Metallic bonding

Metallic bonding is a chemical bond created by the electrostatic attraction between a cloud of delocalized electrons—often called conduction electrons—and positively charged metal ions. In this arrangement, metal atoms lose their valence electrons to a large, shared orbital, leaving behind the nucleus and its closer electrons as positive cations. These cations form a crystal lattice, held together by the negative charge of the delocalized orbital. The bond can be thought of as a more spread-out version of covalent bonding, where free electrons are shared across a structure of positive ions. This type of bonding explains many physical traits of metals, including strength, ductility, electrical and thermal conductivity, opacity, and luster.

Metallic bonding is not the only kind of chemical bond that a pure metal can have. For instance, elemental gallium forms covalently bonded pairs of atoms in both its liquid and solid states; these pairs then arrange into a crystal structure with metallic bonds between them. Another example is the mercurous ion (Hg₂²⁺), which involves a metal–metal covalent bond.

**History**

As chemistry matured into a science, it became obvious that metals made up most of the periodic table, and scientists made great strides in describing the salts formed when metals react with acids. With the rise of electrochemistry, it became clear that metals generally dissolve as positive ions, and their oxidation reactions were well understood through the electrochemical series. This led to a picture of metals as positive ions held together by a sea of negative electrons.

Quantum mechanics later gave this picture a more formal shape with the free electron model and its refinement, the nearly free electron model. Both models treat electrons as a gas moving through the solid, with an energy that depends only on the magnitude of the momentum vector k, not its direction—making it essentially isotropic. In three-dimensional k-space, the highest filled energy levels (the Fermi surface) should therefore form a sphere. The nearly free model adds box-like Brillouin zones to k-space, arising from the periodic potential of the ionic structure, which slightly breaks the isotropy.

The development of X-ray diffraction and thermal analysis allowed scientists to study the structure of crystalline solids, including metals and alloys, leading to phase diagrams. Still, the nature of intermetallic compounds and alloys remained largely mysterious, and their study was often empirical. Chemists tended to avoid anything that didn't follow Dalton’s laws of multiple proportions, leaving the problem to metallurgy.

The nearly free electron model was eagerly adopted by some metallurgists, notably Hume-Rothery, to explain why certain intermetallic alloys form while others do not. His initial attempts were quite successful. He proposed adding electrons to inflate the spherical Fermi balloon inside a series of Brillouin boxes, predicting when a box would become full. This correctly forecast many alloy compositions. However, when cyclotron resonance became available and the actual shape of the Fermi surface could be measured, it turned out the balloon was not spherical—except perhaps in cesium. This showed that a model can yield many correct predictions while still being wrong in its basic assumptions.

This failure pushed researchers to revise the idea of ions floating in a sea of free electrons. Several quantum mechanical models emerged, including band structure calculations based on molecular orbitals and density functional theory. These models either start from the atomic orbitals of neutral atoms sharing electrons or, in the case of density functional theory, from the total electron density. Despite this, 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. Alongside electronic states, vibrational states were also shown to form bands. Rudolf Peierls demonstrated that in a one-dimensional row of metallic atoms, an inevitable instability would break the chain into individual molecules. This raised questions about when collective metallic bonding is stable and when localized bonding takes over, leading to further research on metal atom clusters.

While the band structure model proved powerful for describing metallic bonding, it remains 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 one-electron treatment might work for strongly delocalized s- and p-electrons, but for d-electrons—and even more so for f-electrons—interactions with nearby individual electrons and atomic displacements can become stronger than the delocalized interactions that produce broad bands. This helped explain the transition from localized, unpaired electrons to itinerant ones that participate in metallic bonding.

**The nature of metallic bonding**

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