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Density functional theory (DFT) based first-principles investigations of structural, elastic, electronic band structure, and optical properties of superconducting ternary phosphides (BaM2P2; M = Ni, Rh) have been carried out in this study. This is the first detailed pressure dependent study of these properties for the titled compounds. The calculated ambient condition properties are compared with existing experimental and theoretical results, where available. The pressure dependent variations of the electronic density of states at the Fermi level, N(EF), and the Debye temperature, thetaD, have been studied and their effect on superconducting transition temperature have been explored. N(EF) shows nonmonotonic pressure dependence in BaNi2P2. The pressure dependence of N(EF) for BaRh2P2, on the other hand, is monotonic; decreasing with increasing pressure up to 15 GPa and saturating at higher pressure. Pressure dependence of N(EF) is reflected in the pressure dependent superconducting transition temperature. The Debye temperature increases with increasing pressure. The variation of the optical parameters (real and imaginary parts of the dielectric constant, refractive indices, reflectivity, absorption coefficient, and loss function) with photon energy show metallic behavior complementing the features of electronic band structure calculations. The absorption spectra of BaNi2P2 show strong optical absorption in the ultraviolet region, while BaRh2P2 absorbs photons over a wider energy band including the entire visible range. The reflectivity spectra for both BaNi2P2 and BaRh2P2 reveal that these materials are very strong reflectors of visible spectrum and particularly BaNi2P2 have significant potential to be used as coating material to reduce solar heating.