General compliance transformation relation and applications for anisotropic cubic metals

In anisotropic cubic crystals, the matrices of the compliance (sij) and the stiffness (cij) are usually specified in the crystal axes (Ai) and must be transformed to another orthogonal coordinate system (Xi) chosen to be convenient for the question. Such a transformation has been done in this paper and a simple compliance transformation relation is given. Accordingly, the useful expressions of the Young's modulus E(hkl), Poisson's ratio υ(hkl  ) and so the X-ray elastic constants (XREC) s1⁡(hkl)=−υ⁡(hkl)E⁡(hkl) and 12s2⁡(hkl)=1+υ⁡(hkl)E⁡(hkl) used commonly are also given in terms of the Miller indices of the lattice plane (hkl) in the original crystal axes (Ai).