High precision electronic charge density determination for L1₀-ordered γ-TiAl by quantitative convergent beam electron diffraction

Abstract

Low order structure and Debye–Waller (DW) factors for tetragonal L1₀-ordered γ-TiAl were measured simultaneously using quantitative convergent beam electron diffraction. The high precision and accuracy (largest error <0.5%) measurements allowed the construction of charge density difference maps from full sets of structure and DW factors, suitable for validation of first principles density functional theory (DFT) calculation results. Comparison of the experimentally determined charge density distribution with theoretical DFT predictions shows excellent qualitative agreement in this study. The three-dimensional charge density representations indicate a large electron charge localisation centred about the tetrahedral site at ¼, ¼, ¼, which is coordinated by two Ti atoms at 0, 0, 0 and ½, ½, 0 and two Al atoms at ½, 0, ½ and 0, ½, ½, respectively. Compared to experimental data, the DFT calculations based on full-potential linearised augmented plane wave (LAPW) method (implemented in WIEN2K) were found to quantitatively overestimate charge density between Ti–Ti second nearest neighbour atoms. Moreover, the results from the DFT method based on the projector-augmented wave (PAW) method and a plane wave basis set (implemented in VASP) were found to differ appreciably from both the experimental and LAPW-DFT results, implying that the PAW approach may not accurately describe the bonding in the intermetallic systems with 3 d electrons, such as γ-TiAl.

Keywords:

• titanium aluminides
• electronic structure
• ab initio
• transmission electron microscopy
• convergent beam electron diffraction

Acknowledgements

This work is supported by a grant of the Office of Basic Energy Sciences, Division of Materials Science and Engineering, of US DOE (Grant No DE-FG02-08ER46545). Additional support has been received from the National Science Foundation through access to the TeraGrid resources provided by TACC under grant number (TG-DMR100102) and the Center for Molecular and Materials Simulations at the University of Pittsburgh.

Notes

Note

1. n = integer number for . Generally, for most bcc and fcc metals and alloys, n = 4 23,32–34,65.