Based on Bruggeman's symmetric effective-medium formula and an explicit expression derived for the temperature evolution of the volume fractions of the metallic and isolating domains appearing during the heating and cooling of ${\mathrm{VO}}_2$, respectively, we develop a model to describe the hysteresis of its electrical and thermal conductivities as well as of its specific heat capacity. The model takes into account the average value and standard deviation of the transition temperatures of the individual domains, as well as their activation energies, which represent the driving force for the existence of the ${\mathrm{VO}}_2$ hysteresis. It is shown that the model's predictions driven by these three parameters related to the microstructure of ${\mathrm{VO}}_2$ are in good agreement with robust experimental data. Furthermore, as these parameters are intrinsically correlated to the doping, defect, strain, and interface effects of ${\mathrm{VO}}_2$, the proposed model enables the seamless integration of these effects, and therefore, its predictions are also expected to be useful for describing the thermal and electrical properties of composites based on ${\mathrm{VO}}_2$.

• Received 22 June 2018
• Revised 28 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.075144