The melting lines of model silicon calculated from coexisting solid–liquid phases

Active sparse Bayesian committee machine potential for isothermal-isobaric molecular dynamics simulations

Recent advancements in machine learning potentials (MLPs) have significantly impacted the fields of chemistry, physics, and biology by enabling large-scale first-principles simulations. Among different machine learning approaches, kernel-based MLPs distinguish themselves through their ability to handle small datasets, quantify uncertainties, and minimize over-fitting. Nevertheless, their extensive computational requirements present considerable challenges. To alleviate these, sparsification methods have been developed, aiming to reduce computational scaling without compromising accuracy. In the context of isothermal and isobaric ML molecular dynamics (MD) simulations, achieving precise pressure estimation is crucial for reproducing reliable system behavior under constant pressure. Despite progress, sparse kernel MLPs struggle with precise pressure prediction. Here, we introduce a virial kernel function that significantly enhances the pressure estimation accuracy of MLPs. Additionally, we propose the active sparse Bayesian committee machine (BCM) potential, an on-the-fly MLP architecture that aggregates local sparse Gaussian process regression (SGPR) MLPs. The sparse BCM potential overcomes the steep computational scaling with the kernel size, and a predefined restriction on the size of kernel allows for fast and efficient on-the-fly training. Our advancements facilitate accurate and computationally efficient machine learning-enhanced MD (MLMD) simulations across diverse systems, including ice-liquid coexisting phases, Li10Ge(PS6)2 lithium solid electrolyte, and high-pressure liquid boron nitride.

Evolution of liquid phase during homogenous non-equilibrium melting of Ta at superheating temperature

Homogenous melting at superheating temperature is commonly described by classical nucleation theory (CNT), but the atomic mechanism of the formation and development of critical liquid nuclei is still unclear. Molecular dynamics simulations were conducted to analyze the melting process of Ta. It is found that the process of subcritical liquid clusters evolving into critical liquid nucleus occupies most of the melting time, and merging between neighboring liquid clusters is the main path for subcritical liquid clusters to grow in size. Total melting time is strongly affected by the distribution of formation sites of subcritical liquid clusters, which has been considered random in homogenous melting. This work depicts a clear picture of the formation and development of liquid phase during the homogeneous melting process at superheating temperature and suggests an internal factor of melting mechanism.

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.

Effect of Cooling Rate on the Crystal Quality and Crystallization Rate of SiC during Rapid Solidification Based on the Solid–Liquid Model

The silicon carbide (SiC) that can achieve better electron concentration and motion control is more suitable for the production of high temperature, high frequency, radiation resistance, and high-power electronic devices. However, the fabrication of the high purity single crystal is challenging, and it is hard to observe the structural details during crystallization. Here, we demonstrate a study of the crystallization of single-crystal SiC by the molecular dynamic simulations. Based on several structure analysis methods, the transition of the solid–liquid SiC interface from a liquid to a zinc-blende structure is theoretically investigated. The results indicate that most of the atoms in the solid–liquid interface begin to crystallize with rapid solidification at low cooling rates, while crystallization does not occur in the system at high cooling rates. As the quenching progresses, the number of system defects decreases, and the distribution is more concentrated in the solid–liquid interface. A maximum crystallization rate is observed for a cooling rate of 1010 K/s. Moreover, when a stronger crystallization effect is observed, the energy is lower, and the system is more stable.

Colossal and reversible barocaloric effect in liquid-solid-transition materials n-alkanes

Emerging caloric cooling technology provides a green alternative to conventional vapor-compression technology which brings about serious environmental problems. However, the reported caloric materials are much inferior to their traditional counterparts in cooling capability. Here we report the barocaloric (BC) effect associated with the liquid-solid-transition (L-S-T) in n-alkanes. A low-pressure of ~50 MPa reversibly triggers an entropy change of ~700 J kg⁻¹ K⁻¹, comparable to those of the commercial refrigerants in vapor-based compression systems. The Raman study and theoretical calculations reveal that applying pressure to the liquid state suppresses the twisting and random thermal motions of molecular chains, resulting in a lower configurational entropy. When the pressure is strong enough to drive the L-S-T, the configurational entropy will be fully suppressed and induce the colossal BC effect. This work could open a new avenue for exploring the colossal BC effect by evoking L-S-T materials.

