The Mechaincal Properties Of Bcc Metals (W, Mo, Fe And Ta) Under High Temperature And Pressure:A First-principles Study

First-principles density functional theory?DFT?is used to investigate the mechanical properties of four typical body-centered cubic?BCC?metal materials?W,Mo,Fe,and Ta?under high pressure?0-100 GPa?,uniaxial stress and high temperature?0-3000 K?.The static properties?lattice constants,elastic constants and generalized stacking fault energy?of crystals were calculated using VASP software.Phonon dispersion curves are performed by PHONOPY package which can support VASP code.Through the analysis of the calculation results,the mechanical stability and ductile brittleness of four BCC metal materials under high temperature,high pressure and uniaxial stress were predicted.The main contents are as follows:?1?By using the first principles method based on the density functional theory,the volumes,elastic constants,elastic moduli and the phonon dispersion curves as well as the generalized stacking fault energies of BCC metals W and Mo have been investigated at the pressures from 0 to 100 GPa,and the mechanical stability,the brittle-ductile properties and the shear deformation of the two materials have also been studied at the same pressure.Firstly,by calculating the elastic constants of the two materials at the pressures from 0-100GPa,it is found that the elastic constants of each material satisfy the conditions of mechanical stability,moreover,the frequency of the phonon dispersion curves at 100 GPa is positive and there is no imaginary frequency,therefore,both the structures of W and Mo are mechanically stable at the pressures from 0-100 GPa.Besides,through analyzing the ratio of the bulk modulus and the shear modulus,it is found that high pressure can make the ductility of W and Mo stronger,and the ductility of Mo is better than that of W.Finally,the generalized stacking fault energies?GSFE?,shear moduli G₁₁₁ along the<111>direction and the anisotropy ratios A of the two materials are all investigated and it is found that,both the generalized stacking fault energies and G₁₁₁ as well as A all increase when the pressure becomes higher,and the value of A is very close to 1 at 100GPa,all these indicate that the high pressure makes the shear deformation become more difficult and weakens the anisotropy of W and Mo.?2?The first-principles calculations is performed to investigate the influence of tensile and compressive stresses on[1???1]?110?GSFE curve in the[110]and[1???1]directions for three different BCC metals?Mo,W and Fe?.First,the{110}generalized stacking fault energy surface of three materials is fitted.It is found that the most likely to slip system is the<111>{110}slip system for BCC metal materials,and this sliding system is selected for the next calculation.Second,the tensile elastic modulus and compressive elastic modulus of three materials are calculated in different stress directions.It is found that there are obvious differences in the elastic modulus of different materials along different directions,which indicates that the three materials have different plastic deformation capacities.Finally,the effects of tensile stress and compressive stress on the GSFE curves of three BCC metallic materials are studied.At the[110]direction,as the tensile stress increases,the value of?_uss gradually decreases,and when compressive stress is applied in this direction,the value of?_us increases as the compressive stress increases.In contrast,when tensile and compressive stresses are applied in the[1???1]direction,the stacking fault energy shows the opposite tendency.In addition,the bond lengths of the sliding layers were analyzed and it is demonstrated the main reason of the stacking fault energy changes is the pre-stress changed the interatomic distance of the equilibrium structure.At the same time,the change of GSFE curve under preloading stress indicates that the stress state is an important factor that affects the materials deformation mechanism.?3?In addition to pressure,temperature has a major influence on the mechanical properties of metallic materials.The first-principles density functional theory has also used to calculate the mechanical stability and plastic deformation ability of two BCC metallic materials?Mo and Ta?at high temperature.The free energy,volume,elastic constant,elastic modulus and anisotropy ratio of the two metals are mainly used to investigate the change trend of the mechanical properties of materials at high temperature?0-2000 K?.The calculation results of elastic properties have shown opposite trends compared with the high-pressure.That is,with the increase of temperature,the elastic constant of metal materials tends to decrease slowly,and the temperature dependence of C₁₁ and C₄₄ is the maximum and minimum,respectively.Secondly,the generalized stacking fault energy,shear modulus G₁₁₁ along the<111>dense direction,and the anisotropy ratio A of the two material has investigated,it is found that the generalized stacking fault energy,G₁₁₁,and the anisotropy ratio A decreases gradually with the increase of temperature,which indicates that temperature makes the<111>shear deformation in the close-packed direction easier and enhances the anisotropy of the material.