More than a third of all exoplanets can be classified as super-Earths based on radius (1´2 R C ) and mass (< 10 M C ).Here we model mass-radius relations based on silicate mantle and iron core equations of state to infer to first order the structure and composition range of rocky super-Earths assuming insignificant gas envelopes. As their core pressures exceed those in the Earth by an order of magnitude, significant extrapolations of equations of state for iron are required. We develop a new equation of state of hexagonal close packed (hcp) iron for super-Earth conditions (SEOS) based on density functional theory results for pressures up to 137 TPa. A comparison of SEOS and extrapolated equations of state for iron from the literature reveals differences in density of up to 4% at 1 TPa and up to 20% at 10 TPa. Such density differences significantly affect mass-radius relations. On mass, the effect is as large as 10% for Earth-like super-Earths (core radius fraction of 0.5) and 20% for Mercury-like super-Earths (core radius fraction of 0.8). We also quantify the effects of other modeling assumptions such as temperature and composition by considering extreme cases. We find that the effect of temperature on mass (< 5%) is smaller than that resulting from the extrapolation of the equations of state of iron and lower mantle temperatures are too low to allow for rock and iron miscibility for R < 1.75 R C . Our end-member cases of core and mantle compositions create a spread in mass-radius curves reaching more than 50% in terms of mass for a given planetary radius, implying that modeling uncertainties dominate over observational uncertainties for many observed super-Earths. We illustrate these uncertainties explicitly for Kepler-36b with well-constrained mass and radius. Assuming a core composition of 0.8ρ Fe (equivalent to 50 mol% S) instead of pure Fe leads to an increase of the core radius fraction from 0.53 to 0.64. Using a mantle composition of Mg 0.5 Fe 0.5 SiO 3 instead of MgSiO 3 leads to a decrease of the core radius fraction to 0.33. Effects of thermal structure and the choice of equation of state for the core material on the core radius of Kepler-36b are small but non-negligible, reaching 2% and 5%, respectively.

SummaryThe geometric and electronic structure of the MIL-47(V) metal-organic framework (MOF) is investigated by using ab initio density functional theory (DFT) calculations. Special focus is placed on the relation between the spin configuration and the properties of the MOF. The ground state is found to be antiferromagnetic, with an equilibrium volume of 1554.70 Å3. The transition pressure of the pressure-induced large-pore-to-narrow-pore phase transition is calculated to be 82 MPa and 124 MPa for systems with ferromagnetic and antiferromagnetic chains, respectively. For a mixed system, the transition pressure is found to be a weighted average of the ferromagnetic and antiferromagnetic transition pressures. Mapping DFT energies onto a simple-spin Hamiltonian shows both the intra- and inter-chain coupling to be antiferromagnetic, with the latter coupling constant being two orders of magnitude smaller than the former, suggesting the MIL-47(V) to present quasi-1D behavior. The electronic structure of the different spin configurations is investigated and it shows that the band gap position varies strongly with the spin configuration. The valence and conduction bands show a clear V d-character. In addition, these bands are flat in directions orthogonal to VO6 chains, while showing dispersion along the the direction of the VO6 chains, similar as for other quasi-1D materials.

We provide christoffel, a Python tool for calculating direction-dependent phase velocities, polarization vectors, group velocities, power flow angles and enhancement factors based on the stiffness tensor of a solid. It is built in a modular way to allow for efficient and flexible calculations, and the freedom to select and combine results as desired. All derivatives are calculated analytically, which circumvents possible numerical sampling problems. GNUPlot scripts are provided for convenient visualization. Keywords

Ab initio calculations often do not straightforwardly yield the thermal properties of a material yet. It requires considerable computational efforts, for example, to predict the volumetric thermal expansion coefficient α V or the melting temperature T m from first principles. An alternative is to use semiempirical approaches. They relate the experimental values to first-principles predictors via fits or approximative models. Before applying such methods, however, it is of paramount importance to be aware of the expected errors. We therefore quantify these errors at the density-functional theory level using the Perdew-Burke-Ernzerhof functional for several semiempirical approximations of α V and T m , and compare them to the errors from fully ab initio methods, which are computationally more intensive. We base our conclusions on a benchmark set of 71 ground-state elemental crystals. For the thermal expansion coefficient, it appears that simple quasiharmonic theory, in combination with different approximations to the Grüneisen parameter, provides a similar overall accuracy as exhaustive firstprinciples phonon calculations. For the melting temperature, expensive ab initio molecular-dynamics simulations still outperform semiempirical methods.