Usually the polycrystalline elastic properties have higher practical application

Many low symmetry crystals exhibit a high degree of elastic anisotropy. The elastic anisotropy can be described by the universal anisotropic index AU and the percent anisotropy in BTS 54-505 and shear (Acomp and Ashear). The universal elastic anisotropy index AU [60] and the percent anisotropy for a crystal [61] and [62] with any symmetry are proposed as follows:equation(15)AU=5GVGR+BVBR−6≥0,equation(16)Acomp=BV−BRBV+BR,Ashear=GV−GRGV+GR,where BV (GV) and BR (GR) are the bulk modulus (shear modulus) in the Voigt and Reuss approximations, respectively. A crystal with AU=0 is isotropic. The deviation of AU from zero suggests the extent of single crystal anisotropy and accounts for both the shear and the bulk contributions unlike all other existing anisotropy measures. Thus, AU represents a universal measure to quantify the single crystal elastic anisotropy [60]. The values of Acomp and Ashear can range from zero (isotropic) to 1 representing the maximum elastic anisotropy. Since the investigated crystal systems in present work include cubic and orthorhombic structures, the shear anisotropic factors provide a measure of the degrees of anisotropy in atomic bonding in different planes. Therefore, the shear anisotropic factors A1, A2, A3 are multinucleate calculated and discussed, which are defined as [62]:equation(17)A1=4C44C11+C33−2C13forthe 100 planeequation(18)A2=4C55C22+C33−2C23forthe 010 planeequation(19)A3=4C66C11+C22−2C12forthe 001 plane.