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[SIT16-P17] Charge disproportionation in iron-bearing silicate melts predicted from first-principles calculations
Keywords:Charge disproportionation, Magma ocean, The first-principles thermodynamic integration method
1. Introduction
During the growth of the proto-Earth, collisions of planetesimals are thought to cause large-scale melting and the formation of a magma ocean (MO)[1]. In this MO, the chemical evolution of the Earth proceeded along with the core-mantle separation. Various studies have been conducted on the core formation process and the associated chemical evolution. As a result, the iron-silicate partitioning of siderophile elements suggests core formation pressure conditions at 30-40 GPa[2], while the Basal MO model predicts an iron-silicate equilibrium at the core-mantle boundary condition of 135 GPa[3]. As for the mechanism of iron droplet formation inside the MO, the most popular theory is that it originates from the core of impacters[4], but the possibility of metallic iron formation associated with the charge disproportionation reaction of iron in silicate melts (3Fe2+=2Fe3++Fe0) has also been proposed[5]. Recently, actual charge disproportionation reactions in silicate melts under high-pressure were reported experimentaly[6]. On the other hand, the redox state of MO has been investigated theoreticaly from a thermodynamic model of iron-bearing silicate melts[7], but so far there have been no direct first-principles calculations of the stability of the charge disproportionation reaction of iron in silicate melts.
2. Calculation methods
In this study, we perform first-principles free energy calculations[8] of liquids based on the thermodynamic integration method to determine the stability of the charge disproportionation reaction. We set up the following reaction:
Mg12Fe2+4Si16O48=Mg12Fe2+Fe3+2Si16O48+Fe0
and calculate the free energy of each term and the reaction free energy (ΔG). The silicate melt composition is set to the pyroxene one as a simulation of primordial chondrites, and the considered temperature and pressure conditions are from 0 to 135 GPa and from 3000 to 5000 K.
In the thermodynamic integration method, the potential energy of the reference system, whose free energy can be calculated analytically, is switched to the potential energy of the ab initio system gradually, and the Helmholtz free energy difference between the reference and ab initio systems is obtained by integrating the mixed potential. In this study, the ideal gas is applied to the reference system, and the Gaussian quadrature method is used for the numerical integration. The constant-temperature first-principles molecular dynamics method is used to reproduce the liquid states, and the forces acting on the atoms are calculated based on the density functional theory.
3. Results and discussion
The calculated ΔG at 3000 K is negative, indicating the formation of metallic iron by the charge disproportionation reaction. ΔG is found to be affected more by temperature than by pressure. At 5000 K, the ferrous iron is in contrast greatly stabilized.
The calculated results suggest that metallic iron is produced at MO temperatures up to about 4000 K, but is gradually eliminated at higher temperatures. Therefore, metallic iron would rather decrease and ferrous iron would increase due to the reverse reaction in the deep MO. In order to understand these reaction behavior, electronic and atomic structures are now analyzed in detail.
References
[1] T. Kleine: Nature, 477, 168 (2011).
[2] B. J. Wood, M. J. Walter, and J. Wade: Nature, 441, 825 (2006).
[3] S. Labrosse, J. W. Hernlund, and N. Coltice: Nature, 450, 866 (2007).
[4] D. C. Rubie, et al.: Earth and Planetary Science Letters, 301, 31 (2011).
[5] J. Wade and B. J. Wood: Earth and Planetary Science Letters, 236, 78 (2005).
[6] K. Armstrong, et al.: Science, 365, 903 (2019).
[7] J. Deng, et al.: Nature Communications, 11, 1 (2020). Fig.1. Reaction free energy of iron-charge disproportionation in silicate melts.
[8] Z. Xiong, T. Tsuchiya, and T. Taniuchi: Journal of Geophysical Research: Solid Earth, 123, 6451 (2018).
During the growth of the proto-Earth, collisions of planetesimals are thought to cause large-scale melting and the formation of a magma ocean (MO)[1]. In this MO, the chemical evolution of the Earth proceeded along with the core-mantle separation. Various studies have been conducted on the core formation process and the associated chemical evolution. As a result, the iron-silicate partitioning of siderophile elements suggests core formation pressure conditions at 30-40 GPa[2], while the Basal MO model predicts an iron-silicate equilibrium at the core-mantle boundary condition of 135 GPa[3]. As for the mechanism of iron droplet formation inside the MO, the most popular theory is that it originates from the core of impacters[4], but the possibility of metallic iron formation associated with the charge disproportionation reaction of iron in silicate melts (3Fe2+=2Fe3++Fe0) has also been proposed[5]. Recently, actual charge disproportionation reactions in silicate melts under high-pressure were reported experimentaly[6]. On the other hand, the redox state of MO has been investigated theoreticaly from a thermodynamic model of iron-bearing silicate melts[7], but so far there have been no direct first-principles calculations of the stability of the charge disproportionation reaction of iron in silicate melts.
2. Calculation methods
In this study, we perform first-principles free energy calculations[8] of liquids based on the thermodynamic integration method to determine the stability of the charge disproportionation reaction. We set up the following reaction:
Mg12Fe2+4Si16O48=Mg12Fe2+Fe3+2Si16O48+Fe0
and calculate the free energy of each term and the reaction free energy (ΔG). The silicate melt composition is set to the pyroxene one as a simulation of primordial chondrites, and the considered temperature and pressure conditions are from 0 to 135 GPa and from 3000 to 5000 K.
In the thermodynamic integration method, the potential energy of the reference system, whose free energy can be calculated analytically, is switched to the potential energy of the ab initio system gradually, and the Helmholtz free energy difference between the reference and ab initio systems is obtained by integrating the mixed potential. In this study, the ideal gas is applied to the reference system, and the Gaussian quadrature method is used for the numerical integration. The constant-temperature first-principles molecular dynamics method is used to reproduce the liquid states, and the forces acting on the atoms are calculated based on the density functional theory.
3. Results and discussion
The calculated ΔG at 3000 K is negative, indicating the formation of metallic iron by the charge disproportionation reaction. ΔG is found to be affected more by temperature than by pressure. At 5000 K, the ferrous iron is in contrast greatly stabilized.
The calculated results suggest that metallic iron is produced at MO temperatures up to about 4000 K, but is gradually eliminated at higher temperatures. Therefore, metallic iron would rather decrease and ferrous iron would increase due to the reverse reaction in the deep MO. In order to understand these reaction behavior, electronic and atomic structures are now analyzed in detail.
References
[1] T. Kleine: Nature, 477, 168 (2011).
[2] B. J. Wood, M. J. Walter, and J. Wade: Nature, 441, 825 (2006).
[3] S. Labrosse, J. W. Hernlund, and N. Coltice: Nature, 450, 866 (2007).
[4] D. C. Rubie, et al.: Earth and Planetary Science Letters, 301, 31 (2011).
[5] J. Wade and B. J. Wood: Earth and Planetary Science Letters, 236, 78 (2005).
[6] K. Armstrong, et al.: Science, 365, 903 (2019).
[7] J. Deng, et al.: Nature Communications, 11, 1 (2020). Fig.1. Reaction free energy of iron-charge disproportionation in silicate melts.
[8] Z. Xiong, T. Tsuchiya, and T. Taniuchi: Journal of Geophysical Research: Solid Earth, 123, 6451 (2018).