacting with vacancy complexes, resulting in significant changes in GB properties (Hirel et al., 2022). In this study, we investigate the diffusion of Mg, Fe, and O along GBs in (Mg,Fe)O bicrystals under the CMB conditions using large-scale molecular dynamics (MD) simulations. Bicrystals of high compaction, expected to be most favorable in high-pressure conditions of the CMB, are constructed (Hirel et al., 2019). We explore the dependence of the GB diffusion coefficient on defect concentration and temperature. The diffusion coefficients of iron in ferropericlase single crystals are also calculated. The results are used to examine the efficiency in transporting iron from the core to the mantle through solid-state diffusion.

## 2. Methods

### 2.1. Interatomic Potential

There are two main methods to describe the interaction of atoms in MD simulations: ab initio method based on density functional theory and the force field approach. The ab initio method is considered more accurate because it calculates the electronic structure of materials quantum mechanically, in principle, without relying on empirical parameters. However, this method is computationally demanding, limiting simulations to smaller systems and shorter times. On the other hand, the force field approach uses simplified force parameters, allowing for less intensive computations and enabling longer simulations of larger systems, which is crucial for simulating polycrystalline systems and reducing statistical error. Therefore, in this study, we choose the force field approach and use a new rigid-ion potential developed by Pedone et al. (2006). This approach incorporates long-range Coulomb interactions, a Morse function for short-range interactions, and a repulsive term similar to the Lennard-Jones function. The parameters were calibrated using experimental measurements, including lattice dimensions, elasticity values, both high-frequency and static dielectric constants, lattice energies, piezoelectric constants, and phonon frequencies observed in binary oxides. This potential demonstrates high reliability and applicability in modeling lattice defects, diffusion, and GBs in forsterite (Furstoss et al., 2022; Hirel et al., 2021). Hirel et al. (2021) highlight its ability to accurately reproduce various properties across a pressure range of 0–12 GPa, while Furstoss et al. (2022) further confirm its effectiveness through its good agreement with ab initio calculations in terms of GB atomistic structures, energies, and excess volumes in forsterite. To further verify the reliability of this potential for simulating (Mg, Fe)O GBs, we calculated the formation enthalpy of MgO GBs across pressure conditions of nearly the entire mantle (Figure S1 in Supporting Information S1). The results are in good agreement with Hirel et al. (2019), supporting the applicability of this potential to the periclase system at elevated pressures.

### 2.2. Molecular Dynamics Simulations

The GBs used in this study are symmetric tilt GBs where grains are rotated by opposite angles around the same [001] axis. Our focus is on structures with high-angle GBs as they are more common in polycrystalline MgO
(Saylor et al., 2003), are likely to participate actively in dynamic processes due to their higher energy (Hirel et al., 2021; Ritterbex et al., 2024), and have been used in recent studies on MgO GBs under high pressure (Riet et al., 2021; Ritterbex et al., 2024). Bicrystals are constructed with Atomsk (Hirel, 2015). Two crystals of MgO are rotated by opposite angles (±α/2), cut and then stacked together. We apply translation to one of the two symmetrical single crystals along the GB, and compute relative energies of different configurations, which yields several energy minima. The configurations corresponding to these minima can be called “complexions.” As demonstrated earlier, at the high pressures reigning in the Earth’s mantle, the most compact complexions are energetically most favorable (Hirel et al., 2019), and are used as a starting point. Such a compact complexion can interact with vacancy complexes, thus transforming its atomic configuration further (Hirel et al., 2022). In the following, two symmetric tilt GBs are modeled, corresponding to two different misorientation angles: α = 36.8° where the two crystals meet with {310} planes, and α = 29.5° where the GB plane does not correspond to any high-symmetry crystallographic plane (Figure S2 in Supporting Information S1). Mg-O vacancy pairs are randomly introduced within a region approximately 1 nm wide adjacent to the GB of the complexion to obtain the initial configuration of MgO bicrystals for the following MD simulations. The vacancy concentration Cvac is defined as the ratio between the number of MgO units removed and the number of MgO units in the 1-nm GB region. Following Ammann et al. (2010), the vacancy concentrations considered in this study range from 0.4 at% to 8.0 at%, which are estimated from experimental results (Holzapfel et al., 2003; Yamazaki & Irifune, 2003). The structure of (Mg,Fe)O is generated by randomly substituting Mg with Fe in the aforementioned MgO structure.

To ensure a genuine depiction of real material (Mg, Fe)O single crystal must be of adequate size so that its inner structure mimics that of large grains (Glišović et al., 2015) in the lower mantle. We construct bicrystal systems containing over 50,000 atoms, resulting in an average distance of over 20 nm between the centers of adjacent grains. Each GB operates independently of others, ensuring that atoms involved in one boundary do not interact with any other boundaries throughout the simulation. Supercells with larger GB area and increased number of grains have also been simulated and yielded consistent GB diffusion coefficients, confirming the size convergence of our systems (Figure S3 in Supporting Information S1).

All MD simulations are conducted using LAMMPS (Plimpton, 1995) under periodic boundary conditions. The systems are first equilibrated in isothermal-isobaric conditions (NPT) for 100 ps at a series of temperatures, under two pressures of 0 and 140 GPa for MgO and (Mg, Fe)O, respectively. The resulting structures are then used as the initial configurations to set up the MD simulations for 5 ns under a canonical ensemble (NVT) with the Nosé-Hoover thermostat (Hoover, 1985), in order to evolve the GB structure to reach a steady state. Subsequently, we perform long NVT simulations for 5–10 ns, from which the GB diffusion is analyzed. The timestep of all simulations is 1 fs.

