S2.3 The metallic model

The metallic bond

Metal atoms have few valence electrons, and these are held only weakly by the nucleus: metals have low first ionization energies. When metal atoms pack closely together in a solid, the outer orbitals of neighbouring atoms overlap, and the valence electrons no longer belong to any single atom. They become delocalized: free to move through the whole structure. What remains of each atom is a positive ion, or cation.

This picture is often called the "electron sea" model. The cations are arranged in a regular, closely packed metallic lattice, and the delocalized electrons fill the space between them. Each electron is attracted to many cations at once, and each cation to many electrons, which holds the whole lattice together. In sodium each atom contributes one electron to the sea, so the lattice consists of ${{\mathrm{Na}{\vphantom{X}}^{+}}}$ ions and one delocalized electron per ion; the metal as a whole stays electrically neutral.

Like ionic bonding, the metallic bond is non-directional: the attraction between the cations and the electron sea acts equally in all directions. A cation is not bonded to particular neighbours, so the cations can pack as closely as their size allows. In many metals, such as aluminium and copper, each atom has twelve nearest neighbours, the closest packing possible for spheres of equal size (close packing). Close packing of relatively heavy atoms is the reason most metals have high densities.

Comparing the three models of bonding

The metallic model sits alongside the ionic and covalent models. Each describes a different way of holding atoms together by electrostatic attraction, and each predicts a different set of properties.

Real substances do not always fall neatly into one category, and the bonding of many compounds lies between two of these extremes. The bonding triangle, studied with materials, places a substance on this continuum from the electronegativities of its elements.

Explaining the properties of metals

Metals share a characteristic set of physical properties. They conduct electricity and heat well, can be hammered into sheets and drawn into wires, are shiny when freshly cut, and usually have high melting points and densities. Each property follows from the metallic model.

Electrical conductivity

Metals have high electrical conductivity in both the solid and the liquid state. The delocalized electrons are mobile charge carriers. Without a power supply they move randomly in all directions, so there is no net flow of charge. When a potential difference is applied across the metal, the electrons drift towards the positive terminal, and this flow of charge is the electric current. Electrons leave one end of the metal as fast as new ones enter at the other, so the metal is not changed by conducting.

Because the electron sea is still present when a metal melts, liquid metals conduct too. Mercury, which is liquid at room temperature (melting point $-38.83$ °C, data booklet), was once widely used in electrical switches and is still used in some laboratory and industrial instruments, although its toxicity means it is being replaced. The resistance of a metal increases as its temperature rises, because the cations vibrate more and scatter the moving electrons more often.

Data: conductivities at 20 °C from the table in Wikipedia, "Electrical resistivity and conductivity" (accessed 2026).

All metals conduct, but by very different amounts. Silver and copper are the best conductors; iron conducts only about a sixth as well as copper, and mercury about a sixtieth. Conductivity depends on how easily the delocalized electrons move through the lattice as well as on how many there are, and the simple electron-sea model cannot predict it.

Thermal conductivity

Metals also have high thermal conductivity. When one part of a metal is heated, the delocalized electrons there gain kinetic energy. Because they move freely and rapidly through the lattice, they quickly carry this energy to cooler regions, where they pass it on to the cations in collisions. The closely packed cations also pass vibrations to their neighbours, but this contributes much less in most metals. The best electrical conductors, silver and copper, are also the best thermal conductors, which is evidence that the same mobile electrons carry both charge and heat. Saucepans often have copper or aluminium bases for this reason, so that heat spreads quickly and evenly from the flame or hotplate.

Malleability and ductility

A malleable material can be hammered or pressed into a new shape without breaking; a ductile material can be drawn out into a wire. Metals are both. When a force is applied, layers of cations slide over one another. Because metallic bonding is non-directional, the delocalized electrons move with the cations and continue to attract them in their new positions: the bonding is the same after the layers have moved as before.

An ionic crystal behaves differently: moving one layer of ions brings ions of the same charge next to each other, the layers repel, and the crystal shatters. Gold is so malleable that it can be beaten into gold leaf less than a micrometre thick, and copper is drawn into the thin wires of electrical cables. Adding atoms of a different size to a metal, to make an alloy, disrupts the regular layers and makes it harder for them to slide, which is why alloys are usually harder and stronger than the pure metals.