Barocaloric effect, previously reported in solid-solid phase transition materials, offers a green alternative to current cooling technology. Here the authors report colossal BCE in n-alkanes associated with liquid–solid transition.

Deep potential for face-centered cubic Cu system at finite temperatures

Potential function is critical for molecular dynamics simulation and the state-of-the-art method generating potential functions used in molecular dynamics is based on machine learning with neural networks. This method provides...

Addressing the discrepancy of finding the equilibrium melting point of silicon using molecular dynamics simulations

We performed molecular dynamics simulations to study the equilibrium melting point of silicon using (i) the solid-liquid coexistence method and (ii) the Gibbs free energy technique, and compared our novel results with the previously published results obtained from the Monte Carlo (MC) void-nucleated melting method based on the Tersoff-ARK interatomic potential (Agrawal et al. Phys. Rev. B72, 125206. (doi:10.1103/PhysRevB.72.125206)). Considerable discrepancy was observed (approx. 20%) between the former two methods and the MC void-nucleated melting result, leading us to question the applicability of the empirical MC void-nucleated melting method to study a wide range of atomic and molecular systems. A wider impact of the study is that it highlights the bottleneck of the Tersoff-ARK potential in correctly estimating the melting point of silicon.

The Melting Temperature of Liquid Water with the Effective Fragment Potential

The direct simulation of the solid-liquid water interface with the effective fragment potential (EFP) via the constant enthalpy and pressure (NPH) ensemble was used to estimate the melting temperature (T(m)) of ice-I(h). Initial configurations and velocities, taken from equilibrated constant pressure and temperature (NPT) simulations at P = 1 atm and T = 305 K, 325 K and 399 K, respectively, yielded corresponding T(m) values of 378 ± 16 K, 382 ± 14 K and 384 ± 15 K. These estimates are consistently higher than experiment, albeit to the same degree as previously reported estimates using density functional theory (DFT)-based Born-Oppenheimer simulations with the Becke-Lee-Yang-Parr functional plus dispersion corrections (BLYP-D).

Melting and superheating in solids with volume shrinkage at melting: a molecular dynamics study of silicon

The thermodynamics of homogeneous melting in superheated crystalline solids with volume shrinkage at melting is investigated using extensive molecular dynamics simulation in conjunction with a classical nucleation theory. A liquid-solid co-existing model is established to overcome the difficult in observing liquid phase formation in a superheated Si crystal. We found that melting is governed by two major factors, the volume change induced strain energy and the curvature of the interface between the liquid and the solid phases. The driving force for melting in superheating regime is lowered by the additional strain energy that restricts homogeneous nucleation of a liquid phase till temperature rises above the normal melting point, thus causing superheating. However, due to the abnormal behavior in the compressibility of the silicon liquid in the superheating regime, the degree of superheating in terms of the liquid nucleation gap becomes significantly reduced. More potential complications caused by the change of the atomic bonding in Si at melting are discussed.

A comparison of methods for melting point calculation using molecular dynamics simulations

Accurate and efficient prediction of melting points for complex molecules is still a challenging task for molecular simulation, although many methods have been developed. Four melting point computational methods, including one free energy-based method (the pseudo-supercritical path (PSCP) method) and three direct methods (two interface-based methods and the voids method) were applied to argon and a widely studied ionic liquid 1-n-butyl-3-methylimidazolium chloride ([BMIM][Cl]). The performance of each method was compared systematically. All the methods under study reproduce the argon experimental melting point with reasonable accuracy. For [BMIM][Cl], the melting point was computed to be 320 K using a revised PSCP procedure, which agrees with the experimental value 337-339 K very well. However, large errors were observed in the computed results using the direct methods, suggesting that these methods are inappropriate for large molecules with sluggish dynamics. The strengths and weaknesses of each method are discussed.

