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Thermodynamic modeling of interstitials in titanium alloys


Titanium is recognized as the metal for the 21st century. Its alloys are relevant in diverse fields from aerospace to bio-medical applications. Interstitial elements such as oxygen, nitrogen and carbon can dissolve in a bulk Ti matrix to form solid solutions. Especially oxygen can dissolve up to 33 at % in hcp-Ti. The solute atmosphere created by interstitial elements is crucial for various strengthening mechanics in structural materials. Hence, from materials design perspective, it becomes important to investigate the extent to which titanium alloys can dissolve interstitial elements at finite temperatures. Upon dissolution into titanium alloys, these interstitials form many ordered and disordered compounds. The crystal structures of these compounds are poorly characterized in the literature. Furthermore, interactions between interstitial and substitutional alloying elements in bulk Ti remain poorly understood. This dissertation uses first-principles methods along with coarse grained cluster expansion models to predict accurate phase stability in titanium alloys with interstitial solutes.

The binary Ti-X (X = C, N, O) interstitial systems consist of a multitude of stable and metastable oxides that are used in wide ranging applications. In this dissertation, the stable ordered interstitial compounds were investigated using first-principles methods at 0 K. A systematic search was performed to discover ground state structures as a function of interstitial concentration by considering interstitial-vacancy and/or titanium-vacancy orderings over parent crystal structures such as hcp-Ti, ω-Ti and rocksalt crystals. This dissertation presents the newly discovered ground states while reinforcing observations from previous experimental and computational studies. The phase stability at finite temperature was explored using cluster expansion Hamiltonians and Monte Carlo simulations. The calculations predict a high oxygen solubility in hcp-Ti and the stability of suboxide and vacancy ordered rocksalt phases that undergo order-disorder transitions upon heating in the Ti-O system. In the carbide and the nitride systems, the ordered rocksalts transformed to a disordered rocksalt phase that can tolerate high vacancy concentrations at intermediate to high temperatures. Trends in phase stability, rooted in electronic structure, are revealed upon comparing the calculated Ti-X phase diagrams. Predicted stable and metastable phase diagrams are qualitatively consistent with experimental observations. Some subtle but important discrepancies are revealed between the first-principles based phase stability predictions and the current understanding of phase stability in this system.

In the final part of this dissertation, a phase stability analysis of substitutional titanium alloys that simultaneously contain interstitial species was explored. In particular, the focus was on the effect of substitutional Al in Ti-Al alloys on the solubility of oxygen. There is a strong tendency for short range ordering in alpha-Ti, whereby Al and O atoms avoid being nearest neighbors. This changes phase stability in the Ti-Al binary as a function of the oxygen chemical potential. Pseudo-binary phase diagrams drawn at different degrees of oxygen solubility show a significant change in order/disorder temperature and compositional variance of phases in the binary. The insights from this dissertation can shed light on similar interactions between interstitial solutes and metal atoms observed in other alloy systems. The thermodynamic models developed in this dissertation are part of a crucial first step in building multiscale models to predict oxidation microstructure in titanium alloys.

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