An Empirical Tight-Binding Model for Titanium Phase Transformations

TL;DR

This paper presents an empirical tight-binding model for titanium that accurately reproduces key properties and phase transformations, validated against density-functional calculations and experiments, and suitable for molecular dynamics simulations.

Contribution

The study introduces a novel tight-binding model for titanium that overcomes previous limitations and accurately captures phase transformation behaviors.

Findings

Model reproduces structural energies and electron eigenvalues accurately.

Predicts elastic constants, phonon spectra, and defect energies consistent with experiments.

Overcomes the 'collapse problem' for phase transformation simulations.

Abstract

For a previously published study of the titanium hcp (alpha) to omega (omega) transformation, a tight-binding model was developed for titanium that accurately reproduces the structural energies and electron eigenvalues from all-electron density-functional calculations. We use a fitting method that matches the correctly symmetrized wavefuctions of the tight-binding model to those of the density-functional calculations at high symmetry points. The structural energies, elastic constants, phonon spectra, and point-defect energies predicted by our tight-binding model agree with density-functional calculations and experiment. In addition, a modification to the functional form is implemented to overcome the "collapse problem" of tight-binding, necessary for phase transformation studies and molecular dynamics simulations. The accuracy, transferability and efficiency of the model makes it particularly well suited to understanding structural transformations in titanium.