Structural,electronic,vibrational,and thermodynamic properties of Zr_(1-x)Hf_xCo:A first-principles-based study

The physical properties including structural,electronic,vibrational and thermodynamic properties of Zr1-xHfx Co(x is the concentration of constituent element Hf,and changes from 0 to 1) are investigated in terms of the ABINIT program.The results reveal that all of Zr_(1-x)Hf_x Co have similar physical properties.When Hf concentration x gradually increases from 0.0 to 1.0,the lattice constant decreases from 3.217 ?A to 3.195 ?A very slowly.The calculated density of states(DOS)indicates that the metallic nature is enhanced and the electrical conductivity turns better with the increase of Hf.Moreover,as Hf concentration increases from 0 to 1,the Fermi energy gradually increases from-6.96 e V to-6.21 e V,and the electronic density of states at the Fermi level(N(E_f)) decreases from 2.795 electrons/e V f.u.down to 2.594 electrons/e V f.u.,both of which imply the decrease of chemical stability.The calculated vibrational properties show that the increase of Hf concentration from 0 to 1 causes the maximum vibrational frequency to decrease gradually from about 223 cm~(-1) to 186 cm~(-1),which suggests a lower dispersion gradient and lower phonon group velocities for these modes.Finally,the phonon related thermodynamic properties are obtained and discussed.     

Elastic,vibrational, and thermodynamic properties of Sr_(10)(PO_4)_6F_2 and Ca_(10)(PO_4)_6F_2 from first principles

The electronic, elastic, vibrational, and thermodynamic properties of Sr_(10)(PO_4)_6F_2(Sr-FAP) and Ca_(10)(PO_4)_6F_2(CaFAP) are systematically investigated by the first-principles calculations. The calculated electronic band structure indicates that the Sr-FAP and Ca-FAP are insulator materials with the indirect band gap of 5.273 eV and 5.592 eV, respectively. The elastic constants are obtained by the "stress–strain" method, and elastic modulus are further evaluated and discussed. The vibrational properties, including the phonon dispersion curves, the phonon density of states, the Born effective charge, and associated longitudinal optical and transverse optical(LO–TO) splitting of optical modes, as well as the phonon frequencies at zone-center are obtained within the linear-response approach. Substitution of Ca by Sr causes phonon frequencies to shift to lower values as expected due to the mass effect. Additionally, some phonon-related thermodynamic properties, such as Helmholtz free energy F, internal energy E, entropy S, and specific heat C_V of Sr-FAP and Ca-FAP are predicted with the harmonic approximation. The present calculated results of two apatites are consistent with the reported experimental and theoretical results.