Sharif Digital Repository

In this work a new method for analyzing nanostructured materials has been proposed to accelerate the simulations for solid crystalline materials. The proposed Structural Approximation Method (SAM) is based on Molecular Dynamics (MD) and the accuracy of the results can also be improved in a systematic manner by sacrificing the simulation speed. In this method a virtual material is used instead of the real one, which has less number of atoms and therefore fewer degrees of freedom, compared to the real material. The number of differential equations that must be integrated in order to specify the state of the system will decrease significantly, and the simulation speed increases. To generalize... 

One of the most popular constitutive rules that correlate the continuum and atomic properties in multi-scale models is the Cauchy-Born (CB) hypothesis. Based on this constitutive law of continuum media, it assumes that all atoms follow the deformation subjected to the boundary of crystal. In this paper, the validity and failure of CB hypothesis are investigated for the silicon nano-structure by comparison of the continuum and atomic properties. In the atomistic level, the stresses and position of atoms are calculated using the molecular dynamics (MD) simulation based on the Tersoff inter-atomic potential. The stresses and strains are compared between the atomistic and continuous media to... 

Dynamic and static fracture properties of Graphene Sheets (GSs) and Carbon nanotubes (CNTs) with different sizes are investigated based on an empirical inter-atomic potential function that can simulate nonlinear large deflections of nanostructures. Dynamic fracture of GSs and CNTs are studied based on wave propagation analysis in these nanostructures in a wide range of strain-rates. It is shown that wave propagation velocity is independent from strain-rate while dependent on the nanostructure size and approaches to 2.2×10 4m/s for long GSs. Also, fracture strain shows extensive changes versus strain-rate, which has not been reported before. Fracture stress is determined as 115GPa for GSs and... 

In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework, sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fee metals are given in terms of the parameters of Sutton-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a... 

In this paper, a novel temperature-dependent multi-scale method is developed to investigate the role of temperature on surface effects in the analysis of nano-scale materials. In order to evaluate the temperature effect in the micro-scale (atomic) level, the temperature related Cauchy-Born hypothesis is implemented by employing the Helmholtz free energy, as the energy density of equivalent continua relating to the inter-atomic potential. The multi-scale technique is applied in atomistic level (nano-scale) to exhibit the temperature related characteristics. The first Piola-Kirchhoff stress and tangential stiffness tensor are computed, as the first and second derivatives of the free energy... 

In this paper, the scattering of anti-plane shear waves in an infinite matrix containing a multi-coated nanofiber/nanotube is studied. Based on the fact that the surface to volume ratio for nano-size objects increases, the usual classical theories which generally neglect the surface/interface effects fail to provide reasonable results. Therefore, to analyze the problem the wave-function expansion method is coupled with the surface/interface elasticity theory. In order to provide some quantitative results through consideration of several examples, the knowledge of the relevant surface and/or interface properties of the corresponding constituent materials are required. For this reason, part of... 

In this paper, a novel multi-scale approach is developed for modeling of the surface effect in crystalline nano-structures. The technique is based on the Cauchy-Born hypothesis in which the strain energy density of the equivalent continua is calculated by means of inter-atomic potentials. The notion of introducing the surface effect in the finite element method is based on the intrinsic function of quadratures, called as an indicator of material behavior. The information of quadratures is derived by interpolating the data from probable representative atoms in their proximity. The technique is implemented by the definition of reference boundary CB elements, which enable to capture not only... 

The effect of surface and interface elasticity in the analysis of the Saint-Venant torsion problem of an eccentrically two-phase fcc circular nanorod is considered; description of the behavior of such a small structure via usual classical theories cease to hold. In this work, the problem is formulated in the context of the surface/interface elasticity. For a rigorous solution of the proposed problem, conformal mapping with a Laurent series expansion are employed together. The numerical results well illustrate that the torsional rigidity and stress distribution corresponding to such nanosized structural elements are significantly affected by the size. In order to employ surface and interface... 

In this paper, a multi-scale molecular dynamics-finite element coupling is presented to study the mechanical behavior of heterogeneous nano-crystalline structures. The stiffness and mass matrices of the continuum sub-domain are generated by applying a linear transformation on the matrices obtained via the atomic structure underlying the FE mesh. A Lagrange multiplier method is employed to the transition zone imposing velocity resemblance of the coupling regions. The constraint equations of motion are solved by the multi-time-step decomposition thus giving the opportunity to ascribe different time steps to each individual zone. The molecular dynamics is performed by employing the... 

Based on the fact that the manipulation of fine nanoclusters calls for more precise modelling, the aim of this paper is to conduct an atomistic investigation for interaction analysis of particle-substrate system for pushing and positioning purposes. In the present research, 2D molecular dynamics simulations have been used to investigate such behaviours. Performing the planar simulations can provide a fairly acceptable qualitative tool for our purpose while the computation time is reduced extremely in comparison to 3D simulations. To perform this study, Nose-Hoover dynamics and Sutton-Chen interatomic potential will be used to investigate the behaviour of the aforementioned system. Pushing of... 

