Lattice dynamics, thermodynamics and elastic properties of C22-Zr₆FeSn₂ from first-principles calculations

Since Zr-Fe-Sn is one of the key ternary systems for cladding and structural materials in nuclear industry, it is of significant importance to understand physicochemical properties related to Zr-Fe-Sn system. In order to design the new Zr alloys with advanced performance by CALPHAD method, the thermodynamic model for the lower order systems is required. In the present work, first-principles calculations are employed to obtain phonon, thermodynamic and elastic properties of Zr₆FeSn₂ with C22 structure and the end-members (C22-Zr₆FeFe₂, C22-Zr₆SnSn₂ and C22-Zr₆SnFe₂) in the model of (Zr)₆(Fe, Sn)₂(Fe, Sn)₁. It is found that the imaginary phonon modes are absent for C22-Zr₆FeSn₂ and C22-Zr₆SnSn₂, indicating they are dynamically stable, while the other two end-members are unstable. Gibbs energies of C22-Zr₆FeSn₂ and C22-Zr₆SnSn₂ are obtained from the quasiharmonic phonon approach and can be added in the thermodynamic database: Nuclearbase. The C22-Zr₆FeSn₂’s single-crystal elasticity tensor components along with polycrystalline bulk, shear and Young's moduli are computed with a least-squares approach based upon the stress tensor computed from first-principles method. The results indicate that distortion is more difficult in the directions normal the c-axis than along to it.