Self-diffusion coecient and sound velocity of Fe-Ni-O uid: implications for the stratication of Earth’s outer core

It is experimentally reported that the stratied layer atop Earth’s outer core is hundreds of kilometers thick with a maximum sound velocity reduction of 0.3% relative to the preliminary reference Earth model. However, why the sound velocity atop the outer core is reduced remains theoretically unclear. In this paper, the Ni and vital light O in the outer core were both considered to have implications for the stratication of Earth’s core, including the stratication thickness and the sound velocity prole. Ab initio molecular dynamics simulations were performed on the Fe-Ni-O uid under the conditions of Earth’s outer core, and the self-diffusion coecients and ion-ion dynamic structure factors were calculated. The self-diffusion coecient of O is (19.56±0.83)×10-9 m2s-1 at the core-mantle boundary. Combining the diffusion equation with the time evolution of the O self-diffusion coecient, the calculated stratication thickness at present is 194.7 km. The calculated ion-ion dynamic structural factors indicate that the sound velocity in the outmost outer core near the stratied layer is 7.86 km/s. These results show that Fe-Ni-O is a possible composition of the stratied layer atop the outer core featuring an appropriate thickness and a reduced sound velocity, thereby shedding light on the dynamic behavior of Earth’s core.


Abstract
It is experimentally reported that the strati ed layer atop Earth's outer core is hundreds of kilometers thick with a maximum sound velocity reduction of 0.3% relative to the preliminary reference Earth model. However, why the sound velocity atop the outer core is reduced remains theoretically unclear. In this paper, the Ni and vital light O in the outer core were both considered to have implications for the strati cation of Earth's core, including the strati cation thickness and the sound velocity pro le. Ab initio molecular dynamics simulations were performed on the Fe-Ni-O uid under the conditions of Earth's outer core, and the self-diffusion coe cients and ion-ion dynamic structure factors were calculated. The selfdiffusion coe cient of O is (19.56±0.83)×10-9 m2s-1 at the core-mantle boundary. Combining the diffusion equation with the time evolution of the O self-diffusion coe cient, the calculated strati cation thickness at present is 194.7 km. The calculated ion-ion dynamic structural factors indicate that the sound velocity in the outmost outer core near the strati ed layer is 7.86 km/s. These results show that Fe-Ni-O is a possible composition of the strati ed layer atop the outer core featuring an appropriate thickness and a reduced sound velocity, thereby shedding light on the dynamic behavior of Earth's core.

Full Text
Th strati ed layer underneath the core-mantle boundary (CMB) has a lower sound velocity 1,2 than the corresponding values in the preliminary reference Earth model (PREM) 3 , and its thickness is approximately 200 km 4 to 300 km 2,5 . Studies have suggested that this strati cation is caused by light elements 2 that may have been expelled from the inner core or diffused from the mantle 6 . However, mixtures comprising iron and light elements may increase sound velocity 7 , and the thickness of the strati cation derived from the diffusion equation in a previous paper was only 60-70 km 6 . Hence, a theoretical explanation for the 200-300-km-thick strati cation atop the outer core with a reduced sound velocity remains elusive.
The strati cation in the outer core is both thermal and compositional in nature 8 . In terms of subadiabatic strati cation, the addition of Ni decreases the thermal conductivity by approximately 10%, whereas the Ni effect on the thermal strati cation is limited 9 . The thickness of the compositional strati cation was calculated to be 60-70 km from the self-diffusion coe cient of O in Fe-O uid 6 . In this early analytical model, the self-diffusion coe cient of light O was considered to be 3×10 -9 m 2 s -110 . However, ab initio results indicate that the self-diffusion coe cient of pure Fe is approximately 6×10 -9 m 2 s -111 . O has an anomalously large self-diffusion coe cient in Fe-O uid under CMB conditions: 9×10 -9 m 2 s -1 at 4581 K and 136 GPa, 50×10 -9 m 2 s -1 at 3829 K and 136 GPa 12 , and ~22×10 -9 m 2 s -113 . Although the O concentration is only 1.6-3.8 wt.% in the outer core and O does not exist in the inner core 14 , O is essential for compositional convection 15 and partitions much more strongly than do S and Si from the inner core to the outer core. In addition, the results of nuclear resonance inelastic X-ray scattering demonstrate that Fe enrichment in (Mg,Fe)O has the potential to explain the large velocity drop at the base of the mantle 16 .
