Ab Initio Studies Of ? B Metals And Their Alloys Under High Pressure

High pressure physics is an important subject in the field of materials'research.Pressure increasing can change structure,modify electronic orbits and change bonding patterns.High-pressure phase transition and superconductivity are two hot issues in the field of materials research,which have important values in biology,chemistry,industry,production and life.In this paper,the high-pressure behaviors of materials are studied theoretically.Using ab initio method based on density functional theory,we have studied the following contents:the structure,elasticity,phonon,electron,thermodynamic properties and superconductivity of Hf,as well as the structural stability and superconductivity of the honeycomb high buckled(HB)hafnene;the structure,elasticity,phonon and superconductivity of the equal atomic Ti Zr,Ti Hf and Zr Hf alloys;the structure,electronic structure,magnetic states and elastic properties of the U-Zr alloy systems.For Hf metal,the calculated structural parameters,elastic moduli,phonon spectrum and thermodynamic properties are in good agreement with the experimental results.The calculated transition-pressures are 44.8 GPa for hcp?omega and 73 GPa for omega?bcc.At 0 GPa,the elastic constants and moduli of the hcp,omega and fcc phases agree well with previous experiments and calculations.At 0 GPa,the hcp,omega and fcc phases are mechanically stable phases,while the bcc phase is mechanically unstable phase.The mechanically stable bcc phase can be achieved under compressing.The bulk modulus of these four structures increase with the increase of pressure.The shear modulus of the hcp,fcc and bcc phases also increase with increasing pressure,but it increases first and then decreases for omega phase.The results of elastic anisotropy show that hafnium is anisotropic metal.Under compressing,the general anisotropy index results show that the anisotropy of the hcp and omega phases increase and the anisotropy of the bcc phases decrease.Phonon spectrum results show that the hcp and omega phases are dynamically stable in a wide range of pressure,while bcc phase is not dynamically stable at ambient pressure.But the dynamically stable bcc phase can be achieved when compressing to 62 GPa or raising to a certain temperature.The thermodynamic properties of hcp phase in a wide range of pressure and temperature are in good agreement with the experimental data.The P-T phase diagram of hafnium metal is predicted based on Gibbs energy.The calculated results of superconducting transition temperature T_care in good agreement with the experimental results.The contribution to the density of states at the Fermi level N(E_F)is mainly from the d orbital electrons,and the T_c is closely related to the occupied state of d-electron at the Fermi level.The relatively large electron-phonon coupling constant(EPC)?of the bcc-Hf is mainly derived from the soft mode of TA1 phonon in[1 1 0]direction.Under compressing,the increase or decrease of T_c is closely related to the increase or decrease of?.At ambient conditions,the calculated results of the HB-hafniene show that the predicted HB-hafniene is dynamically stable.Our predicted T_c is2.58 K,which is slightly larger than the calculated result of the bulk hcp-Hf.The results of Ti Zr,Ti Hf and Zr Hf alloys with equal atomic show that the lattice parameters and phase transition pressures of?,?and?phases are in good agreement with other known experimental and theoretical data.The?phases of Ti Zr and Ti Hf alloys are more stable at 0 K and 0 GPa,while the?-Zr Hf has the lowest ground state energy for Zr Hf alloys.Under compressing,?phase transform to?phase,and the predicted phase transition pressures of???are 35,68.3,and 46.7 GPa for Ti Zr,Ti Hf and Zr Hf alloys,respectively.The elastic constants and moduli of?,?and?phases agree well with known experimental and calculated results.at ambient conditions,?and?phases are mechanically stable while?phases are mechanically unstable.In addition,the mechanical stability of?and?is immutable within a given pressure range,and?phase can become mechanical stable phase after compression to a certain extent for Zr Hf alloys.Pressure increasing can increase ductility of?-Zr Hf and?-Zr Hf,and decrease ductility of?-Zr Hf.The?to?(?to?)phase transition reduces(enhance)ductility of Zr Hf alloys.At ambient conditions,?and?phases are dynamically stable and?phase is dynamically unstable.However,the?phase can be dynamics stabilized by increasing the pressure or temperature.In addition,the calculated T_c is in good agreement with the experimental data.Upon compression,the increase or decrease of T_c for Ti Zr,Ti Hf and Zr Hf alloys in all three phases has tight relation with the corresponding behavior of?.The material properties of the alloy systems are in between the corresponding pure metal,and exhibit similar pressure-dependent behaviors to the corresponding single element system.The results show that the lattice parameters of?-UZr₂ are in good agreement with the experimental values for the U-Zr alloy system.In addition,with the increase of pressure,a/a₀ increases gradually,while c/c₀ and V/V₀decrease gradually,indicating that?-UZr₂ is easier to compress in the c direction.?-UZr₂ has good metallic properties.With the pressure increase to about 17 GPa,the curves of electron density spin up and spin down change from asymmetry to symmetry,indicating that?-UZr₂ changes from ferromagnetic state to non-magnetic state.At 0 GPa,?-UZr₂ is a mechanically stable phase.With the pressure increase from 0 to 50 GPa,the bulk modulus B,shear modulus G,Young's modulus E and B/G values increase with the increase of pressure,indicating that the pressure improves the hardness and ductility of the material.The structure,electronic structure,magnetic state and elastic properties of the equal atomic U-Zr alloy system are studied.The optimized structural parameters accord with the experimental values.The results show that ferromagnetic?(U)phase UZr alloy is more stable phase.Based on the?(U,Zr)phase,found by experiment,two possible?(Zr)and?(Zr)phases have been predicted.The dominant electron occupation near the Fermi level is from the U-5f orbital,and there is a very weak correlation effect.The Zr element determines the mechanical strength of UZr alloy.In general,Ti,Zr and Hf metals have many similarities in crystal structure,phase transition,mechanical and kinetic properties,and superconductivity with their three equal atomic alloys.First,although the structures of single crystals and alloys are different at 0 K and 0 GPa,their high temperature or high pressure phases are body-centered cubic structures.Second,phase transition in metals and alloys is thermodynamically driven rather than mechanically driven under elevated pressures,and they are all good ductile materials.Thirdly,the structure with the highest T_c in single crystal and alloy is?phase,and the maximum T_c in alloy is higher than that in single crystal.In addition,for the U-Zr alloy system,zirconium provides the main mechanical properties for the system.This also reflects the application of good mechanical properties for group ? B elements.