Sharif Digital Repository

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... 

The surface, edge and corner effects have significant influences in the electrical and optical properties of silicon nano-structures. In this paper, a novel hierarchical temperature-related multi-scale model is presented based on the boundary Cauchy-Born method to investigate not only the surface but also the edge and corner effects in thermal properties of diamond-like structures such as silicon nano-structures at finite temperature. A combined finite element method and molecular dynamics are respectively employed in macro- and micro-scale levels. The temperature-related Cauchy-Born rule is applied using the Helmholtz free energy, as the energy density of equivalent continua relating to the... 

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... 

Using Tersoff bond order potential, a vibrational analysis of the spherical fullerene family, namely C60, C80, C180, C240, C260, C320, C500, and C720 was performed. To evaluate the validity of our results, we have compared our simulation results with available experimental data and also with DFT B3LYP/6-31G(d) calculations. In general, molecular stiffness tends to decrease with increasing size, but its variation is limited in cases where mostly the tension-compression interaction sites are active such as the breathing mode. Furthermore, the bond length of each molecule is derived and compared with experimental and theoretical values calculated for graphene. Finally, vibrational frequencies... 

The main concern in Molecular Dynamics (MD) simulations is the computational cost, and coarse-graining methods accelerate simulations by reducing the degrees of freedom in the system. Yet, the utilization of these methods should be carefully followed. In this paper, we presented an energy-based coarse-graining method for Tersoff and Stillinger-Weber potential functions. The presented coarse-graining method is based on the domain mapping and modification of potential function. The focus of this paper is on Carbon and Silicon materials; however, this method can be applied to model other materials for which Tersoff and Stillinger-Weber potentials are defined. This method has been validated by...