## 2.3. Trajectory Analysis

Due to the spatially heterogeneous diffusion in polycrystalline systems, direct analysis of the MD trajectory of the entire system would mask the distinct characteristics of the crystal interiors and GBs. Following Riet et al. (2021), we employed an advanced local ionic environment analysis to extract the atomic properties within the GB regions from the bulk system. The first post-processing step is an energy minimization to map instantaneous MD configurations (sampling at 1-ns intervals) to their nearest local energy minima. Through this, we remove the thermal vibrational displacement of atoms and thereby obtain a more distinct representation of the GBs. Subsequently, we examine the distribution of nearest neighbors of all atoms at the energy minima to identify which atoms have complete coordination with the six nearest neighbors and which ones are undercoordinated. The undercoordinated atoms are associated with the GB regions (Riet et al., 2018). This analysis is realized through the nearest neighbor search using the MDAnalysis package (Michaud-Agrawal et al., 2011). Consistent with Riet et al. (2018, 2021), the fraction of undercoordinated atoms at the GBs, denoted as g, remains relatively constant through a single MD trajectory. This insight allowed us to apply the modified Hart equation (Dohmen & Milke, 2010; Hart, 1957; Riet et al., 2021) to compute the GB diffusion coefficient:

$$D_{\text{total}} = gD_{\text{GB}} + (1 - g)D_{\text{lat}}, \quad (1)$$

where Dtotal, DGB, and Dlat are the overall diffusion coefficient, GB diffusion coefficient, and lattice diffusion coefficient within the single crystal interiors, respectively. Since our analysis of atoms within crystal interiors showed negligible diffusion, we assume Dlat ≈ 0. Thus, the GB diffusion coefficient is approximated by:
<figure><img src="image_3.png" /><figcaption>**Figure 1.** The local ionic environment analysis of MgO at 0 GPa and 2,000 K. The results are derived from a snapshot of the MD simulation at 6 ns. The energy minimization is applied to remove the thermal vibration of atoms. (a) The color mapping of the distances from a central ion to its 6th closest neighbor. The view is perpendicular to the rotation angle of the grain boundaries. The atoms enclosed by the white frame are zoomed in to show details. (b) Distributions of distances from a central ion to its 6th closest neighbor. The orange curve is the smoothed histogram using the Savitzky-Golay filter (Savitzky & Golay, 1964), and its minimum value between the two peaks is used to determine the cutoff distance.</figcaption></figure>

$$D_{GB} = \frac{D_{total}}{g} \qquad (2)$$

$D_{total}$ can be easily derived as the slope of mean square displacement (MSD) using the Einstein diffusion relation

$$D_{total} = \lim_{t \to \infty} \frac{\text{MSD}}{6t} = \lim_{t \to \infty} \frac{\langle [\vec{r}(t+t_0) - \vec{r}(t_0)]^2 \rangle_{\alpha}}{6t}, \qquad (3)$$

where $\vec{r}(t)$ is the particle trajectories that are continuous in Cartesian space, and $\langle \cdots \rangle_{\alpha}$ represents an average over atoms of species $\alpha$ (Mg, Fe, O) and over time with different origins (Karki, 2015). When the MSD is a linear function of time, we select the segment of the MSD and calculate the diffusion coefficient by linear fitting. The temperature-dependent diffusion coefficient can be fitted using the Arrhenius equation,

$$D = D_0 e^{-\frac{\Delta H}{RT}}, \qquad (4)$$

where $D_0$ is the pre-exponential factor, $R$ is the ideal gas constant, and $\Delta H$ is the activation enthalpy.

# 3. Results and Discussion

## 3.1. Identification of Grain Boundary Atoms

In this study, we analyze the structure of the GB and identify the GB atoms by examining the local ionic environments following Riet et al. (2021). In the ferropericlase or magnesiowüstite phase of (Mg,Fe)O, ions within the grain typically have six equidistant nearest neighbors. In contrast, ions at the GB exhibit a non-crystalline local environment with varying distances to neighboring ions and often less than six nearest neighbors. Figure 1a shows the color mapping of the distances from a central ion to its sixth-closest neighbor in a snapshot of the MD trajectory of MgO at 0 GPa and 2,000 K, in which the atoms associated with the GB region are clearly visible (i.e., atoms that are not colored purple). The distribution of distances from a central ion to its sixth-closest ion at energy minima structures is shown in Figure 1b, which exhibits a bimodal pattern. The first peak in this distribution indicates ions with six neighbors, characteristic of atoms within a single crystal, not in a GB. The adjacent
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Grain boundary diffusion coefficients of Mg (left) and O (right) as a function of reciprocal temperature (1,700, 1,800, and 2,000 K) in MgO with a $C_{vac}$ of 3.2 at% at ambient pressure. The error bars are estimated from the error bars in Figure S2 of Supporting Information S1, assuming the same relative standard deviation for each element. Results from previous experimental and theoretical studies are plotted in open symbols for comparison (Landuzzi et al., 2015; Liberatore & Wuensch, 1994; Riet et al., 2021). Dashed lines are fitted Arrhenius functions Equation 4.</figcaption></figure>

shoulder on this peak represents atoms near the GB, where relaxation can lead to slightly longer bond distances compared to the crystal interior. The second peak signifies ions that are undercoordinated, typically having five or fewer neighbors, and are located in the GB region. We set the minimum point between the first and second peaks as the cutoff distance for each system to differentiate between lattice and GB ions following Riet et al. (2021).

## 3.2. Grain Boundary Diffusivity

In this section, we discuss the GB diffusion coefficients in MgO at ambient pressure, and in (Mg, Fe)O at 140 GPa, calculated using Equations 2 and 3. The MSD data from all the simulations in this study can be found in Figure S4 of Supporting Information S1. Taking pure MgO as an example, we explore how the GB diffusion coefficients of Mg and O vary with $C_{vac}$, system size, and the misorientation angle of the GB (see Text S1 in Supporting Information S1). This preliminary study allowed us to determine that fully converged results are obtained when $C_{vac}$ reaches 3.2 at% or above, hence, only the diffusivity data at this concentration are presented below.

### 3.2.1. MgO at 0 GPa

Figure 2 summarizes the GB diffusion coefficients of MgO as a function of temperature at ambient pressure. To ensure convergence, we adopt a defect concentration of 3.2 at% to constrain the upper bound of the GB diffusivity (see Text S1 in Supporting Information S1). Our results generally agree well with previous theoretical studies using molecular dynamics simulations, and fall between the results of Riet et al. (2021) and Landuzzi et al. (2015) for both Mg and O.