With increasing computational capabilities, ab initio molecular dynamics can yield accurate adiabatic sound velocities, which can be calculated from equations of state (EOSs) 7  We utilized advanced ab initio molecular dynamics and calculated the time evolution of different particle con gurations with the main aim of determining the compositional strati cation thickness and the strati cation characteristics. On the one hand, the self-diffusion coe cients D were calculated by the velocity autocorrelation function, and the thickness of the strati ed layer was calculated from the diffusion equation and restricted boundary condition. On the other hand, the ion-ion dynamic structure factor S(q,ω) 17 was calculated from the Fourier transform of the particle distribution. Then, the adiabatic sound velocity V for ion acoustic modes was determined as the slope of the dispersion relation.
The calculated self-diffusion coe cients of the Fe-Ni-O uid at the pressures beneath the CMB (Figure 1 (a)) and at the inner core boundary (Figure 1 (b)) are of the same order as the previous ab initio simulation results [11][12][13]18,19 . At CMB pressures, the self-diffusion coe cient of O ranges from (15.28±0.65)×10 -9 m 2 s -1 at 3500 K to (27.13±1.18)×10 -9 m 2 s -1 at 5500 K; in contrast, the self-diffusion coe cient of Fe ranges from (6.74±0.34)×10 -9 m 2 s -1 at 3500 K to (13.56±0.73)×10 -9 m 2 s -1 at 5500 K. The self-diffusion coe cients of Fe and Ni are very small under different temperature and pressure conditions, and the self-diffusion coe cient of Ni is slightly lower than that of Fe. The Ni effect on the thermal conductivity of liquid Fe is also quite limited 9 . Fe and Ni are nearly adjacent in the periodic table and have a similar electron occupation types, which may explain their similar properties.
The above shows that Fe-Ni-O uid has an anomalously high self-diffusion coe cient of O, which is consistent with the self-diffusion coe cient of Fe-O uid 12, 13 . This may originate from the low atomic mass of O, which always corresponds to ease of movement within the uid. This anomalous selfdiffusion coe cient was recently explained by structural 13 and electronic 12 analyses. The higher self-diffusion coe cient of O at high temperatures corresponds to the early formation of Earth and a higher rate of diffusion at that time, which may have an effect on the calculation of the strati cation thickness.
The compositional strati cation atop the outer core is caused by the diffusion of light O 6 . In the strati ed layer, the O concentration distribution C(r, t) varies radially and satis es the diffusion equation. In the convective region, the O concentration is homogeneous, and the contributions of O to the outer core originate from both the inner core and the mantle. The thickness of the compositional strati cation is calculated by the diffusion equation with the time evolution of the O self-diffusion coe cient D(t), which is considered by combining the temperature-dependent self-diffusion coe cient D(t) and cooling rate at the CMB dT c /dt. The thermal conductivity of Fe-Ni uid shows that it is subadiabatic on top of the outer core, and the age of the inner core and the CMB temperature T c (t) are collected 9 . From the time evolution of T c (t), the temperature-dependent equilibrium concentration C eq (T) and self-diffusion coe cient D(T) are transformed into the time evolution of C eq (T) and D(t).
