The possibility to use density-functional theory (DFT) for description of the crystal structure, lattice dynamics, vibrational frequencies, thermodynamical functions and phase transitions will be refered. The DFT is used to provide the minimum ground state energy of a supercell and gives the crystal structure at T=0K. Phonon calculations allow to extend the properties to a finite temperature. Phonons are calculated with the direct method (http://wolf.ifj.edu.pl/phonon/) from the Hellmann-Feynman forces.
The phonon dispersion curves of GaN were predicted before confirming them by X-ray inelastic scattering measurements. We found that in SnO₂ a soft mode accompanies the ferroelastic phase transition occuring under pressure. Phonon dispersion curves and phonon density of states can be calculated in tetragonal chalcopyrites (CuInSe₂, AgGaS₂, AgGaSe₂), orthorhombic MgSiO₃ and cubic Mg₂SiO₄ minerals, and ferroelectric material LiNbO₃. They also allow to calculate the thermodynamical functions, and predict the properties under finite temperature. We have calculated the phonon dispersion curves of the well-known shape memory alloy NiTi. austenite, martensite and R-phase of NiTi and confirmed the R-phase to martensitic phase transition from calculated free energies. Similar phase transition temperature was computed for ceramic ZrO₂. The phonon density of states of Fe dopped intermetalic NiAl lead to a local modes confirmed by the inelastic nuclear absorption.

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1. Ab initiocalculations of phonons and other properties of materials
2. First-principles study of phonon-based properties of magnetic CuFeS₂