Crystal-melt Interfacial Free Energies Research Articles

Modified embedded-atom method potential for high-temperature crystal-melt properties of Ti–Ni alloys and its application to phase field simulation of solidification

We developed new interatomic potentials, based on the second nearest-neighbor modified embedded-atom method (2NN-MEAM) formalism, for Ti, Ni, and the binary Ti–Ni system. These potentials were fit to melting points, latent heats, the binary phase diagrams for the Ti rich and Ni rich regions, and the liquid phase enthalpy of mixing for binary alloys, therefore they are particularly suited for calculations of crystal-melt (CM) interface thermodynamic and transport properties. The accuracy of the potentials for pure Ti and pure Ni were tested against both 0 K and high temperature properties by comparing various properties obtained from experiments or density functional theory calculations including structural properties, elastic constants, point-defect properties, surface energies, temperatures and enthalpies of phase transformations, and diffusivity and viscosity in the liquid phase. The fitted binary potential for Ti–Ni was also tested against various non-fitted properties at 0 K and high temperatures including lattice parameters, formation energies of different intermetallic compounds, and the temperature dependence of liquid density at various concentrations. The CM interfacial free energies obtained from simulations, based on the newly developed Ti–Ni potential, show that the bcc alloys tend to have smaller anisotropy compared with fcc alloys which is consistent with the finding from the previous studies comparing single component bcc and fcc materials. Moreover, the interfacial free energy and its anisotropy for Ti-2 atom% Ni were also used to parameterize a 2D phase field (PF) model utilized in solidification simulations. The PF simulation predictions of microstructure development during solidification are in good agreement with a geometric model for dendrite primary arm spacing.

“Plunger” Method for Simulating Crystal–Melt Interfacial Free Energies

Crystal–melt interfacial free energies are important ingredients in predicting the nucleation barrier for polymers to crystallize. Experimental measurement of polymer crystal–melt interfacial tensions is challenging, particularly for crystal facets other than the lamellar surfaces. We propose a simple way to obtain the interfacial free energy for any polymer crystal surface and melt using molecular dynamics simulation. We measure the force on a simulated nanoscale “plunger”, that restrains a melt from flowing into the gap between two crystals cleaved along the (100) plane. This gives the difference between the crystal–vacuum and crystal–melt interfacial free energies. Separately, the crystal–vacuum interfacial free energy is obtained by measuring the force required to hold two crystals apart and integrating the force with respect to distance. We obtain the crystal–melt interfacial free energy by subtracting the above values. Results from this method applied to n-alkanes can be compared to measurements of ...

Calculation of crystal-melt interfacial free energies of fcc metals

Crystal-melt interfacial free energies of fcc metals were calculated by molecular dynamics simulation. Spherical crystal nucleus was embedded in the undercooled melt to create an ideal model of homogeneous nucleation. Growth and melting behaviors of the nucleus were examined. There was a critical temperature dividing growth and melting of the nucleus. The critical undercooling, as the difference between the critical temperature and the bulk melting point, was proportional to the inverse of the nucleus radius, which is regarded as the Gibbs–Thomson effect. The Gibbs–Thomson coefficient was determined from the relation between the critical undercooling and the nucleus radius. The crystal-melt interfacial free energies, which were estimated from the Gibbs–Thomson coefficients, were consistent with the experimental results of Turnbull.

Comparing crystal–melt interfacial free energies through homogeneous nucleationrates

In this work, we compared several available crystal–melt interfacial free energies viahomogeneous nucleation rates in a pure Lennard-Jones model system using both modelfitting and numerical methods. We examined the homogeneous nucleation temperatureobtained from the classical nucleation theory using the available interfacial free energiesfrom three different methods as inputs, i.e. the free energy integration method, the interfacefluctuation method and the classical nucleation theory based method. We found that thecritical temperature obtained by using the interfacial free energy calculated recently (Baiand Li 2006 J. Chem. Phys. 124 124707) is in better agreement with that obtained fromspontaneous crystallization in an independent molecular dynamics simulation. Thediscrepancies among the interface energies are discussed in light of these results.

