Crystal-liquid interfacial free energy of hard spheres via a thermodynamic integration scheme

Direct Calculation of the Interfacial Free Energy between NaCl Crystal and Its Aqueous Solution at the Solubility Limit

Salty water is the most abundant electrolyte aqueous mixture on Earth, however, very little is known about the NaCl-saturated solution interfacial free energy (γ_{s}). Here, we provide the first direct estimation of γ_{s} for several NaCl crystallographic planes by means of the mold integration technique, a highly efficient computational method to evaluate interfacial free energies with anisotropic crystal resolution. Making use of the JC-SPC/E model, one of the most benchmarked force fields for NaCl water solutions, we measure γ_{s} of four different crystal planes, (100), (110), (111), and (112[over ¯]) with the saturated solution at normal conditions. We find high anisotropy between the different crystal orientations with values ranging from 100 to 150  mJ m^{-2}, and the average value of the distinct planes being γ[over ¯]_{s}=137(20)  mJ m^{-2}. This value for the coexistence interfacial free energy is in reasonable agreement with previous extrapolations from nucleation studies. Our Letter represents a milestone in the computational calculation of interfacial free energies between ionic crystals and aqueous solutions.

A General Method for Calculating Solid/Liquid Interfacial Free Energies from Atomistic Simulations: Application to CaSO4.xH2O

We present a general method for computing interfacial free energies from atomistic simulations, which is particularly suitable for solid/liquid interfaces. Our method uses an Einstein crystal as a universal reference state and is more flexible than previous approaches. Surfaces with dipoles, complex reconstructions, and partially dissolved species are all easily accommodated within the framework. It may also be extended to calculating the relative free energies of different phases and other types of defect. We have applied our method to interfaces of bassanite and gypsum with water and obtained interfacial free energies of the order of 0.15 J/m2, of which approximately 50 % is due to entropic contributions. Our calculations of the interfacial free energy of NaCl with water obtained a value of 0.13 J/m2 of which only 19 % is from entropic contributions. We have also predicted equilibrium morphologies for bassanite and gypsum that compare well with experiments and previous calculations.

Fcc vs. hcp competition in colloidal hard-sphere nucleation: on their relative stability, interfacial free energy and nucleation rate

Hard-sphere crystallization has been widely investigated over the last six decades by means of colloidal suspensions and numerical methods. However, some aspects of its nucleation behaviour are still under debate. Here, we provide a detailed computational characterisation of the polymorphic nucleation competition between the face-centered cubic (fcc) and the hexagonal-close packed (hcp) hard-sphere crystal phases. By means of several state-of-the-art simulation techniques, we evaluate the melting pressure, chemical potential difference, interfacial free energy and nucleation rate of these two polymorphs, as well as of a random stacking mixture of both crystals. Our results highlight that, despite the fact that both polymorphs have very similar stability, the interfacial free energy of the hcp phase could be marginally higher than that of the fcc solid, which in consequence, mildly decreases its propensity to nucleate from the liquid compared to the fcc phase. Moreover, we analyse the abundance of each polymorph in grown crystals from different types of inserted nuclei: fcc, hcp and stacking disordered fcc/hcp seeds, as well as from those spontaneously emerged from brute force simulations. We find that post-critical crystals fundamentally grow maintaining the polymorphic structure of the critical nucleus, at least until moderately large sizes, since the only crystallographic orientation that allows stacking close-packed disorder is the fcc (111) plane, or equivalently the hcp (0001) one. Taken together, our results contribute with one more piece to the intricate puzzle of colloidal hard-sphere crystallization.

Crystal growth of bcc titanium from the melt and interfacial properties: A molecular dynamics simulation study

The crystal growth kinetics and interfacial properties of titanium (Ti) are studied using molecular dynamics computer simulation. The interactions between the Ti atoms are modeled via an embedded atom method potential. First, the free solidification method (FSM) is used to determine the melting temperature T_m at zero pressure where the transition from liquid to body-centered cubic crystal occurs. From the simulations with the FSM, the kinetic growth coefficients are also determined for different orientations of the crystal, analyzing how the coupling to the thermostat affects the estimates of the growth coefficients. At T_m, anisotropic interfacial stiffnesses and free energies as well as kinetic growth coefficients are determined from capillary wave fluctuations. The so-obtained growth coefficients from equilibrium fluctuations and without the coupling of the system to a thermostat agree well with those extracted from the FSM calculations.

Computation of the solid-liquid interfacial free energy in hard spheres by means of thermodynamic integration

We used a thermodynamic integration scheme, which is specifically designed for disordered systems, to compute the interfacial free energy of the solid-liquid interface in the hard-sphere model. We separated the bulk contribution to the total free energy from the interface contribution, performed a finite-size scaling analysis, and obtained for the (100)-interface γ=0.591(11)k_{B}Tσ^{-2}.

