Basic structural units of tilt grain boundaries. Part I. Misorientation axis [100]

The computer simulation methods have been applied to calculate structure and energy of symmetric tilt grain boundaries with the misorientation axis [100]. The calculations have been carried out with the use of the structural-vacancy model previously developed by the authors. The misorientation angles of grain boundaries of common type have varied from 0$^{\circ}$ up to 90$^{\circ}$ while the increment has amounted 1$^{\circ}$. The the reciprocal density of the coincidence sites in special grain boundaries has amounted $\Sigma\le$ 53. The calculations have been carried out with the use of the Morse pair potential and the Cleri–Rosato many-body potential. It is shown that the dependence of the energy of grain boundaries on the misorientation angle when calculated with different potentials has a similar form, and their structure does not depend on the choice of potential and is in good agreement with high-resolution electron microscopic images. Only one special grain boundary is distinguished on the energy curve which is $\Sigma$5(013). It has been found that the structure grain boundaries may be represented by a limited number of atomic groups that have been named basic structural units. The structure of low-angle grain boundaries with the misorientation angle less than 8$^{\circ}$ is described by alternation of basic structural units of D types and ideal crystal, while the structure of low-angle grain boundaries with the misorientation angle ranging from 8$^{\circ}$ up to 13$^{\circ}$ is described by alternation of structural units of C and D types, from 14$^{\circ}$ up to 23$^{\circ}$ – B and C types. High-angle grain boundaries in the range of misorientation angles from 24$^{\circ}$ up to 37$^{\circ}$ contain only of basic structural units of B types, from 38$^{\circ}$ to 50$^{\circ}$ – A and B, more than 50$^{\circ}$ – only A.