Why metals can form alloys

The same features of metallic bonding make alloys possible. The delocalized electrons attract any positive ion in the lattice, and the bonding has no fixed direction or fixed ratio of atoms. A cation of a different metal can therefore take the place of one of the original cations, or a much smaller atom such as carbon can fit into the gaps between them, and the structure is still held together by metallic bonding. Because the second element can be added in almost any proportion, with no fixed formula, alloys are classed as mixtures rather than compounds, even though their atoms are held by metallic bonding.

The different-sized atoms make the layers of cations less regular, so the layers slide less easily and the alloy is usually harder and stronger than the pure metal. An alloy still has delocalized electrons and still conducts, but the irregular lattice scatters the moving electrons more, so alloys are generally poorer conductors than the pure metals they are made from. The compositions, properties and uses of particular alloys are part of the study of materials.

Lustre, melting point and density

• Lustre. Freshly cut or polished metals are shiny. The delocalized electrons absorb light falling on the surface and re-emit it, so the surface reflects most visible light.

• High melting and boiling points. Most metals melt at high temperatures because many strong attractions between the cations and the delocalized electrons must be overcome. There are exceptions where the bonding is weak: mercury is liquid at room temperature, caesium melts at 28.44 °C, and gallium (29.77 °C) melts on the palm of a hand (data booklet).

• High density. Most metals are dense because their atoms are heavy and closely packed. Density depends on the masses of the atoms and how closely they pack, not on the delocalized electrons. The group 1 metals, with large, light atoms, are exceptions: lithium, sodium and potassium float on water.

Relating properties to uses

The choice of metal for a job depends on a combination of properties, and often on cost and availability as well.

Overhead power lines show how properties are balanced. Per unit volume, aluminium conducts only about 60% as well as copper, but it is less than a third as dense. For the same mass of metal, an aluminium cable therefore carries roughly twice the current of a copper one, and lighter cables need fewer and lighter pylons. Most high-voltage overhead lines use stranded aluminium conductors, often wound around a steel core that provides the tensile strength. Inside buildings, where weight matters less and space more, copper is used because a thinner copper wire carries the same current.

Investigating the properties of metals

Simple tests show the properties of metals and allow comparisons between them. Conductivity can be tested by connecting a sample (a strip, wire or rod) into a circuit with a power supply and an ammeter or bulb, and comparing it with non-metals such as sulfur or a glass rod. Malleability can be tested by hammering samples on a steel block: metals flatten, while ionic solids such as a crystal of rock salt and covalent solids such as sulfur shatter or crumble. Trends in melting points across and down the periodic table are best studied with data from a database or the data booklet, since measuring the melting points of most metals accurately needs specialist high-temperature equipment.

The strength of metallic bonding

The strength of metallic bonding varies widely from metal to metal, as melting points show: from $-38.83$ °C for mercury to 3414 °C for tungsten. In the simple model, the strength depends on how strongly the cations attract the delocalized electrons. Two factors control this.

• The charge on the cations. A metal that forms ions with a higher charge gives more electrons per atom to the sea. A higher charge on each cation and a greater density of delocalized electrons around it both increase the electrostatic attraction.

• The radius of the cations. Smaller cations allow the delocalized electrons to be closer to the centre of positive charge, so the attraction is stronger.

These two factors are often combined as the charge density of the cation: its charge divided by its size. Metals whose cations have a high charge density have the strongest metallic bonding, and so the highest melting points and boiling points. The comparison of sodium, magnesium and aluminium drawn to scale shows both factors changing together across period 3.

Trends down a group

Down group 1 every metal forms a 1+ ion and gives one electron per atom to the sea. The ions get larger down the group, from ${{\mathrm{Li}{\vphantom{X}}^{+}}}$ (76 pm) to ${{\mathrm{Cs}{\vphantom{X}}^{+}}}$ (167 pm), because each has an extra occupied energy level. The delocalized electrons are therefore further from the centres of the cations, the attraction is weaker, and the melting point falls steadily from lithium to caesium.

