Periodic table representation of binary, ternary and higher-order systems of inorganic compounds

We enumerate the chemical elements by using the periodicity of the Mendeleev Periodic Table, where the rows reflect the principal quantum number of the electronic configuration of the elements as isolated atoms. By doing that we assign the Periodic Number (PN) to the elements, which expresses much more clearly the chemical similarity between them along the groups. Moving from the unary to higher-order systems, the PN representation shows in an elegantly simple and holistic manner the periodicity of chemical properties and phase stability.By using the PNs of the constituent elements of binary systems, we construct the phase map in which we identify seven regions where phases are not formed, namely the non-former regions. Except for very few distinct systems that violate the identified non-former regions, the seven forbidden regions represent the phase space where phases are not formed in any composition of the constituent elements, whose PNs fall in the given PN ranges also for higher-order systems. In fact, the PN representation of the binary phases map can be easily extended to any higher-order chemical systems to delimit the regions where to search for possible phases, namely the former regions.The powerful usage of the PN representation is seen in the chemical property trends we report for the equiatomic binary phases, for which we calculate, after fully relaxing the crystal structures, the enthalpy of formation, the cohesive energy, the lattice stability and the bulk modulus by using total energy calculations at Density Functional Theory level.