IMF2017

We review the physical geometric constraints of the new simple material model (NSMM) and compare them with Goldschmidt’s tolerance factor formalism, a correlation relation. NSMM geometric constraints serve as an important template for determination of coordination and temperature dependent elemental, genome-like, ion properties, and ionic radii, as shown in “NSMM Review – Part III”. While temperature dependent geometric considerations, including ionic radii, are not sufficient for ultimate determination of crystal structure, importantly, the coordination and temperature ionic radii, which significantly improve the accuracy and precision of lattice volume as a function of temperature, are essential inputs to the Clausius – Mossotti relationship for determination of coordination and temperature dependent ionic polarizability, as shown in “NSMM Review – Part IV”. Importantly, the combined genome-like ion properties, radii and polarizability provide the temperature dependent relative permittivity of materials and the temperature of polarization-induced structural phase transitions. Further, another type of phase transition, a geometrically constrained volume-induced structural phase transition, has been recently identified, see “NSMM Review – Part V. In totality, geometric considerations when coupled with temperature dependent ionic properties, radii and polarizability allow us to physically understand why the majority of “simple” and “simply mixed” Perovskites are not cubic at room temperature and why so many of them undergo structural phase transition from a high temperature cubic-prototype.