First-principles Investigations Of Elastic Properties Of ? Titanium Alloys At Finite Temperature

Titanium and titanium alloys are ideal biomedical materials for hard-tissue replacement because of their excellent biocompatibility,high specific strength,low elastic modulus and high corrosion resistance.Early biomedical titanium alloys such as Ti-6Al-4V,Ti-5Al-2.5Fe and Ti-6Al-7Nb contain the toxic elements(e.g.,Al and V)and their elastic modulI are much higher than that of human bone.The huge gap of the elastic modulus between the implant and the bone makes the stress load focused on the implant,which leads to bone absorption,known as "stress shielding" effect.Third generation biomedical titanium alloys have lower elastic modulus and contain no toxical metal elements,with which the "stress shielding" effect may be effectively avoided.Nb is an important alloying element in third generation biomedical ? titanium alloy,so it is critical to study the influenes of Nb on the stability and elastic property of titanium.First principle methods can calculate accurately the elastic properties of materials at OK.However,the measurement of elastic properties in experiments is carried out at finite temperature.This leads to errors in the calculated elastic properties when compared to the experimental values.Therefore,first-principles calculation of elastic properties at finite temperature is highly demanded.In this work,we used ab initio molecular dynamics(AIMD)and first-principles method in combination with quasi-harmonic approximation(QHA)to evaluate the effect of temperature on the elastic properties of Ti-Nb alloy.The phase stability and elastic properties of Ti-Nb alloy against the Nb content were investigated as well.Employing the first-principles calculations with special quasi-random(SQS)structure and the coherent potential approximation(CPA),we investigated the formation enthalpy and static elastic properties of disordered ?-Ti-Nb alloy against the Nb content.We showed that,with increasing Nb content,the lattice constant of disordered Ti-Nb alloy increases.The elastic constants C11 and C12 increase whereas C44 decreases.The minimum value of Young's modulus shifts from<100>to<111>direction,and the trend of the shear modulus is opposite.When the temperature is lower than 200 K,body centered cubic(BCC)Ti and Nb are not mutually soluble.When the temperature is higher than 400 K,BCC-Ti and BCC-Nb mutually dissolve in the whole composition range.Phase decomposition occurs under 630 K.With Nb content lower than about 30 at.%,the BCC structure of ?-Ti1-xNbx is unstable.The local lattice distortion calculated with SQS structures increases significantly,which makes the free energy and elastic constant of the alloy with atomic relaxation exhibit unphysical change against Nb content.AIMD has been used to calculate the temperature dependent elastic properties of hard materials such as TiN.However,the osilation of the stress with the MD time step makes it uncertain for the calculation of the elastic constants of "soft" metals.To check the feasibility of the AIMD calculations of the elastic modulus of "soft" metals,we calculated the temperature dependent elastic constants of face centered cubic Al as example by using both AIMD and QHA methods.We showed that,by employing carefully chosen strain tensor and strain magnitude,AIMD may generate reliable temperature dependent eleastic constants of Al.The elastic constants and elastic modulus calculated by using both AIMD and QHA decrease linearly with increasing temperature.The calculated elastic properties are in good agreement with the experimental values.The volume thermal expansion contributes 75%-80%to the temperature effect on the elastic properties,followed by the lattice vibration(20%-25%).The contribution of electronic temperature is negligible.Al satisfies the Born elastic stability criteria with temperature up to the experimental melting point.After reaching the equilibrium condition,the elastic constants from AIMD calculations are not sensitive to the number of time steps.Then,the temperature dependent elastic properties of BCC-Ti are calculated by using both AIMD and QHA.AIMD generated elastic constants in better agreement with experiments.At room temperature,BCC-Ti is elastically unstable with negative C11-C12.With increasing temperature,C11 increases whereas C12 decreases.At temperature of 955 K,BCC-Ti becomes elastically stable with positive C11-C12.Near the melting point,C11 and C12 decrease sharply.C44 always decreases with temperature.Lattice vibration contribution is the key factor for BCC-Ti to gradually achieve elastic stability with increasing temperature.The bulk modulus decreases with increasing temperature,and the rate of decline near the melting point increases.The shear modulus and Young's modulus increase with temperature rising from room temperature to the phase transition point,then remain unchanged,and decreased rapidly near the melting point.Finally,the effect of temperature on the elastic properties of BCC Ti-50 at.%Nb was studied.The results showed that the elastic constants C11 and C12 decrease and C44 increase with increasing temperature.Thermal expansion effect and lattice vibration contribute the most to C11 and C12,while lattice vibration and electronic temperature effect play a major role in the rise of C44.The bulk modulus decreases with increasing temperature.The contributions of temperature effect to the bulk modulus decreases in sequence of thermal expansion effect,lattice vibration,electronic entropy.Both shear modulus and Young's modulus increase with temperature.Ti-50 at.%Nb always satisfies the elastic stability.C11-C12 and C44 increase with increasing temperature,while C11+2C12 decrease.