Effective medium theory with hybrid impacts of phase symmetry and asymmetry for analyzing phase transition behavior

Abstract

Recent research found a hysteresis phenomenon of electric conductance against metallic phase ratio during the thermally driven metal-insulator transition in the vanadium trioxide system. Profoundly exploring the hysteresis mechanism might help analyze the phase transition behavior. However, there is no complete analytical theory to give a quantitative description. In this work, we developed an effective medium theory to predict the relationships between the effective electric conductance and the metallic phase ratio during warming and cooling processes. It reveals that the above hysteresis is due to the hybrid impacts of phase symmetry and asymmetry in spatial distribution (termed space factor). Then, we applied this theory to deduce the nucleation and growth behavior of the minority phase in the majority phase during phase transition. The predicted relationship between metallic phase ratio and temperature is consistent with the experimental results obtained by scanning microwave impedance microscopy. It shows that the above dynamic behaviors during the warming and cooling processes are asymmetrical (termed dynamic factor). Combining the space and dynamic factors, we summarized the thermal hysteresis mechanism of the metal-insulator transition. Finally, we analyzed the influence of these two factors on the electric conductance difference during the warming and cooling processes. The result indicates that adjusting asymmetrical elements in space and dynamic factors is key to controlling thermal hysteresis magnitude. Since the electric conductance in our theory can be replaced by other physical properties, such as thermal conductivity, dielectric constant, and magnetic permeability, this work might help analyze many different phase transition behaviors.