Abstract
Average room temperature Debye—Waller factors B and individual (isotropic) temperature factors B Ti and B Al of γ-TiAl alloys containing 51, 54 and 56 at.% Al have been determined by conventional powder X-ray diffraction. The B values for Ti—50 at.% Al and Ti—56 at.% Al were also measured by the critical voltage method in electron diffraction. The temperature factors were calculated from the X-ray intensities using both free-atom relativistic Hartree—Fock structure factors as well as a set of structure factors obtained from first principles local density calculations for the equiatomic γ-TiAl alloy. The B values determined from the X-ray intensities using the free-atom structure factors were found to be in poor agreement with those determined by electron diffraction whereas the B values calculated from the X-ray intensities using structure factors obtained from first-principles calculations were found to be in good agreement with the electron diffraction data. This difference appears to arise because many of the low-angle structure factors of γ-TiAl (up to hkl = 224) are significantly different from the free-atom values owing to crystal bonding. It was found to be difficult to determine the individual temperature factors B Ti and B Al with high accuracy, particularly for the 54 and 56 at.% Al alloys. This is ascribed to the static contributions to the Debye—Waller factors associated with the excess Al atoms on Ti sites and to the ordering of these excess Al atoms on the Ti sublattice as discussed in recent single-crystal X-ray work on this topic.
