| First principles calculations on the structural, vibrational and dielectric properties for β-Si3N4 and BN, using pseudopotential plane wave method, have been conducted. This will be conducive to not only the establishment of the quantitive relationship between microstructure and dielectric property of the materials , but also offering the guide line for the design of the new transmissive materials with low dielectric constant among the materials system of Si-B-O-N. Firstly, the structures have been fully relaxed through first principles molecular dynamical method. Then the zone-center phonon-mode frequencies are evaluated within the framework of density functional perturbation theory(DFPT). Group theory is adopted to identify these phonon modes at the center of Brillouin zone and the LO/TO(longitudinal optic and transverse optic) splittings of the infrared active optic mode are presented. Finally, properties related to electrical perturbation, including electronic dielectric tensors, Born effective charges for all of the atoms, static dielectric tensors and dielectric spectrum, are presented. The strengths and contributions to the dielectric tensors of individual infrared active mode are analyzed, followed by the infrared reflectance spectrum calculations for all of the structures. Excellent agreements have been achieved between the theoretical and experimental results.For β-Si3N4, the calculation indicates that strong infrared reflectivity exists from 800 to 1200 cm4 (24 THz to 36 THz) due to the three strong infrared active modes, leading to a poor electromagnetic wave transmission property. In the spectrum range above 1200 cm-1 or below 800 cm-1 , however, there is relatively good transmission property because of low reflectivity and dissipation resulting from no infrared active mode or weak modes. BN structures, which have a simpler crystal structures and smaller number of infrared active modes, present better electro-magnetic wave transmission properties compared with β-Si3N4...
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