We acknowledge the discrepancy between our results and the experimental results reported by Van Orman et al. (2003). The high diffusivity values measured by Van Orman et al. (2003) may originate from hydrogen segregation at the GBs during sample loading of their high-pressure experiments (Riet et al., 2021). However, the presence of free water on GBs is unlikely to occur in the mantle due to its water-undersaturated conditions (Fei
et al., 2013; Ohtani, 2021). Furthermore, previous studies suggest that the water solubility in ferropericlase is extremely low in the lower mantle (Hernández et al., 2013; Joachim et al., 2013; Muir & Brodholt, 2018) and water is expected to have only a minor effect on the diffusion coefficients (Fei et al., 2013). In addition, Cordier et al. (2023) highlighted that the dislocations and/or other extended defects may also contribute to the results of Van Orman et al. (2003). Dislocations may not be widespread in the lower mantle due to the lack of observed seismic anisotropy (Karato et al., 1995). Previous studies estimate lower mantle dislocation densities to be around $10^8$ to $10^{10} \text{ m}^{-2}$ (Davaille et al., 2018), significantly lower than those in the upper mantle (Farla et al., 2012) by orders of magnitude. Given that dislocation densities below $10^{11} \text{ m}^{-2}$ do not produce any observable effect on Ge diffusion coefficients or their anisotropy (Heldt & Hobstetter, 1963), whether the data reported by Van Orman et al. (2003) can be directly applied to the mantle remains debatable. McKenzie et al. (1971) experimentally obtained $\frac{\delta D_{GB}}{\sqrt{D_{lat}}}$ for oxygen diffusion in periclase at around 2,000 K, where $\delta$ is the GB width. However, since the value of $D_{lat}$ in MgO remains poorly constrained, it is difficult to directly compare this GB diffusivity with our simulation outcomes. Riet et al. (2021) estimated that $\delta D_{GB}$ of oxygen lies between $4 \times 10^{-23} \text{ m}^3 \text{ s}^{-1}$ and $2 \times 10^{-21} \text{ m}^3 \text{ s}^{-1}$, based on the highest and lowest $D_{lat}$ values reported in the literature (Oishi & Kingery, 1960; Yang & Flynn, 1994) and experimental measurements (McKenzie et al., 1971). Our result for $C_{vac} = 3.2 \text{ at\%}$ is $\sim 4 \times 10^{-21} \text{ m}^3 \text{ s}^{-1}$, slightly higher than this range. However, the $C_{vac}$ in pure MgO is significantly lower compared to (Mg,Fe)O due to the absence of multivalent ions (Ammann et al., 2010; Van Orman et al., 2003). Considering lower vacancy concentrations of $C_{vac} < 0.8 \text{ at\%}$, our simulation results fall within the range of experimental estimates. Liberatore and Wuensch (1994) measured oxygen diffusivities in MgO along the symmetric tilt GBs with misorientation angles of both 37° and 22°, which provides a direct comparison as our simulations also target symmetric tilt GBs. Our calculated results align perfectly with the GB diffusivities reported by Liberatore and Wuensch (1994), validating the reliability of our model (Figure 2b).

We find that there may be a slight decrease in the activation enthalpy with increasing temperature when the diffusivity data are fitted with Equation 4, inferred from the apparent change of the slope in Figure 2. This may be due to the more ordered GB structure and higher migration energy barriers at lower temperatures (Peng et al., 2025; Riet et al., 2021). Given the relatively small temperature range in this study, we continue to use a fixed activation enthalpy to fit the diffusivity and more data are required to better resolve this finding. The activation enthalpies for Mg and O are 235(±9) and 225(±61) kJ mol⁻¹, respectively. The only experimental result of the activation enthalpy for GB diffusion of O is $230 \text{ kJ mol}^{-1}$ (measured at 1,380–1,800 K, Passmore et al., 1966), which is closely matched by our simulations. Karki et al. (2015) reported the activation enthalpies for the migration of Mg (221 kJ mol⁻¹) and O (212 kJ mol⁻¹) along the {410} symmetric boundaries of MgO bicrystals at 0 GPa using ab initio calculations. Similar results were obtained by Harris et al. (1997) using MD simulations with empirical potentials. Our simulation results also align very well with these theoretical predictions that assumed ad hoc diffusion pathways. It is noteworthy that in the bulk crystal of periclase, the diffusion activation enthalpy of Mg is smaller than that of O (Ammann et al., 2010), while in the GB, they are quite similar and the activation enthalpy of O is slightly smaller. This may be related to the markedly different chemical environments at the GBs compared to the interior of the crystal. In summary, the GB diffusion properties of MgO at ambient pressure obtained from this study are consistent with previous theoretical and experimental data.

### 3.2.2. (Mg, Fe)O at 140 GPa

The high-pressure diffusion coefficients of Mg, Fe, and O in (Mg, Fe)O with two different iron contents are shown in Figure 3. For (Mg₀.₉ Fe₀.₁)O ferropericlase, the simulation temperatures are set between 4,000 and 5,000 K, corresponding to the upper bounds of the estimated CMB temperatures throughout the Earth's thermal evolution (Andrault et al., 2016). (Mg₀.₁₆ Fe₀.₈₄)O magnesiowüstite is taken as a prototype Fe-rich material that has been suggested to be the main constituent of ULVZs (Wicks et al., 2010, 2017) and the high conductance layer (Buffett, 1992; Knittle & Jeanloz, 1986), and consequently it may serve as an important medium for iron transport from the outer core to the lower mantle. Recent studies suggest that the melting point of FeO wüstite under CMB pressure conditions reaches up to 4140 K (Dobrosavljevic et al., 2023), indicating that our simulation temperature of 4000 K for (Mg₀.₁₆ Fe₀.₈₄)O is below the solidus. Overall, the diffusion coefficients slightly increase with iron content, and the order of diffusion coefficients for the three elements follows $D_{GB}^{Fe} \gtrsim D_{GB}^{Mg} > D_{GB}^{O}$. We find that the diffusion coefficient of Mg is about an order of magnitude larger than that of O, which is closely aligned with the results of Riet et al. (2021). Furthermore, Fe and Mg have similar diffusion coefficients, both significantly larger
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Grain boundary diffusion coefficients as a function of reciprocal temperature (4,000, 4,500, and 5,000 K) in (Mg<sub>0.9</sub>Fe<sub>0.1</sub>)O (solid squares) and (Mg<sub>0.16</sub>Fe<sub>0.84</sub>)O (open circles) with a C<sub>vac</sub> of 3.2 at% at 140 GPa. The diffusivity of Mg, Fe, and O are shown in blue, orange, and green, respectively. The error bars represent 2SD of the diffusion coefficients calculated from four 5-ns-long MD trajectories. Dashed lines are fitted Arrhenius functions Equation 4.</figcaption></figure>

than O, which is consistent with the MD data for GB diffusion in olivine (Mantisi et al., 2017). This suggests that the relative magnitudes of GB diffusion coefficients for different elements are, to a large extent, controlled by ionic radii, considering that the ionic radii of Fe<sup>2+</sup>, Mg<sup>2+</sup>, and O<sup>2-</sup> are 75, 86, and 126 pm, respectively (Slater, 1964). Due to the steric effects (In Nalwa, 2001), smaller ions are better suited to move through the available space, thereby facilitating diffusion. We find that the uncertainty of the diffusion coefficients at 5,000 K is much smaller than at lower temperatures, which may be due to the more stable premelting state of the GBs (see Text S1 in Supporting Information S1) at higher temperatures, reducing the variation in diffusivity. Regarding the temperature dependence, the diffusion activation enthalpies for Mg, Fe, and O are 448(±63), 328(±37), and 479(±97) kJ mol<sup>-1</sup>, respectively. Due to the pressure effect on diffusion, they are significantly higher than the activation enthalpies for MgO under ambient pressure.