Long-time self-diffusion in quasi-two-dimensional colloidal fluids of paramagnetic particles

The effect of hydrodynamic interactions (HI) on the long-time self-diffusion in quasi-two-dimensional fluids of paramagnetic colloidal particles is investigated using a combination of experiments and Brownian dynamics (BD) simulations. In the BD simulations, the direct interactions (DI) between the particles consist of a short-ranged repulsive part and a long-ranged part that is proportional to 1/r^{3}, with r the interparticle distance. By studying the equation of state, the simulations allow for the identification of the regime where the properties of the fluid are fully controlled by the long-ranged interactions, and the thermodynamic state solely depends on the dimensionless interaction strength Γ. In this regime, the radial distribution functions from the simulations are in quantitative agreement with those from the experiments for different fluid area fractions. This agreement confirms that the DI in the experiments and simulations are identical, which thus allows us to isolate the role of HI, as these are not taken into account in the BD simulations. Experiment and simulation fall onto a master curve with respect to the Γ dependence of D_{L}^{★}=D_{L}/(D_{0}Γ^{1/2}), with D_{0} the self-diffusion coefficient at infinite dilution and D_{L} the long-time self-diffusion coefficient. Our results thus show that, although HI affect the short-time self-diffusion, for a quasi-two-dimensional system with 1/r^{3} long-ranged DI, the reduced quantity D_{L}^{★} is effectively not affected by HI. Interestingly, this is in agreement with prior work on quasi-two-dimensional colloidal hard spheres.

Extraction of effective solid-liquid interfacial free energies for full 3D solid crystallites from equilibrium MD simulations

Molecular dynamics simulations of an embedded atom copper system in the isobaric-isenthalpic ensemble are used to study the effective solid-liquid interfacial free energy of quasi-spherical solid crystals within a liquid. This is within the larger context of molecular dynamics simulations of this system undergoing solidification, where single individually prepared crystallites of different sizes grow until they reach a thermodynamically stable final state. The resulting equilibrium shapes possess the full structural details expected for solids with weakly anisotropic surface free energies (in these cases, ∼5% radial flattening and rounded [111] octahedral faces). The simplifying assumption of sphericity and perfect isotropy leads to an effective interfacial free energy as appearing in the Gibbs-Thomson equation, which we determine to be ∼177 erg/cm², roughly independent of crystal size for radii in the 50-250 Å range. This quantity may be used in atomistically informed models of solidification kinetics for this system.

Molecular dynamics simulation of charged colloids confined between hard walls: pre-melting and pre-freezing across the BCC-fluid coexistence

Molecular dynamics (MD) computer simulations are used to study the structure of hard-core Yukawa systems confined between two parallel hard walls. States around the coexistence between a fluid and a body-centered cubic (BCC) crystal are considered. In all cases a pronounced layering in the vicinity of the walls is observed. Using a thermodynamic integration scheme, we determine the wall-fluid interfacial free energy γ which is negative and monotonically decreasing with increasing bulk density of the fluid. In the case of the fluid, the layers next to the walls undergo a transition from a fluid to a hexagonal structure. This pre-freezing transition occurs well below the coexistence bulk density of the fluid. The confined BCC crystal in (111) orientation shows melted regions between crystalline face-centered cubic (FCC) layers close to the wall and the BCC bulk region.

Silicon-wall interfacial free energy via thermodynamics integration

We compute the interfacial free energy of a silicon system in contact with flat and structured walls by molecular dynamics simulation. The thermodynamics integration method, previously applied to Lennard-Jones potentials [R. Benjamin and J. Horbach, J. Chem. Phys. 137, 044707 (2012)], has been extended and implemented in Tersoff potentials with two-body and three-body interactions taken into consideration. The thermodynamic integration scheme includes two steps. In the first step, the bulk Tersoff system is reversibly transformed to a state where it interacts with a structureless flat wall, and in a second step, the flat structureless wall is reversibly transformed into an atomistic SiO₂ wall. Interfacial energies for liquid silicon-wall interfaces and crystal silicon-wall interfaces have been calculated. The calculated interfacial energies have been employed to predict the nucleation mechanisms in a slab of liquid silicon confined by two walls and compared with MD simulation results.

Seeding approach to crystal nucleation

We present a study of homogeneous crystal nucleation from metastable fluids via the seeding technique for four different systems: mW water, Tosi-Fumi NaCl, Lennard-Jones, and Hard Spheres. Combining simulations of spherical crystal seeds embedded in the metastable fluid with classical nucleation theory, we are able to successfully describe the nucleation rate for all systems in a wide range of metastability. The crystal-fluid interfacial free energy extrapolated to coexistence conditions is also in good agreement with direct calculations of such parameter. Our results show that seeding is a powerful technique to investigate crystal nucleation.

Free energy cost of forming an interface between a crystal and its frozen version

Using a thermodynamic integration scheme, we compute the free energy cost per unit area, γ, of forming an interface between a crystal and a frozen structured wall, formed by particles frozen into the same equilibrium structure as the crystal. Even though the structure and potential energy of the crystalline phase in the vicinity of the wall is the same as in the bulk, γ has a nonzero value and increases with increasing density of the crystal and the wall. Investigating the effect of several interaction potentials between the particles, we observe a positive γ at all crystalline densities if the potential is purely repulsive. For models with attractive interactions, such as the Lennard-Jones potential, a negative value for γ is obtained at low densities. A qualitative explanation for the change of sign of γ when going from repulsive to attractive interactions, at low crystal densities, is suggested.