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Boron nitride (BN) is a structurally versatile insulator since it can be found in several crystalline structures with interesting mechanical and electrical properties, making this material attractive for technological applications. Seeking to improve its features, experimental and simulational studies for the amorphous phase (a-BN) have been carried out by some groups, focusing on the electrical and structural properties, pressure-induced phase transformations, and hydrogenated a-BN. In this work two amorphous structures are computationally generated and studied using ab initio Molecular Dynamics on a 216-atom supercell with two different densities, 2.04 and 2.80 g cm$^{-3}$. Our undermelt-quench approach is followed, since it has proven to give good structures for disordered materials and their properties. The topology, the vibrational density of states and some thermodynamic properties of the two samples are reported and compared with existing experiment. Some computational results are also revisited.