Melting points of alkali chlorides evaluated for a polarizable and non-polarizable model

Discovering melting temperature prediction models of inorganic solids by combining supervised and unsupervised learning

The melting temperature is important for materials design because of its relationship with thermal stability, synthesis, and processing conditions. Current empirical and computational melting point estimation techniques are limited in scope, computational feasibility, or interpretability. We report the development of a machine learning methodology for predicting melting temperatures of binary ionic solid materials. We evaluated different machine-learning models trained on a dataset of the melting points of 476 non-metallic crystalline binary compounds using materials embeddings constructed from elemental properties and density-functional theory calculations as model inputs. A direct supervised-learning approach yields a mean absolute error of around 180 K but suffers from low interpretability. We find that the fidelity of predictions can further be improved by introducing an additional unsupervised-learning step that first classifies the materials before the melting-point regression. Not only does this two-step model exhibit improved accuracy, but the approach also provides a level of interpretability with insights into feature importance and different types of melting that depend on the specific atomic bonding inside a material. Motivated by this finding, we used a symbolic learning approach to find interpretable physical models for the melting temperature, which recovered the best-performing features from both prior models and provided additional interpretability.

Estimation of thermodynamic and physicochemical properties of the alkali astatides: On the bond strength of molecular astatine (At2 ) and the hydration enthalpy of astatide (At- )

The recent accurate and precise determination of the electron affinity (EA) of the astatine atom At0 warrants a re-investigation of the estimated thermodynamic properties of At0 and astatine containing molecules as this EA was found to be much lower (by 0.4 eV) than previous estimated values. In this contribution we estimate, from available data sources, the following thermodynamic and physicochemical properties of the alkali astatides (MAt, M = Li, Na, K, Rb, Cs): their solid and gaseous heats of formation, lattice and gas-phase binding enthalpies, sublimation energies and melting temperatures. Gas-phase charge-transfer dissociation energies for the alkali astatides (the energy requirement for M+ At- ➔ M0  + At0 ) have been obtained and are compared with those for the other alkali halides. Use of Born-Haber cycles together with the new AE (At0 ) value allows the re-evaluation of ΔHf (At0 )g (=56 ± 5 kJ/mol); it is concluded that (At2 )g is a weakly bonded species (bond strength <50 kJ/mol), significantly weaker bonded than previously estimated (116 kJ/mol) and much weaker bonded than I2 (148 kJ/mol), but in agreement with the finding from theory that spin-orbit coupling considerably reduces the bond strength in At2 . The hydration enthalpy (ΔHaq ) of At- is estimated to be -230 ± 2 kJ/mol (using ΔHaq [H+ ] = -1150.1 kJ/mol), in good agreement with molecular dynamics calculations. Arguments are presented that the largest alkali halide, CsAt, like the smallest, LiF, will be only sparingly soluble in water, following the generalization from hard/soft acid/base principles that "small likes small" and "large likes large."

First-principles molten salt phase diagrams through thermodynamic integration

Precise prediction of phase diagrams in molecular dynamics simulations is challenging due to the simultaneous need for long time and large length scales and accurate interatomic potentials. We show that thermodynamic integration from low-cost force fields to neural network potentials trained using density-functional theory (DFT) enables rapid first-principles prediction of the solid-liquid phase boundary in the model salt NaCl. We use this technique to compare the accuracy of several DFT exchange-correlation functionals for predicting the NaCl phase boundary and find that the inclusion of dispersion interactions is critical to obtain good agreement with experiment. Importantly, our approach introduces a method to predict solid-liquid phase boundaries for any material at an ab initio level of accuracy, with the majority of the computational cost at the level of classical potentials.

Revisiting the pseudo-supercritical path method: An improved formulation for the alchemical calculation of solid-liquid coexistence

Alchemical free energy calculations via molecular dynamics have been applied to obtain thermodynamic properties related to solid-liquid equilibrium conditions, such as melting points. In recent years, the pseudo-supercritical path (PSCP) method has proved to be an important approach to melting point prediction due to its flexibility and applicability. In the present work, we propose improvements to the PSCP alchemical cycle to make it more compact and efficient through a concerted evaluation of different potential energies. The multistate Bennett acceptance ratio (MBAR) estimator was applied at all stages of the new cycle to provide greater accuracy and uniformity, which is essential concerning uncertainty calculations. In particular, for the multistate expansion stage from solid to liquid, we employed the MBAR estimator with a reduced energy function that allows affine transformations of coordinates. Free energy and mean derivative profiles were calculated at different cycle stages for argon, triazole, propenal, and the ionic liquid 1-ethyl-3-methyl-imidazolium hexafluorophosphate. Comparisons showed a better performance of the proposed method than the original PSCP cycle for systems with higher complexity, especially the ionic liquid. A detailed study of the expansion stage revealed that remapping the centers of mass of the molecules or ions is preferable to remapping the coordinates of each atom, yielding better overlap between adjacent states and improving the accuracy of the methodology.

