Regulatory tolerance and octahedral factors by using vacancy in APbI3 perovskites

Abstract The Goldschmidt tolerance factor and the octahedral factor are widely used to predict stable crystal structures of perovskite materials. A t value between 0.8 and 1.0, and a u value larger than 0.41 usually result in stable perovskite structures. In this study, we set the effective radii of ions of the vacancy at both Pb sites and I sites as zero, decreased the weighted average effective ion radius, and accurately controlled the Goldschmidt tolerance factor and octahedral factor by the content of Pb-sites or I-sites vacancy. Considered by ionization, the results suggest the potential existence of the undiscovered perovskites as APb 1- x I 3 with the single cation vacancies, CsPbI 3- y with y  = 0–1.00 with the single anions vacancies, and double vacancies at both the Pb-sites and I-sites perovskites APb 1- z X 3-2 z (A = Na, K, Rb, and Cs). Finally, a simulation study was performed based on first principle, and the results indicated the structural stability and the effect of the vacancy on the physical properties.