Molecular dynamics simulations are widely used to investigate nucleation in first-order phase transitions. Brute-force simulations, though popular, are limited to conditions of high metastability, where the critical cluster and the nucleation barrier are small. The seeding method has recently emerged as a powerful alternative for exploring lower supersaturation regimes by initiating simulations with a pre-formed nucleus. In confined systems (NVT ensemble), the seeded simulations are particularly effective for determining stable cluster properties and provide a stringent test case for classical nucleation theory (CNT). In this work, we perform NVT seeded simulations of Lennard-Jones condensation in small systems and compare them with CNT predictions based on several thermodynamic models, including equations of state, perturbation theory, and ideal gas approximation. We find that CNT accurately predicts stable cluster radii across a wide range of conditions. Notably, even the very simple ideal gas approximation proves useful for initializing seeded simulations. Furthermore, seeded simulation results correspond to the critical cluster radii of infinite systems: CNT predictions with good equations of state show very good agreement with simulations, while the perturbation theory and the ideal gas approximation perform well at low temperatures but deviate significantly at high temperatures.

Using state-of-the-art rare-event sampling simulations, we precisely characterize the nucleation of liquid droplets from a supersaturated Lennard-Jones gas and uncover a key physical feature: critical clusters nucleate with a density that differs substantially from that of the macroscopic equilibrium liquid. Our atomistic simulations also reveal a nonclassical nucleation pathway showing simultaneous growth and densification in liquid condensation. We then exploit these insights to develop a two-variable nucleation theory, in which the cluster density is allowed to vary. Our accessible model based on the capillary approximation is able to quantitatively retrieve the numerical results in nucleation rate and critical cluster properties over a large range of supersaturation. Remarkably, the two-variable model successfully captures the observed nucleation pathway. The effectiveness of this integrated numerical and theoretical framework demonstrates that the cluster density is a decisive variable in nucleation, highlighting the limitations of the single-variable description while offering a robust foundation for its refinement.

The classical nucleation theory (CNT) and its modified versions provide a convenient framework for describing the nucleation process under the capillary approximation. However, these models often predict nucleation rates that depart significantly from simulation results, even for a simple Lennard-Jones fluid. This large discrepancy is likely due to the inaccurate estimation of the driving force for nucleation, which most traditional models estimate within the ideal solution approximation. In this study, we address this issue by directly calculating the driving force for nucleation using equations of state (EOS) and integrating this approach into the calculation of nucleation rates within the framework of CNT and its modified model. We apply this method to examine the condensation of a Lennard-Jones fluid and compare the resulting nucleation rates with molecular dynamics (MD) simulation data. Our results demonstrate that at relatively low supersaturation, where the capillary approximation is reasonable, our thermodynamic models exhibit excellent agreement with MD results, significantly outperforming traditional models. At moderate and high supersaturation, our approach continues to show a reasonable agreement with MD results. Furthermore, when comparing the results obtained by using different EOS, we find that more precise EOS generally yield better agreement with MD data.

A phase-field model for diffusion-limited crystal growth is formulated that is capable of handling highly anisotropic interfaces. It uses a Willmore regularization that yields corners of finite size. An asymptotic analysis reveals that Herring’s law is recovered for the advancing surfaces. The model is validated by conducting simulations of dendritic growth for low anistorpies and comparing the results to the data from the literature. The model makes it possible to simulate high anisotropy dendrites for which the standard phase-field models are ill-posed. In this regime, the interplay between a Herring instability on the dendrite flanks and the corner regularization creates zig-zag shaped corrugations and leads to a non-monotonic trend of tip velocity as a function of anisotropy strength.

The ternary mixture of uranium, oxygen and zirconium is investigated as a minimal model for corium, the mixture that forms after the meltdown of a nuclear reactor. Like corium, U-O-Zr exhibits a liquid–liquid phase separation between a metal-rich and an oxide-rich phase at high temperatures. A CALPHAD database built on an associate model is used to set up a ternary Cahn–Hilliard model, which can describe two-phase patterns in U-O-Zr. The interface structure and properties, which depend on the choice on the gradient energy coefficients in the free-energy functional, are studied in detail. It is found that interface adsorption is generally present due to the diffuse character of the interface, but that its magnitude is small, such that the model remains a robust and useful tool for future simulations of corium pool stratification dynamics.

At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharp-interface problem, the surface free energy is traditionally augmented with a curvature-dependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface description and present a phase-field model for strongly anisotropic crystals that is regularized using an approximation of the Willmore energy. The Allen–Cahn equation is employed to model kinetically controlled crystal growth. Using the method of matched asymptotic expansions, it is shown that the model converges to the sharp-interface theory proposed by Herring. Then, the stress tensor is used to derive the force acting on the diffuse interface and to examine the properties of a corner at equilibrium. Finally, the coarsening dynamics of the faceting instability during growth is investigated. Phase-field simulations reveal the existence of a parabolic regime, with the mean facet length evolving in t , with t the time, as predicted by the sharp-interface theory. A specific coarsening mechanism is observed: a hill disappears as the two neighbouring valleys merge.

