Homogeneous nucleation and growth of melt in copper

Molecular dynamics simulations are conducted to investigate homogeneous nucleation and growth of melt in copper described by an embedded-atom method (EAM) potential. The accuracy of this EAM potential for melting is validated by the equilibrium melting point obtained with the solid-liquid coexistence method and the superheating-supercooling hysteresis method. We characterize the atomistic melting process by following the temperature and time evolution of liquid atoms. The nucleation behavior at the extreme superheating is analyzed with the mean-first-passage-time (MFPT) method, which yields the critical size, steady-state nucleation rate, and the Zeldovich factor. The value of the steady-state nucleation rate obtained from the MFPT method is consistent with the result from direct simulations. The size distribution of subcritical nuclei appears to follow a power law similar to three-dimensional percolation. The diffuse solid-liquid interface has a sigmoidal profile with a 10%-90% width of about 12 A near the critical nucleation. The critical size obtained from our simulations is in reasonable agreement with the prediction of classical nucleation theory if the finite interface width is considered. The growth of melt is coupled with nucleation and can be described qualitatively with the Johnson-Meh-Avrami law. System sizes of 10(3)-10(6) atoms are explored, and negligible size dependence is found for bulk properties and for the critical nucleation.     

Comparative study of microstructural evolution during melting and crystallization

Molecular dynamics simulations, with the interaction between atoms described by a modified analytic embedded atom method, have been performed to obtain the atomic-scale details of isothermal melting in nanocrystalline Ag and crystallization from supercooled liquid. The radial distribution function and common neighbor analysis provide a visible scenario of structural evolution in the process of phase transition. The results indicate that melting at a fixed temperature in nanocrystalline materials is a continuous process, which originates from the grain boundary network. With the melting developing, the characteristic bond pairs (555), (433), and (544), existing in liquid or liquidlike phase, increase approximately linearly till completely melted. The crystallization from supercooled liquid is characterized by three characteristic stages: nucleation, rapid growth of nucleus, and slow structural relaxation. The homogeneous nucleation occurs at a larger supercooling temperature, which has an important effect on the process of crystallization and the subsequent crystalline texture. The kinetics of transition from liquid to solid is well described by the Johnson-Mehl-Avrami equation.     

氟化钾团簇的相变、成核和重结晶的分子动力学模拟

我们利用Born-Mayer-Huggins相互作用势函数对(KF)_N(N=108，256，500和864)团簇进行了分子动力学(MD)模拟。为了避免周期性边界条件对相变、成核和重结晶的干扰作用，对体系采用了自由边界。基于MD模拟结果，对团簇的熔化温度、熔化焓、扩散系数、成核速率、固液界面自由能、临界核大小等进行了计算和讨论。在对(KF)₈₆₄双晶团簇的热退火模拟中，观察到了固态的重结晶和晶粒的生长。经典的成核理论成功地解释了(KF)₈₆₄双晶团簇的重结晶MD模拟结果。     

Formation mechanism of critical nucleus during nucleation process of liquid metal sodium

To deeply understand the formation mechanism of a critical nucleus during the nucleation process of liquid metal sodium, a system consisting of 10 000 Na atoms has been simulated by using molecular dynamics method. The evolutions of nuclei are traced directly, adopting the cluster-type index method. It is found that the energies of clusters and their geometrical constraints interplay to form the favorable microstructures during the nucleation process. The nucleus can be formed through many different pathways, and the critical size of the nucleus would be different for each pathway. It is also found that the critical nucleus is nonspherical and may include some metastable structures. Furthermore, the size of the cluster and its internal structure both play a crucial role in determining whether it is a critical nucleus, and this is in agreement with the simulations by computing the free energy of the Lennard-Jones system [D. Moroni, P. R. ten Wolde, and P. G. Bolhuis, Phys. Rev. Lett. 94, 235703 (2005)].     

Test of classical nucleation theory on deeply supercooled high-pressure simulated silica

