Kinetics of order-disorder transformations in alloys

Abstract

Relaxation of order (both long-range and short-range) in b.c.c. binary alloys is theoretically worked out based on the vacancy mechanism of atomic migration, using the path-probability method of time-dependent cooperative phenomena and choosing the pair approximation. With this approximation, the system reduces to the equilibrium state specified by the Bethe approximation as the time dependence ceases. The relaxation times τ k for order parameters are calculated as functions of temperature. Necessity of more than one τ k is demonstrated. One of the τ's shows the critical slowing down, and all of the τ's increase sharply at low temperatures. Using τ k , temperature dependence of thermodynamic properties are calculated as the system is first cooled down to the freezing region, and is then heated with a constant rate of temperature change in both ways. Theoretical results show hysteresis. It is noteworthy that a second peak of specific heat appears in addition to the peak at the order-disorder transition point. The second peak is the consequence of “melting” of the “frozen in” state. The results are compared with experiments for FeCo alloys. The limitation of the “corresponding state” concept, often used in the discussion of phase transitions as well as in glass transitions, is shown by calculating the isothermal annealing behavior of the “frozen in” state at the corresponding (fictive) temperature. Since the glass transition is a “frozen in” phenomenon, the theory presented in the paper is also to be used in interpreting some experimental vitrification processes.