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Barium chalcogenides are known for their high-technological importance and great scientific interest. Detailed studies of their elastic, mechanical, dynamical and thermodynamic properties were carried out using density functional theory and plane-wave pseudo potential method within the generalized gradient approximation. The optimized lattice constants were in good agreement when compared with experimental data. The independent elastic constants, calculated from a linear fit of the computed stress–strain function, were used to determine the Young’s modulus (E), bulk modulus (B), shear modulus (G), Poisson’s ratio ([Formula: see text]) and Zener’s anisotropy factor (A). Also, the Debye temperature and sound velocities for barium chalcogenides were estimated from the three independent elastic constants. The calculations of phonon dispersion showed that there are no negative frequencies throughout the Brillouin zone. Hence barium chalcogenides have dynamically stable NaCl-type crystal structure. Finally, their thermodynamic properties were calculated in the temperature range of 0–1000 K and their constant-volume specific heat capacities at room-temperature were reported.

In this work, details density functional theory calculations were performed to obtain the electronic, elastic, phonon and thermodynamic properties of half-Heusler alloys HfNiX (X = Ge and Sn). The PBE functional as implemented in Projector augmented-wave (PAW) pseudopotentials was used for all the calculations. From our results, we reported the energy gap of 0.38 eV for HfNiSn and 0.61 eV for HfNiGe indicating the semiconductor property of these compounds. Also, the mechanical and elastical stabilities of these compounds were confirmed from the comparison of the elastic constants of these compounds with conditions for stabilities. Although the phonon dispersion curves for HfNiGe and HfNiSn are similar with splitting at the Γ point, the shift in their frequency was as a result of the mass different in Ge and Sn. The phonon dispersion curve predicts the dynamically stabilities of these half-Heusler alloys. From the thermodynamic properties of these compounds, it was revealed that these compounds are soft at low temperature, but at a high temperature they tend to be hard materials. Our calculations showed that these two compounds are mechanically, elastically and dynamically stable as cubic half-Heusler alloys.

The mixing properties of liquid Al–Au alloys with respect to the concentration of each constituent is determined using a method based on hard sphere system and pseudo-potential perturbation. These models were used to get relevant information on mixing properties of the Al–Au alloys like the Gibbs energy and the entropy of mixing. The concentration fluctuations, chemical short range order for the hard sphere mixture (quasi-lattice theory) and the activity are calculated to know the extent of order in the liquid alloys. The results revealed that there is a degree of ordering in liquid Al–Au alloy (hetero-coordinated).