We test classical nucleation theory (CNT) in the case of simulations of deeply supercooled, high density liquid silica, as modeled by the van Beest-Kramer-van Santen potential. We find that at density rho=4.38 gcm(3), spontaneous nucleation of crystalline stishovite occurs in conventional molecular dynamics simulations at temperature T=3000 K, and we evaluate the nucleation rate J directly at this T via "brute force" sampling of nucleation events in numerous independent runs. We then use parallel, constrained Monte Carlo simulations to evaluate DeltaG(n), the free energy to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200, and 3300 K. By comparing the form of DeltaG(n) to CNT, we test the ability of CNT to reproduce the observed behavior as we approach the regime where spontaneous nucleation occurs on simulation time scales. We find that the prediction of CNT for the n dependence of DeltaG(n) fits reasonably well to the data at all T studied. Deltamu, the chemical potential difference between bulk liquid and stishovite, is evaluated as a fit parameter in our analysis of the form of DeltaG(n). Compared to directly determined values of Deltamu extracted from previous work, the fitted values agree only at T=3300 K; at lower T the fitted values increasingly overestimate Deltamu as T decreases. We find that n(*), the size of the critical nucleus, is approximately ten silicon atoms at T=3300 K. At 3000 K, n(*) decreases to approximately 3, and at such small sizes methodological challenges arise in the evaluation of DeltaG(n) when using standard techniques; indeed even the thermodynamic stability of the supercooled liquid comes into question under these conditions. We therefore present a modified approach that permits an estimation of DeltaG(n) at 3000 K. Finally, we directly evaluate at T=3000 K the kinetic prefactors in the CNT expression for J, and find physically reasonable values; e.g., the diffusion length that Si atoms must travel in order to move from the liquid to the crystal embryo is approximately 0.2 nm. We are thereby able to compare the results for J at 3000 K obtained both directly and based on CNT, and find that they agree within an order of magnitude. In sum, our work quantifies how certain predictions of CNT (e.g., for Deltamu) break down in this deeply supercooled limit, while others [the n dependence of DeltaG(n)] are not as adversely affected.     

Free energy landscapes for homogeneous nucleation of ice for a monatomic water model

We simulate the homogeneous nucleation of ice from supercooled liquid water at 220 K in the isobaric-isothermal ensemble using the MW monatomic water potential. Monte Carlo simulations using umbrella sampling are performed in order to determine the nucleation free energy barrier. We find the Gibbs energy profile to be relatively consistent with that predicted by classical nucleation theory; the free energy barrier to nucleation was determined to be ~18 k(B)T and the critical nucleus comprised ~85 ice particles. Growth from the supercooled liquid gives clusters that are predominantly cubic, whilst starting with a pre-formed subcritical nucleus of cubic or hexagonal ice results in the growth of predominantly that phase of ice only.     

Molecular dynamics simulations of cluster nucleation during inert gas condensation

Molecular dynamics simulations of vapor-phase nucleation of germanium in an argon atmosphere were performed and a unexpected channel of nucleation was observed. This channel, vapor-induced cluster splitting, is important for more refractory materials since the critical nucleus size can fall below the size of a dimer. As opposed to conventional direct vapor nucleation of the dimer, which occurs by three-body collisions, cluster-splitting nucleation is a second-order reaction. The most important cluster-splitting reaction is the collision of a vapor atom and a trimer that leads to the formation of two dimers. The importance of the cluster-splitting nucleation channel relative to the direct vapor nucleation channel is observed to increase with decreasing vapor density and increasing ratio of vapor to carrier gas atoms.     

Hit and miss of classical nucleation theory as revealed by a molecular simulation study of crystal nucleation in supercooled sulfur hexafluoride

Classical nucleation theory pictures the homogeneous nucleation of a crystal as the formation of a spherical crystalline embryo, possessing the properties of the macroscopic crystal, inside a parent supercooled liquid. In this work we study crystal nucleation in moderately supercooled sulfur hexafluoride by umbrella sampling simulations. The nucleation free energy evolves from 5.2kBT at T=170 K to 39.1kBT at T=195 K. The corresponding critical nucleus size ranges from 40 molecules at T=170 K to 266 molecules at T=195 K. Both nucleation free energy and critical nucleus size are shown to evolve with temperature according to the equations derived from the classical nucleation theory. Inspecting the obtained nuclei we show, however, that they present quite anisotropic shapes in opposition to the spherical assumption of the theory. Moreover, even though the critical nuclei possess the structure of the stable bcc plastic phase, the only mechanically stable crystal phase for SF6 in the temperature range investigated, they are shown to be less ordered than the corresponding macroscopic crystal. Their crystalline order is nevertheless shown to increase regularly with their size. This is confirmed by a study of a nucleus growth from a critical size to a size of the order of 10(4) molecules. Similarly to the fact that it does not affect the temperature dependence of the nucleation free energy and of the critical nucleus size, the ordering of the nucleus with size does not affect the growth rate of the nucleus.     

