Basic structural units of tilt grain boundaries. II. Misorientation axes [110] and [111]

The computer simulation methods have been applied to calculate structure and energy of symmetric tilt grain boundaries (GB) with the misorientation axes [110] and [111]. The calculations have been carried out with the use of the structural-vacancy model. The study of the atomic structure has been carried out within the entire range of misorientation angles. The reverse density of coincidence sites in special grain boundaries has amounted $\Sigma\le$ 57. The calculations have been carried out with the use of the Morse pair potential and the Cleri-Rosato many-body potential. When calculated with different potentials, the dependence of GB energy on the misorientation angle has a similar form, and the atomic structure completely coincides. It has been shown that the structure of any GB with the misorientation axes [110] and [111] may be represented by a limited number of basic structural units. All found basic structural units defined as units of A, B, C and D types are based on the structures of special grain boundaries. Such special GBs shall be $\Sigma$3(111), $\Sigma$3(112), $\Sigma$11(113) and $\Sigma$9(114) for GBs with the misorientation axis [110], and as regarding GBs with the misorientation axis [111], such special GBs shall be $\Sigma$3(112), $\Sigma$7(123) and $\Sigma$13(134). Ranges of angles within which certain basic structural units are found have been defined.