This paper is devoted to the characterization of the surface defects using a recently developed AFM technique named as frequency and force modulation AFM (FFM-AFM). The simulated system includes a recently developed gold coated AFM probe which interacts with a sample including single-atom vacancy and impurities. In order to examine the behavior of the above system including different transition metals, molecular dynamics (MD) simulation with Sutton-Chen (SC) interatomic potential is used. Along this line, an imaging simulation of the probe and sample is performed, and the effects of the horizontal scan speed, the effective frequency set-point, the cantilever stiffness, the tip-sample rest... 

The usual continuum theories are inadequate in predicting the mechanical behavior of solids in the presence of small defects and stress concentrators; it is well known that such continuum methods are unable to detect the change of the size of the inhomogeneities and defects. For these reasons various augmented continuum theories and strain gradient theories have been proposed in the literature. The major difficulty in implication of these theories lies in the lack of information about the additional material constants which appear in such theories. For fcc metals, for the calculation of the associated characteristic lengths which arise in first strain gradient theory, an atomistic approach... 

This paper is devoted to the characterization of the surface defects using a recently developed AFM technique called frequency and force modulation AFM (FFM-AFM). The simulated system includes a recently developed gold coated AFM probe which interacts with a sample including single-atom vacancy and impurities. In order to examine the behavior of the above system on different transition metals, the molecular dynamics (MD) simulation with Sutton-Chen (SC) inter-atomic potential is used. In this study, an online imaging simulation of the probe and sample is performed, and the effects of the horizontal scan speed, the effective frequency set-point, the cantilever stiffness, the tip-sample rest... 

Recent experiments have shown the applicability of single-layer graphene sheets (SLGSs) as electromechanical resonators. Existing theoretical models, based on linear continuum or atomistic methods, are limited to the study of linear vibrations of SLGSs. Here we introduce a hybrid atomistic-structural element which is capable of modelling nonlinear behaviour of graphene sheets. This hybrid element is based on an empirical inter-atomic potential function and can model the nonlinear dynamic response of SLGSs. Using this element, nonlinear vibrational analysis of SLGSs is performed. It is shown that the nonlinear vibrational analysis of SLGSs predicts significantly higher fundamental... 

In this work a new method for analyzing nanostructured materials has been proposed to accelerate the simulations for solid crystalline materials. The proposed Structural Approximation Method (SAM) is based on Molecular Dynamics (MD) and the accuracy of the results can also be improved in a systematic manner by sacrificing the simulation speed. In this method a virtual material is used instead of the real one, which has less number of atoms and therefore fewer degrees of freedom, compared to the real material. The number of differential equations that must be integrated in order to specify the state of the system will decrease significantly, and the simulation speed increases. To generalize... 

In the present work, characterization of the surface trenches and vacancies with Amplitude Modulation AFM (AM-AFM) using Molecular Dynamics (MD) is simulated and the effects of the tip shape on the resulting images are investigated. The simulated system includes a recently developed gold coated AFM probe which interacts with a sample including a surface trench or a single-atom vacancy. In order to examine the behavior of the above system, including different transition metals, a Molecular Dynamics (MD) simulation with Sutton-Chen (SC) interatomic potential is used. Special attention is dedicated to the study of tip geometry effects such as the tip apex radius, the tip cone angle, the probe... 

Precise positioning of nanoclusters through manipulation in the presence of other clusters is one of the main challenging tasks in nanoclusters assembly. Currently, the size of clusters which are used as building blocks is decreasing to a few nanometers. As a result, the particle nature of the matter has a crucial role in manipulator/cluster/substrate interactions. In order to understand and predict the behavior of nanoclusters during the positioning process, it is, therefore, essential to have a deep insight into the aforementioned nanoscale interactions, in this research, 2-D molecular dynamics simulations are used to investigate such behaviors. Performing the planar simulations can... 

Due to the growing applications of silicon in nano-scale systems, a molecular dynamics approach is employed to investigate thermal properties of silicon. Since simulation results rely upon interatomic potentials, thermal expansion coefficient (TEC) and lattice constant of bulk silicon have been obtained using different potentials (SW, Tersoff, MEAM, and EDIP) and results indicate that SW has a better agreement with the experimental observations. To investigate effect of size on TEC of silicon nanowires, further simulations are performed using SW potential. To this end, silicon nanowires of different sizes are examined and their TEC is calculated by averaging in different directions ([100],... 

The molecular-dynamics analysis is presented for 3D compaction simulation of nano-crystalline metals under uniaxial compaction process. The nano-crystalline metals consist of nickel and aluminum nano-particles, which are mixed with specified proportions. The EAM pair-potential is employed to model the formation of nano-particles at different temperatures, number of nano-particles, and mixing ratio of Ni and Al nano-particles to form the component into the shape of a die. The die-walls are modeled using the Lennard-Jones inter-atomic potential between the atoms of nano-particles and die-walls. The forming process is model in uniaxial compression, which is simulated until the full-dense... 

Using seven bond-order potentials and five force fields, the fundamental natural frequency of C60,Ag(1) (breathing mode), and two other basic modes, namely Hg(1) (squashing mode) and T2g(1) are calculated. The same frequencies are derived through a DFT B3LYP/6-31G(d) calculation. Furthermore, the results are compared with Raman and IR scattering data, and previous quantum mechanics calculations, depicting the strength of each interatomic potential in predicting the vibrational properties of Buckminsterfullerene. AIREBO, which is formulated for analyzing hydrocarbons, shows the highest accuracy among all of the potentials under investigation. In general, bond-order potentials predict a...