Dynamics of mesoscopic precipitate lattices in phase separating alloys under external load

We investigate, via three-dimensional atomistic computer simulations, phase separation in an alloy under external load. A regular two-dimensional array of cylindrical precipitates, forming a mesoscopic precipitate lattice, evolves in the case of applied tensile stress by the movement of mesoscopic lattice defects. A striking similarity to ordinary crystals is found in the movement of "meso-dislocations", but new mechanisms are also observed. Point defects such as "meso-vacancies" or "meso-interstitials" are created or annihilated locally by merging and splitting of precipitates. When the system is subjected to compressive stress, we observe stacking faults in the mesoscopic one-dimensional array of plate-like precipitates.Comment: 4 pages, 4 figures, REVTE

From nonlinear to linearized elasticity via Γ-convergence: the case of multiwell energies satisfying weak coercivity conditions

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled non- linear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers

Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: a local mean-field analysis

We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local meanfield approximation of their pseudospin hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their $N_{OP}$-component order parameters, with Landau free energies that have a single zero-strain 'austenite' minimum at high temperatures, and spontaneous-strain 'martensite' minima of $N_V$ structural variants at low temperatures. In a reduced description, the strains at Landau minima induce temperature-dependent, clock-like $\mathbb{Z}_{N_V +1}$ hamiltonians, with $N_{OP}$-component strain-pseudospin vectors ${\vec S}$ pointing to $N_V + 1$ discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local meanfield approximation of their pseudospin hamiltonians, that include the powerlaw interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component, pseudospin taking $N_V +1 =3$ values of $S= 0, \pm 1$, as in a generalized Blume-Capel model. We then consider transitions with two-component ($N_{OP} = 2$) pseudospins: the equilateral to centred-rectangle ($N_V =3$); the square to oblique polygon ($N_V =4$); the triangle to oblique ($N_V =6$) transitions; and finally the 3D cubic to tetragonal transition ($N_V =3$). The local meanfield solutions in 2D and 3D yield oriented domain-walls patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related hamiltonians illustrate that structural-transitions in materials science can be the source of interesting spin models in statistical mechanics.Comment: 15 pages, 9 figure

Phase-field model for grain boundary grooving in multi-component thin films

Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the evolution of the phases, composition, microstructure and morphology of such thin films. The phase-field model is quite general, describing compounds and solid solution alloys with sufficient freedom to choose solubilities, grain boundary and interface energies, and heats of segregation to all interfaces. We present analytical results which describe the interface profiles, with and without segregation, and confirm them using numerical simulations. We demonstrate that the present model accurately reproduces the theoretical grain boundary groove angles both at and far from equilibrium. As an example, we apply the phase-field model to the special case of a Ni(Pt)Si (Ni/Pt silicide) thin film on an initially flat silicon substrate.Comment: 12 pages, 5 figures, submitted to Modelling Simulation Mater. Sci. En

Application of elastostatic Green function tensor technique to electrostriction in cubic, hexagonal and orthorhombic crystals

The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg-Landau free energy expansion of electrostrictive materials.Comment: 4 page

Simulations of cubic-tetragonal ferroelastics

We study domain patterns in cubic-tetragonal ferroelastics by solving numerically equations of motion derived from a Landau model of the phase transition, including dissipative stresses. Our system sizes, of up to 256^3 points, are large enough to reveal many structures observed experimentally. Most patterns found at late stages in the relaxation are multiply banded; all three tetragonal variants appear, but inequivalently. Two of the variants form broad primary bands; the third intrudes into the others to form narrow secondary bands with the hosts. On colliding with walls between the primary variants, the third either terminates or forms a chevron. The multipy banded patterns, with the two domain sizes, the chevrons and the terminations, are seen in the microscopy of zirconia and other cubic-tetragonal ferroelastics. We examine also transient structures obtained much earlier in the relaxation; these show the above features and others also observed in experiment.Comment: 7 pages, 6 colour figures not embedded in text. Major revisions in conten

Self-organization of (001) cubic crystal surfaces

Self-organization on crystal surface is studied as a two dimensional spinodal decomposition in presence of a surface stress. The elastic Green function is calculated for a $(001)$ cubic crystal surface taking into account the crystal anisotropy. Numerical calculations show that the phase separation is driven by the interplay between domain boundary energy and long range elastic interactions. At late stage of the phase separation process, a steady state appears with different nanometric patterns according to the surface coverage and the crystal elastic constants

Prediction of ferroelectricity in BaTiO3/SrTiO3 superlattices with domains

The phase transitions of superlattices into single- and multidomain states were studied using a mesoscale phase-field model incorporating structural inhomogeneity, micromechanics, and electrostatics. While the predictions of transition temperatures of BaTiO3/SrTiO3 superlattices into multidomains show remarkably good, quantitative agreement with ultraviolet Raman spectroscopic and variable-temperature x-ray diffraction measurements, the single-domain assumption breaks down for superlattices in which the nonferroelectric layer thickness exceeds the characteristic domain size in the ferroelectric layers.open463

Intermediate states at structural phase transition: Model with a one-component order parameter coupled to strains

We study a Ginzburg-Landau model of structural phase transition in two dimensions, in which a single order parameter is coupled to the tetragonal and dilational strains. Such elastic coupling terms in the free energy much affect the phase transition behavior particularly near the tricriticality. A characteristic feature is appearance of intermediate states, where the ordered and disordered regions coexist on mesoscopic scales in nearly steady states in a temperature window. The window width increases with increasing the strength of the dilational coupling. It arises from freezing of phase ordering in inhomogeneous strains. No impurity mechanism is involved. We present a simple theory of the intermediate states to produce phase diagrams consistent with simulation results.Comment: 16 pages, 14 figure

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