Extended study of molecular dynamics simulation of homogeneous vapor-liquid nucleation of water

Using the simple point charge/extended water model, we performed molecular dynamics simulations of homogeneous vapor-liquid nucleation at various values of temperature T and supersaturation S, from which the nucleation rate J, critical nucleus size n(*), and the cluster formation free energy DeltaG were derived. As well as providing lots of simulation data, the results were compared with theories on homogeneous nucleation, including the classical, semi-phenomenological, and scaled models, but none of these gave a satisfactory explanation for our results. It was found that two main factors made the theories fail: (1) The average cluster structure including the nonspherical shape and the core structure that is not like the bulk liquid and (2) the forward rate which is larger than assumed by the theories by about one order of magnitude. The quantitative evaluation of these factors is left for future investigations.     

Atomistic mechanisms of phase separation and formation of solid solutions: model studies of NaCl, NaCl-NaF, and Na(Cl1-xBrx) crystallization from the melt

The crystallization of sodium chloride from its melt and mixtures with other sodium halides is investigated by means of transition path sampling molecular dynamics simulations. From this we explore the nucleation mechanisms of both the solidification and the melting process at the atomistic level of detail. By incorporation of impurities the nucleation picture of the eutectic mixtures changes considerably. Doping the NaCl crystal with fluoride ions, we observed the substitutional defects to act as favored nucleation centers for the melting transition. This phenomenon plays a critical role during the solidification process of NaCl-NaF melts of low NaF concentration and is demonstrated to account for the segregation of fluoride ions. While NaCl-NaF corresponds to a eutectic system, we also investigated NaCl-NaBr mixtures. The bromide ions were observed to behave very similarly to chloride ions. As a consequence, no phase separation occurs and Na(Cl1-xBrx) solid solutions are formed. At the example of these two prototypes we demonstrate the study of the atomistic mechanisms related to phase separation processes and solid solution formation during the nucleation and growth of crystals from multinary melts.     

Rate of homogeneous crystal nucleation in molten NaCl

We report a numerical simulation of the rate of crystal nucleation of sodium chloride from its melt at moderate supercooling. In this regime nucleation is too slow to be studied with "brute force" molecular-dynamics simulations. The melting temperature of ("Tosi Fumi") NaCl is approximately 1060 K. We studied crystal nucleation at T = 800 and 825 K. We observe that the critical nucleus formed during the nucleation process has the crystal structure of bulk NaCl. Interestingly, the critical nucleus is clearly faceted, the nuclei have a cubical shape. We have computed the crystal-nucleation rate using two completely different approaches, one based on an estimate of the rate of diffusive crossing of the nucleation barrier, the other based on the forward flux sampling and transition interface sampling methods. We find that the two methods yield the same result within an order of magnitude. However, when we compare the extrapolated simulation data with the only available experimental results for NaCl nucleation, we observe a discrepancy of nearly five orders of magnitude. We discuss the possible causes for this discrepancy.     

Critical nucleus size effects on nanoparticle formation in microemulsions: a comparison study between experimental and simulation results

Monte Carlo simulations were performed to study the influence of critical nucleus size on nanoparticle formation in microemulsions. It was found that critical nucleus size strongly affected nucleation and growth rates, as well as final nanoparticle sizes. An increase of critical nucleus leads to a slower nucleation process. In contrast, it gives rise to acceleration of the growth process. Final nanoparticle sizes increase as the critical nucleus value increases. It is predicted that this dependence will be less pronounced when a high reactant concentration is used. We have compared the simulation results with experimental data taken from different authors. Good agreement between the two kinds of results supports the conclusions of this paper.     

Molecular simulation of the crystallization of aluminum from the supercooled liquid

We report hybrid Monte Carlo molecular simulation results on the crystallization of aluminum from the supercooled liquid. We simulate the entire crystallization process at P=1 atm and at temperatures 20% and 15% below the melting temperature. We demonstrate that crystallization takes place according to the same mechanism for the two degrees of supercooling considered in this work. We show that both nucleation and growth proceed into a random mixing of the hexagonal close packed structure and of the face centered cubic (fcc) phase, with a predominance of the stable fcc form. The concentration of icosahedral (Ih)-like atoms in the supercooled liquid is found to remain constant throughout nucleation and growth, showing that Ih-like atoms do not play an active role in the crystallization process. We also find that the crystallization mechanism of aluminum differs from that observed for simple fluids. While nucleation of simple fluids first proceeds into the metastable body centered cubic (bcc) phase, the fraction of bcc-like atoms in aluminum crystallites always remains very low.     

Reorganization and growth of metastable alpha-N2 critical nuclei into stable beta-N2 crystals

We report on results on the crystal nucleation and growth of nitrogen. Using molecular dynamics simulations, we show that while nucleation proceeds into the metastable alpha-phase (i.e., the crystalline phase associated with the lowest free energy barrier of formation), growth of the crystallite proceeds through a reorganization of the nucleus into the thermodynamically stable beta-phase.     

