Sharif Digital Repository

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, 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... 

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... 

Classical continuum mechanics fails to give accurate solution near the crack tip, moreover, it implies that a solid is able to sustain an infinite stress at the Griffith-Inglis crack tips. Among other critical issues is the inability of the classical approach to sense the size effect. For these reasons, for more in-depth understandings and accurate behavioral predictions, it is essential to develop some atomistic methods which properly accounts, not only for the structure but also the long and short range atomic interactions effectively. In this work the interaction of inhomogeneity and crack under polynomial loading is simulated by using the many body Rafii-Tabar and Sutton potential... 

Often, during fabrication of thin films on substrates, different types of defects may be introduced into the films. Recently, the determination of the elastic fields due to the self-assembly of quantum dots or strained islands in thin films has been of major concern. In the micromechanical studies, such strained islands are modeled by inclusions. This paper aims to develop a theory pertaining to the presence of nano-inclusions of various geometries within thin films having face centered cubic (fcc) structure. To this end, the notion of eigenstrain is combined with a many body inter-atomic potential suitable for fcc crystals. The interaction between atoms is modeled via Sutton-Chen (SC)... 

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 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... 

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... 

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... 

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... 

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... 

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... 

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],... 

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... 

Mechanical properties of materials are an important factor in designing nanoscale systems. Several researches and experiments have shown that the mechanical properties of the nano-scale materials are different from those of bulk. One of the major reasons for this difference is that the ratio of surface to volume increases at the nano-scale, and the effects of free surfaces become very important. In this paper, we have measured the surface elastic constants of silicon crystalline structure using different interatomic potentials. The potentials employed here are EDIP (Environment-Dependent Interatomic Potential), Stillinger-Weber and Tersoff, and also different crystalline orientations are... 

Three independent elastic constants C 11, C 12, and C 44 were calculated and compared using available potentials of eight different metals with FCC crystal structure; Gold, Silver, Copper, Nickel, Platinum, Palladium, Aluminum and Lead. In order to calculate the elastic constants, the second derivative of the energy density of each system was calculated with respect to different directions of strains. Each set of the elastic constants of the metals in bulk scale was compared with experimental results, and the average relative error was for each was calculated and compared with other available potentials. Then, using the Voigt-Reuss-Hill method, approximated values for Young and shear moduli... 

In this research, we have modeled nano-Beams using molecular dynamics. The scope of our study is FCC metals, therefore an appropriate inter-atomic potential for this kind of materials must be chosen. A multi-body long-range potential proposed by Sutton-Chen, which has been used in many physical investigations of FCC metals is applied in our study. Using conducted simulations, the different mechanical properties of material such as elastic modulus, shear modulus and poison's ratio are calculated. The results show that the elastic properties decrease with increase in nano cantilever size. ©2008 IEEE  

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 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...