Solid-liquid Coexistence Research Articles

Efficient mapping of phase diagrams with conditional Boltzmann Generators

Abstract The accurate prediction of phase diagrams is of central importance for both the fundamental understanding of materials as well as for technological applications in material sciences. However, the computational prediction of the relative stability between phases based on their free energy is a daunting task, as traditional free energy estimators require a large amount of simulation data to obtain uncorrelated equilibrium samples over a grid of thermodynamic states. In this work, we develop deep generative machine learning models based on the Boltzmann Generator approach for entire phase diagrams, employing normalizing flows conditioned on the thermodynamic states, e.g., temperature and pressure, that they map to. By training a single normalizing flow to transform the equilibrium distribution sampled at only one reference thermodynamic state to a wide range of target temperatures and pressures, we can efficiently generate equilibrium samples across the entire phase diagram. Using a permutation-equivariant architecture allows us, thereby, to treat solid and liquid phases on the same footing. We demonstrate our approach by predicting the solid-liquid coexistence line for a Lennard-Jones system in excellent agreement with state-of-the-art free energy methods while significantly reducing the number of energy evaluations needed.

Molecular-Level Understanding of Phase Stability in Phase-Change Nanoemulsions for Thermal Energy Storage by NMR Spectroscopy.

Phase change materials (PCMs) are latent heat storage materials that can store or release thermal energy while undergoing thermodynamic phase transitions. Organic PCMs can be emulsified in water in the presence of surfactants to enhance thermal conductivity and enable applications as heat transfer fluids. However, PCM nanoemulsions often become unstable during thermal cycling. To better understand the molecular origins of phase stability in PCM nanoemulsions, we designed a model PCM nanoemulsion system and studied how the molecular-level environments and dynamics of the surfactants and oil phase changed upon thermal cycling using liquid-state nuclear magnetic resonance (NMR) spectroscopy. The model system used octadecane as the oil phase, stearic acid as the surfactant, and aqueous NaOH as the continuous phase. The liquid fraction of octadecane within the nanoemulsions was quantified noninvasively during thermal cycling by liquid-state 1H single-pulse NMR measurements, revealing the extent of octadecane supercooling as a function of temperature. The mean droplet size of the PCM nanoemulsions, measured by dynamic light scattering (DLS), was correlated with the liquid content of octadecane to explain phase instability in the solid-liquid coexistence region. Quantitative 13C single-pulse NMR experiments established that the carbonyl surfactant head groups were present in multiple distinct environments during thermal cycling. After repeated thermal cycling, the 13C signal intensity of the carbonyl surfactant head groups decreased, indicating that the surfactant head groups lost molecular mobility. The results explain, in part, the origin of phase instability of PCM nanoemulsions upon thermal cycling.

Melting temperature of iron under the Earth’s inner core condition from deep machine learning

Constraining the melting temperature of iron under Earth’s inner core conditions is crucial for understanding core dynamics and planetary evolution. Here, we develop a deep potential (DP) model for iron that explicitly incorporates electronic entropy contributions governing thermodynamics under Earth’s core conditions. Extensive benchmarking demonstrates the DP’s high fidelity across relevant iron phases and extreme pressure and temperature conditions. Through thermodynamic integration and direct solid–liquid coexistence simulations, the DP predicts melting temperatures for iron at the inner core boundary, consistent with previous ab initio results. This resolves the previous discrepancy of iron’s melting temperature at ICB between the DP model and ab initio calculation and suggests the crucial contribution of electronic entropy. Our work provides insights into machine learning melting behavior of iron under core conditions and provides the basis for future development of binary or ternary DP models for iron and other elements in the core.

