Complex perovskites draw a great attention of many scientists and engineers due to anomalous properties in the region of morphotropic phase boundary. $PZN-PT((1-x)Pb(Zn_{1/3}Nb_{2/3})O_3-xPbTiO_3)$ exhibits a giant piezoelectricity at x=0.09. Colossal magnetoresistance(CMR) is observed in $LCMO(La_{1-x}Ca_xMnO_3)$ near x=0.33. The origin of the concerned phase coexitence is not understood well.
A new concept of mole ratio transformation is introduced. A scale invariance symmetry is found to exist in a mole ratio transformation. Scale invariance has a crucial role in that different phases can exist at the same thermodynamic condition - an absolute zero temperature. Perovskite materials of given chemical compositions are classified according to this mole ratio.