Although metallic iron from the core may be oxidized and diffuse as ferrous iron upon entering the mantle, we cannot rule out the possibility of metallic iron migrating directly along (Mg, Fe)O GBs on the mantle side. Our calculations indicate that ferrous iron diffuses slightly faster than metallic iron along periclase GBs, thus providing an upper bound on Fe transport efficiency across the CMB. A detailed discussion can be found in Text S4 of Supporting Information S1.

## 4. Implications

The effective diffusion coefficient of iron in a polycrystalline material can be estimated using the following equation (Balluffi et al., 2005; Raj & Ashby, 1971):

$$D_{\text{eff}} = D_{\text{lat}} + \frac{\pi \delta}{d} D_{\text{GB}}, \qquad (5)$$

where δ is the GB width (~1 nm) and d is the grain size (0.01–10 mm, Glišović et al., 2015) in the lower mantle. The lattice diffusion coefficients (D<sub>lat</sub>) are calculated using MD simulations of (Mg, Fe)O single crystals (Text S2 in Supporting Information S1) and are consistent with previous ab initio calculations (Ammann et al., 2010, 2011; Saha et al., 2011). The characteristic length scale of the iron diffusion is given by:

$$L = \sqrt{Dt}, \qquad (6)$$

where the time scale t is set to the age of the Earth (4.54 Gyr, Dalrymple, 2001). To distinguish the respective contributions of GB diffusion and lattice diffusion to the diffusion length scale of iron, we calculated three L values using three different diffusivities: (a) L<sup>eff</sup><sub>GB</sub> from D<sup>eff</sup><sub>GB</sub> = πδ/d D<sub>GB</sub>, which only considers GB diffusion by assuming D<sub>lat</sub> = 0 in Equation 5; (b) L<sub>lat</sub> from D<sub>lat</sub>, which only considers lattice diffusion; (c) L<sup>eff</sup> from D<sup>eff</sup> in Equation 5. The self-diffusion coefficients obtained by the MD simulations were all converted into chemical diffusion coefficients (Text S3 in Supporting Information S1). We explore the diffusivity values at different temperatures (4,000–5,000 K), grain sizes (0.01–10 mm), vacancy concentration (Text S2 in Supporting Information S1), and the ratio of self-to chemical diffusivities (Text S3 in Supporting Information S1) to estimate the upper and lower bounds of the diffusion length scales, as shown in Figure 4. Other iron infiltration mechanisms proposed by previous studies, including capillary rise (Poirier et al., 1998), suction (Kanda & Stevenson, 2006), upward sedimentation of outer core alloys (Buffett et al., 2000), and morphological instability (K. K. Otsuka & Karato, 2012) are also plotted for comparison.

The result of L<sup>eff</sup><sub>GB</sub> does not exceed 30 m, which agrees with the findings of Riet et al. (2021) that transport through periclase GBs is limited to length scales less than ~100 m. This is quite a small value compared with the transport length scales of other mechanisms as well as the spatial scales of ULVZs and the high conductance layer. Since
<figure><img src="image_6.png" /><figcaption>Figure 4. Length scale of iron transport from the core to the mantle compared to length scales of the high conductance layer and ULVZs. The purple dashed line, purple dash-dot line, and purple solid line represent $L_{GB}^{eff}$, $L_{lat}$, and $L_{eff}$, respectively. Other iron infiltration mechanisms are shown for comparison (Poirier et al., 1998; Buffett et al., 2000; Kanda & Stevenson, 2006; K. K. Otsuka & Karato, 2012).</figcaption></figure>

$D_{lat}$ exceeds $D_{GB}^{eff}$ by several orders of magnitude, $D_{lat}$ becomes the absolutely dominant term in Equation 5, resulting in maximum $L_{eff}$ (1,183.1 m) being only about 0.4 m larger than maximum $L_{lat}$ (1,182.7 m). In other words, the diffusion length scale including the GB diffusion is only 0.4 m greater than excluding it. It is worth noting that the lattice diffusion lengths in our model align very well with the estimated thickness of the conducting layer at the CMB (100–1,000 m, Buffett, 2015). To quantitatively analyze the amount of Fe transported via solid-state diffusion, we solve Fick's second law of diffusion to calculate the concentration profile of iron in the mantle:

$$ \frac{\partial C}{\partial t} = -D\nabla^2 C \qquad (7) $$

Assuming that the bottom of the mantle in contact with the core always maintains a composition of pure FeO, and considering an initial condition of zero iron in the mantle, we obtain the concentration profile of FeO in the mantle after the iron diffusion of 4.54 Gyr. The total mass of FeO that has been transported to the mantle calculated from maximum $D_{GB}^{eff}$ is $4.7 \times 10^{19}$ kg, which can only account for less than 17.3 wt% of a ~200-m-high conductance layer composed of pure FeO. On the contrary, the mass calculated from the minimum and maximum $D_{eff}$ values can form conducting layers with thicknesses of 87 and 1,335 m, respectively. Therefore, we conclude that the efficiency of iron transport through GB diffusion is likely to be very small under CMB conditions, and the lattice diffusion in ferropericlase alone can adequately explain the iron enrichment observed within 1 km above the CMB and the resulting high conductance layer. However, for

larger-scale iron enrichment phenomena, such as ULVZs, neither GB diffusion nor lattice diffusion can account for such long-distance iron transport from the core. In this case, alternative hypotheses, such as silicate sediments accumulating at the top of the core during secular cooling (Buffett et al., 2000) or the penetration of blobs of iron-rich liquid into the mantle caused by morphological instability (K. K. Otsuka & Karato, 2012), should be considered as more competitive explanations.