Thermophysical properties of undercooled alloys: an overview of the molecular simulation approaches

We review the studies on the thermophysical properties of undercooled metals and alloys by molecular simulations in recent years. The simulation methods of melting temperature, enthalpy, specific heat, surface tension, diffusion coefficient and viscosity are introduced and the simulated results are summarized. By comparing the experimental results and various theoretical models, the temperature and the composition dependences of the thermophysical properties in undercooled regime are discussed.

Size-dependent nucleation kinetics at nonplanar nanowire growth interfaces

In nanowire growth, kinetic processes at the growth interface can play an important role in governing wire compositions, morphologies, and growth rates. Molecular-dynamics simulations have been undertaken to probe such processes in a system featuring a solid-liquid interface shape characterized by a facet bounded by rough orientations. Simulated growth rates display a dependence on nanowire diameter consistent with a size-dependent barrier for facet nucleation. A theory for the interface mobility is developed, establishing a source for size-dependent growth rates that is an intrinsic feature of systems possessing growth interfaces with faceted and rough orientations.

On the phase diagram of water with density functional theory potentials: The melting temperature of ice I(h) with the Perdew-Burke-Ernzerhof and Becke-Lee-Yang-Parr functionals

The melting temperature (T(m)) of ice I(h) was determined from constant enthalpy and pressure (NPH) Born-Oppenheimer molecular dynamics simulations to be 417+/-3 K for the Perdew-Burke-Ernzerhof and 411+/-4 K for the Becke-Lee-Yang-Parr density functionals using a coexisting ice (I(h))-liquid phase at constant pressures of P=2500 and 10,000 bar and a density rho=1 g/cm(3), respectively. This suggests that ambient condition simulations at rho=1 g/cm(3) will rather describe a supercooled state that is overstructured when compared to liquid water.

Kinetic coefficient of steps at the Si(111) crystal-melt interface from molecular dynamics simulations

Nonequilibrium molecular dynamics simulations are applied to the investigation of step-flow kinetics at crystal-melt interfaces of silicon, modeled with the Stillinger-Weber potential [Phys. Rev. B 31, 5262 (1985)]. Step kinetic coefficients are calculated from crystallization rates of interfaces that are vicinals of the faceted (111) orientation. These vicinal interfaces contain periodic arrays of bilayer steps, and they are observed to crystallize in a step-flow growth mode at undercoolings lower than 40 K. Kinetic coefficients for both [110] and [121] oriented steps are determined for several values of the average step separation, in the range of 7.7-62.4 A. The values of the step kinetic coefficients are shown to be highly isotropic, and are found to increase with increasing step separation until they saturate at step separations larger than approximately 50 A. The largest step kinetic coefficients are found to be in the range of 0.7-0.8 m(sK), values that are more than five times larger than the kinetic coefficient for the rough (100) crystal-melt interface in the same system. The dependence of step mobility on step separation and the relatively large value of the step kinetic coefficient are discussed in terms of available theoretical models for crystal growth kinetics from the melt.

Crystal-melt interface stresses: atomistic simulation calculations for a Lennard-Jones binary alloy, Stillinger-Weber Si, and embedded atom method Ni

Molecular-dynamics and Monte Carlo simulations have been used to compute the crystal-melt interface stress (f) in a model Lennard-Jones (LJ) binary alloy system, as well as for elemental Si and Ni modeled by many-body Stillinger-Weber and embedded-atom-method (EAM) potentials, respectively. For the LJ alloys the interface stress in the (100) orientation was found to be negative and the f vs composition behavior exhibits a slight negative deviation from linearity. For Stillinger-Weber Si, a positive interface stress was found for both (100) and (111) interfaces: f{100}=(380+/-30)mJ/m{2} and f{111}=(300+/-10)mJ/m{2}. The Si (100) and (111) interface stresses are roughly 80 and 65% of the value of the interfacial free energy (gamma) , respectively. In EAM Ni we obtained f{100}=(22+/-74)mJ/m{2}, which is an order of magnitude lower than gamma. A qualitative explanation for the trends in f is discussed.

