arXiv subjects

Arash Yavari

Publications and source records attributed to Arash Yavari.

44 records · Page 3Linked to original sources

arXiv2010

Atomic Structure of Steps on 180^o Ferroelectric Domain Walls in PbTiO_3

Using the method of anharmonic lattice statics, we calculate the equilibrium structure of steps on 180^o ferroelectric domain walls (DW) in PbTiO_3. We consider three different types of steps: i) Ti-Ti step that joins a Ti-centered DW to a Ti-centered DW, (ii) Pb-Pb step that joins a Pb-centered DW to a Pb-centered DW, and (iii) Pb-Ti step that joins a Pb-centered DW to a Ti-centered DW. We show that atomic distortions due to these steps broaden a DW but are localized, i.e., they are confined to regions with dimensions of a few lattice spacings. We see that a step locally thickens the domain wall; the defective domain wall is two to three times thicker than the perfect domain wall depending on the step type. We also observe that steps distort the polarization distribution in a mixed Bloch-Néel like way; polarization rotates out of the domain wall plane near the steps. Our calculations show that Pb-Pb steps have the lowest static energy.

cond-mat.mtrl-sci↗

arXiv2010

Estimating Terminal Velocity of Rough Cracks in the Framework of Discrete Fractal Fracture Mechanics

In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal roughness. We then study the phenomenon of reaching a terminal velocity. Assuming that propagation of a fractal crack is discrete, we predict its terminal velocity using an asymptotic energy balance argument. In particular, we show that the limiting crack speed is a material-dependent fraction of the corresponding Rayleigh wave speed.

cond-mat.mtrl-sci↗

arXiv2010

Structure of Defective Crystals at Finite Temperatures: A Quasi-Harmonic Lattice Dynamics Approach

In this paper we extend the classical method of lattice dynamics to defective crystals with partial symmetries. We start by a nominal defect configuration and first relax it statically. Having the static equilibrium configuration, we use a quasiharmonic lattice dynamics approach to approximate the free energy. Finally, the defect structure at a finite temperature is obtained by minimizing the approximate Helmholtz free energy. For higher temperatures we take the relaxed configuration at a lower temperature as the reference configuration. This method can be used to semi-analytically study the structure of defects at low but non-zero temperatures, where molecular dynamics cannot be used. As an example, we obtain the finite temperature structure of two 180^o domain walls in a 2-D lattice of interacting dipoles. We dynamically relax both the position and polarization vectors. In particular, we show that increasing temperature the domain wall thicknesses increase.

cond-mat.mtrl-sci↗

arXiv2010

Finite-Temperature Atomic Structure of 180^o Ferroelectric Domain Walls in PbTiO3

In this letter we obtain the finite-temperature structure of 180^o domain walls in PbTiO3 using a quasi-harmonic lattice dynamics approach. We obtain the temperature dependence of the atomic structure of domain walls from 0K up to room temperature. We also show that both Pb-centered and Ti-centered 180^o domain walls are thicker at room temperature; domain wall thickness at T=300K is about three times larger than that of T=0K. Our calculations show that Ti-centered domain walls have a lower free energy than Pb-centered domain walls and hence are more likely to be seen at finite temperatures.

cond-mat.mtrl-sci↗

arXiv2010

Effect of strain and oxygen vacancies on the structure of 180^o ferroelectric domain walls in PbTiO_3

In this paper we study the effect of normal and shear strains and oxygen vacancies on the structure of 180^o ferroelectric domain walls in PbTiO_3. It is known that oxygen vacancies move to the domain walls and pin them. Hence, we assume a periodic arrangement of oxygen vacancies on both Pb-centered and Ti-centered domain walls in PbTiO_3. We use a semi-analytic anharmonic lattice statics method for obtaining the relaxed configurations using a shell potential. In agreement with recent ab initio calculations, we observe that a Pb-centered domain wall with oxygen vacancies is not stable even under strain. Our semi-analytic calculations for PbTiO_3 show that oxygen vacancies affect the structure of 180^o domain walls significantly but do not have a considerable effect on the thickness of domain walls; they broaden the domain walls by about fifty percent. We also study the effect of normal and shear strains on both perfect and defective 180^o domain walls. We observe that normal and shear strains affect the structure but do not change the domain wall thickness.

cond-mat.mtrl-sci↗

arXiv2009

A Geometric Theory of Thermal Stresses

In this paper we formulate a geometric theory of thermal stresses. Given a temperature distribution, we associate a Riemannian material manifold to the body, with a metric that explicitly depends on the temperature distribution. A change of temperature corresponds to a change of the material metric. In this sense, a temperature change is a concrete example of the so-called referential evolutions. We also make a concrete connection between our geometric point of view and the multiplicative decomposition of deformation gradient into thermal and elastic parts. We study the stress-free temperature distributions of the finite-deformation theory using curvature tensor of the material manifold. We find the zero-stress temperature distributions in nonlinear elasticity. Given an equilibrium configuration, we show that a change of the material manifold, i.e. a change of the material metric will change the equilibrium configuration. In the case of a temperature change, this means that given an equilibrium configuration for a given temperature distribution, a change of temperature will change the equilibrium configuration. We obtain the explicit form of the governing partial differential equations for this equilibrium change. We also show that geometric linearization of the present nonlinear theory leads to governing equations that are identical to those of the classical linear theory of thermal stresses.

math-ph↗

arXiv2009

A Geometric Theory of Growth Mechanics

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show that time dependency of material metric will affect the energy balance and the entropy production inequality; both the energy balance and the entropy production inequality have to be modified. We then obtain the governing equations covariantly by postulating invariance of energy balance under time-dependent spatial diffeomorphisms. We use the principle of maximum entropy production in deriving an evolution equation for the material metric. In the case of isotropic growth, we find those growth distributions that do not result in residual stresses. We then look at Lagrangian field theory of growing elastic solids. We will use the Lagrange-d'Alembert's principle with Rayleigh's dissipation functions to derive all the governing equations. We make an explicit connection between our geometric theory and the conventional multiplicative decomposition of deformation gradient $\mathbf{F}=\mathbf{F}_e\mathbf{F}_g$ into growth and elastic parts. We linearize the nonlinear theory and derive a linearized theory of growth mechanics. Finally, we obtain the stress-free growth distributions in the linearized theory.

math.DG↗

arXiv2008

Covariant Balance Laws in Continua with Microstructure

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas.

math.DG↗