Related papers: Atomic scale lattice distortions and domain wall p…
We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at all…
Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived…
We present a procedure to map the constitutive laws of elasticity (both in the linear and nonlinear regime) onto a discrete atomic lattice and we apply the resulting elastic lattice model to investigate the strain field within an embedded…
In this paper we propose a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The two lattices have slightly different lattice parameters and there is a small…
Interest in the elastic properties of regular lattices constructed from domain walls has recently been motivated by cosmological applications as solid dark energy. This work investigates the particularly simple examples of triangular,…
We present classical and quantum mechanical descriptions of lattice dynamics, from the atomic to the continuum scale, using atomic scale symmetry modes and their constraint equations. This approach is demonstrated for a one-dimensional…
We present a phenomenological time-dependent Ginzburg-Landau theory of nonlinear plastic deformations in solids. Because the problem is very complex, we first give models in one and two dimensions without vacancies and interstitials, where…
We examine the atomistic scale dependence of material's resistance-to-failure by numerical simulations and analytical analysis in electrical analogs of brittle crystals. We show that fracture toughness depends on the lattice geometry in a…
New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…
In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a…
We discuss a series of 8 energy scales, some of which just speculated by ourselves, and fit the logarithms of these energies as a straight line versus a quantity related to the dimensionalities of action terms in a way to be defined in the…
Domain walls of a discrete model of an anisotropic ferromagnet are studied. They can be described by sequences of two reversible mappings. Competition between the length scale of spatial structures and the lattice constant leads to a rich…
Material properties depend sensitively on picometer scale atomic displacements introduced by local chemical fluctuations. Direct real-space, high spatial-resolution measurements of this compositional variation and corresponding distortion…
We developed a lattice dynamical theory of an atomically-thin compressional piezoelectric resonator. Acoustic and optical dynamic displacement response functions are derived and account for frequency-dependent electromechanical coupling.…
Viscoelasticity has been described since the time of Maxwell as an interpolation of purely viscous and purely elastic response, but its microscopic atomic-level mechanism in solids has remained elusive. We studied three model disordered…
We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $\xi_E$, so that the…
We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to…
We propose a scheme leading to a non-perturbative definition of lattice field theories which are scale-invariant on the quantum level. A key idea of the construction is the replacement of the lattice spacing by a propagating dynamical field…
Using a symmetry-based atomic scale theory of lattice distortions, we demonstrate that elastic textures, such as twin and antiphase boundaries, can generate intricate electronic inhomogeneities in materials with strong electron-lattice…
We study the anomalous elasticity of nematic elastomers by employing the powers of renormalized field theory. Using general arguments of symmetry and relevance, we introduce a minimal Landau-Ginzburg-Wilson elastic energy for nematic…