At the CMB, not only (Mg, Fe)O but also silicate minerals such as bridgmanite and post-perovskite are present. Given that diffusion in bridgmanite is much slower than that in ferropericlase (Ammann et al., 2010; Holzapfel et al., 2003, 2005), we argue that GB diffusion is unlikely to be an effective mechanism to transport Fe from the core to the lower mantle. Considering that some siderophile elements (e.g., W) have larger atomic radii and mass than Fe, we speculate that their GB diffusion coefficients in (Mg, Fe)O might be even smaller than that of Fe. So far the only data available for comparison are experimental results under relatively low pressures (Hayden & Watson, 2007; Yoshino et al., 2020). Therefore, more studies are needed to accurately quantify the efficiency of GB diffusion in exchanging siderophile elements across the CMB to elucidate the scale and extent of the core-mantle interaction.

## Data Availability Statement

Data used in this study are available at Peng and Deng (2024). The software LAMMPS used in this study is developed openly at https://github.com/lammps/lammps and available at Plimpton et al. (2021). The package MDAnalysis is developed openly at https://github.com/MDAnalysis/mdanalysis.

## References

* Ammann, M. W., Brodholt, J. P., & Dobson, D. P. (2011). Ferrous iron diffusion in Ferro-Periclase across the spin transition. *Earth and Planetary Science Letters*, 302(3), 393–402. https://doi.org/10.1016/j.epsl.2010.12.031

* Ammann, M. W., Brodholt, J. P., Wookey, J., & Dobson, D. P. (2010). First-principles constraints on diffusion in lower-mantle minerals and a weak D" layer. *Nature*, 465(7297), 462–465. https://doi.org/10.1038/nature09052

* Andrault, D., Monteux, J., Le Bars, M., & Samuel, H. (2016). The deep Earth may not be cooling down. *Earth and Planetary Science Letters*, 443, 195–203. https://doi.org/10.1016/j.epsl.2016.03.020

* Balluffi, R. W., Allen, S. M., Carter, W. C., & Kemper, R. A. (2005). *Kinetics of materials*. J. Wiley & Sons.

## Acknowledgments

This work was funded by the National Science Foundation under Grant EAR-2242946. The simulations presented in this article were performed on computational resources managed and supported by Princeton Research Computing, a consortium of groups including the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of Information Technology's High Performance Computing Center and Visualization Laboratory at Princeton University.
Buffett, B. A. (1992). Constraints on magnetic energy and mantle conductivity from the forced Nutations of the Earth. *Journal of Geophysical Research*, 97(B13), 19581–19597. https://doi.org/10.1029/92JB00977

Buffett, B. A. (2015). 8.08-Core–mantle interactions. In G. Schubert (Ed.), *Treatise on geophysics* (2nd ed., pp. 213–224). Elsevier. https://doi.org/10.1016/B978-0-444-53802-4.00148-2

Buffett, B. A., Garnero, E. J., & Jeanloz, R. (2000). Sediments at the top of Earth's core. *Science*, 290(5495), 1338–1342. https://doi.org/10.1126/science.290.5495.1338

Buffett, B. A., Mathews, P. M., & Herring, T. A. (2002). Modeling of nutation and precession: Effects of electromagnetic coupling. *Journal of Geophysical Research*, 107(B4), 1–14. https://doi.org/10.1029/2000JB000056

Cordier, P., Gouriet, K., Weidner, T., Van Orman, J., Castelnau, O., Jackson, J. M., & Carrez, P. (2023). Periclase deforms more slowly than bridgmanite under mantle conditions. *Nature*, 613(7943), 303–307. https://doi.org/10.1038/s41586-022-05410-9

Dalrymple, G. B. (2001). The age of the Earth in the twentieth century: A problem (mostly) solved. *Geological Society, London, Special Publications*, 190(1), 205–221. https://doi.org/10.1144/GSL.SP.2001.190.01.14

Davaille, A., Carrez, P., & Cordier, P. (2018). Fat plumes may reflect the complex rheology of the lower mantle. *Geophysical Research Letters*, 45(3), 1349–1354. https://doi.org/10.1002/2017GL076575

Deng, J., Miyazaki, Y., & Lee, K. K. M. (2019). Implications for the melting phase relations in the MgO–FeO system at core-mantle boundary conditions. *Journal of Geophysical Research: Solid Earth*, 124(2), 1294–1304. https://doi.org/10.1029/2018JB015499

Deng, X., Xu, Y., Hao, S., Ruan, Y., Zhao, Y., Wang, W., et al. (2023). Compositional and thermal state of the lower mantle from joint 3D inversion with seismic tomography and mineral elasticity. *Proceedings of the National Academy of Sciences*, 120(26), e2220178120. https://doi.org/10.1073/pnas.2220178120

Dobrosavljevic, V. V., Zhang, D., Sturhahn, W., Chariton, S., Prakapenka, V. B., Zhao, J., et al. (2023). Melting and defect transitions in FeO up to pressures of Earth's core-mantle boundary. *Nature Communications*, 14(1), 7336. https://doi.org/10.1038/s41467-023-43154-w

Dohmen, R., & Milke, R. (2010). Diffusion in polycrystalline materials: Grain boundaries, mathematical models, and experimental data. *Reviews in Mineralogy and Geochemistry*, 72(1), 921–970. https://doi.org/10.2138/rmg.2010.72.21

Farla, R. J. M., Jackson, I., Fitz Gerald, J. D., Faul, U. H., & Zimmerman, M. E. (2012). Dislocation damping and anisotropic seismic wave attenuation in Earth's upper mantle. *Science*, 336(6079), 332–335. https://doi.org/10.1126/science.1218318

Fei, H., Wiedenbeck, M., Yamazaki, D., & Katsura, T. (2013). Small effect of water on upper-mantle rheology based on Silicon self-diffusion coefficients. *Nature*, 498(7453), 213–215. https://doi.org/10.1038/nature12193

Ferrick, A. L., & Korenaga, J. (2023). Long-term core–mantle interaction explains W-He isotope heterogeneities. *Proceedings of the National Academy of Sciences*, 120(4), e2215903120. https://doi.org/10.1073/pnas.2215903120

Furstoss, J., Hirel, P., Carrez, P., & Cordier, P. (2022). Complexions and stoichiometry of the 60.8°/[100](011) symmetrical tilt grain boundary in Mg₂SiO₄ Forsterite: A combined empirical potential and first-principles study. *American Mineralogist*, 107(11), 2034–2043. https://doi.org/10.2138/am-2022-8420