Test of classical nucleation theory via molecular-dynamics simulation

A direct test of classical nucleation theory (CNT) is made using molecular-dynamics simulations. The relation between critical nucleus size and undercooling temperature is extracted and the result yields the solid-liquid interfacial energy. It is shown that the CNT, within the assumptions made for spherical nucleus in supercooled liquid, is valid in the critical regime of nucleation for a large range of undercooling and nucleus size.     

Atomistic simulation of the homogeneous nucleation and of the growth of N2 crystallites

We report on a computer simulation study of the early stages of the crystallization of molecular nitrogen. First, we study how homogeneous nucleation takes place in supercooled liquid N(2) for a moderate degree of supercooling. Using the umbrella sampling technique, we determine the free energy barrier of formation for a critical nucleus of N(2). We show that, in accord with Ostwald's rule of stages, the structure of the critical nucleus is predominantly that of a metastable polymorph (alpha-N(2) for the state point investigated). We then monitor the evolution of several critical nuclei through a series of unbiased molecular dynamics trajectories. The growth of N(2) crystallites is accompanied by a structural evolution toward the stable polymorph beta-N(2). The microscopic mechanism underlying this evolution qualitatively differs from that reported previously. We do not observe any dissolution or reorganization of the alpha-like core of the nucleus. On the contrary, we show that alpha-like and beta-like blocks coexist in postcritical nuclei. We relate the structural evolution to a greater adsorption rate of beta-like molecules on the surface and show that this transition actually starts well within the precritical regime. We also carefully investigate the effect of the system size on the height of the free energy barrier of nucleation and on the structure and size of the critical nucleus.     

纳米粒子相变的分子动力学研究：Cu453的性质、结构与结晶成核

Molecular dynamics （MD） computer simulations have been carried out to study the structures, properties and crystal nucleation of nanoparticles with 453 Cu atoms. Structure information was analyzed from the MD simulations, while properties of nanoparticles of Cu453, such as melting point, freezing temperature, heat capacity and mo- lar volumes, have been estimated. The face center cubic （FCC） phase and icosahedron （Ih） phase were observed during the quenching process, and nucleation rates of crystallization to FCC crystal of Cu453 at temperatures of 650, 700, 750, and 800 K were analyzed. Both classical nucleation theory （CNT） and diffuse interface theory （DIT） were used to interpret our observed nucleation rates. The free energy and diffuse interface thickness between the liquid and the FCC crystal phases were estimated by the CNT and DIT respectively, and the results show that the DIT does not work properly to the system.     

Molecular dynamics simulations of the melting of aluminum nanoparticles

Molecular dynamics simulations are performed to determine the melting points of aluminum nanoparticles of 55-1000 atoms with the Streitz-Mintmire [Phys. Rev. B 1994, 50, 11996] variable-charge electrostatic plus potential. The melting of the nanoparticles is characterized by studying the temperature dependence of the potential energy and Lindemann index. Nanoparticles with less than 850 atoms show bistability between the solid and liquid phases over temperature ranges below the point of complete melting. The potential energy of a nanoparticle in the bistable region alternates between values corresponding to the solid and liquid phases. This bistability is characteristic of dynamic coexistence melting. At higher temperatures, only the liquid state is stable. Nanoparticles with more than 850 atoms undergo a sharp solid-liquid-phase transition characteristic of the bulk solid phase. The variation of the melting point with the effective nanoparticle radius is also determined.     

Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation

Capillarity approximation is used to study the free-energy landscape of nucleation when an intermediate metastable phase exists. The critical nucleus that corresponds to the saddle point of the free-energy landscape as well as the whole free-energy landscape can be studied using this capillarity approximation, and various scenarios of nucleation and growth can be elucidated. In this study, we consider a model in which a stable solid phase nucleates within a metastable vapor phase when an intermediate metastable liquid phase exists. We predict that a composite critical nucleus that consists of a solid core and a liquid wetting layer as well as pure liquid and pure solid critical nuclei can exist depending not only on the supersaturation of the liquid phase relative to that of the vapor phase but also on the wetting behavior of the liquid surrounding the solid. The existence of liquid critical nucleus indicates that the phase transformation from metastable vapor to stable solid occurs via the intermediate metastable liquid phase, which is quite similar to the scenario of nucleation observed in proteins and colloidal systems. By studying the minimum-free-energy path on the free-energy landscape, we can study the evolution of the composition of solid and liquid within nuclei which is not limited to the critical nucleus.