7. Theoretical Ab Initio Calculations in Ordered-Vacancy Compounds at High Pressures

Ab initio calculations within the Density Funtional Theory and the Density Functional Perturbation Theory of the defect chalcopyrite, defect stannite and pseudo-cubic chalcopyrite structures of \(\mathrm{AB}_{2}\mathrm{X}_{4}\) (\(\mathrm{X}=\text {S}\) and Se) compounds are reported. The electronic, dynamical, and elastic properties under hydrostatic pressures are reviewed and discussed in relation with pressure-induced order-disorder phase transitions. Finally, as a matter of example, we present new results of a first-principles study of the pressure dependence of several properties for the pseudo-cubic chalcopyrite structure of \(\text {CdIn}_{2}\text {Se}_{4}\). We found that the generalized Born stability criteria are violated above 11 GPa, thus \(\text {PC-CdIn}_{2}\text {Se}_{4}\) becomes mechanically unstable. Furthermore, we found a phonon dynamical instability around 18 GPa; thus showing that \(\text {PC-CdIn}_{2}\text {Se}_{4}\) becomes unstable at high pressures not only from the static but also from the dynamical point of view.