Garnero, E. J., McNamara, A. K., & Shim, S.-H. (2016). Continent-sized anomalous zones with low seismic velocity at the base of Earth's mantle. *Nature Geoscience*, 9(7), 481–489. https://doi.org/10.1038/ngeo2733

Glišović, P., Forte, A. M., & Ammann, M. W. (2015). Variations in grain size and viscosity based on vacancy diffusion in minerals, seismic tomography, and Geodynamically inferred mantle rheology. *Geophysical Research Letters*, 42(15), 6278–6286. https://doi.org/10.1002/2015GL065142

Harris, D. J., Watson, G. W., & Parker, S. C. (1997). Vacancy migration at the {410}/[001] symmetric tilt grain boundary of MgO: An atomistic simulation study. *Physical Review B*, 56(18), 11477–11484. https://doi.org/10.1103/PhysRevB.56.11477

Hart, E. W. (1957). On the role of dislocations in bulk diffusion. *Acta Metallurgica*, 5(10), 597. https://doi.org/10.1016/0001-6160(57)90127-X

Hayden, L. A., & Watson, E. B. (2007). A diffusion mechanism for core–mantle interaction. *Nature*, 450(7170), 709–711. https://doi.org/10.1038/nature06380

Hayden, L. A., & Watson, E. B. (2008). Grain boundary mobility of carbon in Earth's mantle: A possible carbon flux from the core. *Proceedings of the National Academy of Sciences*, 105(25), 8537–8541. https://doi.org/10.1073/pnas.0710806105

Heldt, L. A., & Hobstetter, J. N. (1963). The effect of dislocations on diffusion in germanium. *Acta Metallurgica*, 11(10), 1165–1168. https://doi.org/10.1016/0001-6160(63)90043-9

Hernández, E. R., Alfè, D., & Brodholt, J. (2013). The incorporation of water into lower-mantle perovskites: A first-principles study. *Earth and Planetary Science Letters*, 364, 37–43. https://doi.org/10.1016/j.epsl.2013.01.005

Hirel, P. (2015). Atomsk: A tool for manipulating and converting atomic data files. *Computer Physics Communications*, 197, 212–219. https://doi.org/10.1016/j.cpc.2015.07.012

Hirel, P., Carrez, P., & Cordier, P. (2022). Why do compact grain boundary complexions prevail in rock-salt materials? *Acta Materialia*, 240, 118297. https://doi.org/10.1016/j.actamat.2022.118297

Hirel, P., Furstoss, J., & Carrez, P. (2021). A critical assessment of interatomic potentials for modelling lattice defects in Forsterite Mg₂SiO₄ from 0 to 12 GPa. *Physics and Chemistry of Minerals*, 48(12), 46. https://doi.org/10.1007/s00269-021-01170-6

Hirel, P., Moladje, G. F. B., Carrez, P., & Cordier, P. (2019). Systematic theoretical study of [001] symmetric tilt grain boundaries in MgO from 0 to 120 GPa. *Physics and Chemistry of Minerals*, 46(1), 37–49. https://doi.org/10.1007/s00269-018-0985-7

Holzapfel, C., Rubie, D. C., Frost, D. J., & Langenhorst, F. (2005). Fe-Mg interdiffusion in (Mg, Fe)SiO₃ perovskite and lower mantle reequilibration. *Science*, 309(5741), 1707–1710. https://doi.org/10.1126/science.1111895

Holzapfel, C., Rubie, D. C., Mackwell, S., & Frost, D. J. (2003). Effect of pressure on Fe–Mg interdiffusion in (FeₓMg₁₋ₓ)O, ferropericlase. *Physics of the Earth and Planetary Interiors*, 139(1), 21–34. https://doi.org/10.1016/S0031-9201(03)00142-0

Hoover, W. G. (1985). Canonical dynamics—Equilibrium phase-space distributions. *Physical Review A*, 31(3), 1695–1697. https://doi.org/10.1103/PhysRevA.31.1695

Jackson, I., Fitz Gerald, J. D., Faul, U. H., & Tan, B. H. (2002). Grain-size-sensitive seismic wave attenuation in polycrystalline olivine. *Journal of Geophysical Research*, 107(B12), 1–16. https://doi.org/10.1029/2001JB001225

Joachim, B., Wohlers, A., Norberg, N., Gardés, E., Petrishcheva, E., & Abart, R. (2013). Diffusion and solubility of hydrogen and water in Periclase. *Physics and Chemistry of Minerals*, 40(1), 19–27. https://doi.org/10.1007/s00269-012-0542-8

Joesten, R. (1991). Grain-boundary diffusion Kinetics in silicate and Oxide minerals. In J. Ganguly (Ed.), *Diffusion, atomic ordering, and mass transport: Selected topics in geochemistry* (pp. 345–395). Springer US. https://doi.org/10.1007/978-1-4613-9019-0_11

Kaare-Rasmussen, J., Peters, D., Rizo, H., Carlson, R., Nielsen, S., & Horton, F. (2023). Tungsten isotopes in Baffin Island lavas: Evidence of Iceland plume evolution. *Geochemical Perspectives Letters*, 28, 7–12. https://doi.org/10.7185/geochemlet.2337

Kanda, R. V. S., & Stevenson, D. J. (2006). Suction mechanism for iron entrainment into the lower mantle. *Geophysical Research Letters*, 33(2), https://doi.org/10.1029/2005GL025009
Karato, S.-i., Zhang, S., & Wenk, H.-R. (1995). Superplasticity in Earth's lower mantle: Evidence from seismic anisotropy and rock physics. *Science*, 270(5235), 458–461. https://doi.org/10.1126/science.270.5235.458

Karki, B. B. (2015). First-principles computation of mantle materials in crystalline and amorphous phases. *Physics of the Earth and Planetary Interiors*, 240, 43–69. https://doi.org/10.1016/j.pepi.2014.11.004

Karki, B. B., Ghosh, D. B., & Verma, A. K. (2015). First-principles prediction of pressure-enhanced defect segregation and migration at MgO grain boundaries. *American Mineralogist*, 100(5–6), 1053–1058. https://doi.org/10.2138/am-2015-5143

Knittle, E., & Jeanloz, R. (1986). High-pressure metallization of FeO and implications for the Earth's core. *Geophysical Research Letters*, 13(13), 1541–1544. https://doi.org/10.1029/GL013i013p01541

