The structural of MgB2 such as lattice constant, volume modulus, volume modulus derivative and compressibility of different degrees have been calculated. The calculations have been performed using a Full Potential-Linearized Augmented Plane Wave (FP-LAPW) method in the framework of Density Functional Theory (DFT) with various Approximation. The results show that the linear compressibility in direction of c is about twice the compressibility in direction of a. In addition, the electronic properties of the compound, including the structure of the energy bands, the density of the states, and the types of bonds in the MgB2 Superconductivity have been studied. The results of a double degeneracy above the Fermi level show that it plays an important role in the superconducting property. According to energy bands, it has been determined that the lattice parameters have a large effect on the  band of boron atoms. The results predict that the constant increase of the lattice along the c-axis has an increase in the density of states at the Fermi level. The results express this fact that the calculation using by GGA has the better agreements with the other theoretical and experimental approximations.

We report systematic investigations of the magnetic superconducting properties of the new superconducting materials (NS): New high temperature superconductors (HTS), Organic superconductors (OS), fullerenes, carbon nanotubes, MgB2 etc. We show that, contrary to conventional superconductors where the superconducting state can be coherent over several tenths of km, the macroscopic coherence range lc of the NS is often as short as 0.1 to 10 mm typically. As a consequence, the magnetic properties are dominated by granular-like effects as well as Josephson coupling between grains. Here, we concentrate on HTS ceramics and organic superconductors exclusively. In the first case we observe three distinct regimes: (i) At very low field (H < 5 Oe to say) all the grains are coupled via Josephson effect and lc can be considered as infinite. (2) At intermediate field (5 <H < 50 Oe, typically) the grains are gradually decoupled by H and/or T. (iii) At higher fields all the grains are decoupled and lc roughly coincides with the diameter of the metallurgical grains. The case of OS is more subtle and is connected with a kind of order-disorder transition that occurs in most of them. For instance, in this study, we exploit quenched disorder (after crossing such a transition) in the k -(BEDTTTF)2 Cu[N(CN)2]Br layered organic superconductor to get new insights on both the superconducting state (T £ 11.6 K) and the glassy transition at Tg, by studying the superconducting properties as functions of annealing time and annealing temperature around the glassy transition. Our main result is that the data can be described by a percolation molecular cluster model in which the topology and the growth of the molecular clusters obey an Ising spin-glass-like model with Tg » 80 K for the hydrogenated compound and Tg » 55 K for the fully deuterated one.