The equilibrium crystal structures,lattice parameters,elastic constants,and elastic moduli of the polymorphs α-,β-,and γ-Si3N4,have been calculated by first-principles method.β-Si3N4 is ductile in nature and has an ionic bonding.γ-Si3N4 is found to be a brittle material and has covalent chemical bonds,especially at high pressures.The phase boundary of the β → γ transition is obtained and a positive slope is found.This indicates that at higher temperatures it requires higher pressures to synthesize γ-Si3N4.On the other hand,the α → γ phase boundary can be described as P =14.37198 + 3.27 × 10-3T-7.83911 × 10-7T2-3.13552 × 10-10T3.The phase transition from α-to γ-Si3N4 occurs at 16.1 GPa and 1700 K.Then,the dependencies of bulk modulus,heat capacity,and thermal expansion on the pressure P are obtained in the ranges of 0 GPa-30 GPa and 0 K-2000 K.Significant features in these properties are observed at high temperatures.It turns out that the thermal expansion of γ-Si3N4 is larger than that of α-Si3N4 over wide pressure and temperature ranges.The evolutions of the heat capacity with temperature for the Si3N4 polymorphs are close to each other,which are important for possible applications of Si3N4.
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