Pressure And Doping Effects On Physical Properties Of Zn₄B₆O₁₃:First-principles Investigation

The transition metal borate Zn₄B₆O₁₃?hereafter abbreviated“ZBO”?has good thermal stability,high mechanical hardness,and excellent thermal conductivity.At the same time,its light transmission range covers almost the entire UV,visible and near-infrared bands.Based on these excellent characteristics,it can used in high-precision optical instruments under cryogenic environments,such as cryogenic optical scanners,space telescopes,and cryogenic fiber temperature transducers.However,ZBO was studied in detail only under ordinary conditions so far,and there are few studies on ZBO under other conditions.Therefore,the focus of this paper is to study the mechanical and optoelectronic properties of ZBO under hydrostatic pressure and ZBO doped with different elements.First,based on the first-principles density functional theory,ZBO under different pressure is analyzed and discussed.The GGA-PBE exchange correlation function is used to optimize the geometrical structure and calculate the elastic properties of ZBO.The calculated cell volume and Vickers hardness of ZBO at 0 GPa were consistent with the experimental values.According to the stability criterion,we know that ZBO is mechanically stable less than a critical pressure?which is 52.98 GPa?.In addition,Young's modulus and Vickers hardness of ZBO decrease with increasing pressure,while the degree of ductility and aeolotropy are going up.From the population and charge difference density,the B-O² bonds are strongest in ZBO while the Zn-O¹ and Zn-O² bonds are covalent with ionic characteristics.The GGA-PBE exchange correlation function may underestimate the band gap of ZBO,so the hybrid functional PBE0 is used for the electronic structure and optical properties.The results show that ZBO is an indirect band gap semiconductor,and the band gap increases with the increase of pressure.The optical properties,such as the dielectric properties,absorption spectrum,refractive index,are also discussed.The calculated results reveal that the mechanical and optical properties of ZBO are weakly dependent on pressure,meaning that ZBO have good stability.Secondly,the O atom at the center position of the ZBO unit cell is replaced by S,Se and Te atom,so ZBO can be reconstructed as three new materials:Zn₄B₆O₁₂S,Zn₄B₆O₁₂Se and Zn₄B₆O₁₂Te.It can be seen that all three materials have negative formation energies,which means the composing processes from the elemental forms are exothermic reactions and those Zn₄B₆O₁₂X are stable.Then,we used first-principles calculations to analyze the mechanical and photoelectron properties of Zn₄B₆O₁₂X?X=S,Se,Te?.The mechanical properties obtained using the GGA-PBE exchange correlation function show that the bulk modulus,shear modulus,Vickers hardness and Young's modulus of Zn₄B₆O₁₂X?X=S,Se,Te?are all less than ZBO.After that,the electronic structures and optical properties of Zn₄B₆O₁₂X?X=S,Se,Te?were obtained using the PBE0 hybrid functional.The results show that Zn₄B₆O₁₂X have direct band gap,and the band gap of Zn₄B₆O₁₂X decreases with the increasing atomic number of X,namely,Zn₄B₆O₁₂S?6.688 eV?>Zn₄B₆O₁₂Se?6.532 eV?>Zn₄B₆O₁₂Te?6.478 eV?.The optical curves of these materials is basically the same,except there is slightly red shifted as the following order:Zn₄B₆O₁₂S-Zn₄B₆O₁₂Se-Zn4B6O12Te.In the end,Zn atoms in ZBO was replaced by 50%Cu atoms and 100%Cu atoms,and Zn₂Cu₂B₆O₁₃ and Cu₄B₆O₁₃ were obtained.After optimization of the geometry,we find out that Zn₂Cu₂B₆O₁₃ belongs to orthorhombic system rather than cubic system,but Cu₄B₆O₁₃ is cubic still.On this basis,we used first-principles calculations to analyze the mechanical properties,electronic structures and optical properties of Zn_xCu_4-xB₆O₁₃?x=2,0?.The results of the mechanical properties obtained by using the GGA-PBE exchange correlation function show that the bulk modulus,shear modulus,Vickers hardness and Young's modulus of Zn_xCu_4-xB₆O₁₃ decrease but the ductility and aeolotropy are increase as the Cu doping ratio increases.The electronic structures and optical properties of Zn_xCu_4-xB₆O₁₃?x=2,0?were obtained using the PBE0 hybrid functional.The electronic structure tells us that the band gap of Zn_xCu_4-xB₆O₁₃decreases sharply with the increasing proportion of Cu atoms,namely,ZBO?5.62 eV?>Zn₂Cu₂B₆O₁₃?1.83 eV?>Cu₄B₆O₁₃?0.33 eV?,which means the performance of ZBO can be changed by doping Cu atoms.From the optical properties,the absorption range is enlarged and the transmission performance is greatly reduced when ZBO is doped by Cu atoms.