Physical Properties Of X-Sn(X=Ti、Zr、Hf) Binary System Via First-principles Calculations

As a new type of biomedical material,Ti-Zr-Nb-Sn based alloys have some advantages such as low density,high specific strength,good corrosion resistance,good bio-tissue compatibility,etc.Recently,it has attracted more and more attentions from materials researchers.The phase stability,mechanical,electronic and thermophysical properties of the related intermetallics are very important for the novel biomedical materials design and development in the future.Therefore,in this paper,the first-principles calculations based on density functional theory（DFT）was used to calculate the phase stability,mechanical,electronic properties of the Ti-Sn,Zr-Sn and Hf-Sn binary intermetallics.The quasi-harmonic Debye model was used to investigate the relationship of thermophysical properties with temperature and pressure.The calculated results have been addressed as following:（1）For the Ti-Sn system,the calculated formation enthalpies show that Ti₃Sn,Ti₂Sn,β-Ti₆Sn₅and Ti₂Sn₃are stable.The calculated elastic constants satisfy the conditions of mechanical stability,which indicates that all compounds are mechanically stable.The calculated elastic moduli show that the compression resistance is stronger than shear resistance.The B/G ratio shows that the six intermetallics have good ductility.（2）For the Zr-Sn system,the miscibility gap in homogeneous region（η₁+η₂）andηis existed,based on the structural similarity of Zr₅Sn₃and Zr₅Sn₄,several interstitial configurations have been taken into account,and the interstitial phase calculated formation enthalpies for the interstitial are all close to the the ground state convex hull,which indicate that the homogeneous region is the interstitial phase with Sn dissolved into interstitialsites of Zr₅Sn₃.For the Zr₄Sn,the calculated results show that Zr₄Sn has a Cr₃Si-prototype and the actual composition was obtained.So,the calculated formation enthalpies show that Zr₄Sn,Zr₅Sn₃,Zr₅Sn₄,Zr Sn₂are stable,the formation enthalpy of Zr₅Sn₄was the lowest.The calculated elastic constants show that the four intermetallics satisfy the mechanical stability conditions.The calculated results of the elastic constants are all in good agreement with other theorectical calculations.The B/G ratio shows that Zr₄Sn and Zr₅Sn₃have good ductility,but Zr Sn₂show brittle behavior.（3）For the Hf-Sn system,there are few reports about the physical properties.In this work,the calculated formation enthalpies of Hf₅Sn₃,Hf₅Sn₄,Hf Sn and Hf Sn₂show that they are all stable except Hf Sn,the formation enthalpy of Hf Sn was above ground state convex hull by 0.09 e V/atom,which is coincide with experimental phase diagram.The calculated elastic constants show that the four phases satisfy the mechanical stability conditions.The calculated results of the elastic moduli show that the compression resistance is stronger than the shear resistance.The B/G ratio shows that the ductilities of Hf₅Sn₃and Hf Sn are better than those of Hf₅Sn₄and Hf Sn₂.（4）By using Debye model,the thermophysical properties of Ti-Sn,Zr-Sn and Hf-Sn have been calculated in this work.The results show that their volume,thermal expansion coefficient,and constant pressure specific heat capacity increase with the increasing temperature,but decrease with pressure.However,the bulk modulus and Gibbs free energy decrease with the increasing temperature,but which increase with pressure.