| Titanium and its alloys are broadly applied to both in aerospace and biomedicine fields,due to their excellent multiple-function.It is worth nothing that β-titanium alloys have been attracting extensive attentions in recent years because of their super-low Young’s modulus and high strength.This type of titanium alloys is often realized by adding a variety of alloying elements,like Nb,Mo,Zr,Ta and other β-phase stable elements.But,the interpalat between structural physical quantities and Young’s modulus is still elusive.One of the hardest questions is what are the key parameters,and how they play the decisive role in modifying the elasticity of titanium alloys.In this work,binary Ti-X(X= Nb,Zr,Mo,Ta)alloys are studied by means of DFT calculation and machine learning method.On the basis of the calculations on the highthroughput obtained database and elected ones from literatures,we successfully find several structures with Young’s modulus less than 40 GPa.By analyzing the selected material genes with the help of multivariate decision tree methods,we find the key parameters affecting the stability and mechanical properties of titanium alloys are varying with different importance coiefficients when changing the alloying elements.This theoretical work also provides a guideline of exploring the composition space of other binary and even multi-element alloys in the future,which can promote the emergence of new materials,particularly on the compositional adjustments.According to formation energy,volume,Young’s modulus and other physical quantities,we find the distribution of volume exhibit obvious boundary,and there is a somewhat hidden relationship between volume and formation energy through analyzing the structural characteristics.The modulus is dependent on the Ti concentration as well as the intrinsic symmetry.For different binary systems,the influence of the above factors on the physical quantity are showing distintic behaviors,which may be bound up with electronic configuration,cell size and atomic radius.In each series,we are able to locate several structures with Young’s modulus lower than40 GPa.Compared with other series,the Ti-Nb have better energetic stability and high possibility of being synthesized for their relatively low formation energy.The bulk modulus and shear modulus of Ti-Zr are much lower than other series,and the effect of adding Zr into titanium alloys alone is not significant interms of the mechanical properties.Ti-Mo structures have much higher bulk modulus and stronger resistance to external compression than other types.The stability of Ti-Ta system is better than that of Ti-Mo and Ti-Zr systems.The low modulus structures found in the studied Ti-X(X= Nb,Zr and Mo)binary systems all show the anisotropy in different degrees,and the materials with the most pronounced effects are expected to produce microcracks and lead to failure under the working conditions.The only exceptional case lies in the Ti-Ta series,which tends to be isotropic,lead to possess a great potential in the future.The density of states of low elasticity structures in different systems show that,there are strong d-orbital hybridization in Ti-Nb,Ti-Mo and Ti-Ta structures,which means enhanced electron bonding and better structural stability.The p-p orbital hybridization exists in the structures with high bulk modulus,which indicates that the compressive strength of the material may be affected by the p-orbital effect.The decision tree results of alloying parametes show that,the formation energy of structures is strongly related to three key variables,which are the bond length,volume and fermi level.The key parameters of Young’s modulus are however alloying element dependent in both quanlity and quantity.However,for Ti-Nb and Ti-Mo,the key variables are much more dispersive,which include the bond length,volume and element content are all of great importantce.But in Ti-Zr system,the element content has little effect on the Young’s modulus,while the bond length plays a decisive role. |
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