A Unified View of the Substitution-Dependent Antiferrodistortive Phase Transition in SrTiO₃

The cubic-to-tetragonal antiferrodistortive transition at 105 K in the most widely studied perovskite, SrTiO₃, is perhaps the preeminent example of a second-order structural phase transition. Extensive investigations since the 1960s have tracked the softening of the phonon mode associated with this transition, the development of octahedral rotations, and the interplay with incipient ferroelectricity and superconductivity. It is less well known that modest ionic substitutions alter the transition temperature (T_a) over a remarkable range in SrTiO₃, from 0 K to above ambient. Here, we first study the thermodynamics of the transition via specific heat and determine a T_a shift of +10.9 K/atomic % in Nb-substituted crystals, the most heavily studied in terms of electronic transport. We then present the first quantitative rationalization of the trends in T_a with substitution in SrTiO₃. We demonstrate that the apparently complex behavior versus tolerance factor occurs simply due to a nonlinear dependence of the rate of change of T_a with substituent concentration. We then connect this to ionic valence mismatch, using bond valence concepts to establish a new parameter, «ϵ⁴», which exhibits a universal linear dependence with T_a for all known substitutions. This provides the first unified view of the substituent-dependent T_a in SrTiO₃, deepens our understanding of the phase transition (including a theoretical maximum in the rate of T_a suppression), and demonstrates predictive power via a simply computed parameter.