The ternary alloy of germanium, antimony, and tellurium (GST) is widely used as a material for phase-change memories. In particular, the stoichiometric compound Ge2Sb2Te5 exhibits a rapid congruent crystallization. To increase the temperature at which spontaneous crystallization erases the stored information, alloys that are enriched in germanium have been investigated. Their crystallization is accompanied by segregation and eventually the nucleation of a new, germanium-rich phase. In order to model the redistribution of alloy components and the time evolution of the microstructure during device operations, we develop a multi-phase-field model for the crystallization of GST that includes segregation and couple it with orientation fields that describe the grain structure. We demonstrate that this model is capable to capture both the emergence of a two-phase polycrystalline structure starting from an initially amorphous material, and the melting and recrystallization during the SET and RESET operations in a memory cell of the “wall” type.

Nucleation kinetics in a multicomponent supersaturated solid solution is examined. Attachment rate of atoms to a nucleus of a size close to the critical one is determined combining a thermodynamic extremum principle and the Fokker-Planck equation. Two limiting cases are examined; when bulk diffusion controls the nucleation kinetics and when the process is limited by the interfacial mobility. The mixed regime is also treated. Moreover, the growth law in multicomponent alloys is derived in the general case, when both mechanisms are considered. Additionally, the attachment rate is derived, in the classical framework, from a new macroscopic growth equations and the fundamental role of the interfacial mobility is examined. These new general expressions, for the attachment rates and the growth laws, determined either applying the thermodynamic extremum principle or derived from the classical formalism are found to be consistent.

The present work aims at understanding the transformation mechanisms of gamma'-L1(2) precipitates in the ternary Co-Al-W system from quenched state to thermodynamic equilibrium. Three alloys with compositions Co-9Al-7W, Co-10Al-12W and Co-7Al-9W (at.%) were aged at 900 degrees C for 10 h, 200 h and 1000 h. The microstructure has been characterized by transmission and scanning electron microscopies, and the phase composition was determined using atom probe tomography. Results show that irrespective of the initial supersaturation, the quenched state is already decomposed into gamma+gamma'. This indicates that even in the Co-7Al-9W alloy that lies in the gamma+Co3W domain of the phase diagram, gamma' phase forms at first, indicating that gamma' is a metastable phase. In the two other alloys, during ageing at 900 degrees C gamma' phase dissolves and the equilibrium state is composed of gamma, CoAl and Co-3 W phases. The gamma' phase in the Co-7Al-9W alloy dissolves more rapidly compared to the two other alloys that are in the gamma+gamma' metastable domain. The volume fraction of Co3W phase increases rapidly with ageing time in the Co-7Al-9W alloy. Whereas gamma' phase is predominant at short ageing times, it becomes a minor phase after 1000 h of ageing, and is replaced mostly by the Co3W phase. As already observed, the transformation from gamma'-L1(2) to Co3W-D0(19) phase is taking place through a stacking fault. This mechanism occurs in the three alloys. In addition, a new dissolution mechanism interpreted as destabilization of the gamma' phase is evidenced in the Co-9Al-7W. The gamma' precipitates tend to split along {111} planes. Transmission electron microscopy investigations show that the dissolution and splitting mechanism of the gamma' phase is initiated by stacking faults, that are subsequently wetted by the gamma phase. (C) 2019 Elsevier B.V. All rights reserved.

The thermodynamics of strongly anisotropic crystalline surfaces is analogous to that of a binary mixture exhibiting phase separation. On a metastable planar surface, formation of stable orientations requires a nucleation process, in which the energy associated with the presence of corners must be considered. In this context, a nucleation event corresponds to the formation of a critical shape for the crystalline surface before the system enters the growth regime. We first derive the Euler-Lagrange equation for crystal surface nucleation, in two dimensions, and show that the saddle-point condition corresponds to a vanishing chemical potential along this critical surface. We then perform numerical simulation of the equation of motion for the crystal surface and show that, as compared with saddle point nucleation, ridge crossing is dynamically favoured.

Lessons-learned from 10 years of noble gas stations operation and dedicated R & D allowed the design of a New Generation of station. In order to produce 60 m(3) air equivalent Xenon samples every 8 h, it implements: (i) larger sampler unit for Xenon extraction (2 compressors and 8 nitrogen membranes), (ii) new noble gas adsorbent (Ag@ZSM5), (iii) hardened components and (iv) new high resolution coincidence low background spectrometer (HPGe/PIPSBox). Station expected radioxenon sensitivity is lower than 0.3 mBq/m(3).

