163 research outputs found
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 -component order parameters, with Landau free energies that
have a single zero-strain 'austenite' minimum at high temperatures, and
spontaneous-strain 'martensite' minima of structural variants at low
temperatures. In a reduced description, the strains at Landau minima induce
temperature-dependent, clock-like hamiltonians, with
-component strain-pseudospin vectors pointing to
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 values of , as in a
generalized Blume-Capel model. We then consider transitions with two-component
() pseudospins: the equilateral to centred-rectangle ();
the square to oblique polygon (); the triangle to oblique ()
transitions; and finally the 3D cubic to tetragonal transition (). 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
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