We present a reliable method to define the interfacial particles for determining the crystal-melt interface position, which is the key step for the crystal-melt interfacial free energy calculations using capillary wave approach. Using this method, we have calculated the free energies gamma of the fcc crystal-melt interfaces for the hard-sphere system as a function of crystal orientations by examining the height fluctuations of the interface using Monte Carlo simulations. We find that the average interfacial free energy gamma(0) = 0.62 +/- 0.02k(B)T/sigma(2) and the anisotropy of the interfacial free energies are weak, gamma(100) = 0.64 +/- 0.02, gamma(110) = 0.62 +/- 0.02, gamma(111) = 0.61 +/- 0.02k(B)T/sigma(2). The results are in good agreement with previous simulation results based on the calculations of the reversible work required to create the interfaces (Davidchack and Laird, Phys. Rev. Lett. 2000, 85, 4571). In addition, our results indicate gamma(100) > gamma(110) > gamma(111) for the hard-sphere system, similar to the results of the Lennard-Jones system.

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.

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.

We investigate the effects of the long-range dipolar interaction on the formation of the stripe patterns in two-dimensional (2D) spin systems with competing short- and long-range interactions by using the continuous time Monte Carlo technique. We find that there exists an optimal temperature region at which the best stripe patterns are prone to be formed, and the stability and the orientational ordering of striped structures mainly depend on the temperature T, while the width of the striped domains is determined by the strength of the long-range dipolar interaction g. Furthermore, a complete T-g phase diagram is obtained. The results provide a simple and universal picture to account for striking and substantial physics revealed in the prevalent striped morphologies of 2D spin systems.

The formation of self-organizing stripe structures in a two-dimensional frustrated system with competing short-range attractive and long-range Coulomb repulsive interactions is investigated by continuous time Monte Carlo simulation technique. We find that intermediate between the frustrated meandering striped phase at low temperatures and the disordered phase at high temperatures is a highly oriented stripe phase where frustrationinduced topological defects are effectively alleviated. The stability and the orientational ordering of stripe structures are mainly controlled by the temperature T, while the stripe thickness is determined by the strength of long-range repulsions g. A metastable branching stripe phase may appear between two ordered striped phases which are different in the width of the stripes. Furthermore, we obtain a complete T-g phase diagram describing the striped phase transitions. Our results clearly indicate a possibility for the production of highly ordered and defect-free nanometer-scale materials with different sizes by tuning the temperature and the relative repulsion strengths, and provide an interesting and universal picture to account for striking and substantial physics revealed in the stripe patterns of soft materials.