Metallic Bonding and Electron Sea Model

Metallic bonding is the attraction between positively charged metal ions and a “sea” of delocalized valence electrons that are free to move throughout the metal, and the electron sea model uses this picture to explain why metals conduct electricity, are malleable and ductile, and have a shiny surface. In brief: in a piece of aluminum each atom contributes three electrons to the sea, so the bonding is stronger than in sodium, which contributes one; this is why aluminum melts at 660 °C and sodium at only 98 °C.

Metals make up about three quarters of the elements, and their properties are very different from those of ionic and covalent substances. They can be bent without breaking, they conduct heat and electricity and they can be polished to a mirror finish. This article describes the electron sea model, relates metallic bonding to melting points, hardness and conductivity, introduces the idea of energy bands, compares metals in tables, works through calculations of electron density and explains the history of the theory.

What is the electron sea model?

The atoms of a metal have few valence electrons and low ionization energies, so these electrons are held loosely. In a solid, the atoms are arranged in a regular lattice. The valence electrons are not bound to individual atoms but are shared among all atoms, and move freely through the lattice. The metal can be pictured as an array of positive metal ions (the atomic cores) immersed in a sea of mobile electrons. The attraction between the cations and the electron sea holds the metal together. Because the electrons are not tied to a particular pair of atoms, the bond is non-directional.

How does the model explain the properties of metals?

• Electrical conductivity: when a voltage is applied, the mobile electrons flow through the metal. Conductivity falls as temperature rises, since the vibrating ions scatter the electrons more.
• Thermal conductivity: the moving electrons also carry thermal energy rapidly from the hot to the cold region of a metal.
• Malleability and ductility: when a force is applied, layers of ions can slide over each other. The electron sea adjusts and keeps holding the ions together, so the metal deforms without breaking. In an ionic crystal, the same shift would bring ions of like charge together and shatter the crystal.
• Luster: the free electrons absorb light of many wavelengths and re-emit it, which gives metals their shiny appearance.
• High melting points and boiling points: strong electrostatic attractions between ions and the electron sea need a lot of energy to overcome. (Mercury is an exception, with a low melting point.)
• Density and strength: metal ions are closely packed in structures with high coordination numbers, such as face-centered cubic and hexagonal close-packed (12 neighbors).

What determines the strength of metallic bonding?

1. Number of delocalized electrons per atom. More electrons in the sea give a stronger attraction.
2. Charge of the metal ion. A 3+ ion attracts the electron sea more strongly than a 1+ ion.
3. Size of the ion. Smaller ions give a closer, stronger attraction.

The effect is seen in period 3: sodium (1 electron), magnesium (2) and aluminum (3) have increasing melting points. Transition metals, which can use d electrons in addition to s electrons, have particularly strong bonding and the highest melting points, such as tungsten at 3,422 °C.

Properties of selected metals

What does band theory add?

In a metal with N atoms, the atomic orbitals combine into N molecular orbitals that are so close in energy that they form a continuous band. The valence band is partly filled with electrons, and so electrons can move to slightly higher energy levels with very little energy, which explains conductivity. In an insulator, the filled band is separated from the next empty band by a large gap. In a semiconductor, the gap is small, so some electrons can cross it, especially when heated. Band theory explains why silicon conducts better as the temperature rises, while metals conduct worse.

Worked examples

1. Free electrons in aluminum. 1.00 cm³ has a mass of 2.70 g, which is 2.70 ÷ 26.98 = 0.1001 mol, or 6.03 × 10²² atoms. With 3 electrons per atom, the number of delocalized electrons is 3 × 6.03 × 10²² = 1.81 × 10²³ per cm³.
2. Free electrons in sodium. 1.00 cm³ has a mass of 0.968 g, which is 0.968 ÷ 22.99 = 0.0421 mol, or 2.54 × 10²² atoms, and so 2.54 × 10²² electrons (one per atom). Aluminum has 1.81 × 10²³ ÷ 2.54 × 10²² = 7.1 times more.
3. Free electrons in copper. 8.96 ÷ 63.55 = 0.141 mol per cm³, and with one electron per atom 8.49 × 10²² electrons per cm³. Copper conducts well, though it has fewer electrons per cm³ than aluminum, because the electrons scatter less.
4. Rank the melting points. Na, Mg and Al. The ranking follows the number of electrons and the charge of the ion: Na (98 °C) < Mg (650 °C) < Al (660 °C).
5. Why does a gold leaf bend instead of shattering? The layers of Au⁺ cores slide over each other, and the electron sea keeps them bonded. A salt crystal would break, since the layers would shift to put like charges next to each other.
6. Resistance of a wire. A copper wire has a conductivity of 59.6 × 10⁶ S/m. For a length of 10.0 m and a cross-sectional area of 1.00 mm² (1.00 × 10⁻⁶ m²), R = L ÷ (σA) = 10.0 ÷ (59.6 × 10⁶ × 1.00 × 10⁻⁶) = 0.168 Ω.

How do alloys fit the model?

In an alloy, atoms of a different element are added to the lattice. The delocalized electrons are still shared among all the atoms, so the bonding remains metallic. The atoms of different size disturb the regular layers, which makes it harder for the layers to slide, so alloys are harder and stronger than pure metals. They are usually poorer conductors, since the irregular lattice scatters the electrons.

How did the theory of metals develop?

In 1900, Paul Drude proposed that the electrons in a metal behave like a gas of free particles, which explained electrical and thermal conduction. Hendrik Lorentz and Arnold Sommerfeld improved the model with statistics for electrons. In the late 1920s and early 1930s, Felix Bloch, Rudolf Peierls and Alan Wilson developed the band theory of solids, based on quantum mechanics, which explained the differences between metals, semiconductors and insulators.

Which mistakes are common?

Mistake 1: Saying that the electrons belong to one atom

They are delocalized and belong to the whole crystal.

Mistake 2: Thinking that metals are made of neutral atoms with free electrons added

The metal as a whole is neutral. The ions are positively charged, and the electrons balance the charge.

Mistake 3: Believing that all metals have high melting points

Mercury is a liquid at room temperature, and cesium melts at 28 °C.

Mistake 4: Expecting conductivity to increase with temperature

For metals, conductivity decreases as the temperature rises. For semiconductors, it increases.