A comparison of crystal–melt interfacial free energies using different Al potentials

We have calculated the crystal–melt interfacial stiffnesses using simulations with three different interatomic potentials for Al, and from these derived the anisotropic crystal–melt interfacial free energies. We find that there is a strong dependence of the results on the potential, and that this dependence cannot be explained by the usual Turnbull relation between the interfacial free energy and the latent heat. The potentials which produce liquid structures in closer agreement with experiments give free energies in good agreement with nucleation data.

Crystal-melt interfacial free energies of hard-dumbbell systems

The crystal-melt interfacial free energies of different crystal orientations and crystal forms for the hard-dumbbell systems have been calculated directly using a multistep thermodynamic perturbation method via nonequilibrium work measurements with a cleaving procedure. We found that for the plastic crystal phase, the interfacial free energies decrease as the reduced bond length L* increases and the anisotropy is very weak as in isotropic systems. On the other hand, for the orientationally ordered crystal phase, the interfacial free energies become more than three times larger and the anisotropy is about 13%. These results may have significant implications for our understanding on the nucleation kinetics in molecular systems and the search of optimal conditions of protein crystallization.

Crystal-melt interfacial free energies in hcp metals: A molecular dynamics study of Mg

Crystal-melt interfacial free energies $(\ensuremath{\gamma})$ are computed for hcp Mg by employing equilibrium molecular-dynamics (MD) simulations and the capillary-fluctuation method (CFM). This work makes use of a newly developed embedded-atom-method (EAM) interatomic potential for Mg fit to crystal, liquid, and melting properties. We describe how the CFM, which has previously been applied to cubic systems only, can be generalized for studies of hcp metals by employing a parametrization for the orientation dependence of $\ensuremath{\gamma}$ in terms of hexagonal harmonics. The method is applied in the calculation of the Turnbull coefficient $(\ensuremath{\alpha})$ and crystalline anisotropies of $\ensuremath{\gamma}$. We obtain a value of $\ensuremath{\alpha}=0.48$, with interfacial free energies for different high-symmetry orientations differing by approximately 1%. These results are compared to those obtained in previous MD-CFM studies for cubic EAM metals as well as experimental studies of solid-liquid interfaces in hcp alloys. In addition, the implications of our results for the prediction of dendrite growth directions in hcp metals are discussed.

Calculations of crystal-melt interfacial free energies by nonequilibrium work measurements

We developed a multistep thermodynamic perturbation method to compute the interfacial free energies by nonequilibrium work measurements with cleaving potential procedure. Using this method, we calculated the interfacial free energies of different crystal orientations for the Lennard-Jones system. Our results are in good agreement with the results by thermodynamic integration method. Compared with thermodynamic integration method, the multistep thermodynamic perturbation method is more efficient. For each stage of the cleaving process, only a few thermodynamic perturbation steps are needed, and there is no requirement on the reversibility of the path.

Crystal-melt interfacial free energies and mobilities in fcc and bcc Fe

Molecular-dynamics simulations have been used to compute thermodynamic and kinetic properties of the solid-liquid interface for both the fcc and bcc phases of Fe. Pure Fe was modeled using two different interatomic potentials of the embedded atom type as well as an effective pair potential. Free solidification simulations were used to determine the kinetic coefficient $\ensuremath{\mu}$ for the different models of pure Fe. The anisotropy of $\ensuremath{\mu}$ with respect to growth direction in the bcc phase is similar to that observed in fcc systems, namely ${\ensuremath{\mu}}_{100}g{\ensuremath{\mu}}_{110}\ensuremath{\sim}{\ensuremath{\mu}}_{111},$ and the kinetic coefficient of bcc is larger than $\ensuremath{\mu}$ for the fcc phase. The kinetic coefficient results are discussed in terms of a kinetic density-functional-theory-based model of crystal growth. In addition, results for solid-liquid interfacial free energies $\ensuremath{\gamma}$ computed via the capillary fluctuation method, are summarized.

