Kinetics of Order–Disorder Transformation in Alloys under Electron Irradiation

Abstract

A simple kinetic model is presented which describes the order–disorder reaction under irradiation. The model is based on the Bragg‐Williams approximation. It is assumed that radiation‐induced disordering is opposed by radiation‐enhanced reordering. The ordering process is modeled by a chemical reaction whose elementary step occurs via vacancy jumps. The activation energy of such jumps is a linear function of the degree of order. Compared to the value in disordered material it is higher for a jump contributing to disordering and lower in the opposite case. A set of rate equations is derived which allow to calculate the steady‐state vacancy concentrations as a function of the degree of order. The treatment is given in general form applicable to alloys with B2, LI2, and D1a, structure. Details are worked out numerically for B2 and D1a alloys. The results for D1a are compared with those of recent experiments on Ni4Mo.

Cu3Pd Observed by High-Voltage Electron Microscopy

“…4(a). This effect is similar to that observed previously in Ni 4 Mo by other investigators [22][23][24][25]. At this temperature, th.e high energy electrons are inducing disorder through several different mechanisms including replacement collision sequences and random point-defect annihilation.…”

“…This growth of concentration waves is what has occurred, for example, in the Cu-Pd specimens quenched from 1270 K. More significantly, it is this same phenomenon which was observed in situ in the specimens which had been disordered at 90 K and heated to room temperature where the kinetics (enhanced by the electron beam) allowed the development of the SRO state. This same explanation has also been successfully applied to the growth of the SRO state in irradiated Ni 4 Mo [23][24][25]. That the SRO state below T 0 is qualitatively similar to the fluctuating state above T 1 follows because in both cases it is the second order term in the free energy expansion which governs the configuration of the alloy.…”

“…lattice and, consequently, must have extrema at certain special points, namely, <000>, <100>, <1 70> and <777> [28]. Often, the absolute minimum of f2(k) will be at one of these special points as it is, for example, in Ni 4 Mo [23][24][25]. What distinguishes Cu-Pd in this regard is that for Pd content greater than about 16% f2(k) presents minima away from the special point (100] in the Brillouin zone; it is at the [q 10] and equivalent positions that the diffuse intensity appears as the disordered state evolves into the SRO state.…”

Spinodal ordering beyond the lifshitz point in Cu3Pd observed by high voltage electron microscopy

“…It is well known that, below 500·C, Cu-Pd fcc solid solutions undergo ordering reactions in the range of about 10 to 30 The earlier explanation by Sato and Toth 16 for the stability of LPS, based on Fermi surface considerations, is certainly valid, but inadequate for explaining the thermodynamics of LPS stability. The ANNNI model, in its original form 17,18, makes some drastic oversimplifying assumptions, for the sake of convenience, but does predict remarkably well the sequence of polytypes encountered, for example, in Al3 Til 4 and Ag 3Mg 19 systems.…”

A first-principles thermodynamic approach to ordering in Ni-Mo alloys

“…Some unique features of ordering transformation in this system have attracted the attention of several research groups. An extensive amount of research work [2][3][4] has been dedicated to understand the behavior of phase transformations that occur in this system [5,6]. There have been a number of studies on the ordering of Ni 4 Mo and Ni 3 Mo based alloys.…”