Charge Density Determination for Al-rich Composition L1o-ordered gamma-TiAl by Convergent Beam Electron Diffraction
Microscopy and Microanalysis
The electron density difference map, ∆ρ(r)= ρ(r) Cryst -ρ(r) IAM , here defined as the difference between the electron density of a crystal, ρ(r) Cryst , and that of the equivalent independent atom model (IAM), ρ(r) IAM , represents one of the quantum mechanical characteristics central for developing fundamental understanding of materials. Convergent beam electron diffraction (CBED) experiments performed with modern transmission electron microscope (TEM) instruments equipped with energy filter
... with energy filter and charge coupled devices (CCD) permit probing of nano-scale volumes of perfect crystal and have been shown to enable the measurements of low-order structure factor, F g , with sufficient accuracy to obtain Δρ(r) for 3d-electron system transition metals (e.g. Cr, Fe, Co, Ni) and some binary intermetallic phases (e.g. NiAl, TiAl and FePd) [1, 2] . The facility to determine experimentally the Δρ(r) for these d-electron materials warrants use of the CBED measurements as additional metrics in validation of density functional theory (DFT) calculations . Using multi-beam off-zone axis (MBOZA) CBED diffraction geometries sets of multiple Fg and the Debye Waller factors have been determined here for the chemically ordered intermetallic phase γ-TiAl with slightly Al-rich off-stoichiometric composition, i.e., Ti-52at%Al. The lattice parameters of the offstoichiometric γ-TiAl phase, with the tetragonal L1 0 structure, and the elemental composition have been determined by combining X-ray diffraction, locally resolved CBED HOLZ line analyses  and X-ray energy dispersive spectroscopy using binary standards [2, 4] . Experimental details and the dynamical diffraction theory based iterative refinements for the CBED data quantifications have been described previously [1, 2] . It has been shown for equiatomic γ-TiAl that DFT calculations based on the local density approximation (LDA) fail to treat accurately the 3d-electron system related bonding effects, while using the generalized gradient approximations (GGA) achieved considerably improved match and qualitatively excellent agreement with experimentally determined low-order F g and ∆ρ(r) [2, 4]. However, GGA DFT calculations predicted larger electron charge delocalization than is observed in the CBED based experimentally determined Δρ(r) for equiatomic γ-TiAl . Figure 1 shows the difference between the X-ray structure factors, F g , determined here for the two different composition TiAl phase crystals and the IAM based X-ray structure factors. Based on sets of the first five low-order structure factors, F g , those with Miller indices hkl satisfying h 2 +k 2 +l 2 <5, charge density maps, ∆ρ(r), have been obtained from the CBED experiments and GGA DFT calculations (e.g. Fig. 2) . Comparison of the ∆ρ(r) obtained from CBED and DFT indicated that effects from the small (2at.%) Al-excess in the binary intermetallic phase γ-TiAl are most discernible for the compositionally all-Ti planes, e.g. the (001)sections (Fig. 2) . Incorporating the excess Al by substitution on Ti sites appears to enhance delocalization of charge density between second nearest neighbor Ti atoms along <010>, while reducing it for nearest neighbor Ti atom bonds along <110> (Fig. 2) .