Solving the Christoffel equation: phase and group velocities

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

γ'-Fe4N: facts, hypotheses and open questions

By reviewing the experimental and theoretical literature on γ’-Fe4N, and by a systematic survey of predictions by the LDA, PBE, WC, LDA+U (2x), PBE+U (2x), and B3PW91 exchange-correlation functionals, the structural, magnetic and hyperfine properties of this material as well as their pressure dependencies are interpreted. The hypothesis is put forward that γ’-Fe4N as found in nature is exactly at a sharp transition between low-spin and high-spin behaviour. PBE+U (U=0.4 eV) is identified as the most accurate exchangecorrelation functional for this material, although it is needed to fix the magnetization at the experimental value to obtain a satisfying description. Remaining disagreement between theory and experiment is pointed out. A recent experimental claim for a giant magnetic moment in γ’-Fe4N is discussed, and is not reproduced by our calculations

Spin-density wave in Cr: nesting versus low-lying thermal excitations

It is well known that present versions of density functional theory do not predict the experimentally observed spin-density wave state to be the ground state of Cr. Recently, a so-called "nodon model" has been proposed as an alternative way to reconcile theory and experiment: the ground state of Cr is truly antiferromagnetic, and the spin-density wave appears due to low-lying thermal excitations ("nodons"). We examine in this paper whether the postulated properties of these nodons are reproduced by ab initio calculations

Ranking the stars : a refined Pareto approach to computational materials design

We propose a procedure to rank the most interesting solutions from high-throughput materials design studies. Such a tool is becoming indispensable due to the growing size of computational screening studies and the large number of criteria involved in realistic materials design. As a proof of principle, the binary tungsten alloys are screened for both large-weight and high-impact materials, as well as for fusion reactor applications. Moreover, the concept is generally applicable to any design problem where multiple competing criteria have to be optimized

Ab initio based thermal property predictions at a low cost : an error analysis

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 alpha(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 alpha(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 Gruneisen parameter, provides a similar overall accuracy as exhaustive first-principles phonon calculations. For the melting temperature, expensive ab initio molecular-dynamics simulations still outperform semiempirical methods

Error estimates for density-functional theory predictions of surface energy and work function

Density-functional theory (DFT) predictions of materials properties are becoming ever more widespread. With increased use comes the demand for estimates of the accuracy of DFT results. In view of the importance of reliable surface properties, this work calculates surface energies and work functions for a large and diverse test set of crystalline solids. They are compared to experimental values by performing a linear regression, which results in a measure of the predictable and material-specific error of the theoretical result. Two of the most prevalent functionals, the local density approximation (LDA) and the Perdew-Burke-Ernzerhof parametrization of the generalized gradient approximation (PBE-GGA), are evaluated and compared. Both LDA and GGA-PBE are found to yield accurate work functions with error bars below 0.3 eV, rivaling the experimental precision. LDA also provides satisfactory estimates for the surface energy with error bars smaller than 10%, but GGA-PBE significantly underestimates the surface energy for materials with a large correlation energy

Assessment of a low-cost protocol for an ab initio based prediction of the mixing enthalpy at elevated temperatures: the Fe-Mo system

We demonstrate how a limited number of ab initio calculations in combination with a simple Debye model can predict a concentration- and temperature-dependent mixing enthalpy for a binary system. Fe-Mo is taken as a test case, and our predictions are compared with phase diagram information and a recently measured heat of solution for Mo in Fe. Crystallographic and magnetic information is calculated for the lambda and mu intermetallic phases in the Fe-Mo phase diagram as well. The present methodology can be useful for making a quick survey of mixing enthalpies in a large set of binary systems, in particular in the dilute concentration ranges where tabulated data are often lacking and where CALPHAD-style modeling is less reliable