Anisotropy And Physical Properties Of Metal Dodecaborides Under High Pressure

Based on the first principles and quasi-harmonic Debye model,the dependence of the anisotropy and physical properties of MB₁₂(M=Zr,Hf,Y and Sc)compounds on pressure and temperature has been calculated and analyzed comprehensively.The negative values of cohesive energy indicate these compounds show thermodynamic stability.The conduction and valence bands of MB₁₂crystal structures all overlap near Fermi energy levels,indicating that HFB₁₂,Yb₁₂,Zr B₁₂and Sc B₁₂all have metallic properties.By analyzing the pressure dependence of state density,it is observed that the total state density at the Fermi energy level decreases with the pressure going up.Besides,with the increased pressure,Fermi plane deviates from the high level to the low level,implying that the stability of MB₁₂is increasing with the increase of pressure.Meanwhile,the differential charge density of MB₁₂is analyzed,and the results show that the B₁₂cluster separates the transition metal atoms Hf,Y,Zr and Sc,isolating them from each other.The transition metal atoms and cluster B₁₂are bound by a TM-B bond,which has both ionic bond and covalent bond characteristics.Using the stress-strain method,the elastic constants of the optimized structure are investigated.The results reveal that these compounds exhibit high hardness and strong anti-uniaxial stress ability.Young's modulus E is 50%larger than bulk modulus B and shear modulus G,which are very close to each other.Poisson's ratio?,fracture toughness and B/G grow up with the increased pressure,but the hardness H_vdecreases with the increased pressure.The B/G ratio and Poisson's ratio?reveal that YB₁₂and Zr B₁₂show a more brittle state within the considered pressure range,while Hf B₁₂and Sc B₁₂transform from brittle to ductile materials when the pressures exceed 80 GPa and 95 GPa,respectively.Zr B₁₂and Hf B₁₂possess similar fracture toughness,while Sc B₁₂possesses the lowest one.The elastic anisotropy is evaluated by the universal anisotropy index A^U,E_max/E_min,anisotropic shear A_shear,shear factor A₁and the three-dimensional surface structures of Young's modulus.Pressure can increase the anisotropy for MB₁₂,which is in good agreement with the correlation results of the universal elastic anisotropy index A^Uand E_max/E_min.Besides,the 3D contours of the Young's modulus of four materials are very similar at both 0 and 100 GPa.Also,the analysis of sound velocity and minimum thermal conductivity reveals that four dodecaborides all show poor anisotropy.All MB₁₂compounds have the smallest minimum thermal conductivity k_min^[111]and the largest minimum thermal conductivity k_min^[110].The minimum thermal conductivity k_minfollows the order of Sc B₁₂>YB₁₂>Zr B₁₂>Hf B₁₂.It should be noted that MB₁₂compounds have both high sound velocity and low thermal conductivity,which forms a strong contrast with the common low thermal conductivity,low sonic velocity and brittle materials.The dependence of thermodynamic properties on pressure and temperature of MB₁₂(M=Zr,Hf,Y and Sc)compounds are also comprehensively investigated via quasi-harmonic Debye model.The heat capacity and thermal expansion coefficient among the four compounds have very little difference.(except 0 GPa).Temperature and pressure have similar effects on heat capacity and thermal expansion coefficient.Futhermore,the effect of temperature on heat capacity and thermal expansion coefficient is more prominent than that of pressure.The sensitivity of Debye temperature to pressure is higher than temperature.Moreover,the normalized volume,Debye temperature and Gruneisen parameters are more sensitive to pressure than temperature.The effect of pressure on Gruneisen parameters is opposite to that of temperature.These findings are of great value for the applications of these multifunctional materials in electromechanical and medical engineering.