The structural stabilities of the intermetallics and the solid-state phase transformations induced by lattice vibration
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investigated the structural stabilities of the intermetallics and the solid-state phase transformations induced by lattice vibration effects in the Al–Zr system by first-principles calculations. The calculated lattice parameters of all the phases and the phonon dispersion relations for pure Al and Zr are in good agreement with the experimental data. AlZr(oC8), Al4Zr5(hP18), and Al3Zr5(tI32) are predicted to be the high-temperature phases. To study the structural stabilities at high temperatures, the thermodynamic properties of the intermetallics are calculated via the linear response approach within the harmonic approximation. Thanks to the calculated enthalpies of formation at high temperatures, Al3Zr5 is predicted to be stabilized above 1163 K with respect to AlZr2 and Al2Zr3, in good agreement with the phase transformation temperature (1273 K) in the experimental phase diagram.
I. INTRODUCTION
More than 10 intermetallics exist with extremely narrow concentration ranges in the binary Al–Zr phase diagram.1 The ground-state structural stabilities of these intermetallics had been investigated by some previous theoretical researches.2–5 In agreement with the experimental phase diagram, the enthalpies of formation of Al3Zr5 (tI32) and Al4Zr5 (hp18) were predicted to lie above the ground-state convex hull at 0 K by Ghosh and Asta.5 However, the enthalpies of formation of AlZr (oC8), Al2Zr3(tP20), and AlZr2(hP6) were also predicted to lie above the ground-state convex hull about several kJ/mol at 0 K, while these phases exist as the stable phases at lower than 600 C as the composition of Zr changes in the experimental phase diagram. These phases were expected to be stabilized at high temperatures due to the lattice vibration entropy by the authors. Lattice vibration effects were proved to play an important role in determining the phase stabilities by many researches.6–10 However, the theoretical calculations on the Al–Zr system mainly focused on the ground-state properties. The importance of the lattice vibration free energy on the solubility of Zr in Al was demonstrated.11 As most of the intermetallics in the Al–Zr system change in narrow concentration ranges, it is an effective way to investigate the phase stabilities in various compositions by a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0227 J. Mater. Res., Vol. 25, No. 9, Sep 2010
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calculating the free energies of these ordered intermetallics as a function of the temperature from lattice dynamic calculations. It is known by the authors that no lattice dynamic calculations were made to investigate the solid-state structural phase transformations in the Al–Zr system yet. As described in this work, we use first-principles methods based on density-functional theory (DFT) and density-functional perturbation theory (DFPT) to investigate the ground-state structural stabilities and the influence of lattice vibration effects on the solid-state structural phase trans
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