Cooper, R. & Kohlstedt, D. in High-Pressure Research in Geophysics Vol. 12 (eds Akimoto, S. & Manghnani, M. H.) 217–228 (Springer, 1982).
Montazerian, M. & Zanotto, E. D. Nucleation, growth, and crystallization in oxide glass-formers. A current perspective. Rev. Mineral. Geochem. 87, 405–429 (2022).
James, P. F. Kinetics of crystal nucleation in silicate glasses. J. Non-Cryst. Solids 73, 517–540 (1985).
Canup, R. M. Forming a Moon with an Earth-like composition via a giant impact. Science 338, 1052–1055 (2012).
Nomura, R. et al. Spin crossover and iron-rich silicate melt in the Earth’s deep mantle. Nature 473, 199–202 (2011).
Labrosse, S., Hernlund, J. W. & Coltice, N. A crystallizing dense magma ocean at the base of the Earth’s mantle. Nature 450, 866–869 (2007).
Deng, J., Miyazaki, Y., Yuan, Q. & Du, Z. Deep mantle heterogeneities formed through a basal magma ocean contaminated by core exsolution. Nat. Geosci. 18, 1056–1062 (2025).
Mukhopadhyay, S. & Parai, R. Noble gases: a record of Earth’s evolution and mantle dynamics. Annu. Rev. Earth Planet. Sci. 47, 389–419 (2019).
Solomatov, V. in Treatise on Geophysics 2nd edn (ed. Schubert, G.) 81–104 (Elsevier, 2015).
Solomatov, V. S. & Stevenson, D. J. Suspension in convective layers and style of differentiation of a terrestrial magma ocean. J. Geophys. Res. Planets 98, 5375–5390 (1993).
Monteux, J., Qaddah, B. & Andrault, D. Conditions for segregation of a crystal-rich layer within a convective magma ocean. J. Geophys. Res. Planets 128, e2023JE007805 (2023).
Patočka, V., Calzavarini, E. & Tosi, N. Settling of inertial particles in turbulent Rayleigh-Bénard convection. Phys. Rev. Fluids 5, 114304 (2020).
Boukaré, C.-E. & Ricard, Y. Modeling phase separation and phase change for magma ocean solidification dynamics. Geochem. Geophys. Geosyst. 18, 3385–3404 (2017).
Rose, L. A. & Brenan, J. M. Wetting properties of Fe-Ni-Co-Cu-O-S melts against olivine: implications for sulfide melt mobility. Econ. Geol. 96, 145–157 (2001).
Fokin, V. M., Zanotto, E. D., Yuritsyn, N. S. & Schmelzer, J. W. P. Homogeneous crystal nucleation in silicate glasses: a 40 years perspective. J. Non-Cryst. Solids 352, 2681–2714 (2006).
Zaragoza, A. et al. Competition between ices Ih and Ic in homogeneous water freezing. J. Chem. Phys. 143, 134504 (2015).
Niu, H., Bonati, L., Piaggi, P. M. & Parrinello, M. Ab initio phase diagram and nucleation of gallium. Nat. Commun. 11, 2654 (2020).
Deng, J., Niu, H., Hu, J., Chen, M. & Stixrude, L. Melting of MgSiO3 determined by machine learning potentials. Phys. Rev. B 107, 064103 (2023).
Niu, H., Piaggi, P. M., Invernizzi, M. & Parrinello, M. Molecular dynamics simulations of liquid silica crystallization. Proc. Natl Acad. Sci. 115, 5348–5352 (2018).
Potapov, O. V., Fokin, V. M. & Filipovich, V. N. Nucleation and crystal growth in water containing soda–lime–silica glasses. J. Non-Cryst. Solids 247, 74–78 (1999).
Andrault, D. et al. Solidus and liquidus profiles of chondritic mantle: implication for melting of the Earth across its history. Earth Planet. Sci. Lett. 304, 251–259 (2011).
Fiquet, G. et al. Melting of peridotite to 140 gigapascals. Science 329, 1516–1518 (2010).
Turnbull, D. Correlation of liquid-solid interfacial energies calculated from supercooling of small droplets. J. Chem. Phys. 18, 769–769 (1950).
Fokin, V. M. & Zanotto, E. D. Crystal nucleation in silicate glasses: the temperature and size dependence of crystal/liquid surface energy. J. Non-Cryst. Solids 265, 105–112 (2000).
