The First-principle Calculations For MgB₂, Ternary Silicides And KMgF₃

The recent discovery of superconductivity in MgB2 at temperature as high as 39K has generated great interest, and has spurred extensive work on its properties and the discovery of closely related materials. In this dissertation, we carry out first-principle calculations based on the full-potential linearized Muffin-tin orbital (FP-LMTO) method to study the crossover from 3D to 2D for MgB₂-type systems, the quantum size effects in MgB₂ film and the superconductivity in ternary silicides MAlSi (M=Ca, Sr, Ba). Furthermore, the intrinsic defects in KMgF₃ are modelled by the ab initio method and the extended-ion method. The main work and results are as follows:1. Using the FP-LMTO method, we calculate the electronic band structure and the density of states for MgB₂ with large lattice constant c and ideal 2D B. The "empty spheres" technique is used to simulate the vacuum region on both sides of the B plane. With increasing c, the charge transfer from Mg to B gradually decreases and the Mg So-bonding band is also partial filled. As c is increased to 4co, the B layer in MgB₂ would be regarded as an ideal 2D plane, the B σ band would have more holes than that in MgB₂ with c = C₀. We further estimate the most important E_2g phonon frequency at point and the electron-phonon coupling constant A by using the frozen phonon method. The enhancements of the density of states at Fermi level and the electron-phonon coupling constant with increasing c indicate that T_c in MgB₂ could be further increased if the inter-layer coupling might be reduced.2. The LMTO within the atomic sphere approximation (LMTO-ASA) and the LMTO within the plane wave method (LMTO-PW) are used to calculate the electronic structures of free-standing MgB₂ (0001) films with 2 to 10 Mg/B bilayers (BLs). For the calculations in MgB₂ films, periodic slab geometries are employed. The "empty spheres" technique is used to simulate the vacuum region on both sides of the film. For 2 6 BLs, both LMTO-ASA and LMTO-PW methods are employed, and the results are in good agreement with each other. For more than 6 BLs, only LMTO-ASA method can be used under the currently available computational resources. We identify the quantum welllevels using the calculated local density of states. Owing to the quantum size effects, the total energy, the incremental energy with the bilayer added, the electron energy of the occupied quantum well states and the density of states at the Fermi level, all of them exhibit oscillatory behavior with the number of Mg/B bilayers. The incremental energy and the quantum-well state energy are used to study the MgB2 film stability, suggesting the existence of the "magic numbers" in film growth.3. The FP-LMTO and the linear response LMTO methods are used to calculate the electronic structure, phonon spectra and electron-phonon (EP) interaction of ternary silicides MAISi with M=Ca, Sr and Ba. The dynamical matrix is generated for 40 phonon wave vectors in the irreducible Brillouin zone, corresponding to a mesh of (6,6,6) reciprocal lattice divisions. The Brillouin zone integrations for the dynamical matrix and the electron-phonon matrix are done for a mesh of (18,18,18) reciprocal lattice divisions. The results show that the metallic d-like bands which are admixed with (Al,Si) p bands cross the Fermi level, the main contribution to the DOS at Ep comes from the metallic d-states, indicating that the alkali earth metals may play a more active role in the properties of these compounds. As the alkali earth metal is changed from Ca to Ba, N(Ei?) increases monotonically, but the EP coupling constant A decreases, leading to a reduction of Tc. A striking feature of the phonon spectra is the existence of very soft Big mode, which has a large contribution to the integrated A and plays an important role in variation of Tc in the MAISi compounds. The estimated Tc may be close to the experimental values if the anharmonicity of the B\g mode is appropriately taken into account.4. The ab initio method based on our modified Gaussian 94 (G94) quantum chemical program and the extended-ion method are used to model the intrinsic defects in KMgF3, such as Yk centers, self-trapped excitons (STEs) and F centers. The G94 code has been modified to create the infinite ionic crystal field effect by the Ewald's method. The calculated Madelung potential enters into the Fock matrix and the Hartree-Fock-Roothaan equation is then solved self-consistently. It is found that the Yk center moves toward the nearby interstitial site, still keeping C2y symmetry;the STE is unstablein the on-center symmetry, undergoing a relaxation consisting of an axial translation superimposed with a rotation;the relaxation of the lattice around the F center is very small, the ground state wavefunction of F center is well localized, but the excited state wavefunction of F center is more diffuse. Only the extended-ion method is used to study the reorientation of the Yk center and the decay of STE, for it is difficult for the ab initio method to be used as the cluster is big enough. The calculated energy barriers in the processes of the reorientation of the Yk center are close to but slightly larger than the experimental values. For the STE decay, the separation between the electron and hole is favorable for path "b" addressed in this dissertation due to the asymmetry on both sides of [110] row of fluorides. The structure of the STE and its decay behavior are compared with those in other ionic crystals. The calculated excitation energies of F center, Yk center and the emission energy of self-trapped exciton by using the unrestricted Hartree-Fock method in G94 code are compared with their experimental values.