Ginzburg-Landau theory of static domain walls in shape-memory alloys

Falk, F.

doi:10.1007/bf01308772

Cited by 193 publications

(93 citation statements)

References 9 publications

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“…The key feature of this solution is that the transverse component of the polarization (p 0 r ) shows a dip at the domain wall, and consequently one has a drop in voltage of 0.115 V across the 90 domain wall. It is interesting to note that Mayer and Vanderbilt [4] obtained a comparable voltage drop (0.15-0.2 V) across the 90 domain wall in PbTiO 3 using ab initio methods; in their paper [4], they call this result ''surprising'' as it is not anticipated on the basis of the classical description of domain walls [20]. Here, we have shown that the voltage drop is a natural outcome of solving the set of coupled equations in (7).…”

Section: Prl 95 247603 (2005) P H Y S I C a L R E V I E W L E T T E mentioning

confidence: 89%

Depletion Layers and Domain Walls in Semiconducting Ferroelectric Thin Films

2005

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Commonly used ferroelectric perovskites are also wide-band-gap semiconductors. In such materials, the polarization and the space-charge distribution are intimately coupled, and this Letter studies them simultaneously with no a priori ansatz on either. In particular, we study the structure of domain walls and the depletion layers that form at the metal-ferroelectric interfaces. We find the coupling between polarization and space charges leads to the formation of charge double layers at the 90 domain walls, which, like the depletion layers, are also decorated by defects like oxygen vacancies. In contrast, the 180 domain walls do not interact with the defects or space charges. Implications of these results to domain switching and fatigue in ferroelectric devices are discussed. DOI: 10.1103/PhysRevLett.95.247603 PACS numbers: 77.80.Dj, 73.40.ÿc, 75.60.Ch Ferroelectric perovskites that are widely used as actuators, sensors, and memories have classically been modeled as insulators following the Devonshire-Ginsburg-Landau (DGL) theory [1]. These materials, however, are also wideband-gap semiconductors [2]. Consequently, one has bandbending and depletion layers at electrodes and charge layer formation at domain walls, which in turn affect the polarization distribution. These in turn contribute to fatigue and domain-wall pinning.Recent efforts have sought to augment the DGL theory for these effects [3]. However, they assume a priori the depletion layer and space-charge distribution and calculate the resulting polarization distribution, or vice versa. There have also been ab initio studies of the electronic band structure and atomistic studies of defects [4 -6]. However, they provide limited information at the device scale due to enormous computational effort required to handle realistic length scales and geometries. This Letter provides a comprehensive presentation of a semiconducting ferroelectric at the device scale with no a priori assumptions on the polarization or space charge.We focus on the [001]-polarized tetragonal phase of BaTiO 3 to be specific, though many of our findings are generic. This well-studied material displays both 180 and 90 domain walls. Oxygen vacancies are a common defect and they act as donors [6,7]. We focus on the parallel-plate capacitor geometry (electrode-ferroelectric-electrode), which is the building block of many devices. Our results show the formation of depletion layers and the alteration of the polarization near electrodes, reveal some essential differences between 180 and 90 domain walls, show the redistribution of oxygen vacancies to electrodes and across 90 domain walls during annealing, and provide a concrete mechanism for imprinting a 90 domain wall. These results shed new light on various experimental observations.The state of the semiconducting ferroelectric crystal is determined by the polarization density p, the strain , the space-charge density , and the defect density N d , each of which we treat as field quantities. We assume here that all defects are donors motivated...

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Section: Prl 95 247603 (2005) P H Y S I C a L R E V I E W L E T T E mentioning

confidence: 89%

Depletion Layers and Domain Walls in Semiconducting Ferroelectric Thin Films

2005

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“…5-7 can be rationalized using a systematic power series expansion of the energy in terms of ǫ α . Although such expansions are quite common in the literature [5,10], our results show that fourth order terms in ǫ α , especially cross couplings of the form ǫ 2 1 ǫ 2 3 and ǫ 2 2 ǫ 2 3 , together with coupling to the external hydrostatic pressure P need to be included in order to reproduce the T = 0 results accurately. The coefficients of all these terms are however not independent.…”

Section: Zero Temperature Resultsmentioning

confidence: 93%

“…It is however not clear apriori, what are the relevant continuum degrees of freedom, especially in situations where the solid undergoes large deformations from the parent. In most theoretical studies of this problem, the only continuum degrees of freedom relevant at these scales have been taken to be the components of the strain tensor [9,10]. However, short length scale phenomena like atomic rearrangements [11,12] are not captured by these strainonly theories and may in some cases affect the kinetics of the transformation.…”

Section: Introductionmentioning

confidence: 99%

A mesoscopic model of a two-dimensional solid state structural transformation: statics and dynamics

