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

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

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state

Modelling avalanches in martensites

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45612-6_

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

The SLUGGS Survey: stellar kinematics, kinemetry and trends at large radii in 25 early-type galaxies

Due to longer dynamical time-scales, the outskirts of early-type galaxies retain the footprint of their formation and assembly. Under the popular two-phase galaxy formation scenario, an initial in situ phase of star formation is followed by minor merging and accretion of ex situ stars leading to the expectation of observable transitions in the kinematics and stellar populations on large scales. However, observing the faint galactic outskirts is challenging, often leaving the transition unexplored. The large-scale, spatially resolved stellar kinematic data from the SAGES Legacy Unifying Galaxies and GlobularS (SLUGGS) survey are ideal for detecting kinematic transitions. We present kinematic maps out to 2.6 effective radii on average, kinemetry profiles, measurement of kinematic twists and misalignments, and the average outer intrinsic shape of 25 SLUGGS galaxies. We find good overall agreement in the kinematic maps and kinemetry radial profiles with literature. We are able to confirm significant radial modulations in rotational versus pressure support of galaxies with radius so that the central and outer rotational properties may be quite different. We also test the suggestion that galaxies may be more triaxial in their outskirts and find that while fast rotating galaxies were already shown to be axisymmetric in their inner regions, we are unable to rule out triaxiality in their outskirts.We compare our derived outer kinematic information to model predictions from a two-phase galaxy formation scenario. We find that the theoretical range of local outer angular momentum agrees well with our observations, but that radial modulations are much smaller than predicted

Technical summary

The Working Group III (WGIII) contribution to the IPCC's Fifth Assessment Report (AR5) assesses literature on the scientific, technological, environmental, economic and social aspects of mitigation of climate change. It builds upon the WGIII contribution to the IPCC's Fourth Assessment Report (AR4), the Special Report on Renewable Energy Sources and Climate Change Mitigation (SRREN) and previous reports and incorporates subsequent new findings and research. Throughout, the focus is on the implications of its findings for policy, without being prescriptive about the particular policies that governments and other important participants in the policy process should adopt. In light of the IPCC's mandate, authors in WGIII were guided by several principles when assembling this assessment: (1) to be explicit about mitigation options, (2) to be explicit about their costs and about their risks and opportunities vis-a-vis other development priorities, (3) and to be explicit about the underlying criteria, concepts, and methods for evaluating alternative policies. This summary offers the main findings of the report

Restoration of Altered MicroRNA Expression in the Ischemic Heart with Resveratrol

Resveratrol, a constituent of red wine, is important for cardioprotection. MicroRNAs are known regulators for genes involved in resveratrol-mediated cardiac remodeling and the regulatory pathway involving microRNA has not been studied so far.We explored the cardioprotection by resveratrol in ischemia/reperfusion model of rat and determined cardiac functions. miRNA profile was determined from isolated RNA using quantitative Real-time PCR based array. Systemic analyses of miRNA array and theirs targets were determined using a number of computational approaches.Cardioprotection by resveratrol and its derivative in ischemia/reperfusion [I/R] rat model was examined with miRNA expression profile. Unique expression pattern were found for each sample, particularly with resveratrol [pure compound] and longevinex [commercial resveratrol formulation] pretreated hearts. Longevinex and resveratrol pretreatment modulates the expression pattern of miRNAs close to the control level based on PCA analyses. Differential expression was observed in over 25 miRNAs, some of them, such as miR-21 were previously implicated in cardiac remodeling. The target genes for the differentially expressed miRNA include genes of various molecular function such as metal ion binding, sodium-potassium ion, transcription factors, which may play key role in reducing I/R injury.Rats pretreated with resveratrol for 3 weeks leads to significant cardioprotection against ischemia/reperfusion injury. A unique signature of miRNA profile is observed in control heart pretreated with resveratrol or longevinex. We have determined specific group of miRNA in heart that have altered during IR injuries. Most of those altered microRNA expressions modulated close to their basal level in resveratrol or longevinex treated I/R mice