Anisotropic elasticity in hexagonal crystals

Abstract The general expressions for the compliance s ijkl ′ , Young's modulus E ( hkl ) and Poisson's ratio υ ( hkl ) are given for an arbitrary plane ( hkl ) of hexagonal crystal. The calculations have also been made for 12 hexagonal metals Be, Cd, Co, Hf, Mg, Re, Ru, Sc, Ti, Y, Zr and Zn, and the representation surfaces, for which the radius vector deviated an angle ψ from the crystallographic Z -axis is proportional to 1 E ( h k l ) or υ ( hkl ) are constructed. For convenient applications, the expressions of Young's modulus E ( hkl ) and Poisson's ratio υ ( hkl ) are also given in terms of the Miller indices of the lattice plane ( hkl ). With these expressions, the X-ray elastic constants (REC) can be obtained readily for a particular plane ( hkl ) chosen for measurement.