Hi Muhammad, I think Goldschmidt's tolerance (t)  is a key factor to prepare Perovskite structure, ABO3.  In more detail, the structural family of perovskites , ABO3 can be described as consisting of corner sharing [BO6] octahedra with the A cation occupying the 12-fold coordination site formed in the middle of the cube of eight such octahedra. The ideal cubic perovskite structure is not very common and also the mineral perovskite itself is slightly distorted. Pioneering structural work on perovskites were conducted by Goldschmidt et al in the 1920s that formed the basis for further exploration of the perovskite family of compounds. Distorted perovskites have reduced symmetry, which is important for their magnetic and electric properties. If the large oxide ion is combined with a metal ion having a small radius the resulting crystal structure can be looked upon as close packed oxygen ions with metal ions in the interstitials. In some perovskites, the distortion of the structure can be assigned to Jahn – Teller active ions at the B position. For example in LnMnO3 (Ln = La, Pr or Nb) with Mn3+ ions the 3d4 electrons divide up into 3 tg and 1 eg electron.

In the ideal cubic case the cell axis, a, is geometrically related to the ionic radii (rA, rB, and rO) as described in this equation: a = square root of 2 (rA + ro) = 2 (rA + rB) 

The ratio of the two expressions for the cell length is called the Goldschmidt’s tolerance factor t and allows us to estimate the degree of distortion. t =  (rA + rB)/ square root of 2 (rA + ro), where the cubic structure will be happened if : 0.89 < t < 1 . Lower values of t will lower the symmetry of the crystal structure and higher the values of t will form hexagonal structure.  Another case of modification is happened if the octahedral B4+ position shifts into two sites for B’+ and B’’3+ (as super structure of perovskite) or forms a vacancy. In addition to, Perovskites with transition metal ions  on the B site show an enormous variety of intriguing electronic or magnetic properties. This variety is not only related to their chemical flexibility, but also  to a larger extent related to the complex character that transition metal

ions play in certain coordinations with oxygen or halides. While magnetism and electronic correlations are usually related to unfilled 3d electron shells of the transition metal ions, pronounced dielectric properties are connected with filled 3d electron shells. 

I hope this information will be useful

Rudy S

Yes, I agree with Rudy; but in general, perovskite structure is defined by ABX3 configuration because the X anion could be another chemical element (e.g. fluoroperovskite ABF3) not only oxygen. I recommend that you probe a simulation using SPuDS (this program works with Goldschmidt's equation and it calculates the Tolerance Factor -t- and the Global Instability Index -GII-). Those parameters have a big importance in the chemical and structure stability, also, it allows to verify some combinations for your production process.

About photovoltaic properties, it depends: some researchers talk about new materials with complex perovskites doped with Rare Earths (see Springer page) and tell us for possible photovoltaic behavior related with a structure distortions and tilts.

The possible photovoltaic behavior is based in a INSTABILITY (not stability) for the crystalline structure of a perovskite, specially, about charge or spin variations; however the first one is the most important phenomenon that the photovoltaic reaction appears.

Regards,

Edward Caro