Computational methods to simulate molten salt thermophysical properties

Molten salts are important thermal conductors used in molten salt reactors and solar applications. To use molten salts safely, accurate knowledge of their thermophysical properties is necessary. However, it is experimentally challenging to measure these properties and a comprehensive evaluation of the full chemical space is unfeasible. Computational methods provide an alternative route to access these properties. Here, we summarize the developments in methods over the last 70 years and cluster them into three relevant eras. We review the main advances and limitations of each era and conclude with an optimistic perspective for the next decade, which will likely be dominated by emerging machine learning techniques. This article is aimed to help researchers in peripheral scientific domains understand the current challenges of molten salt simulation and identify opportunities to contribute.

Computing the Liquidus of Binary Monatomic Salt Mixtures with Direct Simulation and Alchemical Free Energy Methods

We describe and validate a free-energy-based method for computing the liquidus for binary solid-liquid phase diagrams in molecular simulations of monatomic salts. The method is demonstrated by calculating the liquidus for LiCl-KCl and MgCl₂-KCl salt mixtures with the polarizable ion model (PIM). The free-energy-based method is cross-validated with direct coexistence simulations. Both techniques show excellent agreement with one another. Though the predictions of the PIM disagree with experiments, we use our free-energy-based approach to decouple the contributions of liquid mixture nonidealities and pure component solid-liquid equilibrium to the phase diagram. In both mixtures, the PIM accurately reproduces the liquid phase nonidealities but fails to predict the liquidus because it does not accurately predict the pure component melting temperature of LiCl or MgCl₂.

Eutectics: formation, properties, and applications

Various eutectic systems have been proposed and studied over the past few decades. Most of the studies have focused on three typical types of eutectics: eutectic metals, eutectic salts, and deep eutectic solvents. On the one hand, they are all eutectic systems, and their eutectic principle is the same. On the other hand, they are representative of metals, inorganic salts, and organic substances, respectively. They have applications in almost all fields related to chemistry. Their different but overlapping applications stem from their very different properties. In addition, the proposal of new eutectic systems has greatly boosted the development of cross-field research involving chemistry, materials, engineering, and energy. The goal of this review is to provide a comprehensive overview of these typical eutectics and describe task-specific strategies to address growing demands.

Modeling LiF and FLiBe Molten Salts with Robust Neural Network Interatomic Potential

Lithium-based molten salts have attracted significant attention due to their applications in energy storage, advanced fission reactors, and fusion devices. Lithium fluorides and particularly 66.6%LiF-33.3%BeF₂ (Flibe) are of considerable interest in nuclear systems, as they show an excellent combination of favorable heat transfer, neutron moderation, and transmutation characteristics. For nuclear salts, the range of possible local structures, compositions, and thermodynamic conditions presents significant challenges in atomistic modeling. In this work, we demonstrate that atom-centered neural network interatomic potentials (NNIPs) provide a fast method for performing molecular dynamics of molten salts that is as accurate as ab initio molecular dynamics. For LiF, these potentials are able to accurately reproduce ab initio interactions of dimers, crystalline solids under deformation, crystalline LiF near the melting point, and liquid LiF at high temperatures. For Flibe, NNIPs accurately predict the structures and dynamics at normal operating conditions, high-temperature-pressure conditions, and in the crystalline solid phase. Furthermore, we show that NNIP-based molecular dynamics of molten salts are scalable to reach long time scales (e.g., nanosecond) and large system sizes (e.g., 10⁵ atoms) while maintaining ab initio density functional theory accuracy and providing more than 3 orders of magnitude of computational speedup for calculating structure and transport properties.

Automated Development of Molten Salt Machine Learning Potentials: Application to LiCl

The in silico modeling of molten salts is critical for emerging "carbon-free" energy applications but is inhibited by the cost of quantum mechanically treating the high polarizabilities of molten salts. Here, we integrate configurational sampling using classical force fields with active learning to automate and accelerate the generation of Gaussian approximation potentials (GAP) for molten salts. This methodology reduces the number of expensive ab initio evaluations required for training set generation to O(100), enabling the facile parametrization of a molten LiCl GAP model that exhibits a 19 000-fold speedup relative to AIMD. The developed molten LiCl GAP model is applied to sample extended spatiotemporal scales, permitting new physical insights into molten LiCl's coordination structure as well as experimentally validated predictions of structures, densities, self-diffusion constants, and ionic conductivities. The developed methodology significantly lowers the barrier to the in silico understanding and design of molten salts across the periodic table.