Metallic Bonding

Metallic bonding can be understood as a limiting form of covalent bonding in which the shared electrons are not localised between any specific pair of atoms but are instead free to roam throughout the entire crystal structure. ^[1] The mental picture is of positively charged metal cores packed together in a regular lattice, bathed in a mobile sea of electrons that acts as a kind of electrostatic glue binding them in place. ^[1] The attraction is the same as in covalent bonding - the delocalised electrons spend most of their time in the spaces between the cores, creating a region of net negative charge that draws the positive cores together - but the electrons are not committed to any individual bond. They belong to the metal as a whole, not to any pair of adjacent atoms.

Conditions for Metallic Bonding

Three factors favour the formation of metallic bonds over covalent or ionic alternatives. ^[1] The first is weak electron affinity: metals have low electronegativity values and therefore hold their outer valence electrons loosely. They give them up easily to the communal electron sea rather than localising them in directional bonds.

The second factor is the number of electrons that would need to be shared to reach a noble-gas configuration. When that number is large, forming enough localised covalent bonds to distribute all of those electrons is impractical. Sodium, for example, would need to share seven additional electrons to acquire the argon configuration - far more than is feasible through pairwise covalent overlap. Non-metals, by contrast, need to gain only one or two electrons, making localised covalent or ionic bonding much more accessible to them. ^[1]

The third factor is the availability of vacant energy levels into which valence electrons can move. This availability is controlled in part by the spacing between atoms and is most directly explained through the concept of energy bands.

Energy Bands and Electrical Conduction

When isolated atoms are brought into the close proximity they occupy in a solid, the Pauli exclusion principle - which forbids any two electrons from having identical quantum numbers - forces the energy levels of each subshell to spread out. ^[1] What was a single energy level in an isolated atom becomes a band of closely spaced levels in the solid. In crystals containing on the order of 10²² atoms, these levels are so densely packed within each band that they are effectively continuous. ^[1] As atoms are brought closer together, the bands grow wider. Conduction - the free movement of electrons - becomes possible in two situations: when the outer valence subshell is only partially filled, or when the energy band of a filled subshell overlaps with an adjacent empty band.

Magnesium illustrates the first mechanism. When Mg atoms are packed to metallic densities, the 3s and 3p energy bands broaden until they overlap. Every available 3s energy level is occupied, but the 3p band - vacant in isolated atoms - now overlaps in energy with the filled 3s band. Electrons from the 3s band are free to move into the 3p band, where the abundance of vacant energy levels lets them migrate through the crystal in response to an applied voltage. ^[1] In this framework the occupied 3s band is the valence band (the source of the mobile electrons) and the empty 3p band is the conduction band (the destination into which they move). The inner filled subshells do not participate because a band gap - an energy range with no available states - separates them from the conduction band. ^[1]

Sodium illustrates the second mechanism. Its 3s subshell is only half-occupied, so the 3s band in metallic sodium is simultaneously the valence band and the conduction band - it provides mobile electrons and it has vacant levels for them to move into, all within the same band. ^[1] The transition metals, such as iron, use both mechanisms simultaneously: their d subshells typically carry unfilled orbitals that support conduction within the d bands, and the d band energy also overlaps with the higher s and p bands. ^[1]

Physical Consequences

Because metallic bonds require no specific orbital orientation, they are non-directional. Metal atoms pack together in highly symmetrical, close-packed arrangements - the structure is governed by the drive to fill space efficiently and maximise the number of nearest neighbours, not by the need to align specific orbitals. ^[1]

The electron sea also confers another important property: easy substitution. Because metallic bonds make no demands on the identity of the atom providing the core - they only require that the atom donate electrons to the communal sea - one metal atom can substitute for another with essentially no disruption to the structure. ^[1] This is precisely why metal alloys can mix such different metals in continuous proportions, and why two pieces of the same metal can be welded together.

Because the bonding is relatively weak - the electron sea is diffuse and the electrostatic attraction modest compared with ionic or covalent bonds - metals tend to be soft and malleable. ^[1] Sliding one plane of metal atoms past another does not require disrupting a tightly localised bond; the electron sea simply redistributes around the new arrangement. This is why native gold can be hammered into thin sheets and why copper bends without breaking - physical properties that follow directly from the non-directionality and moderate strength of the metallic bond.

The width of energy bands increases as atoms are brought closer together by pressure. At sufficiently high pressures, the bands of the highest filled and next unfilled subshells spread enough to overlap even in materials that would be insulators at surface conditions. This is why the electrical conductivity observed in the deep crust and mantle of the Earth may partly reflect pressure-induced metallic conduction in silicate minerals that are insulators at lower pressures. ^[1]

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