Dependence of stresses on grain orientations in BCC polycrystalline films on substrates

Most thin films have different thermal expansion coefficients from their substrates, thus thermal stresses will be introduced into the films when the temperature is changed during annealing and service. Calculations of these stresses for grains in various crystallographic orientations have been made for seven BCC transition metals Cr, Fe, Mo, Nb, Ta, V and W. Neglecting W, which is isotropic and the stresses are equiaxial and without grain orientation (hkl) dependence, the BCC metals may be grouped into two classes. In the first class (Cr, Mo, Nb and V), the (100)-oriented grains have the largest stresses, while the stresses \sigma _1 and \sigma _2 in other (hkl)-oriented grains decrease linearly with the increase of the angle between (hkl) and (100), and with \sigma _1 < \sigma _2 except in (100)- and (111)-oriented grains. In the second class (Fe and Ta), on the contrary, the (100)-oriented grains have the lowest stresses, and the stresses \sigma _1 and \sigma _2 in other (hkl)-oriented grains increase linearly with the increase of the angle between (hkl) and (100), and with \sigma _1 > \sigma _2 except in (100)- and (111)-oriented grains.