Elastic Properties of Nanowires - an Atomistic Evaluation

Abstract: Nanowires constitute one of the fundamental building blocks in assembled nanodevices. Due to the high surface to volume ratio, the fraction of surface atoms is not negligible for nanosized elements. Because of the reduced coordination of surface atoms, the physical properties deviate from those of the bulk, which influences the overall physical properties of nanostructures. Consequently, this provides the structure with physical properties that may deviate significantly from the bulk and it may therefore be inappropriate to employ macroscopic continuum mechanical concepts at this scale, as it could lead to inaccurate predictions of the response. The major purpose of this thesis is to study how well the behavior of metallic nanowires can be predicted by elementary macroscopic continuum mechanics. This includes to investigate at what sizes of the cross sectional dimensions and in what way macroscopic continuum mechanical models fail to describe the mechanical response accurately. The presented work is of a theoretical nature, related to experiments reported in the literature, and the mechanical properties and responses are modeled through classical molecular dynamics and molecular statics simulations with empirical potentials to describe the interatomic interactions. The thesis begins with a short introduction and discussion of the main topics and numerical methods addressed and used in the appended papers, followed by a brief summary and discussion of the obtained results. The bulk of the thesis consists of four appended papers, A-D. In these, different atomistic simulations are employed to study the elastic properties of single crystal metallic nanowires subjected to different types of loading and dynamic excitation: tensile loading (Papers A and B), transverse loading (Paper A), transverse free vibrations (Papers B and C), and compressive loading leading to buckling (Paper D). The simulations show that the stiffness varies with size and that Young's modulus may increase or decrease with decreasing size, depending on how the crystal is oriented. The behavior is a consequence of what kind of crystallographic surfaces that are present at the bounding surfaces and the non-linear character of the bulk. Consequently, the flexural rigidity can be either higher or lower than what is estimated using macroscopic material properties, depending on the crystallographic orientation and the surface elastic properties. Moreover, it is shown that the surface influence on the flexural rigidity increases as the cross sectional dimensions decrease. This implies that the inhomogeneous elastic character of the cross section may have to be explicitly taken into account when predicting the flexural rigidity accurately for nanowires of small cross sections. This influence has been found to be particularly important when considering static bending and buckling, and it manifests itself in a lowering of the flexural rigidity, leading to a lowering of critical strain and an increase in deflection. Aside from these features, it is shown that the nanowires deform quite similar to what is expected from elementary beam theory. Moreover, it is found that the elastic behavior converges towards that expected from a bulk structure as the cross sectional dimensions increase.