171 research outputs found
Three-Dimensional Elastic Compatibility: Twinning in Martensites
We show how the St.Venant compatibility relations for strain in three
dimensions lead to twinning for the cubic to tetragonal transition in
martensitic materials within a Ginzburg-Landau model in terms of the six
components of the symmetric strain tensor. The compatibility constraints
generate an anisotropic long-range interaction in the order parameter
(deviatoric strain) components. In contrast to two dimensions, the free energy
is characterized by a "landscape" of competing metastable states. We find a
variety of textures, which result from the elastic frustration due to the
effects of compatibility. Our results are also applicable to structural phase
transitions in improper ferroelastics such as ferroelectrics and
magnetoelastics, where strain acts as a secondary order parameter
Droplet Fluctuations in the Morphology and Kinetics of Martensites
We derive a coarse grained, free-energy functional which describes droplet
configurations arising on nucleation of a product crystal within a parent. This
involves a new `slow' vacancy mode that lives at the parent-product interface.
A mode-coupling theory suggests that a {\it slow} quench from the parent phase
produces an equilibrium product, while a {\it fast} quench produces a
metastable martensite. In two dimensions, the martensite nuclei grow as
`lens-shaped' strips having alternating twin domains, with well-defined front
velocities. Several empirically known structural and kinetic relations drop out
naturally from our theory.Comment: 4 pages, REVTEX, and 3 .eps figures, compressed and uuencoded,
Submitted to Phys. Rev. Let
Catastrophic Fermi surface reconstruction in the shape-memory alloy AuZn
AuZn undergoes a shape-memory transition at 67 K. The de Haas van Alphen
effect persists to 100 K enabling the observation of a change in the quantum
oscillation spectrum indicative of a catastrophic Fermi surface reconstruction
at the transition. Coexistence of both Fermi surfaces at low temperatures is
suggestive of an intrinsic phase separation in the bulk of the material. In
addition, a Dingle analysis reveals a sharp change in the scattering mechanism
at a threshold cyclotron radius, which we suggest to be related to the
underlying microstructure that drives the shape-memory effect.Comment: 4 pages, 4 figure
Twin wall of cubic-tetragonal ferroelastics
We derive solutions for the twin wall linking two tetragonal variants of the
cubic-tetragonal ferroelastic transformation, including for the first time the
dilatational and shear energies and strains. Our solutions satisfy the
compatibility relations exactly and are obtained at all temperatures. They
require four non-vanishing strains except at the Barsch-Krumhansl temperature
TBK (where only the two deviatoric strains are needed). Between the critical
temperature and TBK, material in the wall region is dilated, while below TBK it
is compressed. In agreement with experiment and more general theory, the twin
wall lies in a cubic 110-type plane. We obtain the wall energy numerically as a
function of temperature and we derive a simple estimate which agrees well with
these values.Comment: 4 pages (revtex), 3 figure
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
Fermi Surface as a Driver for the Shape-Memory Effect in AuZn
Martensites are materials that undergo diffusionless, solid-state
transitions. The martensitic transition yields properties that depend on the
history of the material and may allow it to recover its previous shape after
plastic deformation. This is known as the shape-memory effect (SME). We have
succeeded in identifying the primary electronic mechanism responsible for the
martensitic transition in the shape-memory alloy AuZn by using Fermi-surface
measurements (de Haas-van Alphen oscillations) and band-structure calculations.
This strongly suggests that electronic band structure is an important
consideration in the design of future SME alloys
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
Disorder-Driven Pretransitional Tweed in Martensitic Transformations
Defying the conventional wisdom regarding first--order transitions, {\it
solid--solid displacive transformations} are often accompanied by pronounced
pretransitional phenomena. Generally, these phenomena are indicative of some
mesoscopic lattice deformation that ``anticipates'' the upcoming phase
transition. Among these precursive effects is the observation of the so-called
``tweed'' pattern in transmission electron microscopy in a wide variety of
materials. We have investigated the tweed deformation in a two dimensional
model system, and found that it arises because the compositional disorder
intrinsic to any alloy conspires with the natural geometric constraints of the
lattice to produce a frustrated, glassy phase. The predicted phase diagram and
glassy behavior have been verified by numerical simulations, and diffraction
patterns of simulated systems are found to compare well with experimental data.
Analytically comparing to alternative models of strain-disorder coupling, we
show that the present model best accounts for experimental observations.Comment: 43 pages in TeX, plus figures. Most figures supplied separately in
uuencoded format. Three other figures available via anonymous ftp
Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics
We study the statics and the dynamics of domain patterns in proper
hexagonal-orthorhombic ferroelastics; these patterns are of particular interest
because they provide a rare physical realization of disclinations in crystals.
Both our static and dynamical theories are based entirely on classical,
nonlinear elasticity theory; we use the minimal theory consistent with
stability, symmetry and ability to explain qualitatively the observed patterns.
After scaling, the only parameters of the static theory are a temperature
variable and a stiffness variable. For moderate to large stiffness, our static
results show nested stars, unnested stars, fans and other nodes, triangular and
trapezoidal regions of trapped hexagonal phase, etc observed in electron
microscopy of Ta4N and Mg-Cd alloys, and also in lead orthovanadate (which is
trigonal-monoclinic); we even find imperfections in some nodes, like those
observed. For small stiffness, we find patterns like those observed in the
mineral Mg-cordierite. Our dynamical studies of growth and relaxation show the
formation of these static patterns, and also transitory structures such as
12-armed bursts, streamers and striations which are also seen experimentally.
The major aspects of the growth-relaxation process are quite unlike those in
systems with conventional order parameters, for it is inherently nonlocal; for
example, the changes from one snapshot to the next are not predictable by
inspection.Comment: 9 pages, 3 figures (1 b&w, 2 colour); animations may be viewed at
http://huron.physics.utoronto.ca/~curnoe/sim.htm
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
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