Compression data for all 26 data sets, separated as individual Excel sheets with the composition and temperature in the title of each sheet. As noted in the headers of each sheet, the first column is the length of the supercell (units: Å), the second column is the volume (units: Å3), the third column is the density (units: g/cm3), the fourth column is the pressure (units: GPa), the fifth column is the standard deviation on pressure (units: GPa), the sixth column is the temperature (units: K), and the seventh column is the standard deviation on temperature (units: K). Standard deviations on pressure and temperature were determined from the simulations
We employ first-principles molecular-dynamics simulations to study the pressure and temperature dependence of a series of realistic silicate melts. In molecular dynamics, the particles, i.e. the atoms, move under the action of interatomic forces according to Newtonian mechanics. With first-principles we accurately compute these interatomic forces without relying on any approximations and fits to experimental data. We use the density-functional theory in the planar-augmented wavefunction flavor as implemented in the VASP package [Kresse and Hafner, 1993] to compute the interatomic forces. The kinetic energy-cutoff of the planewaves was set at 550 eV and of the augmentation charge at 800 eV. The electronic density is sampled in the reciprocal space in the Gamma point. With these parameter the accuracy of the pressure value is on the order of a few kilobars. We employ the generalized-gradient approximation in the Perdew-Burke-Ernzerhof formulation [Perdew et al., 1996]. Because of the presence of iron, all the simulations are spin-polarized, with the spin on each Fe atom being allowed to freely fluctuate at each time step. All simulations are NVT-type, meaning the Number of particles and the Volume are kept fixed throughout the simulations. The Temperature is fixed using a Nose-Hoover thermostat, whose equivalent VASP mass is set at 4; this ensures fluctuations of the temperature of 7% above and below the target temperature. The timestep for all simulations is 1 femtosecond. Simulations were conducted at temperatures of 2000(140) K, 3000(200) K, 4000(270) K and 5000(320) K where values in parentheses denote average standard deviations of the thermal fluctuations. In typical NVT simulations both pressure and temperature fluctuate around average values. Their excursions describe a normal distribution. For example, at 4000 K, for the pressure we obtain a standard deviation of 1.5 GPa at ambient pressure, increasing to 3 GPa at 150 GPa; the median, i.e. the range between 25% and 75% of the values, is on the order of 2 GPa at ambient pressure, increasing to 3.5 GPa at high pressure. These values show a small deviation of the pressure from the average, with limited and symmetric excursions above and below it.
The reference melt has pyrolite composition, which is an approximant to the bulk silicate Earth (BSE) composition [McDonough & Sun, 1995], and which already served in previous studies [Caracas et al., 2019; Solomatova & Caracas, 2019; Solomatova et al., 2019]. It is a six-component melt with molar composition 0.5Na2O – 2CaO – 1.5 Al2O3 – 4FeO – 30MgO – 24 SiO2. This composition is closer than 1 wt% to the proposed BSE composition. We use cubic cells with 153 atoms to mimic the pyrolitic composition.