Simulation of dielectric behavior in RFeO$$_{}$$ orthoferrite ceramics (R = rare earth metals)

Due to their colossal dielectric constant (CDC), \(\hbox {RFeO}_{3}\), orthoferrite ceramics (R = rare earth metal) have recently attracted much attention. In the present research, the dielectric constants of \(\hbox {RFeO}_{3}\) orthoferrite ceramics, whether with or without CDC, have been simulated. The type of synthesis method, the type of R material, temperature, and frequency as the effective parameters on the dielectric behavior are introduced to the model. Another input parameter is the ratio of \(\hbox {Fe}^{+2}/\hbox {Fe}^{+3}\) peak area (in the XPS diagram), which is the most important parameter that affects the CDC behavior. Initially, a colossal database is formed by means of WebPlotDigitizer software and 2930 experimental data, and then the simulation is carried out through gene expression programming. Two case studies are also performed on \(\hbox {PrFeO}_{3}\) and \(\hbox {NdFeO}_{3}\) orthoferrite ceramics to validate the accuracy of the presented model. \(\hbox {PrFeO}_{3}\) exhibits significant CDC behavior whereas the \(\hbox {NdFeO}_{3}\) ceramic samples possess little CDC property, both of which were precisely simulated by the model. Two-dimensional tenth-degree equations resulting from the model predict the dielectric constant variations accurately.