X-ray determination of the Debye–Waller factors and order parameters of Ni₃Al alloys

Integrated intensities of Bragg reflections have been measured at room temperature for Ni₃Al alloys containing various amounts of boron, hafnium, zirconium and titanium and the data have been used to evaluate the mean Debye–Waller factors (〈B〉), Debye temperatures (Θ_M) and long-range-order parameters (S). The Debye temperatures are observed to show a slight decrease with the decrease of aluminium content within the Ni₃Al phase. The results for the Debye–Waller factors indicate that additions of the ternary elements hafnium, zirconium and titanium cause the mean Debye–Waller factor to increase linearly, while boron addition results in a nonlinear increase. The long-range-order parameter of stoichiometric Ni₃Al is 0.97, which decreases with decreasing aluminium concentration from the stoichiometric composition. The long-range-order parameter of Ni₃Al increases until 0.75 at.% B has been added, beyond that it remains constant. The long-range-order parameter of Ni₃Al increases initially with the addition of hafnium, zirconium and titanium up to 0.50 at.% Hf and 0.52 at.%Zr, with further addition of hafnium and zirconium, it decreases. The results are discussed in relation to the crystal structure and chemical bonding in Ni₃Al.