The classical Goldschmidt factor is defined for the ABO3 system with perovskite structure (as in CaTiO3) and depends on the diameter of the A- and B-site cation or rather their ratio.

Since the Ruddlesden-Popper phase is (simplified) considered a NaCl-like stacking fault, I am not sure how you could calculate a tolerance factor that is defined for another crystal structure. Can you elaborate on that?

Fabian J. Altermann

thanks for your answer;

actually, I want to know how I can get the suitable ionic radius in A'2An-1BnX3n+1 (general formula of 2DRP perovskite) for a stable structure.

in halide Ruddlesden-Popper perovskite we have a spacer cation (A') and I think it is different from oxide Ruddlesden-Popper perovskite.

I don't know how I can consider the role of the ionic radius of spacer cation on the stability of the structure. on the other hand, I guess, the (n) has to play an important role in the stability of the structure because when n tends to infinity, we will have a simple perovskite structure and when n is 1, we will have a 2D structure.

The precise and probabilistic nature of τ, as well as its simple functional form—depending only on widely available Shannon radii (and the oxidation states required to determine the radii)—enables the rapid search across composition space for stable perovskite materials. Before attempting synthesis, it is common for new materials to be examined using computational approaches; therefore, it is useful to compare the predictions from τ with those obtained using density functional theory (DFT). The stabilities (decomposition enthalpies, ΔHd) of 73 single and double perovskite chalcogenides and halides were recently examined with DFT using the Perdew-Burke-Ernzerhof ) exchange-correlation functional (DFT). τ is found to agree with the calculated stability for 64 of 73 calculated materials. Importantly, the probabilities that result from classification with τ linearly correlate with ΔHd, demonstrating the value of the monotonic behavior of τ and P(τ) (Fig. 2D and table S3).

Article New Tolerance Factor to Predict the Stability of Perovskite ...