Single Crystal Elastic Constants of β-Silicon Nitride Determined by X-Ray Powder Diffraction

Abstract

The X-ray elastic constants of pressureless sintered β-silicon nitride (Si₃N₄), were experimentally determined for ten different diffractions by using Kα radiations of Cu, Co, Fe, Cr and V. The X-ray compliances, (1+v'_x)/E'_x and v'_x/E'_x (E'_x=Young's modulus, v'_x=Poisson's ratio), change as a second power function of cos²φ (φ=angle between the diffraction plane normal and the c-axis of hexagonal crystal). Using the simplex method, the elastic constants of single crystals of β-silicon nitride were determined from the measured values of the X-ray compliances on the basis of the average of Voigt and Reuss models and Kröner's model, combined with the self-consistent analysis of multi-phase materials. The obtained result shows a high stiffness in the c-direction of hexagonal crystals, but the degree of anisotropy is not so large as the whisker data reported by Hay et al.