Calculation of elastic constants of BCC transition metals: tight-binding recursion method

Abstract
The elastic constants of BCC transition metals (Fe, Nb, Mo and W) are calculated by using the tight-binding d band and the Born-Mayer repulsive potential. Introducing a small distortion characteristic to C44 (or C') elastic deformation and calculating the energy change up to second order in the atomic displacement, the authors determine the shear elastic constants C44 and C'. The elastic constants C11 and C12 are then calculated by using the relations B=1/3(C11+2C12) and C'=1/2(C11-C12), where B is the bulk modulus. In general, the agreement between the present results and the experimental values is satisfactory. The characteristic elasticity behaviour, i.e. the strong Nd (number of d electrons) dependence of the observed anisotropy factor A=C44/C', is also discussed.