Metallic bonding

Metallic bonding is a chemical bond created by the electrostatic attraction between conduction electrons—which exist as a delocalized electron cloud—and positively charged metal ions. In this process, metal atoms lose their valence electrons to a large, delocalized orbital, leaving the nucleus and its closer electrons as positive cations. These cations arrange into a crystal lattice, held together by the negative charge of the delocalized orbital. The bond can be seen as free electrons shared across a framework of positive ions, making it a more spread-out version of covalent bonding. This bonding explains many metal properties, including strength, ductility, thermal and electrical resistivity and conductivity, opacity, and luster.

Metallic bonding isn't the only bond a pure metal can show. For instance, elemental gallium forms covalently-bound pairs of atoms in both liquid and solid states; these pairs then create a crystal structure linked by metallic bonding. Another example is the mercurous ion (Hg₂²⁺), which involves a metal–metal covalent bond.

**History**

As chemistry became a science, it was clear that metals made up most of the periodic table, and progress was made in describing salts formed from reactions with acids. With electrochemistry, it became evident that metals generally enter solution as positive ions, and their oxidation reactions were understood through the electrochemical series. This led to a picture of metals as positive ions held together by an ocean of negative electrons.

Quantum mechanics gave this picture a formal interpretation with the free electron model and its extension, the nearly free electron model. In both, electrons behave like a gas moving through the solid, with energy that is essentially isotropic—depending only on the magnitude of the momentum vector k, not its direction. In three-dimensional k-space, the highest filled energy levels (the Fermi surface) should thus form a sphere. In the nearly-free model, box-like Brillouin zones are added to k-space due to the periodic potential from the ionic structure, slightly breaking the isotropy.

X-ray diffraction and thermal analysis allowed the study of crystalline solids, including metals and alloys, leading to phase diagrams. Despite this, the nature of intermetallic compounds and alloys remained mysterious, often studied empirically. Chemists generally avoided anything that didn't follow Dalton's laws of multiple proportions, leaving the problem to metallurgy.

The nearly-free electron model was adopted by some metallurgists, like Hume-Rothery, to explain why certain intermetallic alloys form and others don't. His early attempts were successful: he added electrons to inflate the spherical Fermi-balloon inside a series of Brillouin-boxes, predicting when a box would fill. This matched many observed alloy compositions. However, when cyclotron resonance allowed measurement of the balloon's shape, it turned out not to be spherical—except possibly for caesium. This showed that a model can make correct predictions while being wrong in its basic assumptions.

This failure led researchers to modify the idea of ions flowing in a sea of free electrons. Quantum mechanical models emerged, such as band structure calculations based on molecular orbitals and density functional theory. These start from atomic orbitals of neutral atoms sharing electrons, or from total electron density. Still, the free-electron picture remains dominant in introductory metallurgy courses.

The electronic band structure model became a major focus for studying metals and even more so semiconductors. Vibrational states also formed bands. Rudolf Peierls showed that a one-dimensional row of metallic atoms would inevitably break into individual molecules due to instability. This raised questions about when collective metallic bonding is stable versus when localized bonding takes over, leading to research on metal atom clusters.

Though powerful, the band structure model is a one-electron approximation of a many-body problem: each electron's energy states are described as if all other electrons form a uniform background. Researchers like Mott and Hubbard realized this treatment works for strongly delocalized s- and p-electrons, but for d- and especially f-electrons, interactions with nearby individual electrons and atomic displacements can become stronger than the delocalized interaction that creates broad bands. This better explained the transition from localized unpaired electrons to itinerant ones involved in metallic bonding.

**The nature of metallic bonding**

Metallic bonding arises from two phenomena: electron delocalization and the availability of many more delocalized energy states than delocalized electrons. The latter could be called electro...