Rare earth Ruddlesden-Popper nickelates (Rn+1NinO3n+1±δ, R = La, Pr) have recently been found to host superconductivity (SC) under pressure when n ≥ 2, generally accompanied by a tetragonal structural phase transition. However, differences between samples such as oxygen off-stoichiometry δ and intergrowth of different polytypes cause large variations in the observed properties, including differences in the SC onset as large as 76 K (e.g. 80 K for bilayer-bilayer La3Ni2O7 [1], but only 3.6 K for the monolayer-trilayer polytype studied by the same group [2]), reduced dimensionality of the propagation space of the spin density waves (Δδ = -0.05) [3], and even the existence of SC in an orthorhombic structure as in La3Ni2O6.85 under 19 GPa of pressure [4]. Through representation-adapted Rietveld analysis of the structural distortions and domain evolution of the zero A-site size variance archetypal system Pr2-xCaxNiO4+δ, we decouple the intrinsic charge-lattice coupling across a wide phase space (10 ≤ T ≤ 500 K; 0 ≤ x ≤ 0.6; -0.4 ≤ δ ≤ 0.23) in both hole and electron-doped regimes, finding that three symmetry-breaking modes sufficiently parameterise nearly all possible structural phase transitions: two ferroelastic shear modes Γ4+(a) and Γ2+(a) with magnitudes as strong as 2.5%, and one displacive mode X3+(a;b) with a variable order parameter direction. The δ ≈ 0 phase space is nearly universally Bmab, with intrinsic phase separation existing at low temperatures across the phase diagram, similar to the LTT-LTO nanoscopic domains in the 214 cuprates [5], but with an additional Immm + I4/mmm irreversible phase separation existing in certain negative δ regions on quenching. We also show that negative δ is directly coupled to the Γ2+(a) mode (arising from vacancy ordering) and anisotropic domain broadening, whereas tetragonality (i.e. zero or minimal shear) correlates with a very positive δ, showing how other researchers can infer the approximate δ of their nickelates by simply knowing the lattice parameters and decomposing the distortions using the tool ISODISTORT [6]. Lastly, we map the shear space of the SC and charge-modulated nickelates, showing that SC predominates in hole-doped nickelate systems with a small but finite shear at ambient conditions, with strong implications on high-Tc materials design.

[1] Sun, H. et al., Nature, 2023, 621 (493-498). [2] Huang, C. et al., 2025, arXiv:2510.12250 [cond-mat.supr-con]. [3] Chen, K. et al., Phys. Rev. Res., 2025, 7 (L032014). [4] Shi, M. et al., Nat. Commun., 2025, 16 (9141). [5] Ladbrook, E. et al., arXiv:2511.18938 [cond-mat.supr-con] [6] Stokes, H. et al., ISOTROPY Software Suite, iso.byu.edu.