Anisotropic dynamical scaling in a spin model with competing interactions

Results are presented for the kinetics of domain growth of a two-dimensional Ising spin model with competing interactions quenched from a disordered to a striped phase. The domain growth exponent are $\beta=1/2$ and $\beta=1/3$ for single-spin-flip and spin-exchange dynamics, as found in previous simulations. However the correlation functions measured in the direction parallel and transversal to the stripes are different as suggested by the existence of different interface energies between the ground states of the model. In the case of single-spin-flip dynamics an anisotropic version of the Ohta-Jasnow-Kawasaki theory for the pair scaling function can be used to fit our data.Comment: 4 pages, REVTeX fil

Grain boundary pinning and glassy dynamics in stripe phases

We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value $R_g \sim \lambda_0\ \epsilon^{-1/2}\exp(|a|/\sqrt{\epsilon})$, where$\epsilon\ll 1$is the dimensionless distance away from threshold,$\lambda_0$the stripe wavelength, and$a$ a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.Comment: 17 pages, 8 figures. Corrected version with one new figur

Instabilities and disorder of the domain patterns in the systems with competing interactions

The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at certain temperatures the ordered hexagonal pattern becomes unstable with respect to the two types of instabilities: the radially-nonsymmetric distortions of the domains and the repumping of the order parameter between the neighbors. Both these instabilities may lead to the transformation of the regular hexagonal pattern into a disordered pattern.Comment: ReVTeX, 4 pages, 3 figures (postscript); submitted to Phys. Rev. Let

Ordering of the lamellar phase under a shear flow

The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free-energy and the evolution follows a convection-diffusion equation. Lamellae order preferentially with the normal along the vorticity direction. Typical lengths grow as $\gamma t^{5/4}$ (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3

Modeling Elasticity in Crystal Growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.Comment: 4 pages, 10 figure

Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$

A Viscoelastic model of phase separation

We show here a general model of phase separation in isotropic condensed matter, namely, a viscoelastic model. We propose that the bulk mechanical relaxation modulus that has so far been ignored in previous theories plays an important role in viscoelastic phase separation in addition to the shear relaxation modulus. In polymer solutions, for example, attractive interactions between polymers under a poor-solvent condition likely cause the transient gellike behavior, which makes both bulk and shear modes active. Although such attractive interactions between molecules of the same component exist universally in the two-phase region of a mixture, the stress arising from attractive interactions is asymmetrically divided between the components only in dynamically asymmetric mixtures such as polymer solutions and colloidal suspensions. Thus, the interaction network between the slower components, which can store the elastic energy against its deformation through bulk and shear moduli, is formed. It is the bulk relaxation modulus associated with this interaction network that is primarily responsible for the appearance of the sponge structure peculiar to viscoelastic phase separation and the phase inversion. We demonstrate that a viscoelastic model of phase separation including this new effect is a general model that can describe all types of isotropic phase separation including solid and fluid models as its special cases without any exception, if there is no coupling with additional order parameter. The physical origin of volume shrinking behavior during viscoelastic phase separation and the universality of the resulting spongelike structure are also discussed.Comment: 14 pages, RevTex, To appear in Phys. Rev

Sheared Solid Materials

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volume {\it m}. For very small $m$ the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasing {\it m}, accumulation of {\it m} around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.Comment: 16pages, 11figure

The Energy-Scaling Approach to Phase-Ordering Growth Laws

We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on a scaling assumption for pair correlations, determines $L(t)$ self-consistently for purely dissipative dynamics by computing the time-dependence of the energy in two ways. We derive growth laws for conserved and non-conserved $O(n)$ models, including two-dimensional XY models and systems with textures. We demonstrate that the growth laws for other systems, such as liquid-crystals and Potts models, are determined by the type of topological defect in the order parameter field that dominates the energy. We also obtain generalized Porod laws for systems with topological textures.Comment: LATeX 18 pages (REVTeX macros), one postscript figure appended, REVISED --- rearranged and clarified, new paragraph on naive dimensional analysis at end of section I