Nonequilibrium Diffusional Phase Transformations in Alloys Induced by Migration of Grain Boundaries and Dislocations

Abstract

The main scenarios of nonequilibrium diffusional transformations induced by moving defects (dislocations, grain boundaries) in alloys under severe plastic deformation are considered. It has been shown that the phase state locally changes in the area of a defect where thermodynamic properties of alloy are locally changed, and the attained state is frozen after the displacement of a defect due to the difference between the rates of bulk diffusion and diffusion on a defect. For this reason, an alloy shifts from the state of its thermodynamic equilibrium under treatment, thus different nonequilibrium states, such as the disordering of alloy, the dissolution of equilibrium phase precipitates, the appearance of nonequilibrium phases, and the formation of regular structures, are possible depending on the type of the system. These effects may take place if the treatment of an alloy is performed at moderate temperatures, when diffusion is frozen in the bulk and rather active on defects. The phenomena of phase and structural instability developing under severe plastic deformation at moderate temperatures are considered within the framework of the proposed model.

APPENDIX

1.1 MODEL PARAMETRIZATION

In the presented calculation, the size of a grain is characterized by the ratio L/d and attains 30–200 nm (the characteristic width of a defect d was taken equal to 1 nm). The disturbance shape function near a defect was taken in the form

$$\Omega ({\mathbf{r}} - {{{\mathbf{r}}}_{{{\text{def}}}}}) = {{\left( {1 + {{{\left[ {\frac{2}{d}({\mathbf{r}} - {{{\mathbf{r}}}_{{{\text{def}}}}})} \right]}}^{{12}}}} \right)}^{{ - 1}}}.$$

((A.1))

In the case of switching in the energy of dissolution in the phases depending on the concentration (see Eq. (14)), we used the smoothened Heaviside function

$$h = {{\left( {1 + \exp \left( { - \frac{{c({\mathbf{r}}) - 0.5}}{{0.02}}} \right)} \right)}^{{ - 1}}}.$$

((A.2))

The temperature was selected from the range of 500–700 K, at which the typical values of D_GB are 10^‒13–10^–19 m²/s [59]. As follows from the formula ${{{v}}_{{{\text{def}}}}}$ = V_defL/D_def, the range considered in the calculations for the velocities of defects V_def is 10^–5–10^–14 m/s, and the characteristic time of processes are estimated by the formula τ = D_def/L²t with a spread of values of 10^–4–10⁵ s. In experiments, the abnormal transformations under SPD are usually completed for several seconds and, in principle, agree with this estimate. It is also worth noting that the generation of nonequilibrium vacancies under SPD [60] may increase the diffusion coefficient D_def (and, correspondingly, the characteristic rates of processes) by 10 orders of magnitude. Moreover, the grain boundary diffusion coefficient on nonequilibrium grain boundaries formed under SPD may grow by 3–5 orders of magnitude in comparison with ordinary conditions as a result of distortion in the lattice within the broad near-boundary area [61].

The rate of ordering processes in the theoretical models [44, 45] is determined by the time of a single atomic jump, which is much shorter than the characteristic diffusion times, whence it follows that κ₀L² $\gg$ 1. In experiments, the incubation period of ordering was observed [11, 62], probably due to the need for the implementation of long-range ordering and, in certain cases, crystal lattice rearrangement decelerating the development of this transformation.