Intermetallic Compounds and Alloy Bonding Theory Derived from Quantum Mechanical One‐Electron Models

Abstract

This chapter traces, to the current day, one‐electron quantum mechanical concepts as applied to intermetallic compounds and alloys. Three main threads are followed: the evolution over time of the tight‐binding model, the role of nearly free‐electron theory, and the adaption of one‐electron ideas to experimentally derived phenomenological theories as applied to these systems.Analysis of tight‐binding theory begins with the two‐electron bond: The case of hydrogen is contrasted to the alkali metals. The connection between tight‐binding theory and density functional theory is explored: Tight‐binding theory is found to reproduce well the more computationally precise DFT band structures. Models that emanate from tight‐binding theory include the COOP and COHP analysis of the metallic bond, site preferences (the coloring problem), and Mulliken populations. Tight‐binding moment theory is also shown to account for crystalline structural preferences. The Dronskowski–Landrum model for magnetically ordered systems is presented. Recent developments focused on localized orbitals (Wannier functions), and transition metal electron‐counting (for half‐Heusler, Nowotny chimney ladder phases, and other phases) is explored. Reversed approximation molecular orbital analysis to these latter systems is presented.The role of nearly free electron theory and its role in the understanding of Hume‐Rothery electron phases is presented. The importance of the Jones zone is made clear, not just for these phases but also for more complex phases, including the Samson phase, Cd3Cu4, with 1124 atoms in its unit cell. Recent work combining the Jones model of orbital mixing with the Zintl concept of electropositive to electronegative atom electron transfer is found to lead to corrected Jones zones for the quasi‐crystalline approximant phase Li52.0Al88.7Cu19.3. An explanation of the unusual electron count of the 1e−/aγ‐brass structure Li33Ag19is derived. The role of pseudopotentials in accounting for structural distortions is reviewed.Finally, a look at how well‐known phenomenological analyses have evolved into modern quantum theory‐based models is explored. Among these is the role of structure maps, where the Pettifor tight‐binding model for structure maps is presented. The phenomenological Pearson analysis of steric strain is shown to lead to chemical pressure analysis via ‐based Hückel theory. The classic Brewer analysis of electron transfer from electropositive to electronegative atoms evolves into the ‐Lewis acidity model.

Understanding element solution energies in nickelbase alloys using machine learning

“…In [6], the atomic radius was found to be a crucial parameter in determining the tendency of an element to form TCP phases. In our case of a Ni 3 A-phase, the size difference between nickel and the phase-forming element causes a chemical pressure [33], with Ni-Ni bonds being strained (for example, the distance between two nickel atoms in γ″ in our calculations is 2,57Å and 2.61 Å, compared to a bond length of 2.489 Å in pure Ni) and the Ni-A bonds being compressed. Replacing the phase-forming element with a smaller atom or Ni with a larger atom thus relieves this chemical pressure and is energetically favourable.…”