Elucidation and verification of cracking behavior in additive manufacturing of alloy 718 based on fractography

This study identified a cracking that occurred continuously in the built direction of an additive manufactured part of alloy 718 by the laser metal deposition method and clarified the cracking behavior. The solidification microstructure of alloy 718 was evaluated by EDS, EPMA, and extraction residue, and it was found that Laves phase, Ti carbides, and Al oxides were formed between the dendrite microstructures. A fracture surface analysis of the cracks revealed that the cracking in the additive manufacturing was hot cracking associated with the liquid film and that the cracking occurred along the grain boundaries. The fracture surface at the beginning of the cracking showed a solidification cracking fracture surface. The experimental investigation for crack propagation during additive manufacturing and the analytical evaluation of the mechanical state around the cracking using thermal elastic-plastic analysis elucidated the cracking behavior during additive manufacturing. If the cracking exists at the fusion boundary, it is suggested that the cracking initiates from the solid-liquid interface towards the solidification direction. Moreover, tensile strain occurred around the cracks during additive manufacturing, particularly the strain was biggest at the crack edge on the fusion boundary. Therefore, the continuous cracking that occurred beyond each layer in the additive manufacturing of alloy 718 in this study can be considered solidification cracking, and its behavior can be further explained as a notch extension cracking that starts from the solidification cracking and continuously occurs in the solid-liquid coexistence temperature region.

Compositional transferability of deep learning potentials: a case study for LiCl-KCl melt.

One of the crucial issues related to machine learning potentials is the formation of representative dataset. For multicomponent systems, it is a general methodology to scan the composition range with a certain step. However, there is a lack of information on the compositional transferability of machine learning potentials. In this paper, we extend the knowledge in this area by studying the transferability of deep learning potential over the range of compositions of LiCl-KCl molten mixtures. The training dataset was formed using only the near-eutectic composition of 60% LiCl-40% KCl. Then, we tested the ability of the model to predict physicochemical properties of the melts far from the reference composition. It was found that for the composition range from 0 to 100% of LiCl, the calculated properties concur closely with those of other studies and ab initio calculations. Therefore, the model shows prominent non-intuitive compositional transferability. Moreover, the solid states and solid-liquid coexistence were reproduced. The calculated melting temperatures of LiCl and KCl show the errors of 6.6% and 0.4%, respectively. We argue that such good transferability stems from the local structure configurations that are typical both for pure LiCl and for pure KCl which are implicitly presented in the training dataset because of local fluctuations in composition. To collect the data for the initial dataset, density functional theory was employed. Then, the DeePMD package was used to train a neural network potential. To calculate the properties of the melts, standard equilibrium and non-equilibrium molecular dynamic approaches were utilized.

Effect of distribution shape on the melting transition, local ordering, and dynamics in a model size-polydisperse two-dimensional fluid

Abstract We study the effect of particle size polydispersity (δ) on the melting transition (T *), local ordering, solid–liquid coexistence phase and dynamics of two-dimensional Lennard–Jones fluids up to moderate polydispersity by means of computer simulations. The particle sizes are drawn at random from the Gaussian (G) and uniform (U) distribution functions. For these systems, we further consider two different kinds of particles, viz., particles having the same mass irrespective of size, and in the other case the mass of the particle scales with its size. It is observed that with increasing polydispersity, the value of T * initially increases due to improved packing efficiency (ϕ) followed by a decrease and terminates at δ ≈ 8% (U-system) and 14% (G-system) with no significant difference for both mass types. The interesting observation is that the particular value at which ϕ drops suddenly coincides with the peak of the heat capacity (CP ) curve, indicating a transition. The quantification of local particle ordering through the hexatic order parameter (Q 6), Voronoi construction and pair correlation function reveals that the ordering decreases with increasing δ and T. Furthermore, the solid–liquid coexistence region for the G-system is shown to be comparatively wider in the T–δ plane phase diagram than that for the U system. Finally, the study of dynamics reveals that polydisperse systems relax faster compared to monodisperse systems; however, no significant qualitative differences, depending on the distribution type and mass polydispersity, are observed.

Theoretical investigation on the solid-liquid phase transition of gallium through free energy analysis.

Gallium, renowned for its notably low melting point and unique property of becoming liquid at room temperature, is a valuable constituent in phase change materials. In this study, we investigate the solid-liquid phase transition of gallium using the modified embedded atom method (MEAM) potential. It addresses the technique to compute the free energy difference between the solid and liquid without using a reference state. We examine various thermodynamic and dynamic properties, including density, specific heat capacity, diffusivity, and radial distribution functions. We compute the coexistence temperature of the solid-liquid phase transitions of gallium from free energy analysis. This information is crucial for understanding the behavior of the material under different pressure conditions and can be valuable for various applications, such as materials processing and high-pressure studies. The analysis, findings, and insights of the present work will be of great significance to the broad scientific and engineering communities in the field of phase transformation of materials. A series of molecular dynamics(MD) simulations were conducted using the LAMMPS software packages. The gallium atoms are modeled using the modified embedded atom method (MEAM) potential. To accurately predict the solid-liquid phase transitions of gallium, we calculated free energy by employing the "constrained λ integration" method, coupled with multiple histogram reweighting (MHR). The solid-liquid coexistence line is determined through the Gibbs-Duhem integration technique.

