Potential Size-Dependent Temperature Hysteresis of the First-Order Phase Transition in a Nanoscale Metallic Powder

The paper describes the evolution of a nanoscale powder in the cyclic heat treatment process that induces first-order phase transition. Transformation α-Fe ↔ γ-Fe in the temperature cycling range 800 ↔ 1450 K is used as an example to obtain a thermal hysteresis (temperature difference between the forward and inverse transformations). The existence of a thermodynamic hysteresis is justified in conditions when the ergodic hypothesis is not valid for nanosystems, resulting in the difference between forward and inverse transformations α-Fe ↔ γ-Fe because of the difference in their energy barriers. The thermal hysteresis is determined by the superposition of size-dependent kinetic hysteresis and size-dependent thermodynamic hysteresis. Three different cases of size dependence of the hysteresis loop width for the volume content of the new phase are identified. A potential weak size effect or zero size effect in a wide nanosize range resulting from the compensation of kinetic and thermodynamic hystereses is justified for the first time. The correlations between the size of nanopowder particles, cycling rate, and hysteresis loop width for the volume content of the new phase exhibit logarithmic dependence.