Explicit anharmonicity, defined as the vibrational contribution beyond the quasiharmonic approximation, is qualitatively different between the group V and group VI bcc refractory elements. Group V elements show a small and mostly negative anharmonic entropy, whereas group VI elements have a large positive anharmonic entropy, strongly increasing with temperature. Here, we explain this difference utilizing highly accurate anharmonic free energies and entropies from ab initio calculations for Nb and Ta (group V), and Mo and W (group VI). The numerically calculated entropies are in agreement with prior experimental data. The difference in behavior between the two sets of elements arises not from their high-temperature behavior but rather from the 0K quasiharmonic reference state. We understand this by analyzing the 0K and the high-temperature phonon density of states and the electronic density of states. The qualitative difference disappears when the anharmonicity is instead referenced with a high-temperature effective harmonic potential. However, even for an optimized effective harmonic reference, the remaining effective anharmonicity is significant. The reason is that the anharmonicity in the bcc systems - carried by asymmetric distributions in the nearest neighbors - can never be accounted for by a harmonically restricted potential.

We present the magnetic Moment Tensor Potentials (mMTPs), a class of machine-learning interatomic potentials, accurately reproducing both vibrational and magnetic degrees of freedom as provided, e.g., from first-principles calculations. The accuracy is achieved by a two-step minimization scheme that coarse-grains the atomic and the spin space. The performance of the mMTPs is demonstrated for the prototype magnetic system bcc iron, with applications to phonon calculations for different magnetic states, and molecular-dynamics simulations with fluctuating magnetic moments.

We present an analysis of temperature-dependent atomic short-range ordering and phase stability of the face-centered cubic CrCoNi medium-entropy alloy employing a combination of ab initio calculations and on-lattice machine learning interatomic potentials. Temperature-dependent properties are studied with canonical Monte Carlo simulations. At around 975 K a phase transition into an ordered Cr(Ni,Co)2 phase (MoPt2-type) is found. This hitherto not reported state has an ordering energy twice as large than the ordered structures previously suggested. We show that magnetism is not responsible for the observed chemical ordering.

An active learning approach to train machine-learning interatomic potentials (moment tensor potentials) for multicomponent alloys to ab initio data is presented. Employing this approach, the disordered body-centered cubic (bcc) TiZrHfTax system with varying Ta concentration is investigated via molecular dynamics simulations. Our results show a strong interplay between elastic properties and the structural ω phase stability, strongly affecting the mechanical properties. Based on these insights we systematically screen composition space for regimes where elastic constants show little or no temperature dependence (elinvar effect).

The phase stability of a bcc AlNbTiV high-entropy alloy at elevated temperatures is studied using a combination of machine-learning interatomic potentials, first-principles calculations, and Monte Carlo simulations. The simulations reveal a B2 ordering below about 1700 K, mainly caused by a strong site preference of Al and Ti. A much weaker site preference for V and Nb is observed, strongly affecting the alloys total configurational entropy. The underlying mechanisms of the B2 phase stability as opposed to the random solid solution are discussed in terms of a high persisting configurational entropy of the B2 phase due to strong sublattice site disorder.

Concentrated solid solutions including the class of high entropy alloys (HEAs) have attracted enormous attention recently. Among these alloys a recently developed face-centered cubic (fcc) equiatomic VCoNi alloy revealed extraordinary high yield strength, exceeding previous high-strength fcc CrCoNi and FeCoNiCrMn alloys. Significant lattice distortions had been reported in the VCoNi solid solution. There is, however, a lack of knowledge about potential short-range order (SRO) and its implications for most of these alloys. We performed first-principles calculations and Monte Carlo simulations to compute the degree of SRO for fcc VCoNi, namely, by utilizing the coherent-potential approximation in combination with the generalized perturbation method as well as the supercell method in combination with recently developed machine-learned potentials. We analyze the chemical SRO parameters as well as the impact on other properties such as relaxation energies and lattice distortions.

Recently, high-entropy alloys (HEAs) have attracted wide attention due to their extraordinary materials properties. A main challenge in identifying new HEAs is the lack of efficient approaches for exploring their huge compositional space. Ab initio calculations have emerged as a powerful approach that complements experiment. However, for multicomponent alloys existing approaches suffer from the chemical complexity involved. In this work we propose a method for studying HEAs computationally. Our approach is based on the application of machine-learning potentials based on ab initio data in combination with Monte Carlo simulations. The high efficiency and performance of the approach are demonstrated on the prototype bcc NbMoTaW HEA. The approach is employed to study phase stability, phase transitions, and chemical short-range order. The importance of including local relaxation effects is revealed: they significantly stabilize single-phase formation of bcc NbMoTaW down to room temperature. Finally, a so-far unknown mechanism that drives chemical order due to atomic relaxation at ambient temperatures is discovered.

The unique and unanticipated properties of multiple principal component alloys have reinvigorated the field of alloy design and drawn strong interest across scientific disciplines. The vast compositional parameter space makes these alloys a unique area of exploration by means of computational design. However, as of now a method to compute efficiently, yet with high accuracy the thermodynamic properties of such alloys has been missing. One of the underlying reasons is the lack of accurate and efficient approaches to compute vibrational free energies—including anharmonicity—for these chemically complex multicomponent alloys. In this work, a density-functional-theory based approach to overcome this issue is developed based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.