Structural transformation of dusty plasma crystal in dc discharge plasma by changing confinement ring bias

We report an experimental study of the structural transition of a stable complex plasma crystal to a solid-liquid phase coexistence by the controlled adjustment of the confinement potential, while keeping all other parameters constant. The experiments are carried out on a tabletop linear dusty plasma experimental device, which consists of a circular powered electrode and an extended grounded cathode plate. A stationary crystal of melamine formaldehyde particles is formed in a background of argon plasma inside a confining ring that is isolated from the cathode by a ceramic cover. The stable crystal structure breaks in the core region and transitions to a coexistent state by carefully changing the confining potential, thereby modifying the sheath structure. The transition is confirmed by evaluating the variation in different characteristic parameters such as the pair correlation function, local bond order parameter, and dust kinetic temperature as a function of confining bias potential. It is found that melting in the core is due to the onset of dust fluctuations in the layers beneath the topmost layer, which grow in amplitude as the confining bias potential is reduced below a threshold value. The present technique of changing confinement provides a unique feature to study structural transitions of plasma crystals without affecting the overall plasma parameters. Published by the American Physical Society 2024

A comprehensive investigation on the accuracy and efficiency of methods for melting temperature calculation using molecular dynamics simulations

Machine learning approaches have been extensively applied to improve the accuracy and reliability of potentials, addressing inherent limitations in molecular dynamics (MD) simulations. Notably, the precise determination of the melting temperature (Tm) relies on MD simulations, necessitating a comprehensive review of available melting models. This study aims to present a thorough comparison of various melting methods, including the single–phase method, hysteresis method, Z method, modified Z method, void method, modified void method, two–phase method, and sandwich method, considering both accuracy and efficiency. These melting models are systematically categorized into three groups: perfect crystals, crystal defects, and solid–liquid interfaces. The impact of factors such as atomic numbers, heating and cooling rates, crystal defects, and nucleation processes on Tm is discussed. Additionally, the temperatures corresponding to the superheating limit and the amorphous transition induced by heating and cooling rates during melting and crystallization processes are analyzed. Furthermore, the study explores the impact of different proportions of solid and the number of solid–liquid interfaces on melting behaviors. To further enhance the accuracy of Tm calculations, we propose a new approach termed the modified two–phase method, integrating the void method and two–phase method to account for crystal defects and solid–liquid coexistence, respectively.

Evaluation of Interfacial Thermal Resistance of Al-Si Alloy by Using Image-Based Simulation

Interfacial thermal resistances of Al-Si alloys were evaluated by comparing the measured thermal conductivities and the simulated thermal conductivities. Al-7%Si, Al-18%Si and Al-18%Si held in the solid-liquid coexistence temperature for 90 minutes were fabricated by gravity casting. Thermal conductivities were measured with the steady state thermal conductivity measuring device. Thermal conductivities were also simulated by using optical microscope images. Comparing the measured thermal conductivities and the simulated thermal conductivities, interfacial thermal resistances in Al-Si interfaces were evaluated as about 2.5-4.8×10-9 m2K/W.

In-Situ Investigation on Structure Transformation of Single-walled Carbon Nanotubes

The in-situ structure transformations by high-temperature energy beam in single-walled carbon nanotubes (SWCNTs) in real-time are investigated by experiment and molecular dynamics (MD) simulation. Experimental results showed that electron beam irradiation dramatically changed the size and structure of SWCNTs, leading defects, fracture, fusion, amorphization, evaporation and so on. The mechanism that causes these phenomena in experiments are explored and explained by using MD simulation. Thermodynamic and energy properties such as Lindeman index, potential energy plots and radial distribution function obtained by MD simulations revealed that 4200 K (±100 K) is the critical temperature for the damage or premetling of (6,6) SWCNTs, which are in solid–liquid coexistence stage between 4200 K and 4800 K. Once the temperature exceeded 4800 K, the SWCNTs will be dismembered and vaporized. This work is significant to establish a link between SWCNTs transformations and its temperature and provides a support for welding between SWCNTs and manufacturing SWCNT-based devices.

