Pressure–temperature phase diagram of lithium, predicted by embedded atom model potentials

In order to study the performance of interatomic potentials and their reliability at higher pressures, the phase diagrams of two different embedded-atom-type potential models (EAMs) and a modified embedded-atom model (MEAM) of lithium are compared. The calculations were performed by using the nested sampling technique in the pressure range 0.01–20 GPa, in order to determine the liquid–vapor critical point, the melting curve, and the different stable solid phases of the compared models. The low-pressure stable structure below the melting line is found to be the body-centered-cubic (bcc) structure in all cases, but the higher pressure phases and the ground-state structures show a great variation, being face-centered cubic (fcc), hexagonal close-packed (hcp), a range of different close-packed stacking variants, and highly symmetric open structures are observed as well. A notable behavior of the EAM of Nichol and Ackland (Phys. Rev. B: Condens. Matter Mater. Phys.2016, 93, 184101) is observed, that the model displays a maximum temperature in the melting line, similarly to experimental results

Nested sampling of materials’ potential energy surfaces : case study of Zirconium

The nested sampling (NS) method was originally proposed by John Skilling to calculate the evidence in Bayesian inference. The method has since been utilised in various research fields, and here we focus on how NS has been adapted to sample the Potential Energy Surface (PES) of atomistic systems, enabling the straightforward estimation of the partition function. Using two interatomic potential models of zirconium, we demonstrate the workflow and advantages of using nested sampling to calculate pressure-temperature phase diagrams. Without any prior knowledge of the stable phases or the phase transitions, we are able to identify the melting line, as well as the transition between the body-centred-cubic and hexagonal-close-packed structures

Insight into liquid polymorphism from the complex phase behavior of a simple model

We systematically explored the phase behavior of the hard-core two-scale ramp model suggested by Jagla [Phys. Rev. E 63, 061501 (2001)] using a combination of the nested sampling and free energy methods. The sampling revealed that the phase diagram of the Jagla potential is significantly richer than previously anticipated, and we identified a family of new crystalline structures, which is stable over vast regions in the phase diagram. We showed that the new melting line is located at considerably higher temperature than the boundary between the low- and high-density liquid phases, which was previously suggested to lie in a thermodynamically stable region. The newly identified crystalline phases show unexpectedly complex structural features, some of which are shared with the high-pressure ice VI phase

Neural-network force field backed nested sampling: Study of the silicon p−T phase diagram

Nested sampling is a promising method for calculating phase diagrams of materials. However, if accuracy at the level of ab-initio calculations is required, the computational cost limits its applicability. In the present work, we report on the efficient use of a neural-network force field in conjunction with the nested-sampling algorithm. We train our force fields on a recently reported database of silicon structures evaluated at the level of density functional theory and demonstrate our approach on the low-pressure region of the silicon pressure-temperature phase diagram between 0 and . The simulated phase diagram shows a good agreement with experimental results, closely reproducing the melting line. Furthermore, all of the experimentally stable structures within the investigated pressure range are also observed in our simulations. We point out the importance of the choice of exchange-correlation functional for the training data and show how the r2SCAN meta-GGA plays a pivotal role in achieving accurate thermodynamic behaviour. We furthermore perform a detailed analysis of the potential energy surface exploration and highlight the critical role of a diverse and representative training data set

Nested sampling for materials: the case of hard spheres

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three dimensional hard sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered

Polytypism in the ground state structure of the Lennard-Jonesium.

We present a systematic study of the stability of nineteen different periodic structures using the finite range Lennard-Jones potential model discussing the effects of pressure, potential truncation, cutoff distance and Lennard-Jones exponents. The structures considered are the hexagonal close packed (hcp), face centred cubic (fcc) and seventeen other polytype stacking sequences, such as dhcp and 9R. We found that at certain pressure and cutoff distance values, neither fcc nor hcp is the ground state structure as previously documented, but different polytypic sequences. This behaviour shows a strong dependence on the way the tail of the potential is truncated

Surface phase diagrams from nested sampling

Studies in atomic-scale modeling of surface phase equilibria often focus on temperatures near zero Kelvin due to the challenges in calculating the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling (NS) algorithm allows for modeling phase equilibria at arbitrary temperatures by directly and efficiently calculating the partition function, whose relationship with free energy is well known. This work extends NS to calculate adsorbate phase diagrams, incorporating all relevant configurational contributions to the free energy. We apply NS to the adsorption of Lennard-Jones (LJ) gas particles on low-index and vicinal LJ solid surfaces and construct the canonical partition function from these recorded energies to calculate ensemble averages of thermodynamic properties, such as the constant-volume heat capacity and order parameters that characterize the structure of adsorbate phases. Key results include determining the nature of phase transitions of adsorbed LJ particles on flat and stepped LJ surfaces, which typically feature an enthalpy-driven condensation at higher temperatures and an entropy-driven reordering process at lower temperatures, and the effect of surface geometry on the presence of triple points in the phase diagrams. Overall, we demonstrate the ability and potential of NS for surface modeling