Bragg-Williams Model Research Articles

Bragg-williams and other models of the omega phase transformation

Abstract Various previously proposed models of the β → ω phase transformation in Ti, Zr, Hf alloys are briefly reviewed. A new Bragg-Williams model of the displacive order-disorder transition is introduced in the single-variant approximation. A closed-form free energy expression is derived which exhibits typical first-order characteristics. A quantitative but approximate prediction is made for the temperature dependence of the long-range order parameter. This parameter measures the degree of advancement of (111)-plane collapse or, equivalently, the amplitude of the 2 3 [111] ω-wave.

Ni8X phases in the systems Ni-V, Ni-V-Nb, and Ni-V-Ta

In nickel-base alloys at the composition Ni8X, where “X” may be combinations of V, Nb, and Ta, the ordering reactions have been investigated by employing electrical resistivity and electron diffraction techniques. The critical temperature for the order-disorder reaction is estimated to be 405° C for Ni8V and is shown to decrease linearly with increasing vanadium content across the pseudo-binary sections Ni8Nb-Ni8V and Ni8Ta-Ni8V, in agreement with calculations based upon the Bragg-Williams model. A secondary ordering reaction between V and Nb atoms has been observed in nickel-base alloys at the composition Ni8(V0.5Nb0.5).