Molecular dynamics simulations of melting and the glass transition of nitromethane

Molecular dynamics simulations have been used to investigate the thermodynamic melting point of the crystalline nitromethane, the melting mechanism of superheated crystalline nitromethane, and the physical properties of crystalline and glassy nitromethane. The maximum superheating and glass transition temperatures of nitromethane are calculated to be 316 and 160 K, respectively, for heating and cooling rates of 8.9 x 10(9) Ks. Using the hysteresis method [Luo et al., J. Chem. Phys. 120, 11640 (2004)] and by taking the glass transition temperature as the supercooling temperature, we calculate a value of 251.1 K for the thermodynamic melting point, which is in excellent agreement with the two-phase result [Agrawal et al., J. Chem. Phys. 119, 9617 (2003)] of 255.5 K and measured value of 244.73 K. In the melting process, the nitromethane molecules begin to rotate about their lattice positions in the crystal, followed by translational freedom of the molecules. A nucleation mechanism for the melting is illustrated by the distribution of the local translational order parameter. The critical values of the Lindemann index for the C and N atoms immediately prior to melting (the Lindemann criterion) are found to be around 0.155 at 1 atm. The intramolecular motions and molecular structure of nitromethane undergo no abrupt changes upon melting, indicating that the intramolecular degrees of freedom have little effect on the melting. The thermal expansion coefficient and bulk modulus are predicted to be about two or three times larger in crystalline nitromethane than in glassy nitromethane. The vibrational density of states is almost identical in both phases.

Melting temperature of ice Ih calculated from coexisting solid-liquid phases

We carried out molecular-dynamics simulations by using the two-phase coexistence method with the constant pressure, particle number, and enthalpy ensemble to compute the melting temperature of proton-disordered hexagonal ice I(h) at 1-bar pressure. Four models of water were considered, including the widely used TIP4P [W. L. Jorgensen, J. Chandrasekha, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys.79, 926 (1983)] and TIP5P [M. W. Mahoney and W. L. Jorgensen J. Chem. Phys.112, 8910 (2000)] models, as well as recently improved TIP4P and TIP5P models for use with Ewald techniques-the TIP4P-Ew [W. Horn, W. C. Swope, J. W. Pitera, J. C. Madura, T. J. Dick, G. L. Hura, and T. Head-Gordon, J. Chem. Phys.120, 9665 (2004)] and TIP5P-Ew [S. W. Rick, J. Chem. Phys.120, 6085 (2004)] models. The calculated melting temperature at 1 bar is T(m) = 229 +/- 1 K for the TIP4P and T(m) = 272.0 +/- 0.6 K for the TIP5P ice I(h), both are consistent with previous simulations based on free-energy methods. For the TIP4P-Ew and TIP5P-Ew models, the calculated melting temperature is T(m) = 257.0 +/- 1.1 K and T(m) = 253.9 +/- 1.1 K, respectively.

Metallic single-walled silicon nanotubes

Atomistic computer-simulation evidences are presented for the possible existence of one-dimensional silicon nanostructures: the square, pentagonal, and hexagonal single-walled silicon nanotubes (SWSNTs). The local geometric structure of the SWSNTs differs from the local tetrahedral structure of cubic diamond silicon, although the coordination number of atoms of the SWSNTs is still fourfold. Ab initio calculations show that the SWSNTs are locally stable in vacuum and have zero band gap, suggesting that the SWSNTs are possibly metals rather than wide-gap semiconductors.