Multiple structural phase transitions in single crystal silicon subjected to dynamic loading

Single crystal Silicon (SC Si), as one of the most extensively used elements, has a series of complex phase changes, however, it is not fully understood under dynamic loading conditions. In this letter, both the shock induced multiple solid-solid phase transformations and solid-liquid transition are systematically investigated using large-scale molecular dynamics (MD) simulations. With the increase of particle velocities up to 2.8 km/s, the SC Si is revealed to undergo a continuous structural phase transitions from cubic diamond (cd) to β-tin, bct5, near-simple cubic (sc), and body centered cubic (bcc) structure. Furthermore, the liquid Si is distinguished and shows solid-liquid coexistence under intensive shocks. Our work dissects the continues multiple phase transitions in shocked Si for the first time in MD simulations, which provides new understandings of phase transitions of Si under dynamic loadings, and strongly supports and complements the relevant reported experimental researches.

Estimation of solid-liquid coexistence curve for coarse-grained water models through reliable free energy method

The anomalies properties of water have been interpreted theoretically using several all-atom and coarse-grained water models. Here we use a robust and traditional free energy approach to develop the solid-liquid coexistence curve for water using coarse-grained monatomic mW and machine-learned bond order potential (ML-BOP) water models. We employ the pseudo-supercritical thermodynamic path in combining multiple histogram reweighting (MHR) and Gibbs-Duhem integration. The ML-BOP model has a broad density-temperature hysteresis loop and shows lower maximum and minimum densities as compared to the mW model. The computed excess Helmholtz free energy and the Gibbs free energy at the approximate melting temperature are higher for the ML-BOP model in comparison with the mW model. The pressure dependence fusion curve for both water models aligns with the literature. This analysis indicates that the free energy method accurately captures the solid-liquid transformation and the thermodynamic melting point of water.

Transferable Force Field for Gallium Nitride Crystal Growth from the Melt Using On-The-Fly Active Learning.

Atomic-scale simulations of reactive processes have been stymied by two factors: the lack of a suitable semiempirical force field on one hand and the impractically large computational burden of using ab initio molecular dynamics on the other hand. In this paper, we use an "on-the-fly" active learning technique to develop a nonparameterized force field that, in essence, exhibits the accuracy of density functional theory and the speed of a classical molecular dynamics simulation. We developed a force field capable of capturing the crystallization of gallium nitride (GaN) during a novel additive manufacturing process featuring the reaction of liquid Ga and gaseous nitrogen precursors to grow crystalline GaN thin films. We show that this machine learning model is capable of producing a single force field that can model solid, liquid, and gas phases involved in the process. We verified our computational predictions against a range of experimental measurements relevant to each phase and against ab initio calculations, showing that this nonparametric force field produces properties with excellent accuracy as well as exhibits computationally tractable efficiency. The force field is capable of allowing us to simulate the solid-liquid coexistence interface and the crystallization of GaN from the melt. The development of this transferable force field opens the opportunity to simulate the liquid-phase epitaxial growth more accurately than before to analyze reaction and diffusion processes and ultimately to establish a growth model of the additive manufacturing process to create the gallium nitride thin films.

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.

Effect of supercooling phenomenon on liquid freezing in cylindrical vessel

AbstractFreezing has been used to extend the shelf life of food products. In freezing, the large ice crystals which are unfavorable for the texture and quality of food are mainly generated during a solid–liquid coexistence phase. It is well known the ice crystals produced after undergoing a supercooling state were finer than those produced without supercooling. This implies that the supercooling phenomenon affects the solid–liquid coexistence time during freezing. Therefore, in this study, the effect of the supercooling phenomenon on the solid–liquid coexistence time was investigated using a cylindrical vessel. The experimental results indicated that the solid–liquid coexistence time decreased with increasing degrees of supercooling. This result suggests that increasing the degree of supercooling is effective for producing finer ice crystals. Generally, the temperature distribution is uniform to promote the supercooled state. Thus, rotational motion of the vessel with a periodical switching the rotational direction every 180° clockwise and counter‐clockwise was imposed to relax the temperature distribution in the vessel. Below a certain rotational speed, it was observed that supercooling deepened; above that, multiple instances of supercooling release were observed owing to the inversion.

