First-Principles Calculations for Structural, Elastic, Electronic and Thermodynamic Properties of $HfZn_{2}$ under Pressure

By using density functional theory within the Perdew-Burke-Ernzerhof generalized gradient approximation implemented in the VASP code, we study the structural, elastic, electronic, and thermodynamic properties of C15 Laves-phase compound $HfZn_{2}$. Comparing the lattice constants calculated from the Perdew-Burke-Ernzerhof generalized gradient approximation and local density approximation, we find that the former is in better agreement with the experimental data. The elastic constants of $HfZn_{2}$ calculated by strain-stress method indicate that they keep stable up to 100 GPa. The bonding characteristics are discussed by analyzing the energy band structure, charge density distribution and charge density difference. Phonon dispersion curves and phonon density of states of HfZn_{2} at the different pressure are predicted for the first time. In addition, there is no imaginary frequency in the phonon band at different pressure, which also shows that $HfZn_{2}$ is stable up to 100 GPa. Vibrational models are also illustrated based on phonon and group theory. The thermodynamic properties under high temperature and high pressure are calculated by different thermodynamic models. The heat capacity at constant pressure and low temperature calculated by quasi-harmonic approximation is more close to the measurement than that calculated by quasi-harmonic Debye models.