We examine the influence of different forms of the free-energy functionals used in the phase-field-crystal ͑PFC͒ model, and compare them with the second-order density-functional theory ͑DFT͒ of freezing, by using bcc iron as an example case. We show that there are large differences between the PFC and the DFT and it is difficult to obtain reasonable parameters for existing PFC models directly from the DFT. Therefore, we propose a way of expanding the correlation function in terms of gradients that allows us to incorporate the bulk modulus of the liquid as an additional parameter in the theory. We show that this functional reproduces reasonable values for both bulk and surface properties of bcc iron, and therefore it should be useful in modeling bcc materials. As a further demonstration, we also calculate the grain boundary energy as a function of misorientation for a symmetric tilt boundary close to the melting transition.

Articles you may be interested in Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media J. Chem. Phys. 141, 244903 (2014); 10.1063/1.4904728Green's function for a spherical dielectric discontinuity and its application to simulation J. Chem. Phys. 140, 044903 (2014) (2003)]. To this aim, we introduce two computational approaches that allow to solve the selfconsistent equations beyond the loop expansion. The first method is based on a perturbative Green's function technique, and the second one is an extension of a previously introduced semiclassical approximation for single dielectric interfaces to the case of slit nanopores. Both approaches can handle the case of dielectrically discontinuous boundaries where the one-loop theory is known to fail. By comparing the theoretical results obtained from these schemes with the results of the Monte Carlo simulations that we ran for ions at neutral single dielectric interfaces, we first show that the weak coupling Debye-Huckel theory remains quantitatively accurate up to the bulk ion density ρ b 0.01 M, whereas the self-consistent theory exhibits a good quantitative accuracy up to ρ b 0.2 M, thus improving the accuracy of the Debye-Huckel theory by one order of magnitude in ionic strength. Furthermore, we compare the predictions of the self-consistent theory with previous Monte Carlo simulation data for charged dielectric interfaces and show that the proposed approaches can also accurately handle the correlation effects induced by the surface charge in a parameter regime where the mean-field result significantly deviates from the Monte Carlo data. Then, we derive from the perturbative self-consistent scheme the one-loop theory of asymmetrically partitioned salt systems around a dielectrically homogeneous charged surface. It is shown that correlation effects originate in these systems from a competition between the salt screening loss at the interface driving the ions to the bulk region, and the interfacial counterion screening excess attracting them towards the surface. This competition can be quantified in terms of the characteristic surface charge σ *, where B = 7 Å is the Bjerrum length. In the case of weak surface charges σ s σ * s where counterions form a diffuse layer, the interfacial salt screening loss is the dominant effect. As a result, correlation effects decrease the mean-field density of both coions and counterions. With an increase of the surface charge towards σ * s , the surface-attractive counterion screening excess starts to dominate, and correlation effects amplify in this regime the mean-field density of both type of ions. However, in the regime σ s > σ * s , the same counterion screening excess also results in a significant decrease of the electrostatic mean-field potential. This reduces in turn the mean-field counterion density far from the charged surface. We also show that for σ s σ * s , electrostatic correlations result in a charge inversion effect. However, the electrostatic coupling regime where this...

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well-known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.

The growth of quasicrystals, i.e., aperiodic structures with long-range order, seeded from the melt is investigated using a dynamical phase field crystal model. Depending on the thermodynamic conditions, two different growth modes are detected, namely defect-free growth of the stable quasicrystal and a mode dominated by phasonic flips which are incorporated as local defects into the grown structure such that random tiling-like ordering emerges. The latter growth mode is unique to quasicrystals and can be verified in experiments on one-component mesoscopic systems.PACS numbers: 61.44. Br,81.10.Aj,82.70.Dd Quasicrystals are aperiodic structures that possess long range positional and orientational order [1,2]. Since their discovery by Shechtman [1], hundreds of quasicrystals have been reported and confirmed. Most of them are metallic alloys (see, e.g., [3,4]) but more recently they have also beend found in soft-matter systems that are made, e.g., by amphiphilic molecules [5], supramolecular dendritic systems [6,7], or by star block copolymers [8,9]. Such soft matter quasicrystals can provide scaffolds for photonic materials [10] and serve as well-characterized mesoporous matrices [11,12]. In general, quasicrystals occur either as defect-free structures stabilized by energy [13][14][15][16][17] or as locally disordered phases, leading to random tiling like structures, stabilized by entropy [18].One of the key issues for quasicrystal formation is to understand their growth mechanism out of an undercooled melt. Unlike ordinary growth of periodic crystals where a layer-by-layer mode is possible, quasicrystals lack any strict sequential growth mode due to their aperiodicity which renders their formation quite complex. Based on atomistic simulations, it has been proposed that instead first clusters are formed in the fluid which then assemble in the growing solid-fluid interface [19] but the fundamentals and details for quasicrystal growth are far from being understood. In particular, the incorporation of defects into the emerging structure during the growth process plays the leading role to discriminate between grown defect-free and random-tiling-like quasicrystals.In this letter we explore the growth behavior of quasicrystals using an appropriate dynamical phase field crystal model with two incommensurate length scales which exhibits stable defect-free quasicrystals in equilibrium. Depending on the thermodynamic conditions (such as undercooling and distance from the triple point), we find two different growth regimes for quasicrystals. There is either a defect-free growth into the stable quasicrystal or a mode dominated by phasonic flips which are incorporated as local defects into the grown structure such that a metastable random tiling-like ordering emerges. The latter growth mode is unique to quasicrystals and can be verified in experiments on one component mesoscopic systems which exhibit quasicrystalline order. Our findings do not only provide a microscopic (i.e. particleresolved) understanding of the growth pro...

We study the phase diagram and the commensurate-incommensurate transitions in a phase field model of a two-dimensional crystal lattice in the presence of an external pinning potential. The model allows for both elastic and plastic deformations and provides a continuum description of lattice systems, such as for adsorbed atomic layers or two-dimensional vortex lattices. Analytically, a mode expansion analysis is used to determine the ground states and the commensurate-incommensurate transitions in the model as a function of the strength of the pinning potential and the lattice mismatch parameter. Numerical minimization of the corresponding free energy shows reasonable agreement with the analytical predictions and provides details on the topological defects in the transition region. We find that for small mismatch the transition is of first order, and it remains so for the largest values of mismatch studied here. Our results are consistent with results of simulations for atomistic models of adsorbed overlayers.