where t is called the tolerance factor, r_A is the radius of the A-site cation, r_B is the radius of the B-site cation, and r_X is the radius of the anion. The compound could be in an ideal perovskite structure when the tolerance factor is equal to precisely 1. Generally, the perovskite structure is stable when the tolerance factor is in the range of 0.75 to 1.00 [22]. If t lies in the approximately range of 0.9 to 1.0, the perovskite tends to exist in the ideal cubic structure. When t is lower than 0.9 but higher than 0.71, the octahedral structure will distort to break the cuboctahedral coordination and form a structure with a lower symmetry than the cubic one.

In addition to the simple ABX₃ type, the family of perovskite materials also contains many other derivatives that show different atomic ratios, such as the Ruddlesden–Popper perovskite (RP-type) [22], Dion-Jacobson perovskite [23], Aurivillius perovskite [24], etc. All these perovskite derivatives can be realized by adjusting the thickness of perovskite units or inter-layer species. Regular and repeated phases can be synthesized when the structures are ordered, while disordered modules are non-stoichiometric. Such perovskites can be regarded as “layered materials”, which leads to their special physical structures and chemical characterizations. What is more, the special crystal structure of perovskites allows some elements to exist in unusual or mixed valence states with non-stoichiometric ratios of oxygen, leading to tunable and unique chemical properties that would further benefit the catalytic reactions. Actually, the positive roles of oxygen vacancies in perovskites for catalysis have been extensively investigated. It has been found that the moderate concentration of oxygen vacancies on the catalyst surface could effectively suppress the competitive hydrogen evolution reaction (HER) and also facilitate charge transfer during the CO₂RR process [25].

The electrical conductivity of perovskites is another significant property when applied as an electrocatalyst. The RP-type perovskite materials were found to have high electrical conductivity due to the BO₆ octahedra structure [26], which benefits the charge transfer process during electrochemical reactions [27]. Compared with the simple ABO₃ perovskite, the RP-type perovskite (A₂BO₄) shows better electrical conductivity; moreover, the capability can be improved with the increasing n number because of the higher three-dimensional layered structure. In addition, the RP-type perovskite materials are stable enough under different pH conditions and oxidative potentials [28], making them promising electrocatalysts for many energy conversion reactions. In summary, the unique physicochemical properties of perovskite materials endow them with a broad application in various fields, such as energy conversion, storage, and electrochemical sensors [29,30].

In addition to chemical composition and crystal structure, particle size and microstructure also affect the performance of catalysts. Consequently, many approaches have been developed to synthesize perovskites with controlled particle size and morphology, such as wet chemistry methods, deposition-based approaches, templated-assisted synthesis, electrospinning, infiltration, exsolution, etc. In wet chemical synthesis, sol-gel processes are widely used to prepare nanosized perovskites [31,32]. In this method, citric acid [33] and ethylenediamine tetra-acetic acid [34] are often applied as the complexing agents to coordinate with the metal ions. A subsequent high-temperature calcination process should be carried out to remove the organics and facilitate the growth of perovskite crystals. Although the sol-gel method can produce purer-phase perovskites with higher surface areas when compared with the conventional solid-state method, the high-temperature calcination would inevitably lead to large agglomerated particles with a size of tens to hundreds of nanometers [35]. Template-assisted approaches have also been developed to synthesize perovskites with a porous microstructure [36]. Generally, a porous soft or hard template will be introduced in the preparation procedures, and then removed via calcination or chemical etching. The soft templates usually are self-assembled amphiphilic molecules [37,38] such as surfactants, and the hard ones can be silica-based molecular sieves [39,40] and organic polymethyl methacrylate (PMMA) [41,42]. The choice of templates should be based on the requirements for the pore size of the targeted structure of perovskites. Until now, perovskites with micropores, mesopores, three-dimensional ordered macropores, and hierarchical pores have been successfully prepared [43,44]. The porous microstructure could not only increase the surface area and hence provide more active sites but also provide convenient mass transfer channels, contributing to the greatly improved catalytic performance of perovskite-based materials for CO₂RR.