ABSTRACT
Most of the novel half-Heuslers are either half-metallic (semiconducting) or metallic . Also , these half-Heuslers are either ferromagnetic or non-magnetic . Some have good thermal capacities , electronic and magnetic values , good optical applications e.t.c while some do not have good applications in the above properties. Besides , it is entirely difficult to ascertain whether some novel half-Heuslers can be synthesized experimentally or not . Hence , the need to study the structural , mechanical , half-metallic , electronic , magnetic , thermodynamic and optical properties of ZrFeBi in α ,β and γ phases. This is aimed at confirming the structural stability , half-metallicity, good mechanical value , electronic band gaps , magnetic properties, thermodynamic significance and optical applications of all the three phases . More so , the semiconducting character of ZrFeBi has good optical applications in spintronics and optoelectronics . There is need to investigate the optical properties of only half-metallic phases of ZrFeBi.
The first principle Density Functional Theory (DFT) method is used to investigate the structural, mechanical , half-metallic , electronic , magnetic , thermodynamic and optical properties ZrFeBi in α ,β and γ phases. DFT-based Quantum Espresso is used to calculate the structural properties of ZrFeBi in α ,β and γ phases such as Bulk , Young’s and Shear moduli , Pressure derivative , Energy of formation , Cohesive Energy e.t.c to determine their structural stability. Electronic and magnetic properties such as Band structures , Densities of states , and Ferromagnetism , Non-magnetism , magnetic moments , spin – polarization are respectively investigated using DFT-implemented Quantum Espresso .The respective mechanical properties of ZrFeBi in α ,β and γ phases such as Young’s , Bulk and Shear Moduli , elastic constants , Pugh’s ratio , Poisson’s ratio , Cauchy Pressure , Anisotropy factor , Klein man Parameter , Vickers Hardness , and thermodynamic properties such as Free Energy , Entropy , Heat Capacity , Debye Temperature e.t.c are computed using Quantum Espresso-based Thermo_pw code . The optical properties of α ,β and γ phases of ZrFeBi such as Dielectric function , Absorption spectra , Energy loss coefficient , Reflectivity coefficient and Refractive index are investigated using Quantum Espresso-incorporated Yambo Code.
It is found that α and γ phase of ZrFeBi have lower total energy than β-phase showing that they are more structurally stable than the β-phase The results of energy of formation and cohesive energy of α ,β and γ phases of ZrFeBi show that the half-Heusler alloy can be synthesized experimentally. Results of mechanical properties of α ,β and γ phases of ZrFeBi indicate that the ZrFeBi has good mechanical applications in terms of their high ductility , malleability , tensile strength ,resistance against deformation e.t.c . The spin-up channels in the electronic band structures of α and γ phases of ZrFeBi have indirect band gap along X and Г-points of their symmetry points while their spin-down channels have no band gap , indicating that they exhibit half-metallic or semiconducting character. On the other hand , the β-phase of ZrFeBi has zero band gap in both spin-up and spin-down channels of their band structures , showing that β-phase exhibits metallic behaviour. Results of the magnetic moments , ferromagnetics , non-magnetics ,spin-polarization , Curie Temperature of α ,β and γ phases of ZrFeBi show that all the three phases are accurately ferromagnetic , despite β-phase has greater magnetic capacity. The magnetic properties of all the three (α, β and γ) phases perfectly obey Slater Pauling’s rule as the total magnetic moments are greater than or equal to one (Mt). The heat capacity, free energy, entropy and internal energy of of α-phase (ZrFeBi) and γ-phase (BiFeZr) of ZrfeBi which constitute the thermodynamic properties were also investigated. All the thermodynamic properties have various relationship with temperature. The heat capacity obeys Dulong-petit law which states that at high temperature, heat capacity of ZrFeBi in α, and γ-phase remains constant but , at sufficiently low temperature, the heat capacity is proportional to T3. A system perfectly ordered at OK has zero entropy. Optical properties such as Dielectric function, Absorption spectrum, Energy loss, Reflectivity coefficient and Refractive index of only α and γ phases were calculated using Yambo code. Optical properties of β-phase (FeBiZr) were not studied because of its metallic character. It is only Half-metallic Phases of ZrFeBi that have good applications in spintronics . Results show that ZrFeBi in both α and γ phases are optically useful in optoelectronic devices ,e.g. magnetic tunnel Junctions (MTJs), giant magneto-resistance devices (GMRs) , injecting spin-polarized currents into semiconductors , as solar reflector e.tc.
