Kalkopirit yarıiletken cualse$_2$'nin ve nadir-toprak oksit, hidrit ve boratlarının basınç-bağımlı örgü dinamiksel ve elastik özelliklerinin Ab initio yöntemlerle incelenmesi

Theoretical investigation of the physical properties of materials from first-principles (ab initio), today, is a very popular and powerful method in condensed matter physics and also in many other disciplines. First-principles here means that there is no experimental value used in the calculations as an input parameter. In this thesis we have performed an ab initio study of pressure-dependent structural, elastic and lattice dynamical properties of chalcopyrite semiconductor CuAlSe$_2$ and oxides, hydrides and borides of rare-earths. The calculations have been carried out by using the density-functional and density-functional perturbation theory within the local density approximation using norm conserving and optimized pseudopotentials and a plane-wave basis. Structural properties such as equilibrium lattice constants, bulk modulus, elastic constants, compressibilities and their pressure dependencies are calculated from the ground-state density functional theory. Born effective charge tensors, dielectric permittivity tensors, the phonon dispersion curves and their mode Grüneisen parameters and phonon density of states are calculated using density functional perturbation theory. In addition to these properties the temperature dependent lattice constant, bulk modulus, volume expansion, entropy and specific heat of LaB$_6$ and CeB$_6$ are investigated by performing the quasiharmonic approximation for the free energy. The calculated results agree well with the experiments. In the case of CuAlSe$_2$, we compare the mode Grüneisen parameters of the calculated quantities with those of zinc-blende type materials and find similar trends. The calculated elastic stiffness constants of CuAlSe$_2$ show pseudocubic behaviour. We have also found that treating the 4f electrons of cerium as valence states is crucial for a satisfactory description of the lattice dynamical properties of CeO$_2$. In the study of cerium hydrides, it has been observed that while the mode Grüneisen parameters for acoustic modes of CeH$_2$ are calculated mostly negative throughout the Brillouin zone, they are found positive in the case of CeH$_3$. Thermodynamical properties of LaB$_6$ and CeB$_6$ obtained from quasi-harmonic approximation are in a good agreement with the available experimental data.