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Molecular dynamics results showing continuum theory failure in describing the elastic behavior of nanoparticles embedded in Si-based systems

Pier Luca Palla ,  Stefano Giordano ,  Luciano Colombo 

CNR-INFM SLACS and Dept of Physics, University of Cagliari, Cittadella Universitaria di Monserrato, Dept of Physics, University of Cagliari, Cagliari I-09042, Italy

Abstract

In recent technological developments Si-based nanostructures have been widely investigated and utilized in many advanced applications, i.e. in optoelectronics, photonics and nanomechanics: typically, crystalline nanograins are dispersed into a silicon matrix in order to obtain desired physical properties such as the optical response, the quantum efficiency and the effective elastic moduli of different systems. The typical sizes of such nanostructures can range from the microscale to the nanoscale, generating several difficulties in the applications of the standard continuum approach to analyze the physical system response. From the mechanical point of view, the classical Eshelby theory describing the behavior of an inhomogeneity embedded in a matrix, does not take into consideration the actual size of the system at all, being this continuum approach a scale-free theory. Therefore, the atomistic structure of the medium is not considered and the results of the elasticity theory are meaningful only for geometrical structures ranging from the mesoscale to the macroscale. When the size of the embedded particles is comparable with the inter-atomic distance of the crystal lattice such results lose their validity and the atomistic simulation can be used to investigate the response at the nanoscale. In the present work we draw a comparison among the continuum theory and molecular dynamics results for Si-based composite systems formed by crystalline (or amorphous) inclusions embedded in a crystalline (or amorphous) bulk matrix. We performed a large campaign of simulations with decreasing radius (starting from a quite macroscopic one) of the cylindrical (or spherical) inhomogeneity. In particular, we observed a characteristic size of the embedded inhomogeneity, which represents the threshold of applicability of the Eshelby theory predictions.  Moreover, we obtained the behavior of the elastic fields under such a scale threshold, for different properties of the involved phases.

 

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Related papers

Presentation: Oral at E-MRS Fall Meeting 2008, Symposium K, by Pier Luca Palla
See On-line Journal of E-MRS Fall Meeting 2008

Submitted: 2008-06-16 17:36
Revised:   2009-06-07 00:48