Fig. 2

The total energies of the La defects a, Si defects b, and their mixtures c in HfO2. The big colored diamonds mark single data points. The box diagrams depict the distributions of data points: the colored box body marks the lower and upper quartiles, the line in the box is the median, the whiskers are the lowest and the highest values neglecting the outliers, which are marked by small black diamonds. The quartets of colored diamonds or box diagrams represent the sets, as described in Table 1. They are sorted in an ascending order of concentration along the horizontal axis. The background color associates the sets with defect concentration labels at the bottom edge and the defect type itself is labeled at the top edge. The four colors mark different crystal phases as described in the legend. All sets are referenced to the corresponding m-phase data point or distribution median \(\tilde E_{{\mathrm{tot}}}^{\mathrm{m}}\)