Dependence of stresses on grain orientations in BCC polycrystalline films on substrates
Zhang Jian-Min (张建民)a, Zhang Yan (张研)a, Xu Ke-Wei (徐可为)b
a College of Physics and Information Technology, Shaanxi Normal University, Xian 710062, China; b State Key Laboratory for Mechanical Behavior of Materials,Xian Jiaotong University, Xian 710049, China
Abstract 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.
Received: 03 December 2004
Revised: 25 May 2005
Accepted manuscript online:
Fund: Project supported by the State Key Development Programme for Basic Research of China (Grant No
2004CB619302), and the National Natural Science Foundation of China (Grant No 50271038).
Cite this article:
Zhang Jian-Min (张建民), Zhang Yan (张研), Xu Ke-Wei (徐可为) Dependence of stresses on grain orientations in BCC polycrystalline films on substrates 2005 Chinese Physics 14 1862
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