Rao

Sengupta

2004

J. Phys.: Condens. Matter

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We study equilibrium properties of a system of particles in two dimensions, interacting with pair and three body potentials, which undergoes a structural transition from a square to a rhombic lattice and thus constitutes a simple model for a generic tetragonal to orthorhombic transition. We aim at an intermediate level of description lying in-between that of coarse grained elastic strain hamiltonians and microscopic ab -initio approaches. Macroscopic thermodynamic properties and phase diagram at zero and finite temperatures as a function of the density and the relative strengths of the pair and three body energies are obtained using lattice sums, an approximate 'cell-model' theory and molecular dynamics simulations in the NVT ensemble. We propose that this model solid can be used as a test bed for studies of statics and dynamics of structural transitions.

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“…are taken into consideration by some researchers e.g. Falk [29][30][31][32], Ball and James [9], Abeyarantne and co-workers [1][2][3][4], Krumhansl [51], Lindgrad [55], etc., to develop a microscopic model for PTs. Patoor, Eberhardt, and Berveiller [62] initiated to work at macro scale using the information from microscopic scale.…”

Section: State Of the Art Of Engineering Theories And Computational Mmentioning

confidence: 99%

“…The constitutive equations (26), (29), (30), the mass conservation condition (31), and above explained constraints (32)-(34) following from the stationary conditions of the Lagrangian functional, yield the final coupled incremental equations for every material point of the whole system or -in spatially discretized form -in every Gaussian integration point of the finite elements; they read:…”

Section: Time Integration Of Constitutive Equations In Each Materials mentioning

confidence: 99%

Contributions on the theory and computation of mono‐ and poly‐crystalline cyclic martensitic phase transformations

Sagar

Stein

2010

Z Angew Math Mech

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In this article new contributions to the theory and computation of cyclic martensitic phase transformations (PT) in monoand poly-crystalline metallic shape memory alloys are presented. The PT models of the non-convex variational problem are based on the Cauchy-Born hypothesis and Bain's principle. A quasi-convexified C 1 -continuous thermo-mechanical micromacro constitutive model for metallic monocrystals is developed which is represented together with the phase transformation constraints by a unified Lagrangian variational functional including phase evolution equations with mass conservation. The unified setting presented here includes poly-crystalline shape memory alloys whose microstructure is modeled using lattice variants. A pre-averaging scheme for randomly distributed poly-crystalline variants of transformation strains is used to transform them into those of a fictitious monocrystal. Thus, the incremental integration in process time and the spatial integration algorithms of the discrete variational problems for both mono-and poly-crystalline phase transformations can be implemented into a unified algorithm with branching for mono-and poly-crystalline phase transformations. Furthermore, an error-controlled adaptive 3D finite element method in space is presented for phase transformation problems using explicit error indicator with gradient smoothing and mesh refinements via new mesh generation in each adaptive step. Computations of informative examples with convergence studies, and comparisons with published experimental results are presented using 3D finite elements. Shape memory alloys: phenomenology, physical effects, and applicationsShape memory alloys (SMAs) have immense technological potential because of various aspects of their special thermomechanical behavior, such as shape memory effect (SME) in form of reversible quasiplastic (QP) deformation, superelasticity (SE), and bio-compatibility. Nowadays, it is widely used for biomedical systems e.g. endovascular stents, orthodontic arc wires; for controlling and activating mechanical systems such as actuators and connectors and also for structural systems e.g. vibration control devices.SMAs exhibit a strong nonlinear thermomechanical behavior associated with abrupt changes in their lattice structure called martensitic phase transformation (PT). They have intrinsic ability to transform between austenite (parent phase) and a number of symmetry-related martensitic variants (product phases). Those SMAs considered here are copper based alloy CuAlNi and nickel based alloy NiTi, which both can behave as QP and SE depending on the operating temperature.Martensitic PT is considered as a diffusionless first-order transformation between 'high' temperature, θ > A s , austenite and 'low' temperature martensitic phases, θ < M s , Fig. 1. A s and M s are the so-called austenite and martensite start temperatures. Other critical temperatures are austenite and martensite finish temperatures which are denoted by A f and M f , respectively. SMAs exhibit a specific feature...

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Ginzburg-Landau theory of static domain walls in shape-memory alloys

Cited by 193 publications

References 9 publications

Depletion Layers and Domain Walls in Semiconducting Ferroelectric Thin Films

Depletion Layers and Domain Walls in Semiconducting Ferroelectric Thin Films

A mesoscopic model of a two-dimensional solid state structural transformation: statics and dynamics

Contributions on the theory and computation of mono‐ and poly‐crystalline cyclic martensitic phase transformations

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