Landuzzi, F., Pasquini, L., Giusepponi, S., Celino, M., Montone, A., Palla, P. L., & Cleri, F. (2015). Molecular dynamics of ionic self-diffusion at an MgO grain boundary. *Journal of Materials Science*, 50(6), 2502–2509. https://doi.org/10.1007/s10853-014-8808-9

Liberatore, M., & Wuensch, B. J. (1994). Oxygen self-diffusion in Mgo grain boundaries. *MRS Online Proceedings Library*, 357(1), 389–393. https://doi.org/10.1557/PROC-357-389

Mantisi, B., Sator, N., & Guillot, B. (2017). Structure and transport at grain boundaries in polycrystalline olivine: An atomic-scale perspective. *Geochimica et Cosmochimica Acta*, 219, 160–176. https://doi.org/10.1016/j.gca.2017.09.026

McKenzie, D. R., Searcy, A. W., Holt, J. B., & Condit, R. H. (1971). Oxygen grain-boundary diffusion in MgO. *Journal of the American Ceramic Society*, 54(4), 188–190. https://doi.org/10.1111/j.1151-2916.1971.tb12261.x

Michaud-Agrawal, N., Denning, E. J., Woolf, T. B., & Beckstein, O. (2011). MDAnalysis: A toolkit for the analysis of molecular dynamics simulations. *Journal of Computational Chemistry*, 32(10), 2319–2327. https://doi.org/10.1002/jcc.21787

Muir, J. M. R., & Brodholt, J. P. (2018). Water distribution in the lower mantle: Implications for hydrolytic weakening. *Earth and Planetary Science Letters*, 484, 363–369. https://doi.org/10.1016/j.epsl.2017.11.051

Nagao, H., Iyemori, T., Higuchi, T., & Araki, T. (2003). Lower mantle conductivity anomalies estimated from geomagnetic jerks. *Journal of Geophysical Research*, 108(B5). https://doi.org/10.1029/2002JB001786

Nalwa, H. S. (Ed.) (2001). *Handbook of surfaces and interfaces of materials*. Academic Press.

Ohta, K., Hirose, K., Ichiki, M., Shimizu, K., Sata, N., & Ohishi, Y. (2010). Electrical conductivities of Pyrolitic mantle and MORB materials up to the lowermost mantle conditions. *Earth and Planetary Science Letters*, 289(3), 497–502. https://doi.org/10.1016/j.epsl.2009.11.042

Ohtani, E. (2021). Hydration and dehydration in Earth's interior. *Annual Review of Earth and Planetary Sciences*, 49(1), 253–278. https://doi.org/10.1146/annurev-earth-080320-062509

Oishi, Y., & Kingery, W. D. (1960). Oxygen diffusion in periclase crystals. *The Journal of Chemical Physics*, 33(3), 905–906. https://doi.org/10.1063/1.1731286

Otsuka, K., & Karato, S.-I. (2012). Deep penetration of molten iron into the mantle caused by a morphological instability. *Nature*, 492(7428), 243–246. https://doi.org/10.1038/nature11663

Passmore, E. M., Duff, R. H., & Vasilos, T. (1966). Creep of Dense, polycrystalline magnesium Oxide. *Journal of the American Ceramic Society*, 49(11), 594–600. https://doi.org/10.1111/j.1151-2916.1966.tb13175.x

Pedone, A., Malavasi, G., Menziani, M. C., Cormack, A. N., & Segre, U. (2006). A new self-consistent empirical interatomic potential model for Oxides, silicates, and Silica-based Glasses. *The Journal of Physical Chemistry B*, 110(24), 11780–11795. https://doi.org/10.1021/jp0611018

Peng, Y., & Deng, J. (2024). Grain boundary diffusion of ferropericlase: Implications for the core-mantle interaction [Dataset]. OSF. https://doi.org/10.17605/OSF.IO/2DJYH

Peng, Y., Yoshino, T., & Deng, J. (2025). Grain boundary diffusion cannot explain the W isotope heterogeneities of the deep mantle. *Nature Communications*, 16(1), 1866. https://doi.org/10.1038/s41467-025-57120-1

Plimpton, S. (1995). Fast parallel algorithms for short-range molecular-dynamics. *Journal of Computational Physics*, 117(1), 1–19. https://doi.org/10.1006/jcph.1995.1039

Plimpton, S., Kohlmeyer, A., Thompson, A., Moore, S., & Berger, R. (2021). LAMMPS Stable release 29 September 2021 (stable_29Sep2021_update3) [Software]. Zenodo. https://doi.org/10.5281/zenodo.6386596

Poirier, J. P., Malavergne, V., & Le Mouël, J. L. (1998). Is there a thin electrically conducting layer at the base of the mantle? In M. Gurnis, M. E. Wyssession, E. Knittle, & B. A. Buffett (Eds.), *Geodynamics series* (Vol. 28, pp. 131–137). American Geophysical Union. https://doi.org/10.1029/GD028p0131

Raj, R., & Ashby, M. F. (1971). On grain boundary sliding and diffusional creep. *Metallurgical Transactions A*, 2(4), 1113–1127. https://doi.org/10.1007/BF02664244

Riet, A. A., Van Orman, J. A., & Lacks, D. J. (2018). The interplay of structure and dynamics at grain boundaries. *The Journal of Chemical Physics*, 149(19), 194501. https://doi.org/10.1063/1.5052188

Riet, A. A., Van Orman, J. A., & Lacks, D. J. (2021). A molecular dynamics study of grain boundary diffusion in MgO. *Geochimica et Cosmochimica Acta*, 292, 203–216. https://doi.org/10.1016/j.gca.2020.09.012

Ritterbex, S., Tsuchiya, T., Drury, M., & Plümper, O. (2024). Atomic-scale study of intercrystalline (Mg, Fe)O in planetary mantles: Mechanics and thermodynamics of grain boundaries under pressure. *Journal of Geophysical Research: Solid Earth*, 129(5), e2023JB028375. https://doi.org/10.1029/2023JB028375

Rudolph, M. L., Lekić, V., & Lithgow-Bertelloni, C. (2015). Viscosity jump in Earth's mid-mantle. *Science*, 350(6266), 1349–1352. https://doi.org/10.1126/science.aad1929

