Results and Conclusions

Concerning the bulk calculations, we find that a realistic description of the order-disorder transition of Cu$_{\rm 3}$Au and CuAu can be obtained; the lattice constant, mean square displacement and the potential energy show a step-like discontinuity in qualitative and quantitative agreement with experimental findings.

As for the Cu$_{\rm 3}$Au system, the study of the twist boundaries (3) resulted, that within the accuracy of 5% no noticeable segregation of either Cu or Au to the boundary could be found, which holds also for the tilted boundaries (4). Wetting occurred at temperatures about T/T$_{\rm c}$ = 0.8 for the twisted boundaries, while for the tilted boundaries we found no wetting for the temperatures T/T$_{\rm c}$ = 0.8 and 0.9.

For the Cu$_{\rm 3}$Au antiphase boundaries (5) we found that from the two possible antiphase boundaries (the conservative and the non-conservative), the conservative boundary can not be distinguished from the rest of the material, while the non-conservative shows higher disorder than the bulk material for temperatures 20% below the transition temperature. Our simulations indicate that only the non-conservative boundary wets, in accordance with experimental results.

The examination of the [001] surfaces of Cu$_{\rm 3}$Au (6) showed that the only possible surface structure is the mixed Cu-Au structure. We found segregation of Au to the surface and a very small oscillatory behavior of the segregation profile.

For CuAu we examined the [001] periodic antiphase boundaries. We used the ab-initio calculations to exclude some of the popular models for the periodic antiphase boundaries of CuAu-II. Then we extended the ab-initio results for T $\neq$ 0 K (7). We found that the boundaries are disordered well below the transition temperature and this is probably the reason for the stabilization of the CuAu-II phase.

The different size of the gold and copper atoms induces strains. These strains are zero in the bulk because of symmetry. Furthermore, in Cu$_{\rm 3}$Au gold atoms prefer to have copper atoms as first neighbors in order to reduce the strains, even at temperatures over T$_{\rm c}$ , and therefore the short-range order parameter is never zero. These strains affect the atomic arrangements at the interfaces and surfaces. We found that at the surface the gold atoms move outwards and the copper atoms inwards, in accordance with experimental findings, causing rippling of the surface and in this way reducing the strains. At the interfaces, the planes adjacent to the boundary have some sites with tensile and some sites with compressive stress. This leads to a new ordering at the interface, for example at the $\Sigma$ = 5 [001] twisted boundary of Cu$_{\rm 3}$Au , where the gold atoms occupy the CSL sites, or at the $\Sigma$ = 13, 17, 25 [001] twisted boundaries of Cu$_{\rm 3}$Au and the antiphase boundaries of Cu$_{\rm 3}$Au , where we find an interplanar ordering with domains of gold atoms of the one adjacent plane having as nearest atoms the copper atoms of the other plane and vise versa.