We develop and analyze a two-mode phase-field-crystal model to describe fcc ordering. The model is formulated by coupling two different sets of crystal density waves corresponding to <111> and <200> reciprocal lattice vectors, which are chosen to form triads so as to produce a simple free-energy landscape with coexistence of crystal and liquid phases. The feasibility of the approach is demonstrated with numerical examples of polycrystalline and (111) twin growth. We use a two-mode amplitude expansion to characterize analytically the free-energy landscape of the model, identifying parameter ranges where fcc is stable or metastable with respect to bcc. In addition, we derive analytical expressions for the elastic constants for both fcc and bcc. Those expressions show that a nonvanishing amplitude of [200] density waves is essential to obtain mechanically stable fcc crystals with a nonvanishing tetragonal shear modulus (C11-C12)/2. We determine the model parameters for specific materials by fitting the peak liquid structure factor properties and solid-density wave amplitudes following the approach developed for bcc [K.-A. Wu and A. Karma, Phys. Rev. B 76, 184107 (2007)]. This procedure yields reasonable predictions of elastic constants for both bcc Fe and fcc Ni using input parameters from molecular dynamics simulations. The application of the model to two-dimensional square lattices is also briefly examined.

Previous simulation and experimental studies have shown that some grain boundaries (GBs) can couple to applied shear stresses and be moved by them, producing shear deformation of the lattice traversed by their motion. While this coupling effect has been well confirmed for symmetrical tilt GBs, little is known about the coupling ability of asymmetrical boundaries. In this work we apply a combination of molecular dynamics and phase field crystal simulations to investigate stress-driven motion of asymmetrical GBs between cubic crystals over the entire range of inclination angles. Our main findings are that the coupling effect exists for most of the asymmetrical GBs and that the coupling factor exhibits a non-trivial dependence on both the misorientation and inclination angles. This dependence is characterized by a discontinuous change of sign of the coupling factor, which reflects a transition between two different coupling modes over a narrow range of angles. Importantly, the magnitude of the coupling factor becomes large or divergent within this transition region, thereby giving rise to a sliding-like behavior. Our results are interpreted in terms of a diagram presenting the domains of existence of the two coupling modes and the transition region between them in the plane of misorientation and inclination angles. The simulations reveal some of the dislocation mechanisms responsible for the motion of asymmetrical tilt GBs. The results of this study compare favorably with existing experimental measurements and provide a theoretical ground for the design of future experiments.

We use the phase-field-crystal (PFC) method to investigate the equilibrium premelting and nonequilibrium shearing behaviors of [001] symmetric tilt grain boundaries (GBs) at high homologous temperature over the complete range of misorientation 0 < θ < 90 • in classical models of bcc Fe. We characterize the dependence of the premelted layer width W as a function of temperature and misorientation. In addition, we compute the thermodynamic disjoining potential whose derivative with respect to W represents the structural force between crystal-melt interfaces due to the spatial overlap of density waves. The disjoining potential is also computed by molecular dynamics (MD) simulations, for quantitative comparison with PFC simulations, and coarse-grained amplitude equations (AE) derived from PFC that provide additional analytical insights. We find that, for GBs over an intermediate range of misorientation (θmin < θ < θmax), W diverges as the melting temperature is approached from below, corresponding to a purely repulsive disjoining potential, while for GBs outside this range (θ < θmin or θmax < θ < 90 • ), W remains finite at the melting point. In the latter case, W corresponds to a shallow attractive minimum of the disjoining potential. The misorientation range where W diverges predicted by PFC simulations is much smaller than the range predicted by MD simulations when the small dimensionless parameter ǫ of the PFC model is matched to liquid structure factor properties. However it agrees well with MD simulations with a lower ǫ value chosen to match the ratio of bulk modulus and solid-liquid interfacial free-energy, consistent with the amplitude-equation prediction that θmin and 90 • − θmax scale as ∼ ǫ 1/2 . The incorporation of thermal fluctuations in PFC is found to have a negligible effect on this range. In response to a shear stress parallel to the GB plane, GBs in PFC simulations exhibit coupled motion normal to this plane or sliding. Furthermore, the coupling factor exhibits a discontinuous change as a function of θ that reflects a transition between two coupling modes. Sliding is only observed over a range of misorientation that is a strongly increasing function of temperature for T /TM ≥ 0.8 and matches roughly the range where W diverges at the melting point. The coupling factor for the two coupling modes is in excellent quantitative agreement with previous theoretical predictions [J. W. Cahn, Y. Mishin, and A. Suzuki, Acta Mater. 54, 4953 (2006)].

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The rate of curvature-driven grain growth in polycrystalline materials is well-known to be limited by interface dissipation. We show analytically and by simulations that, for systems forming modulated phases or non-equilibrium patterns with crystal ordering, growth is limited by bulk dissipation associated with lattice translation, which dramatically slows down grain coarsening. We also show that bulk dissipation is reduced by thermal noise so that those systems exhibit faster coarsening behavior dominated by interface dissipation for high Peierls barrier and high noise. Those results provide a unified theoretical framework for understanding and modeling polycrystalline pattern evolution in diverse systems over a broad range of length and time scales.PACS numbers: 61.72. Mm, 05.40.Ca, 61.72.Hh, 62.20.Hg Polycrystalline patterns are observed in very diverse systems including crystalline solids [1], colloidal systems [2,3], various spatially modulated phases of macromolecular systems such as diblock copolymers [4,5], and nonequilibrium (NE) dissipative structures [6]. When grain boundaries (GBs) between domains of different crystal orientation are mobile, those patterns generally coarsen in time to reduce GB length or area by elimination of smaller grains. This coarsening behavior has been extensively studied because of its practical importance for engineering polycrystalline materials [7] and its fundamental relevance for our general understanding of nonequilibrium ordering phenomena.The ordering dynamics of modulated phases and NE patterns has been extensively studied theoretically [8][9][10][11][12][13][14][15][16] in the framework of model equations of the formwhere ψ is an order parameter appropriate to each system that can be globally conserved (n = 1) or non-conserved (n = 0), η is a noise uncorrelated in space and time with a variance determined by the fluctuation-dissipation relation η( r, t)η( r , t) = 2αT (−∇ 2 ) n δ( r − r )δ(t − t ), and F is a Lyapounov functional with a minimum in a lattice ordered state. Eq. (1) has also been proposed as a theoretical framework− the phase-field-crystal (PFC) model− to study polycrystalline materials on diffusive time scales with ψ representing the crystal density field [17,18]. While Eq. (1) has been traditionally studied for purely relaxational (p = 0) dynamics [8][9][10][11][12][13][14][15][16][17], propagative (p = 1) wave-like dynamics has also been introduced in the PFC framework to mimic phonon-mediated relaxation of the strain field [18].Extensive computational studies of Eq. (1) have shown that the characteristic domain or grain size for both roll patterns [9][10][11][12] and hexagonal lattices [13][14][15][16] grows ∼ t q . The exponent q is typically much smaller than the q = 1/2 value expected for "normal grain growth" in polycrystalline materials [19], and depends on parameters and noise strength [15,16]. While there have been theoretical attempts to explain those exponents for roll patterns [9][10][11][12], the origin of this sluggish (low q) coarse...