Laird, B. B. & Davidchack, R. L. Direct calculation of the crystal−melt interfacial free energy via molecular dynamics computer simulation. J. Phys. Chem. B 109, 17802–17812 (2005).
Fokin, V. M., Zanotto, E. D. & Schmelzer, J. W. P. Homogeneous nucleation versus glass transition temperature of silicate glasses. J. Non-Cryst. Solids 321, 52–65 (2003).
Monteux, J., Andrault, D. & Samuel, H. On the cooling of a deep terrestrial magma ocean. Earth Planet. Sci. Lett. 448, 140–149 (2016).
Stixrude, L., de Koker, N., Sun, N., Mookherjee, M. & Karki, B. B. Thermodynamics of silicate liquids in the deep Earth. Earth Planet. Sci. Lett. 278, 226–232 (2009).
Boukaré, C. E., Ricard, Y. & Fiquet, G. Thermodynamics of the MgO-FeO-SiO2 system up to 140 GPa: application to the crystallization of Earth’s magma ocean. J. Geophys. Res. Solid Earth 120, 6085–6101 (2015).
Nabiei, F. et al. Investigating magma ocean solidification on Earth through laser-heated diamond anvil cell experiments. Geophys. Res. Lett. 48, e2021GL092446 (2021).
Dowty, E. in Physics of Magmatic Processes (ed. Hargraves, R. B.) Ch. 10, 419–486 (Princeton Univ. Press, 1980).
Asahara, Y. et al. Formation of metastable cubic-perovskite in high-pressure phase transformation of Ca(Mg, Fe, Al)Si2O6. Am. Mineral. 90, 457–462 (2005).
Ito, E., Kubo, A., Katsura, T. & Walter, M. J. Melting experiments of mantle materials under lower mantle conditions with implications for magma ocean differentiation. Phys. Earth Planet. Inter. 143–144, 397–406 (2004).
Fei, H., Faul, U. & Katsura, T. The grain growth kinetics of bridgmanite at the topmost lower mantle. Earth Planet. Sci. Lett. 561, 116820 (2021).
Yamazaki, D., Yoshino, T., Matsuzaki, T., Katsura, T. & Yoneda, A. Texture of (Mg,Fe)SiO3 perovskite and ferro-periclase aggregate: implications for rheology of the lower mantle. Phys. Earth Planet. Inter. 174, 138–144 (2009).
Panero, W. R., Pigott, J. S., Reaman, D. M., Kabbes, J. E. & Liu, Z. Dry (Mg,Fe)SiO3 perovskite in the Earth’s lower mantle. J. Geophys. Res. Solid Earth 120, 894–908 (2015).
Ghosh, D. B. & Karki, B. B. Transport properties of carbonated silicate melt at high pressure. Sci. Adv. 3, e1701840 (2017).
Caracas, R., Hirose, K., Nomura, R. & Ballmer, M. D. Melt–crystal density crossover in a deep magma ocean. Earth Planet. Sci. Lett. 516, 202–211 (2019).
Dragulet, F. & Stixrude, L. Partitioning of iron between (Mg,Fe)SiO3 liquid and bridgmanite. Geophys. Res. Lett. 51, e2023GL107979 (2024).
Xing, C.-M., Wang, C. Y., Charlier, B. & Namur, O. Ubiquitous dendritic olivine constructs initial crystal framework of mafic magma chamber. Earth Planet. Sci. Lett. 594, 117710 (2022).
Deguen, R., Alboussière, T. & Brito, D. On the existence and structure of a mush at the inner core boundary of the Earth. Phys. Earth Planet. Inter. 164, 36–49 (2007).
Bergman, M. I. Estimates of the Earth’s inner core grain size. Geophys. Res. Lett. 25, 1593–1596 (1998).
Tsujino, N. et al. Viscosity of bridgmanite determined by in situ stress and strain measurements in uniaxial deformation experiments. Sci. Adv. 8, eabm1821 (2022).
Garnero, E. J. & McNamara, A. K. Structure and dynamics of Earth’s lower mantle. Science 320, 626–628 (2008).
Talavera-Soza, S., Cobden, L., Faul, U. H. & Deuss, A. Global 3D model of mantle attenuation using seismic normal modes. Nature 637, 1131–1135 (2025).
Herzberg, C. & Zhang, J. Melting experiments on anhydrous peridotite KLB-1: compositions of magmas in the upper mantle and transition zone. J. Geophys. Res. Solid Earth 101, 8271–8295 (1996).
Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).
Wang, H., Zhang, L., Han, J. & Weinan, E. DeePMD-kit: a deep learning package for many-body potential energy representation and molecular dynamics. Comput. Phys. Commun. 228, 178–184 (2018).
Zhang, S., Hu, J., Sun, X., Deng, J. & Niu, H. Structural heterogeneity of MgSiO3 liquid and its connection with dynamical properties. Phys. Rev. Lett. 134, 204101 (2025).
Piaggi, P. M. & Parrinello, M. Multithermal-multibaric molecular simulations from a variational principle. Phys. Rev. Lett. 122, 050601 (2019).
Barducci, A., Bussi, G. & Parrinello, M. Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Phys. Rev. Lett. 100, 020603 (2008).
Branduardi, D., Bussi, G. & Parrinello, M. Metadynamics with adaptive Gaussians. J. Chem. Theory Comput. 8, 2247–2254 (2012).
McDonough, W. F. & Sun, S. S. The composition of the Earth. Chem. Geol. 120, 223–253 (1995).
Stixrude, L. & Lithgow-Bertelloni, C. Thermodynamics of mantle minerals – II. Phase equilibria. Geophys. J. Int. 184, 1180–1213 (2011).
Davis, M. J., Ihinger, P. D. & Lasaga, A. C. Influence of water on nucleation kinetics in silicate melt. J. Non-Cryst. Solids 219, 62–69 (1997).
Fenn, P. M. The nucleation and growth of alkali feldspars from hydrous melts. Can. Mineral. 15, 135–161 (1977).
Hammer, J. E. Crystal nucleation in hydrous rhyolite: experimental data applied to classical theory. Am. Mineral. 89, 1673–1679 (2004).
Arzilli, F. et al. Plagioclase nucleation and growth kinetics in a hydrous basaltic melt by decompression experiments. Contrib. Mineral. Petrol. 170, 55 (2015).
Fletcher, N. H. Size effect in heterogeneous nucleation. J. Chem. Phys. 29, 572–576 (1958).
Solomatov, V. S. Batch crystallization under continuous cooling: analytical solution for diffusion limited crystal growth. J. Cryst. Growth 148, 421–431 (1995).
Alfè, D. Melting curve of MgO from first-principles simulations. Phys. Rev. Lett. 94, 235701 (2005).
Castro, R. H. R., Tôrres, R. B., Pereira, G. J. & Gouvêa, D. Interface energy measurement of MgO and ZnO: understanding the thermodynamic stability of nanoparticles. Chem. Mater. 22, 2502–2509 (2010).
Christensen, U. R. Dynamo scaling laws and applications to the planets. Space Sci. Rev. 152, 565–590 (2010).
Bower, D. J., Sanan, P. & Wolf, A. S. Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets. Phys. Earth Planet. Inter. 274, 49–62 (2018).
Stixrude, L., Scipioni, R. & Desjarlais, M. P. A silicate dynamo in the early Earth. Nat. Commun. 11, 935 (2020).
Ziegler, L. B. & Stegman, D. R. Implications of a long-lived basal magma ocean in generating Earth’s ancient magnetic field. Geochem. Geophys. Geosyst. 14, 4735–4742 (2013).
Sosso, G. C. et al. Crystal nucleation in liquids: open questions and future challenges in molecular dynamics simulations. Chem. Rev. 116, 7078–7116 (2016).
Auer, S. & Frenkel, D. Prediction of absolute crystal-nucleation rate in hard-sphere colloids. Nature 409, 1020–1023 (2001).
Espinosa, J. R., Sanz, E., Valeriani, C. & Vega, C. Homogeneous ice nucleation evaluated for several water models. J. Chem. Phys. 141, 18C529 (2014).
Kurz, W., Fisher, D. J. & Trivedi, R. Progress in modelling solidification microstructures in metals and alloys: dendrites and cells from 1700 to 2000. Int. Mater. Rev. 64, 311–354 (2019).
Xu, J. et al. Silicon and magnesium diffusion in a single crystal of MgSiO3 perovskite. J. Geophys. Res. Solid Earth 116, JB008444 (2011).
Yoshino, T., Makino, Y., Suzuki, T. & Hirata, T. Grain boundary diffusion of W in lower mantle phase with implications for isotopic heterogeneity in oceanic island basalts by core-mantle interactions. Earth Planet. Sci. Lett. 530, 115887 (2020).

