A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA). The calculated values compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. From this the calculated linear bulk moduli are found to be in good agreement with the experiments. The shear modulus, Young’s modulus, and Poisson’s ratio for ideal polycrystalline TiSi2 are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young’s modulus for single crystal TiSi2 are estimated from the elastic constants obtained from LDA as well as GGA calculations and are compared with the experimental results. The shear anisotropic factors and anisotropy in the linear bulk modulus are obtained from the single crystal elastic constants. From the site and angular momentum decomposed density of states combined with a charge density analysis and the elastic anisotropies, the chemical bonding nature between the constituents in TiSi2 is analyzed. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal. The calculated elastic properties are found to be in good agreement with experimental values when the generalized gradient approximation is used for the exchange and correlation potential.

We demonstrate that the magnetic properties of diluted magnetic semiconductors are dominated by short ranged interatomic exchange interactions that have a strong directional dependence. By combining first principles calculations of interatomic exchange interactions with a classical Heisenberg model and Monte Carlo simulations, we reproduce the observed critical temperatures of a broad range of diluted magnetic semiconductors. We also show that agreement between theory and experiment is obtained only when the magnetic atoms are randomly positioned. This suggests that the ordering of diluted magnetic semiconductors is heavily influenced by magnetic percolation, and that the measured critical temperatures should be very sensitive to details in the sample preparation, in agreement with observations.

The vacancy formation energy and the vacancy formation volume of the 3d, 4d, and 5d transition and noble metals have been calculated within the local-density approximation. The calculations employ the order-N locally self-consistent Green's-function method in conjunction with a supercell approach and include electrostatic multipole corrections to the atomic sphere approximation. The results are in excellent agreement with available full-potential calculations and with the vacancy formation energies obtained in positron annihilation measurements. The variation of the vacancy formation energy through a transition-metal series and the effects of crystal and magnetic structure are investigated and discussed. ͓S0163-1829͑99͒07717-6͔

The formation energies of point defects and the interaction energies of various defect pairs in NiAl are calculated from first principles within an order N, locally self-consistent Green's-function method in conjunction with multipole electrostatic corrections to the atomic sphere approximation. The theory correctly reproduces the ground state for the off-stoichiometric NiAl alloys. The constitutional defects ͑antisite Ni atoms and Ni vacancies in Ni-rich and Al-rich NiAl, respectively͒ are shown to form ordered structures in the ground state, in which they tend to avoid each other at the shortest distance on their sublattice. The dominant thermal defects in Ni-rich and stoichiometric NiAl are calculated to be triple defects. In Al-rich alloys another type of thermal defect dominates, where two Ni vacancies are replaced by one antisite Al atom. As a result, the vacancy concentration decreases with temperature in this region. The effective defect formation enthalpies for different concentration regions of NiAl are also obtained.

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A quantitative description of the configurational part of the total energy of metallic alloys with substantial atomic size difference cannot be achieved in the atomic sphere approximation: It needs to be corrected at least for the multipole moment interactions in the Madelung part of the one-electron potential and energy. In the case of a random alloy such interactions can be accounted for only by lifting the atomic sphere and single-site approximations, in order to include the polarization due to local environment effects. Nevertheless a simple parameterization of the screened Coulomb interactions for the ordinary single-site methods, including the generalized perturbation method, is still possible. We obtained such a parameterization for bulk and surface NiPt alloys, which allows one to obtain quantitatively accurate effective interactions in this system.

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