Fig. 3

Total energies against the defect concentration plots for a LaHf, b (LaHfVO), c SiHf, and d SiHfLaHf defects in HfO2. All the points are extracted from Fig. 2 for a better representation of the linear dependencies. The points for the pure HfO2 and 3.125 f.u.% LaHf and SiHf defect concentration are single data points. All other points in the plots are the medians of the corresponding distributions. The second row of plots e–h shows half the interquartile range IQR(E)/2, as a measure of energy variations caused by dopant interaction, versus defect concentration for the four defects. The third row of plots i–l shows \(\sigma (\bar E)\), caused by dopant concentration, versus defect concentration for the four defects