The First Principles Study Of The Temperature-pressure Effects For The Elastic Properties Of BCC Metals

The elastic properties are the physical properties of the solid itself,and the magnitude of the elasticity can be expressed by the elastic constants.In recent years,the BCC(Body-Centered-Cubic)metals Ta,Fe,W,Mo have been used in all walks of life at different temperature and pressures.Therefore,it is of great theoretical and practical significance to study the elastic properties of materials at a certain temperature and pressure.According to the density functional theory,the elastic constants of BCC metals have been calculated by using the first-principles method with the VASP and Phonon software at the temperature of 0-1500 K.Besides,the thermodynamic properties of BCC metals and the velocities of sound have been calculated at the temperature of 0-1500 K.The main contents of this paper are as follows:(1)Firstly,the lattice constants of BCC metals are optimized by using two different exchange correlation functions(GGA-PAW and LDA).It is shown that all the results of the lattice constants obtained from GGA-PAW and LDA are different from the experimental results,but,the elastic constants calculated in this work will be closer to the experimental data if the lattice constants are closerto the experimental data.Compared with the results from LDA,the results from the GGA-PAW are more closer to the experimental results.Therefore,the exchange correlation function GGA-PAW is used in the later calculations.(2)According to the density functional theory and density functional perturbation theory,the elastic constants of the BCC metals Ta,Fe,W,Mo at the temperature 0-1500 K have been calculated by using the first-principles method.It is shown that the elastic constants C11 ,C12 and C44 of the four metals all decrease when the temperature increases.Moreover,the three elastic constants at different temperature satisfy the standard C11?0,C44?0,C11-C12?0,which can indicate that the phase of the metal is stable at the temperature.Besides,according to the Voigt-Reuss-Hill equation,the bulk modulus B and shear modulus G as well as the ratio B/G at the temperature of 0-1500 K can all be calculated by using the elastic constants obtained,and it is indicated by the ratio B/G that the four metals all show the toughness at the temperature of 0-1500 K.(3)At the temperature 0-1500 K,the sound velocities have been predicted according to the elastic constants obtained,and the sound velocities decrease when the temperature increases,because the atomic vibration becomes severer when the temperature increases and it hinders the propagation of sound wave.Besides,the thermal expansion coefficients of the metals are predicted when the temperature increases and the conclusion can be obtained that when the temperature increases,larger the expansion rate of the crystal volume is,greater the elastic constants' rate of the decrease will be.Meanwhile,thethermodynamic properties of Ta,Fe,W and Mo have been investigated.It is found that at the low temperature range(0-300 K),the heat capacity at constant volume CV and the isobaric heat capacity CP increase obviously when the temperature increases,and at the range of 300-1500 K,the trend of CV and the isobaric heat capacity CP are gently,especially at the range of 1000-1500 K,CV follows the equipartition theorem.(4)Based on the density functional theory,the elastic constants at the pressure of 0-30 GPa with the temperature of 0 K have been calculated,and the elastic constants increase with the increase of the pressure.And the elastic constants at higher pressure of 50 GPa and 100 GPa and at the temperature of0-1500 K are also investigated.It is found the higher the pressure is,the decrease rate of the elastic constants will be smaller when the temperature increases,and this indicates that the influence of the pressure on the elastic constants is more obvious than that of temperature.