Stability and Structural Transitions in Crystal Lattices (original) (raw)

Modeling of strains and stresses of material nanostructures

Bulletin of the Polish Academy of Sciences: Technical Sciences, 2009

Modeling of strains and stresses of material nanostructuresStress and deformation analysis of materials and devices at the nanoscale level are topics of intense research in materials science and mechanics. In these investigations two approaches are observed. First, natural for the atomistic scale description is based on quantum and molecular mechanics. Second, characteristic for the macroscale continuum model description, is modified by constitutive laws taking atomic interactions into account. In the present paper both approaches are presented. For a discrete system of material points (atoms, molecules, clusters), measures of strain and stress, important from the mechanical viewpoint, are given. Numerical examples of crack propagation and deformation of graphite sheets (graphens) illustrate the behavior of the discrete systems.

Atomistic mechanisms governing elastic limit and incipient plasticity in crystals

Nature, 2002

Nanometre-scale contact experiments 1-6 and simulations 7-10 demonstrate the potential to probe incipient plasticity-the onset of permanent deformation-in crystals. Such studies also point to the need for an understanding of the mechanisms governing defect nucleation in a broad range of fields and applications. Here we present a fundamental framework for describing incipient plasticity that combines results of atomistic and finite-element modelling, theoretical concepts of structural stability at finite strain, and experimental analysis. We quantify two key features of the nucleation and subsequent evolution of defects. A position-sensitive criterion based on elastic stability determines the location and character of homogeneously nucleated defects. We validate this stability criterion at both the atomistic and the continuum levels. We then propose a detailed interpretation of the experimentally observed sequence of displacement bursts to elucidate the role of secondary defect sources operating locally at stress levels considerably smaller than the ideal strength required for homogeneous nucleation. These findings provide a self-consistent explanation of the discontinuous elastic-plastic response in nanoindentation measurements, and a guide to fundamental studies across many disciplines that seek to quantify and predict the initiation and early stages of plasticity.

Mechanical Behavior of Nano Structures Using Atomic-Scale Finite Element Method (AFEM)

Latin American Journal of Solids and Structures

This work presents a detailed description of the formulation and implementation of the Atomistic Finite Element Method AFEM, exemplified in the analysis of one-and two-dimensional atomic domains governed by the Lennard Jones interatomic potential. The methodology to synthesize element stiffness matrices and load vectors, the potential energy modification of the atomistic finite elements (AFE) to account for boundary edge effects, the inclusion of boundary conditions is carefully described. The conceptual relation between the cutoff radius of interatomic potentials and the number of nodes in the AFE is addressed and exemplified for the 1D case. For the 1D case elements with 3, 5 and 7 nodes were addressed. The AFEM has been used to describe the mechanical behavior of one-dimensional atomic arrays as well as twodimensional lattices of atoms. The examples also included the analysis of pristine domains, as well as domains with missing atoms, defects, or vacancies. Results are compared with classical molecular dynamic simulations (MD) performed using a commercial package. The results have been very encouraging in terms of accuracy and in the computational effort necessary to execute both methodologies, AFEM and MD. The methodology can be expanded to model any domain described by an interatomic energy potential.

Lattice model describing scale effects in nonlinear elasticity of nanoinhomogeneities

Physical Review B, 2010

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 nano-inhomogeneity. We prove that its elastic behavior at the nanoscale is governed by relevant atomistic effects. In particular, we demonstrate that such effects on the linear and nonlinear elastic properties are described by the same scaling exponent, in a large range of elastic contrast between the matrix and the nano-inhomogeneity. This suggests that the linear and nonlinear elastic behaviors of the composite system belong to the same universality class (at least within the nanometer length scale here investigated).

Calculation of Elastic Bond Constants in Atomistic Strain Analysis

Nanoscale research letters, 2015

Strain analysis has significance both for tailoring material properties and designing nanoscale devices. In particular, strain plays a vital role in engineering the growth thermodynamics and kinetics and is applicable for designing optoelectronic devices. In this paper, we present a methodology for establishing the relationship between elastic bond constants and measurable parameters, i.e., Poisson's ratio ν and systematic elastic constant K. At the atomistic level, this approach is within the framework of linear elastic theory and encompasses the neighbor interactions when an atom is introduced to stress. Departing from the force equilibrium equations, the relationships between ν, K, and spring constants are successfully established. Both the two-dimensional (2D) square lattice and common three-dimensional (3D) structures are taken into account in the procedure for facilitating, bridging the gap between structural complexity and numerical experiments. A new direction for unders...

Nonlinear theoretical formulation of elastic stability criterion of crystal solids

Physical Review B, 2012

Elastic stability criterion is generally formulated based on local elasticity where the second order elastic constants of a crystalline system in an arbitrary deformed state are required. While simple in formalism, such formulation demands extensive computational effort in either ab initio calculation or atomistic simulation, and often lacks clear physical interpretation. Here we present a nonlinear theoretical formulation employing higher order elastic constants beyond the second-order ones; the elastic constants needed in the theory are those at zero stress state, or in any arbitrary deformed state, many of which are now available. We use the published second and higher order elastic constants of several cubic crystals including Au, Al, Cu, as well as diamondstructure Si, with transcription under different coordinate frames, to test the stability conditions of these crystals under uniaxial and hydrostatic loading. The stability region, ideal strength, and potential bifurcation mode of those cubic crystals under loading are obtained using this theory. The results obtained are in very good agreement with the results from ab initio calculation or embedded atom method. The overall good quality of the results confirms the desired utility of this new approach to predict elastic stability and related properties of crystalline materials without involving intense computation.

Atomistic studies of strain relaxation in heteroepitaxial systems

Journal of Physics: Condensed Matter, 2009

We present a review of recent theoretical studies of different atomistic mechanisms of strain relaxation in heteroepitaxial systems. We explore these systems in two and three dimensions using different semi-empirical interatomic potentials of Lennard-Jones and many-body embedded atom model type. In all cases we use a universal molecular static method for generating minimum energy paths for transitions from the coherent epitaxial (defect free) state to the state containing an isolated defect (localized or extended). This is followed by a systematic search for the minimum energy configuration as well as self-organization in the case of a periodic array of islands. In this way we are able to understand many general features of the atomic mechanisms and energetics of strain relaxation in these systems. Finally, for the special case of Pd/Cu(100) and Cu/Pd(100) heteroepitaxy we also use conventional molecular dynamics simulation techniques to compare the compressively and tensilely strained cases. The results for this case are in good agreement with the existing experimental data.