Origins of elastic properties in ordered nanocomposites

We predict a diblock copolymer melt in the lamellar phase with added spherical nanoparticles that have an affinity for one block to have a lower tensile modulus than a pure diblock copolymer system. This weakening is due to the swelling of the lamellar domain by nanoparticles and the displacement of polymer by elastically inert fillers. Despite the overall decrease in the tensile modulus of a polydomain sample, the shear modulus for a single domain increases dramatically

Atomic scale lattice distortions and domain wall profiles

We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained {\it atomic length} scale variations to {\it continuum} elasticity and describes elasticity at several length scales. We apply the approach to a two-dimensional square lattice with a monatomic basis, and find the elastic deformations and hierarchical atomic relaxations in the vicinity of a domain wall between two different homogeneous strain states. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Ginzburg-Landau theory, by showing that they are anisotropic.Comment: 6 figure

Re-equilibration after quenches in athermal martensites:Conversion-delays for vapour to liquid domain-wall phases

Entropy barriers and ageing states appear in martensitic structural-transition models, slowly re-equilibrating after temperature quenches, under Monte Carlo dynamics. Concepts from protein folding and ageing harmonic oscillators turn out to be useful in understanding these nonequilibrium evolutions. We show how the athermal, non-activated delay time for seeded parent-phase austenite to convert to product-phase martensite, arises from an identified entropy barrier in Fourier space. In an ageing state of low Monte Carlo acceptances, the strain structure factor makes constant-energy searches for rare pathways, to enter a Brillouin zone `golf hole' enclosing negative energy states, and to suddenly release entropically trapped stresses. In this context, a stress-dependent effective temperature can be defined, that re-equilibrates to the quenched bath temperature.Comment: 11 pages, 12 figures. Under process with Phys. Rev. B (2015

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

Oscillating elastic defects: competition and frustration

We consider a dynamical generalization of the Eshelby problem: the strain profile due to an inclusion or "defect" in an isotropic elastic medium. We show that the higher the oscillation frequency of the defect, the more localized is the strain field around the defect. We then demonstrate that the qualitative nature of the interaction between two defects is strongly dependent on separation, frequency and direction, changing from "ferromagnetic" to "antiferromagnetic" like behavior. We generalize to a finite density of defects and show that the interactions in assemblies of defects can be mapped to XY spin-like models, and describe implications for frustration and frequency-driven pattern transitions.Comment: 4 pages, 5 figure

Elastic Deformation of Polycrystals

We propose a framework to model elastic properties of polycrystals by coupling crystal orientational degrees of freedom with elastic strains. Our model encodes crystal symmetries and takes into account explicitly the strain compatibility induced long-range interaction between grains. The coupling of crystal orientation and elastic interactions allows for the rotation of individual grains by an external load. We apply the model to simulate uniaxial tensile loading of a 2D polycrystal within linear elasticity and a system with elastic anharmonicities that describe structural phase transformations. We investigate the constitutive response of the polycrystal and compare it to that of single crystals with crystallographic orientations that form the polycrystal.Comment: 4 pages, 4 ps figure