Figure 2

3D phase diagram that shows the most stable phases of (a) \(\hbox {Rh}_\text {Ti}\hbox {S}_\text {O}\), (b) \(\hbox {Rh}_\text {Ti}\hbox {N}_\text {O}\), (c) \(\hbox {Mn}_\text {Ti}\hbox {S}_\text {O}\) and (d) \(\hbox {Mn}_\text {Ti}\hbox {N}_\text {O}\) codoped \(\hbox {TiO}_2\) charged configurations, and (e) S-Rh, (f) N-Rh, (g) S-Mn and (h) N-Mn⁶⁵ codoped \(\hbox {SrTiO}_3\) charged configurations with minimum formation energy as a function of \(\Delta \mu _\text {O}\) and \(\mu _\text {e}\). Here, \(\Delta \mu _\text {O}\) (on x-axis) is varied according to environmental growth conditions [T and \(p_{\text {O}_2}\) (on top axes)] and \(\mu _\text {e}\) (on y-axis) is varied from VBM to CBm of pristine system. The experimental growth conditions for \(\hbox {TiO}_2\) are \(T = 848\) K, \(p_{\text {O}_2} = 2.6\times 10^{-8}\) atm⁷³ and for \(\hbox {SrTiO}_3\) are T = 1373 K, \(p_{\text {O}_2} = 1\) atm³⁷.