The early stages of precipitation of the gamma' phase in a model Co based superalloy (Co-9.1Al-7W (at.%)) have been investigated at 900 degrees C using electron microscopy and atom probe tomography. Nucleation, growth and coarsening stages have been studied with a focus on the temporal evolution of the precipitate composition in the light of recent theoretical developments on phase separation in multicomponent alloys. The experimental data have been confronted to the theories of nucleation and coarsening recently developed for such alloys, which are valid for non-ideal and non-dilute systems, and predict the temporal evolution of both the matrix and precipitate compositions. The rate constant for the mean size evolution of the particles, as derived from experiments, has been compared to the one predicted by the mentioned coarsening theory that accounts for a more accurate description of the thermodynamics of the phases, as compared with more classical approaches. From this comparison the gamma/gamma' interfacial energy was derived and found equal to similar to 48 mJ/m(2) The exponents for the temporal evolution of average particles size, number of particles per unit volume were found identical to those for binary alloys during the coarsening regime, as expected, and the temporal evolutions of compositions in both gamma and gamma' phases were found to evolve as predicted by theory. Indeed, the W content in the particles, measured from atom probe tomography (APT) experiments, was found to significantly decrease with time and the observed evolution is remarkably well described by the theory and therefore is shown to originate from the competition between diffusion and capillarity. (C) 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.

Phase transitions are known to present peculiarities in small systems that are related to depletion effects of the ambient phase. Mass conservation affects the conditions of thermodynamic equilibrium between a nucleus of the new phase and the matrix as compared with nucleation in infinite systems. This finite-size effect is known to delay the phase transition but can also impede nucleation in very small systems as it stabilizes the initial state, originally metastable in infinite systems. In this work, we investigate this superstabilization effect in the context of classical nucleation theory in multicomponent solutions and we derive an analytical expression for the system size below which nucleation becomes thermodynamically impossible. Comparing with the exact solution, our simple result is shown to accurately predict the superstabilization effect, and can therefore be used, for instance, as a guideline for the design of novel nanomaterials.

The analysis by atom probe tomography (APT) of InAlAsSb layers with applications in triple junction solar cells (TJSCs) has shown the existence of In- and Sb-rich regions in the material. The composition variation found is not evident from the direct observation of the 3D atomic distribution and because of this a statistical analysis has been required. From previous analysis of these samples, it is shown that the small compositional fluctuations determined have a strong effect on the optical properties of the material and ultimately on the performance of TJSCs.

We examine binary nucleation in the size and composition space {R,c} using the formalism of the multivariable theory [N. V. Alekseechkin, J. Chem. Phys. 124, 124512 (2006)]. We show that the variable c drops out of consideration for very large curvature of the new phase Gibbs energy with composition. Consequently nuclei around the critical size have the critical composition, which is derived from the condition of criticality for the canonical variables and is found not to depend on surface tension. In this case, nucleation kinetics can be investigated in the size space only. Using macroscopic kinetics, we determine the general expression for the condensation rate when growth is limited by bulk diffusion, which accounts for both diffusion and capillarity and exhibits a different dependence with the critical size, as compared with the interface-limited regime. This new expression of the condensation rate for bulk diffusion-limited nucleation is the counterpart of the classical interface-limited result. We then extend our analysis to multicomponent solutions.

The classic framework of Johnson-Mehl-Avrami-Kolmogorov (JMAK) has been commonly used in studies of thin film phase transformation kinetics despite its inherent limitation to transformations that occur in finite size domains or via heterogeneous nucleation on surfaces. To address the effects of finite size and heterogeneous nucleation on a JMAK analysis, we employ the level-set method to simulate phase evolution in thin film systems. Isothermal transformations under a constant nucleation rate and isotropic interface growth, with both bulk and surface nucleation cases are considered for broad range of film thicknesses. In agreement with past work, we find that when the thickness of the film is sufficiently small or heterogeneous nucleation on surface is present, it is possible to have a non-constant Avrami exponent over the course of phase transformation. Our results also show that the rate constant varies with the film thickness in contrast to bulk phase transformations. Furthermore, we obtain the grain size distributions at the end of the transformation for various film thicknesses that vary strongly in shape for small changes in film thickness when the film thickness is on the order of the characteristic length. By analyzing this information and determining the change of the average grain size with film thickness, we find that, the film thickness relative to the characteristic length is a reliable indicator of the dominant growth dimensionality in thin film phase transformations.

The analysis by atom probe tomography (APT) of InAlAsSb layers with applications in triple junction solar cells (TJSCs) has shown the existence of Inand Sb-rich regions in the material. The composition variation found is not evident from the direct observation of the 3D atomic distribution and because of this a statistical analysis has been required. From previous analysis of these samples, it is shown that the small compositional fluctuations determined have a strong effect on the optical properties of the material and ultimately on the performance of TJSCs.

A new general model dealing with nucleation, growth and coarsening simultaneously has been developed for the simulation of precipitation in non-dilute multicomponent alloys. Nucleation is implemented using the Zeldovich theory that includes regression effects. Growth and coarsening are modeled using the recently developed growth law in multicomponent alloys that accounts for capillarity, mass balance at the interface matrix-precipitate and diffusion-flux couplings. Numerical results are confronted to atom probe tomography (APT) experiments on model NiCrAl superalloys and to rigid lattice kinetics Monte Carlo (LKMC) simulations and are found in very good agreement with both APT experiments and LKMC simulations. We emphasize this work on the evolution of phase concentrations. The temporal evolution of the mean precipitate composition is found to be non-monotonic during the phase transformation, and phase composition does not follow the tie line due to a complex interplay between capillarity and diffusion process. The widespread availability of both thermodynamic and mobility databases makes this new model very suitable for material design.