Effect of graphene on solid–liquid coexistence in Cu nanodroplets

The microstructure determines the macro properties, so the chemical and physical properties of nanoparticles can be tuned by changing their structures. A molecular dynamics simulation for the rapid solidification of Cu nanodroplets on the graphene sheet is conducted to investigate the effect of substrate on nanoparticles. The phase transition, structure evolution, and crystallinity are quantified by the potential energy, the largest standard cluster analysis, and Bond-orientation order parameters. It is found that the solidification is inhomogeneous and stepwise crystallization. Interestingly, originating from the graphene wettability, different solid–liquid coexistence states are obtained that may have the potential to modify the chemical and physical reactions on nanoparticles. The temperature of this solid–liquid coexistence state depends strongly on the structural evolution of crystallization and thus can be regulated by the wetting properties of the graphene substrate. These results significantly extend the fundamental understanding of heterogeneous nucleation in nanodroplets, providing important insights for designing and fabricating composite materials with multifunctional properties.

Strategy of Suppressing the Solidification Cracking Susceptibility of 247LC Superalloy Weld Metals using Commercial Ni-Based Fillers

The solidification cracking susceptibility of 247LC superalloy dissimilar welds with ERNiCrCoMo-1, ERNiCrMo3, and ERNiFeCr-2 commercial fillers was quantitatively evaluated using Varestraint testing for the sound weld geometries of gas turbine blades. We confirmed that the solidification brittle temperature range (BTR) of the 247LC/ ERNiCrMo-3 dissimilar weld was 217 K, which was measured using a thermo-vision camera during the Varestraint testing, and the BTR increased to 260, and 485 K with the ERNiCrCoMo-1 and ERNiFeCr-2 fillers, respectively, Based on theoretical calculations of the weld solidification path (i.e., using Scheil’s model; performed via the software Thermo-Calc) for each dissimilar weld, the variation in the BTR can be considered to be highly dependent on the solid-liquid coexistence temperature range of the dissimilar welds, and it is also correlated with the low-temperature formation of topologically closed packed phases during the terminal stage. Based on the experimental and theoretical results, the commercial Ni-based filler ERNiCrMo-3 is expected to be an effective welding material for 247LC dissimilar welding and the successful manufacturing of high-soundness blades.

2D multi-phase-field lattice Boltzmann simulations of semi-solid shear deformation

The deformation of solid–liquid coexistence regions strongly affects the formation of solidification defects in casting applications. Thus, understanding the mechanism of semi-solid deformation is crucial. This study used the multi-phase-field lattice Boltzmann model (MPF-LBM), which can simulate polycrystalline solidification with solid motion and liquid flow, to simulate two-dimensional semi-solid shear deformation with various grain shapes and solid fractions. It was concluded that the MPF-LBM could express the characteristic behaviors of semi-solid deformation, such as the Reynolds’ dilatancy and shear band, depending on the grain shape and solid fraction.

The macrosegregation behaviour of Fe-C-Cr-Mo type steel in laboratory scale model ingot.

In ingot casting, it is important to predict and control segregation and casting defects that occur during the solidification process, because they have a significant effect on the quality of the steel ingot. In some special steels, in typical Fe-C-Cr-Mo type high carbon tool steels, macro-segregation tends to be more pronounced due to their wide solid-liquid coexistence temperature range and molten steel properties such as relatively higher liquid viscosity than basic carbon steels. In order to investigate segregation and defect formation phenomena during solidification, many experiments have been conducted using specially designed laboratory scale model ingots that can induce partial difference of solidification to cause macrosegregation phenomena. However, these kind of experimental approaches for special steels are less conducted and influence of alloy types on the macrosegregation behaviour is still not well understood. In this study, a model ingot which have a steel chill ring in the middle region of a mullite mold was prepared, then Fe-0.45C(mass%) carbon steel, Fe-1C-1.8Cr(mass%) bearing steel and Fe-1C-8Cr-2Mo(mass%) high carbon tool steel were cast into 30kg ingots and the macrosegregation behaviour was investigated.