Quantum-defect theory of heats of formation and structural transition energies of liquid and solid simple metal alloys and compounds

Abstract

The tables of $l$-dependent ion-core radii ($l=0,1,2\mathrm{}$) derived from free-ion quantum defects and previously presented by Simons and Bloch are extended to include halogens and the group-$\mathrm{I}-B$ metals (Cu, Ag, and Au). From these radii hybridized bond-orbital coordinates with $\sigma$ and $\pi$ character are formed. The dual bond-orbital coordinates are used to discuss the structures, uniaxial distortions, and melting points of more than 100 simple binary compounds belonging either to the octet family $A^N{B}^{P-N}$ with $P=8\mathrm{}$ or to the suboctet family $2\le P\le 6$. Two conclusions emerge: the quantum bond-orbital $\sigma$ and $\pi$ dual coordinates describe the physical properties of these materials much more accurately than traditional classical coordinates such as size and electronegativity, and the dual quantum coordinates are equally accurate for octet and suboctet compounds. The success of the quantum coordinates implies that bond charges with $\sigma$ and $\pi$ components make important contributions to the structural energies of these materials. The dual coordinate cellular scheme developed by Miedema and co-workers to describe the sign of the heat of formation of liquid and solid metal alloys is examined within the context of orbital, $l$-dependent ion-core radii. We show that Miedema's original coordinate set is unphysical, but that his inductively revised coordinates which are derived from more than 500 binary phase diagrams are remarkably accurate. Apparent irregularities in the revised coordinates are shown by comparison with the orbital shell model to be correct and the consequence of core shell structure.