Isotropic and anisotropic Debye-Waller factors in off-stoichiometric ?-TiAl
Abstract (Summary)The lack of ductility exhibited by the intermetallic phase ?-TiAl, has been related to the directional nature of the interatomic bonding, as predicted by several calculations of electron charge density distribution in this compound. It is important to verify these predictions with experimental determination of the charge density distribution in TiAl. The experimental determination of electron charge density requires an accurate measurement of a number of structure factors. The energy-filtered convergent beam electron diffraction (CBED) method has been established as an accurate method for the accurate measurement of structure factors. However, the accuracy of this method is limited by the lack of knowledge of accurate values of the appropriate Debye-Waller factors. In the work presented in this thesis accurate and precise Debye-Waller factors have been measured in off-stoichiometric ?-TiAl from single crystal x-ray diffraction experiments. These Debye-Waller factors have further been used to determine the 200 structure factor in TiAl with the CBED method.A procedure for the preparation of un-deformed TiAl single crystals for the four-circle x-ray diffraction experiments has been developed in this work. Weak, diffuse intensities were observed in the x-ray diffraction experiment, which correspond to the kinematically forbidden reflections (hkl) in TiAl with indices h+k=2n+l. Calculated static structure factors were fitted with the experimental structure factors which were corrected for polarization, absorption and extinction using a non-linear least square refinement to obtain the Debye-Waller factors. Isotropic and anisotropic, site specific Debye-Waller factors were extracted from Ti-54A1 and Ti-56A1 single crystal data. Accurate lattice parameters were also determined from the x-ray diffraction experiments.The anisotropic Debye-Waller factor calculations result in a better fit between the calculated and experimental structure factors. These calculated structure factors also explain the scatter in the experimental structure factors for higher order reflections, which has previously been attributed to experimental error. The ordering of excess Al atoms on one of the Ti sites, with the anisotropic Debye-Waller factors, explains the diffuse intensities obtained for the forbidden reflections with h+k=2n+l. Compositional uncertainty did not affect the Debye-Waller factors of the Al sites, whereas it affected the Ti site which accommodated the excess Al atoms.The 200 structure factor in TiAl was determined from the CBED method by using the accurate anisotropic Debye-Waller factors extrapolated to the appropriate composition. The effects of compositional accuracy and changes in sample thickness on the 200 structure factor were also studied. The most accurate measurement of structure factors is obtained for a composition of Ti-52.3 at.% Al. The present results for changes in structure factors with thickness of the sample are contrary in tendency to those previously reported.Diffuse intensities corresponding to a Ti3 Al5 type ordering were observed in the electron diffraction experiments. These intensities exhibited characteristics commonly ascribed to short-range order, in this case, associated with small clusters of Ti3 Al5 embedded in the ?-TiAl matrix. However, sufficient intensities corresponding to this ordering were not observed in the x-ray diffraction experiments, which could be attributed to the overall small volume fraction of this secondary phase. Hence, the Ti3 Al5 ordering was not used to model the Debye-Waller factors here. However, it is important to understand the effect of such ordering on the determination of structure factors in TiAl in the future.
School:The Ohio State University
School Location:USA - Ohio
Source Type:Master's Thesis
Date of Publication:01/01/1997