Saha, S., Bengtson, A., Crispin, K. L., Van Orman, J. A., & Morgan, D. (2011). Effects of spin transition on diffusion of Fe²⁺ in ferropericlase in Earth's lower mantle. *Physical Review B*, 84(18), 184102. https://doi.org/10.1103/PhysRevB.84.184102

Savitzky, A., & Golay, M. J. E. (1964). Smoothing and differentiation of data by simplified least squares procedures. *Analytical Chemistry*, 36(8), 1627–1639. https://doi.org/10.1021/ac60214a047

Saylor, D. M., Morawiec, A., & Rohrer, G. S. (2003). Distribution of grain boundaries in magnesia as a function of five macroscopic parameters. *Acta Materialia*, 51(13), 3663–3674. https://doi.org/10.1016/S1359-6454(03)00181-2

Sherman, D. M. (1989). The nature of the pressure-induced metallization of FeO and its implications to the core-mantle boundary. *Geophysical Research Letters*, 16(6), 515–518. https://doi.org/10.1029/GL016i006p00515

Slater, J. C. (1964). Atomic Radii in crystals. *Journal of Chemical Physics*, 41(10), 3199–3204. https://doi.org/10.1063/1.1725697

ten Grotenhuis, S. M., Drury, M. R., Peach, C. J., & Spiers, C. J. (2004). Electrical properties of fine-grained olivine: Evidence for grain boundary transport. *Journal of Geophysical Research*, 109(B6). https://doi.org/10.1029/2003JB002799

Van Orman, J. A., Fei, Y., Hauri, E. H., & Wang, J. (2003). Diffusion in MgO at high pressures: Constraints on deformation mechanisms and chemical transport at the core-mantle boundary. *Geophysical Research Letters*, 30(2). https://doi.org/10.1029/2002GL016343
Vilella, K., Bodin, T., Boukaré, C.-E., Deschamps, F., Badro, J., Ballmer, M. D., & Li, Y. (2021). Constraints on the composition and temperature of LLSVPs from seismic properties of lower mantle minerals. *Earth and Planetary Science Letters*, **554**, 116685. https://doi.org/10.1016/j.epsl.2020.116685

Wicks, J. K., Jackson, J. M., & Sturhahn, W. (2010). Very low sound velocities in iron-rich (Mg, Fe)O: Implications for the core-mantle boundary region. *Geophysical Research Letters*, **37**(15). https://doi.org/10.1029/2010GL043689

Wicks, J. K., Jackson, J. M., Sturhahn, W., & Zhang, D. (2017). Sound velocity and density of magnesiowüstites: Implications for ultralow-velocity zone topography. *Geophysical Research Letters*, **44**(5), 2148–2158. https://doi.org/10.1002/2016GL071225

Williams, Q., & Garnero, E. J. (1996). Seismic evidence for partial melt at the base of Earth's mantle. *Science*, **273**(5281), 1528–1530. https://doi.org/10.1126/science.273.5281.1528

Yamazaki, D., & Irifune, T. (2003). Fe–Mg interdiffusion in magnesiowüstite up to 35 GPa. *Earth and Planetary Science Letters*, **216**(3), 301–311. https://doi.org/10.1016/S0012-821X(03)00534-X

Yang, M. H., & Flynn, C. P. (1994). Intrinsic diffusion properties of an Oxide: MgO. *Physical Review Letters*, **73**(13), 1809–1812. https://doi.org/10.1103/PhysRevLett.73.1809

Yoshino, T. (2019). Penetration of molten iron alloy into the lower mantle phase. *Comptes Rendus Geoscience*, **351**(2), 171–181. https://doi.org/10.1016/j.crte.2018.06.013

Yoshino, T., Makino, Y., Suzuki, T., & Hirata, T. (2020). Grain boundary diffusion of W in lower mantle phase with implications for isotopic heterogeneity in oceanic island basalts by core-mantle interactions. *Earth and Planetary Science Letters*, **530**, 115887. https://doi.org/10.1016/j.epsl.2019.115887

Young, C. J., & Lay, T. (1987). The core-mantle boundary. *Annual Review of Earth and Planetary Sciences*, **15**(1), 25–46. https://doi.org/10.1146/annurev.ea.15.050187.000325

Yuan, Q., Li, M., Desch, S. J., Ko, B., Deng, H., Garnero, E. J., et al. (2023). Moon-forming impactor as a source of Earth's basal mantle anomalies. *Nature*, **623**(7985), 95–99. https://doi.org/10.1038/s41586-023-06589-1

## References From the Supporting Information

Deng, J., & Lee, K. K. M. (2017). Viscosity jump in the lower mantle inferred from melting curves of ferropericlase. *Nature Communications*, **8**(1), 1997. https://doi.org/10.1038/s41467-017-02263-z

Dillon, S. J., & Harmer, M. P. (2007). Multiple grain boundary transitions in ceramics: A case study of alumina. *Acta Materialia*, **55**(15), 5247–5254. https://doi.org/10.1016/j.actamat.2007.04.051

Frolov, T., Olmsted, D. L., Asta, M., & Mishin, Y. (2013). Structural phase transformations in metallic grain boundaries. *Nature Communications*, **4**(1), 1899. https://doi.org/10.1038/ncomms2919

Glicksman, M. E., & Vold, C. L. (1972). Heterophase dislocations — An approach towards interpreting high temperature grain boundary behavior. *Surface Science*, **31**, 50–67. https://doi.org/10.1016/0039-6028(72)90253-1

Lesher, C. E. (2010). Self-diffusion in silicate Melts: Theory, observations and applications to magmatic systems. *Reviews in Mineralogy and Geochemistry*, **72**(1), 269–309. https://doi.org/10.2138/rmg.2010.72.7

Mackwell, S., Bystricky, M., & Sproni, C. (2005). Fe–Mg interdiffusion in (Mg, Fe)O. *Physics and Chemistry of Minerals*, **32**(5), 418–425. https://doi.org/10.1007/s00269-005-0013-6

Otsuka, L., Longo, M., & Karato, S.-I. (2013). Ferric iron content of ferropericlase as a function of composition, Oxygen Fugacity, temperature and pressure: Implications for redox conditions during diamond formation in the lower mantle. *Earth and Planetary Science Letters*, **365**, 7–16. https://doi.org/10.1016/j.epsl.2012.11.030

Torabi Rad, M., Boussinot, G., & Apel, M. (2020). Dynamics of grain boundary premelting. *Scientific Reports*, **10**(1), 21074. https://doi.org/10.1038/s41598-020-77863-9