A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for ${\mathrm{TiSi}}_2$ 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 ${\mathrm{TiSi}}_2$ are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young’s modulus for single crystal ${\mathrm{TiSi}}_2$ 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 ${\mathrm{TiSi}}_2$ 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.

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.

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.

Within the conventional single-site coherent potential approximation (CPA) used to calculate thermodynamic properties of random alloys, the effect of charge transfer is neglected. We discuss a number of recent models based on the same mathematical form but with a different prefactor β which allow one to include charge-transfer effects in the framework of the CPA. We show how the models work in actual calculations for selected metallic alloy systems, Al-Li, Li-Mg, and Ni-Pt, which exhibit charge transfer. We find that the so-called screened impurity model (β=1), which is derived completely within the mean-field single-site approximation, leads to the best agreement with experimental lattice parameter and mixing energy data for Al-Li and Li-Mg alloys. However, for the Ni-Pt system exhibiting strong ordering tendency this model seems to overestimate the Madelung energy of the completely random alloy, and in this case the screened-CPA method (β=1/2) gives more correct results. It is suggested that a comparison with the results obtained by the Connolly-Williams method may be used to determine an optimal value for β depending on the alloy under consideration.

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, respectively) 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.