Novel Methods for Electronic Structure Calculations.


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Gonzalo Gutiérrez

Felip e González-Cataldo, Sergio Davis

Grupo de NanoMateriales, Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile,



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Ab-initio melting curve of silica at ultra-high pressure: implications for gas giants and super-earths

Silicon and oxygen are among the most abundant rock-forming elements. Their bonding gives rise to silica, SiO2, one of the most extensively studied materials in condensed matter physics, chemistry, engineering and planetary sciences. SiO2 and silicates, such as MgSiO3 and CaSiO3, are not only the major components of the Earths lower mantle, but also of the rock-ice protocores that result in gas giants through core accretion. They are also widely believed to form the bulk composition of super-Earths. It has been determined that MgSiO3 dissociates in the cores of gas giants and terrestrial exoplanets, leaving SiO2 and MgO as separate compounds that form the rocky interior of these planets.
The discovery of extrasolar giant planets with masses ranging from that of Saturn to a few times the mass of Jupiter has opened new possibilities for understanding planetary formation and composition. Hundreds of these gas giants and some super-Earths have been found in the last decade, providing enormous datasets of their atmospheric composition, size and mass. Estimating the internal composition of these planets is based on a mass to radius relation that relies heavily on EOS, which are calculated from electronic structure theory and sometimes measured experimentally on Earth. For example, EOS for hydrogen, helium, “ices” such as water, ammonia, methane, silicate rocks, and iron serve as initial inputs to these models. In this sense, the giant planets resemble natural laboratories for studying the behavior of materials at high pressure and temperature, which typically reach values outside the realm of experiment on Earth. This leaves theoretical approaches, such as ab-initio calculation, as our only window to understand the properties of matter in these extreme regimes.
SiO2 goes through a series of phase transitions as the pressure increases: quartz → coesite → stishovite → CaCl2- type → α-PbO2-type → pyrite-type → cotunnite-type → Fe2P-type structure. Tsuchiya (1) postulated the last transition, which according to their calculation would occur near 700 GPa. Recent ab-initio calculations of the melting curve of SiO2 up to 160 GPa (using the two-phase molecular dynamics method) show good agreement with previous calculations, which were done with the same method but using classical potentials. However, the solid-liquid boundary for silica at higher pressures remains unknown.
In this work we extend the melting curve of SiO2 up to 6000 GPa (60 Mbar) and 20000 K, covering the range of pressures and temperatures that exist at the interiors of gas giants and massive super-Earths. We use ab-initio molecular dynamics simulation, based on Density Functional Theory (DFT), together with the Z method and Bayesian statistics to estimate the melting curve in the microcanonical ensemble. The Z-method is a powerful one-phase technique to estimate melting curves (2,3). It needs, however, several simulations and long simulation times as one approaches the melting temperature (4). In order to compensate for this we have applied a Bayesian statistical analysis (5), drastically reducing the number of simulations needed to constrain the melting point.
According to our ab-initio simulations, silica, if present, is solid within the cores of all Solar System gas giants and, together with MgO, is a key component of the stable rocky cores of extrasolar gas giants. The results allow us to determine the solid-solid boundary between high pressure silica phases at the melting point. We estimated the pyrite-cotunnite phase transition at 480 GPa, and the cotunnite-Fe2P at 900 GPa.
We acknowledge support from CONICYT 201090712 (FG-C) and CONICYT ACT-1115 (GG).

(1) T. Tsuchiya and J. Tsuchiya, Prediction of a hexagonal SiO2 phase affecting stabilities of MgSiO 3 and CaSiO 3 at multimegabar pressures. PNAS, 108(4):1252–5, (2011).
(2) A. Belonoshko, N. Skorodumova, A. Rosengren, and B. Johansson, Melting and critical superheating. Phys. Rev. B,
73(1):012201, (2006).
(3) S. Davis, A. Belonoshko, B. Johansson, N. Skorodumova, and A. C T van Duin, High-pressure melting curve of hydrogen.
J. Chem. Phys., 129(19):194508, (2008).
(4) D. Alf`e, C. Cazorla, and M. J. Gillan. The kinetics of homogeneous melting beyond the limit of superheating. J. Chem.
, 135(2):19, (2011).
(5) S. Davis and G. Gutiérrez, Bayesian inference as a tool for analysis of first-principles calculations of complex materials: an
application to the melting point of Ti 2GaN. Model. Simul. Mater. Sci. Eng., 21(7):075001, (2013).