Solving the diffusion equation with boundary conditions yields the time evolution of the location of strati cation s(t), the time evolution of the equilibrium O concentration C m (t) in the convective outer core, and the spatial distribution of the O concentration C(r,t=4.5 Ga) in the strati cation with radial distance r, all of which are plotted in Figure 2. The thickness of the compositional strati cation at present is 194.7 km, and the maximum thickness of strati cation was 285.1 km after the accretion of the inner core. It is obvious that an anomalously large self-diffusion coe cient induces an ~200-km-thick strati cation layer, which is of the same order as the reported compositional strati cation 4 . Some factors that could affect the strati cation have been discussed, such as the barodiffusioninduced buoyancy frequency and double diffusive convection 6 . However, the current thickness of the compositional strati cation is not affected by the age of the inner core, as the diffusion time and the amount of O expelled from the inner core are de nite. Further research has been conducted on Fe-O uids in recent years, including the Fe-O phase transition 20 , the partition coe cient, the partitioning of O between ferropericlase and the liquid core 21 , and the long-lived magma ocean 22 . Nevertheless, further and more systematic research must be performed to thoroughly understand the compositional strati cation from the perspective of S, Si and other light elements. Moreover, the convective motion atop the outer core may be suppressed or unstable, and this strati ed layer is formed as a result of either subadiabatic strati cation or the diffusion of light elements 8 . Hence, the thermal evolution of the strati cation should also be included to better understand the thermal state and dynamics of Earth's core.
Ion-ion dynamic structure factors were calculated from the traces of particles from ab initio molecular dynamics simulations, and the dispersion relationship of the collective excitations was determined by analyzing the positions of the side peaks. The resulting slope of the dispersion relation for small wave vectors is the adiabatic sound velocity. The ion-ion dynamic structure factors and dispersion relationship of Fe-Ni-O uid are presented in Figure 3(a) and (b). The adiabatic sound velocity of Fe-Ni-O uid is 7.86 km/s at 4000 K and 136 GPa. The sound velocity of this Fe-Ni-O uid at CMB pressure is highly sensitive to temperature and thus ranges from 9.29 km/s at 3500 K to 6.45 km/s at 5000 K; that is, the temperature effect on the sound velocity is nonnegligible. The ion-ion dynamic structure factors correspond to inelastic X-ray scattering experiments, where angle-dispersive X-ray diffraction (XRD) spectra can be converted into structure factors. The sound velocity of pure Fe is lower than 8.0 km/s at 136 GPa and 5000 K according to inelastic X-ray scattering measurements combined with shock-wave data based on the Mie-Grüniesen EOS 14 .  16 . To further understand the nature of the strati cation atop Earth's core, more ab initio molecular dynamic simulations should be adopted to ascertain the self-diffusion coe cients and sound velocities of other possible Fe-Ni-X (X being another possible light element) uids.
The thickness and sound velocity of the strati ed layer provide fundamental seismic insights into Earth's core. From our ab initio molecular dynamics simulations, for the rst time, we derived the self-diffusion coe cients and adiabatic sound velocity of Fe-Ni-O uid under the conditions of Earth's core. The ab initio approach for calculating the self-diffusion coe cient and the dynamic structure factor represent complementary methods for determining the sound velocity with inelastic X-ray scattering measurements and seismic observation pro les of the strati cation atop Earth's core. Hence, the use of ab initio molecular dynamics to calculate the self-diffusion coe cients and adiabatic sound velocities of uids reveals new pathways to study the compositional evolution of Earth's core.
In conclusion, the self-diffusion coe cient of O can reach (19.56±0.83)×10 -9 m 2 s -1 at the CMB. The compositional strati cation thickness derived from the diffusion equation is 194.7 km in the present day, whereas it was 285.1 km after the accretion of the inner core. The adiabatic sound velocity of the Fe-Ni-O uid at the CMB is 7.86 km/s according to ion-ion dynamic structure factors. We report both the shortrange and the long-range structures of Fe-Ni-O uid to describe the dynamics of Earth's core. Ab initio molecular dynamics simulations concurrently show that the Fe-Ni-O uid exhibits a large self-diffusion coe cient and low seismic velocity. These unique features of the Fe-Ni-O uid might be responsible for the strati cation structure of Earth's outer core. Ultimately, this paper provides new insights into the dynamics and evolution of Earth's core. Davies