Abstract
Titanium (Ti)-based halide perovskites with A(2)TiX(6) and ATiX(3) stoichiometry can be promising alternatives to lead-based perovskites due to their high cuboctahedral stability and reduced internal stresses. It is important to study compositional stability and crystal chemistry controlling the formation of BX6 octahedral periodic arrays in Ti-based perovskites. Here, we investigate on the formability of Ti-based mixed organic-inorganic and all-inorganic perovskite crystals via establishing a library of tolerance (t) and octahedral (mu) stability factors using random sampling of ionic radii. Structural mapping and machine learning analysis are performed for twelve Ti-perovskites selected by mixing/matching cations with halide anions. Formation probabilities from normal/binomial distributions are integrated into a statistical algorithm used in a "Decision tree classifier" to obtain training/testing datasets. We relate perovskites stability to cuboctahedral formation considering complex crystal chemistry including ionic radii, bond length from ions electronegativity, and bond-valence sums from coordination numbers. Results revealed that cuboctahedral B-sites should be occupied by Ti cations to have a stable structural composition. High formation tendencies are estimated for methylammonium Ti-based chloride or bromide perovskites. Game theory methods determined six formable structures (Cs2TiX6 and RbTiX3 for X = F-, Cl-, Br-). Probabilities of formation of future datasets with different halides are A(m)TiBr(3m) (0.93) > A(m)TiCl(3m) (0.91) > A(m)TiF(3m) (0.79) > A(m)TiI(3m) (0.52) matching statistical results with +/- 8% marginal error and 96.3% classification accuracy; there is optimality in having a (Ti-Br)-like structure for a balanced cuboctahedral. This work shows a potential towards the discovery of novel lead-free perovskites for photoluminescence, tunable bandgaps, tunneling junctions, and photovoltaic applications.