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Elastic properties of Mg_(1−x)Al_xB₂ have been studied from first principles. The elastic constants (c₁₁, c₁₂, c₁₃, c₃₃ and c₅₅) have been calculated, in the regime of x = 0 to 0.25. From these calculations the ratio between the bulk modulus and shear modulus (B/G) as well as the ratio between the two directional bulk moduli (B_a/B_c) have been evaluated. Our calculations show that the ratio B_a/B_c decreases monotonically as the aluminium content is increased, whereas the ratio B/G is well below the empirical ductility limit, 1.75, for all concentrations. In addition, we analyse the electronic structure and the nature of the chemical bonding, using the balanced crystal orbital overlap population (BCOOP) (Grechnev et al 2003 J. Phys.: Condens. Matter 15 7751) and the charge densities. Our analysis suggests that, while aluminium doping decreases the elastic anisotropy of MgB₂ in the a and c directions, it will not change the brittle behaviour of the material considerably. 

Superplastic transition metal alloys and compounds are predicted from first principles calculations. Provided a suitable tuning of the alloying is done, materials with vanishingly low shear modulus C[prime] have recently been identified among the 3d, 4d, and 5d elements if the valence electron average number is close to 4.24 (i.e., Ti-Ta-Nb-V-Zr-O and Ti-Nb-Ta-Zr-O alloys). The vanishingly low C[prime] elastic constant of these bcc alloys is, according to the joint experimental and theoretical studies [T. Saito et al., Science 300, 464 (2003)], the crucial material parameter that is responsible for the superplasticity. We predict here, using first principles calculations, that superplastic alloys should also be found for alloys with drastically different valence electron concentrations, i.e., for W-Re-, W-Tc-, Mo-Re-, Mo-Tc-, and Fe-Co-based alloys.

The electron and phonon contributions to the free energy of gold are calculated from a first-principles method. From the free energy the equation of state (EOS) along with the shock Hugoniot with initial conditions at ambient pressure and room temperature are calculated. The results show good agreement with the corresponding experimental EOS and Hugoniot up to compressions of V/V-0=0.65-i.e., up to the solid-liquid phase transition in the Hugoniot. Optimal agreement between experiment and theory is obtained after a small adjustment of the calculated equilibrium lattice constant to the experimental lattice constant. (the correction is of the order of a few percent). The current calculations are consistent with recent suggestions of an underestimation of the pressures obtained with the ruby pressure scale R-1 line.

We provide a complete quantitative explanation for the anisotropic thermal expansion of hcp Ti at low temperature. The observed negative thermal expansion along the c axis is reproduced theoretically by means of a parameter free theory which involves both the electron and phonon contributions to the free energy. The thermal expansion of titanium is calculated and found to be negative along the c axis for temperatures below ∼170 K, in good agreement with observations. We have identified a saddle point van Hove singularity near the Fermi level as the main reason for the anisotropic thermal expansion in α-titanium.

Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self-consistently from first principles has been developed to address this issue. The method combines concepts from Born's interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. The method has been tested on the high-temperature bcc phase of Ti, Zr, and Hf, as representative examples, and is found to reproduce the observed high-temperature phonon frequencies with good accuracy.