First-principles study of the phase stability and elastic properties of Ti-X alloys (X = Mo, Nb, Al, Sn, Zr, Fe, Co, and O)

Wenchong Zhou, Ryoji Sahara, Koichi Tsuchiya

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41 Citations (Scopus)


Phase stability and elastic properties of Ti1-x-Xx alloys (X = substitutional Mo, Nb, Al, Sn, Zr, Fe, Co, and interstitial O) in body-centered cubic (bcc) (β phase) and hexagonal close-packed (hcp) (α phase) crystal structures were studied using first-principles calculations. The formation energy was used to determine the dependence of the phase stability on the atomic concentration x (0 ≤ x ≤ 0.5 for substitutional elements and 0 ≤ x < 0.02 for O) of the alloying elements and atomic configurations (ordered, disordered, and other compound structures). The disordered configurations of the atoms in the alloys were considered within the framework of the special quasi-random structures (SQS) method. The composition dependence of elastic constants, isotropic elastic moduli and density of states (DOS) were also evaluated. The predicted formation energies and elastic properties agrees well with previous experimental and theoretical results. Addition of Mo was found to stabilize the β phase significantly while destabilizing the α phase. Nb was found to be a weaker β-stabilizer. In Ti-Al and Ti-Sn systems, the compounds form preferentially at a higher concentration. Zr shows little effect on the phase stability, thus Zr is a neutral element. For Ti-O systems, the octahedral site is the most stable site for interstitial oxygen in both bcc and hcp structures. The comparison of formation energies showed that O acts as an α stabilizer. Considering the configurational entropy contribution, we concluded that temperature effect can be significant to stabilize the phases. The elastic constants calculation revealed that adding Mo, Nb, Fe, or Co increases the mechanical stability of bcc Ti, whereas bcc Ti-Al, Ti-Sn, and Ti-Zr systems are mechanically unstable for all the calculated concentrations. For their hcp counterparts, Ti-Mo and Ti-Nb have lower mechanical stability than the Ti-Al, Ti-O, and Ti-Sn systems. It was found in the electronic structures calculation that increasing addition of Nb, Mo, Fe, and Co weakens the covalent-like bonding of hcp system and strengthens the metallic bonding of bcc system. This variation of the TDOSs of these Ti alloys explains why the bcc phase becomes more stable than the hcp phase at high concentration. Due to the similarity of electronic structure, Zr does not change the DOS of the bcc and hcp phases significantly: The Fermi level in DOS profile of Ti-Zr was found to be identical to that of pure Ti system. Ti-Al and Ti-Sn alloys keep the covalent-like bonding, which explains why hcp Ti-Al and Ti-Sn are stable.

Original languageEnglish
Pages (from-to)579-595
Number of pages17
JournalJournal of Alloys and Compounds
Publication statusPublished - 2017 Dec 15
Externally publishedYes


  • Elastic property
  • First-principles calculation
  • Phase stability
  • Ti alloys

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Metals and Alloys
  • Materials Chemistry


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