The group 2 metals follow the same general pattern, with the melting point falling from beryllium (1287 °C) to barium (725.0 °C), but the trend is not smooth: magnesium (650.0 °C) melts below calcium (842.0 °C). The group 2 metals do not all have the same crystal structure, and melting depends on the arrangement of the atoms as well as on the strength of the bonding. Irregularities like this are a reminder that the electron-sea model is a simplification that explains broad trends rather than every value.

Data: IB Chemistry data booklet (2025), sections 8 and 10.

Trends across a period

Across period 3 from sodium to aluminium, the charge on the cation rises from 1+ to 3+, the number of delocalized electrons per atom rises from one to three, and the ionic radius falls from 102 pm to 54 pm. All three changes strengthen the metallic bonding, and both the melting points and the boiling points increase.

The boiling points show the trend far more clearly than the melting points: aluminium boils at 2519 °C, nearly three times the boiling point of sodium, but melts only 10 °C above magnesium. When a metal melts, the cations gain enough energy to move past each other but remain surrounded by the electron sea, so most of the metallic bonding survives in the liquid. Boiling separates the atoms completely, so the boiling point is the better guide to the strength of metallic bonding.

For the same reasons, a group 2 metal has a higher melting point than the group 1 metal in the same period: calcium melts at 842.0 °C and potassium at 63.38 °C. The trend across a period ends at the metals; silicon, the next element after aluminium, has a giant covalent structure.

The same ideas help to explain trends in the chemical reactivity of metals. Metals whose atoms lose their valence electrons most easily are the most reactive, which is why reactivity increases down group 1 as the melting point falls; trends in the reactivity of metals are studied with electron transfer reactions.

Limitations of the electron-sea model

The electron-sea model is a simple picture: point-like positive ions in a uniform cloud of mobile electrons. It explains the properties that all metals share and the broad trends in melting points, but it cannot account for the differences between individual metals.

• Conductivity. It predicts that every metal conducts, but not how well. Aluminium delocalizes three electrons per atom and calcium two, yet aluminium conducts only about 20% better than calcium, and lead, with four outer electrons, conducts far worse than either.

• Irregular melting points. It cannot explain why magnesium melts below calcium, or why manganese melts far below its neighbours, because melting also depends on the crystal structure.

• Hardness and brittleness. It predicts that all metals are malleable, but some, such as tungsten and chromium, are hard and fairly brittle at room temperature.

• Magnetism and colour. It does not explain why iron, cobalt and nickel are magnetic, or why copper and gold are coloured while most metals are silvery.

A more complete description, the band theory of solids, treats the outer orbitals of all the atoms in a crystal as forming bands of closely spaced energy levels. It accounts for these differences, and for why semiconductors such as silicon conduct far less than metals, but it is not needed to explain the properties and trends of metals at this level.

Transition elements and delocalized d-electrons (HL)

In the first-row transition elements the 4s and 3d sublevels are very close in energy. When the atoms form a metallic lattice, electrons from both sublevels can become delocalized. A transition element therefore contributes more electrons per atom to the electron sea than an s-block metal of the same period, and its cations are small and highly charged. The density of delocalized electrons is high, and the attraction between the cations and the electron sea is strong.

The effect on melting points is large. Potassium, which can delocalize only its single 4s electron, melts at 63.38 °C, and calcium, with two 4s electrons, at 842.0 °C. Every transition element in period 4 except zinc melts above 1000 °C, and vanadium and chromium above 1900 °C. Tungsten, a transition element of period 6, has the highest melting point of any metal, 3414 °C (data booklet), which is why it is used for lamp filaments and for electrodes that must survive the heat of an electric arc.

Why melting points change little across the d-block

Across the s and p blocks the melting points of the metals change sharply, because each step adds a proton and a valence electron that joins the sea, and the cations shrink markedly (${{\mathrm{Na}{\vphantom{X}}^{+}}}$ 102 pm, ${{\mathrm{Mg}{\vphantom{X}}^{2+}}}$ 72 pm, ${{\mathrm{Al}{\vphantom{X}}^{3+}}}$ 54 pm). Across the d-block the changes are much smaller. Each extra electron enters an inner 3d sublevel, which shields the outer electrons quite well, so the atomic radius changes only a little, from 159 pm for scandium to 122 pm for copper (data booklet), and the number of electrons available for delocalization stays similar.

