Thermodynamic properties of ZrC are calculated up to the melting point (T melt ≈ 3700 K), using density functional theory (DFT) to obtain the fully anharmonic vibrational contribution, and including electronic excitations. A significant improvement is found in comparison to results calculated within the quasiharmonic approximation. The calculated thermal expansion is in better agreement with experiment and the heat capacity reproduces rather closely a CALPHAD estimate. The calculations are presented as an application of a development of the upsampled thermodynamic integration using Langevin dynamics (UP-TILD) approach. This development, referred to here as two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD), is the inclusion of tailored interatomic potentials to characterize an intermediate reference state of anharmonic vibrations on a two-stage path of thermodynamic integration between the original DFT quasiharmonic free energy and the fully anharmonic DFT free energy. This approach greatly accelerates the convergence of the calculation, giving a factor of improvement in efficiency of ∼50 in the present case compared to the original UP-TILD approach, and it can be applied to a wide range of materials.

We present an approach that enables an efficient and accurate study of dynamically unstable crystals over the full temperature range. The approach is based on an interatomic potential fitted to ab initio molecular dynamics energies for both the high-and low-temperature stable phases. We verify by comparison to explicit ab initio simulations that such a bespoke potential, for which we use here the functional form of the embedded atom method, provides accurate transformation temperatures and atomistic features of the transformation. The accuracy of the potential makes it an ideal tool to study the important impact of finite size and finite time effects. We apply our approach to the dynamically unstable β (bcc) titanium phase and study in detail the transformation to the low-temperature stable hexagonal ω phase. We find a large set of previously unreported linear-chain disordered (LCD) structures made up of three types of [111] β linear-chain defects that exhibit randomly disordered arrangements in the (111) β plane.

In this paper, we present a model which allows bridging the atomistic description of two-phase systems to the continuum level, using Ni-H as a model system. Considering configurational entropy, an attractive hydrogen-hydrogen interaction, mechanical deformations and interfacial effects, we obtained a fully quantitative agreement in the chemical potential, without the need for any additional adjustable parameter. We find that nonlinear elastic effects are crucial for a complete understanding of constant volume phase coexistence, and predict the phase diagram with and without elastic effects.