Effect of Grain Boundaries on the Vibrational Properties of Phononic Crystals
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Effect of Grain Boundaries on the Vibrational Properties of Phononic Crystals Ralf Meyer1 1 Department of Mathematics and Computer Science and Department of Physics, Laurentian University, 935 Ramsey Lake Road, Sudbury, ON P3E 2C6, Canada ABSTRACT The influence of grain boundaries on the vibrational properties of nanoscale phononic crystals is studied with the help of molecular dynamics simulations. The low-frequency vibrational density of states of phononic crystals made from single crystal and polycrystalline silicon are derived from the simulations. The results show that the presence of grain boundaries leads to an increase of the density of states and a change of its peak structure at low frequencies. Calculations of the band structure of the model systems along one direction reveal that the grain boundaries affect the bands differently and in a non-uniform manner. INTRODUCTION Phononic crystals are artificially created materials that promise to be useful in numerous applications. Phononic crystals are characterized by periodic variations of their elastic properties, which make it possible to control the propagation of elastic waves in the material. Phononic crystals can be designed to have vibrational band gaps, i.e. forbidden frequency ranges in which vibrational waves cannot travel through the material. An overview of the physics of phononic crystals can be found in references [1-3]. It has been shown theoretically [4] and experimentally [5,6] that phononic crystals with periodicity length on the nanometer scale can have reduced thermal conductivities. This makes them candidates for thermoelectric materials with high figures of merit ZT and has raised interest in the properties of thermal phonons in phononic crystals. In this study, the vibrational properties of nanoscale silicon phononic crystals are calculated from molecular dynamics simulations. The effect of grain boundaries on the vibrational spectrum is studied by comparing the properties of phononic crystals with and without grain boundaries. Results are shown for the low frequency vibrational density of states as well as the band structure along one direction in k-space. COMPUTATIONAL DETAILS Two similar model configurations have been used for the molecular dynamics simulations in this work. Both configurations consist of 72 silicon nanoparticles with a diameter of 9 nm that are placed on the sites of a honeycomb lattice with a nearest-neighbor distance of 16.7 nm. The nanoparticles are connected through silicon nanowires with a diameter of 6 nm. One of the two model configurations was cut out of a block of single crystal silicon and contains no grain boundaries. The other configuration was built from nanoparticles and nanowires with different crystalline orientations. This configuration is polycrystalline with grain boundaries at the junctions between particles and wires. Figure 1 shows the polycrystalline configuration as an example for the model systems simulated in this work.
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