The melting points rise to a maximum near the middle of the series (vanadium and chromium) and then fall. In the second half of the d-block the 3d electrons are increasingly paired and held more tightly by the growing nuclear charge, so fewer of them take part in metallic bonding. At zinc the 3d sublevel is full ($[\text{Ar}]\,3d^{10}\,4s^2$) and only the two 4s electrons are delocalized, so zinc melts at only 419.5 °C, closer to the s-block metals than to its neighbours. Manganese (1246 °C) falls well below the trend. Its unusually complex crystal structure is part of the reason, and its half-filled $3d^5$ sublevel is often suggested to hold the d electrons more tightly, so that fewer are delocalized.

Electrical conductivity of transition elements

Transition metals are good electrical conductors because their delocalized s and d electrons are mobile charge carriers. Copper, with a conductivity second only to silver, is the standard metal for electrical circuits: it combines very high conductivity with ductility, resistance to corrosion, and a cost far below that of silver.

Having more delocalized electrons does not by itself make a metal a better conductor. Iron, with eight electrons outside its argon core, conducts only about a sixth as well as copper, and less well than calcium. How easily the electrons move through the lattice matters as much as how many there are, and a full explanation needs the band theory of solids. The simple model explains why transition metals conduct and why they melt at high temperatures, but not the exact order of their conductivities.

The other characteristic properties of transition elements, such as variable oxidation states, coloured compounds and catalytic activity, are part of the study of the periodic table, and their reactions with ligands are part of electron-pair sharing reactions.

Applying the ideas in exam questions

Paper 1A: the strongest metallic bond

Paper 1A: properties and delocalized electrons

Paper 1A: malleability

Paper 1B: testing a trend in the group 2 metals

(Paper 1B style) A student uses a database to test the hypothesis that "the melting point of the group 2 metals decreases down the group because the ionic radius increases". The student records the data in a table.

Paper 2: calcium and calcium chloride

Paper 2: bonding in magnesium, oxygen and magnesium oxide

Paper 2: copper in electrical circuits (HL)

Paper 1A: identifying a transition element from data (HL)

Self-check

• To do:

  I can define the metallic bond and describe the structure of a metal as a lattice of cations in a sea of delocalized electrons.

• To do:

  I can explain why the valence electrons of metal atoms become delocalized.

• To do:

  I can compare the ionic, covalent and metallic models of bonding.

• To do:

  I can explain the electrical conductivity of metals in the solid and liquid states.

• To do:

  I can explain the thermal conductivity of metals.

• To do:

  I can explain malleability and ductility in terms of non-directional bonding, and contrast metals with brittle ionic solids.

• To do:

  I can identify which properties of metals depend on the delocalized electrons and which (such as density) do not.

• To do:

  I can relate the properties of copper, aluminium, iron, tungsten and gold to their uses.

• To do:

  I can explain how the charge and radius of the cations affect the strength of metallic bonding.

• To do:

  I can explain the trends in melting points down group 1 and group 2 and across period 3, and recognize where the simple model breaks down.

• To do:

  I can explain why metallic bonding makes alloys possible, and why alloys are harder than the pure metals.

• To do:

  I can outline the limitations of the electron-sea model.

• To do:

  I can explain the high melting points of transition elements in terms of delocalized 3d and 4s electrons (HL).

• To do:

  I can explain why melting points change less across the d-block than across the s and p blocks (HL).

• To do:

  I can explain why transition metals such as copper are good electrical conductors (HL).

Which substance is ionic?

1. A

   W

2. B

   X

3. C

   Z

4. D

   Y

Relate mass to area and density. Mass = density × volume, and the lengths are equal, so the masses are in the ratio of density × area:

The aluminium cable has about 1.7 times the cross-sectional area of the copper one but only about half its mass (0.51 of it). This is the calculation behind the use of aluminium on pylons, where the weight of the cable between supports matters most.