Crystal-melt interfacial free energies in metals: fcc versus bcc

The structural dependence of crystal-melt interfacial free energies $(\ensuremath{\gamma})$ is investigated for fcc and bcc solids through molecular-dynamics calculations employing interatomic potentials for Fe. We compute $\ensuremath{\approx}30--35%$ lower values of $\ensuremath{\gamma}$ for the bcc structure, and find that our results cannot be explained simply in terms of differences in latent heats (L) or densities $(\ensuremath{\rho})$ for bulk bcc and fcc phases. We observe a strong structural dependence of the Turnbull coefficient $\ensuremath{\alpha}=\ensuremath{\gamma}/L{\ensuremath{\rho}}^{2/3},$ and find a trend towards lower crystalline anisotropies of $\ensuremath{\gamma}$ for the bcc structure relative to fcc.

Direct calculation of the crystal–melt interfacial free energies for continuous potentials: Application to the Lennard-Jones system

Extending to continuous potentials a cleaving wall molecular dynamics simulation method recently developed for the hard-sphere system [Phys. Rev. Lett. 85, 4751 (2000)], we calculate the crystal–melt interfacial free energies, γ, for a Lennard-Jones system as functions of both crystal orientation and temperature. At the triple point, T*=0.617, the results are consistent with an earlier cleaving potential calculation by Broughton and Gilmer [J. Chem. Phys. 84, 5759 (1986)], however, the greater precision of the current calculation allows us to accurately determine the anisotropy of γ. From our data we find that, at all temperatures studied, γ111<γ110<γ100. A comparison is made to the results from our previous hard-sphere calculation and to recent results for Ni by Asta, Hoyt, and Karma [Phys. Rev. B 66 100101(R) (2002)].

Application of Nucleation Theory to the Process of Droplet Freezing on an Ice Substrate

Abstract The probability P that ice embryos, nucleated inside droplets colliding with an ice surface, have crystallographic orientations different from that of the substrate, is correlated with the mean number of droplets which form each crystal in accretions grown in dry regime (substrate temperature T s < 0°C). The theory of heterogeneous nucleation is applied to represent the ice embryo nucleation rate and the approximate expression is obtained, where ΔG y * is the nucleation energy for randomly oriented critical embryos. Assuming cap-shaped embryos and taking into account the crystal size in accretions grown at T s = —15°C and air temperatures , it is found that erg The relationship between the value of ΔG y * and those of the crystal-embryo and crystal-melt interfacial free energies is discussed. Finally the dependence of P 0 on the growth conditions and on the ice substrate orientation is analysed, considering the effect of embryo breeding by collision and that of orientation selection, which is responsible for the establishment of preferential orientations in the accretions.

Application of Nucleation Theory to the Process of Droplet Freezing on an Ice Substrate

AbstractThe probability P that ice embryos, nucleated inside droplets colliding with an ice surface, have crystallographic orientations different from that of the substrate, is correlated with the mean number of droplets which form each crystal in accretions grown in dry regime (substrate temperature Ts < 0°C). The theory of heterogeneous nucleation is applied to represent the ice embryo nucleation rate and the approximate expression is obtained, where ΔGy* is the nucleation energy for randomly oriented critical embryos. Assuming cap-shaped embryos and taking into account the crystal size in accretions grown at Ts = —15°C and air temperatures , it is found that ergThe relationship between the value of ΔGy* and those of the crystal-embryo and crystal-melt interfacial free energies is discussed. Finally the dependence of P0 on the growth conditions and on the ice substrate orientation is analysed, considering the effect of embryo breeding by collision and that of orientation selection, which is responsible for the establishment of preferential orientations in the accretions.