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S2.3

The metallic model

Structure 2 · Models of bonding and structure · SL and HL

🎯What you need to be able to do

  • Describe a metallic bond as the electrostatic attraction between a lattice of cations and delocalized electrons.
  • Explain the electrical conductivity, thermal conductivity and malleability of metals in terms of that model.
  • Relate characteristic properties of metals to their uses.
  • Explain how the charge of the cation and the radius of the metal ion determine the strength of the metallic bond, and use this to explain trends in the melting points of s- and p-block metals.
  • AHL Explain the high melting points and electrical conductivity of transition elements in terms of delocalized d-electrons.

📚The chemistry

The metallic bond

A metallic bond is the electrostatic attraction between a lattice of positive metal ions (cations) and a “sea” of delocalized electrons.

Metal atoms have low ionization energies, so the outer electrons are released into the structure as a whole rather than belonging to any particular atom. What remains is a regular lattice of cations held together by their common attraction to the mobile electrons between them. Like the ionic bond, the metallic bond is non-directional and acts throughout the structure, which is why metals form giant structures with (usually) high melting points.

All three bonding models introduced so far are electrostatic. What distinguishes them is where the electrons are: transferred in the ionic model, shared between two atoms in the covalent model, and delocalized across the whole lattice in the metallic model. That is the comparison S2.4 then turns into a continuum.

Explaining the properties

  • Electrical conductivity. The delocalized electrons are free to move through the lattice, so applying a potential difference makes them drift and a current flows. Crucially, metals conduct as solids — unlike ionic compounds, which must be molten or dissolved — and conducting does not decompose them, because nothing is transported except electrons.
  • Thermal conductivity. Mobile electrons carry kinetic energy rapidly from a hot region to a cold one; the vibrating cations pass energy along too, but the electron contribution is the larger, which is why good electrical conductors are also good thermal conductors.
  • Malleability and ductility. Because the bonding is non-directional, layers of cations can slide over one another without the attraction being destroyed — the delocalized electrons simply move with them, so the new arrangement is bonded exactly as well as the old. This is the sharpest contrast with an ionic solid, where sliding brings like charges together and the crystal shatters.
  • Lustre and opacity. The delocalized electrons absorb and re-emit light of many frequencies, giving the characteristic metallic shine.

Uses follow from properties, and the syllabus asks you to make the link explicitly: copper for wiring and cooking pans (electrical and thermal conductivity, ductility); aluminium for aircraft and drinks cans (low density, malleable, corrosion-resistant because of its oxide layer); iron and steel for construction (high melting point, strength); gold and silver for contacts and jewellery (conductivity, resistance to oxidation, lustre).

“Metals conduct because the ions can move.” They cannot — the cations are in fixed lattice positions. It is the delocalized electrons that move in a metal, and the ions that move in a molten or aqueous ionic compound. Swapping the two is the single most common error across S2.1 and S2.3, and it is also why electrolysis decomposes an ionic melt but passing a current through copper wire does not decompose the copper.

What makes the bond strong or weak

The strength of metallic bonding — and therefore the melting point, boiling point, hardness and enthalpy of atomization — depends on two things:

Charge on the cation
More delocalized electrons per atom means a higher cationic charge and a greater electron density in the sea, so a stronger attraction.
Radius of the cation
A smaller ion puts the positive charge closer to the delocalized electrons, so the attraction is stronger.

This explains the trends the syllabus asks for:

  • Across period 3, Na (1+), Mg (2+), Al (3+): the cationic charge increases, the ionic radius decreases, and the number of delocalized electrons per atom increases from one to three. All three factors strengthen the bond, so melting point rises sharply — sodium 98 °C, magnesium 650 °C, aluminium 660 °C.
  • Down group 1, Li to Cs: the charge stays at 1+, but the cations get steadily larger, so the delocalized electrons are further from the nuclei and the attraction weakens. Melting points fall — lithium 181 °C, sodium 98 °C, potassium 63 °C, caesium 29 °C, which will melt in your hand.

The guide is explicit that only a simple treatment in terms of the charge of the cations and the electron density is required — you are not expected to discuss band theory or crystal packing.

AHL Transition elements

Transition elements have delocalized d-electrons in addition to their s-electrons. Because the 3d and 4s sublevels are close in energy, electrons from both can be released into the delocalized sea.

Two consequences:

  • Very high melting points. More delocalized electrons per atom means a much greater electron density in the sea, and the cations are also relatively small, so the metallic bonding is far stronger than in the s-block. Iron melts at 1538 °C, tungsten at 3422 °C, against 98 °C for sodium.
  • High electrical conductivity, for the same reason: more mobile charge carriers per unit volume.

It also explains why the melting-point trend across the d-block is comparatively flat compared with the sharp rise across period 3. In the s- and p-block, each step across adds a delocalized electron and shrinks the ion appreciably. Across the d-block the electrons are being added to an inner 3d sublevel, so the number contributed to the sea and the atomic radius both change only slightly from one element to the next — there is no dramatic change to drive a dramatic trend. The chemical properties of transition elements — variable oxidation state, coloured complexes, catalysis — are in S3.1.

✏️Worked example

(a) Explain, in terms of structure and bonding, why magnesium has a much higher melting point (650 °C) than sodium (98 °C).
(b) Explain why a metal can be hammered into a sheet while an ionic crystal shatters.
(c) Both magnesium and molten magnesium chloride conduct electricity. Explain the difference in the mechanism, and state one further observable difference.
(d) AHL Suggest why chromium melts at 1907 °C while calcium, its neighbour two places to the left in period 4, melts at 842 °C.

(a) Both are giant metallic lattices of cations in a sea of delocalized electrons, so both are melted by overcoming the electrostatic attraction between the two. Magnesium differs on all three of the relevant counts:

  • magnesium releases two electrons per atom into the delocalized sea rather than one, so the electron density is higher;
  • the cation is \( \mathrm{Mg^{2+}} \) rather than \( \mathrm{Na^{+}} \), so the charge attracting those electrons is doubled;
  • \( \mathrm{Mg^{2+}} \) is smaller than \( \mathrm{Na^{+}} \) (greater nuclear charge on the same number of electrons), so the charge is closer to the delocalized electrons.

All three strengthen the metallic bond, so much more energy is needed to break the lattice down and the melting point is far higher.

(b) In a metal, the bonding is non-directional and the electrons are delocalized. When a force makes one layer of cations slide over another, the cations move into equivalent new positions and the electron sea flows with them, so the attraction is unchanged and the metal deforms without breaking — it is malleable.

In an ionic crystal, the lattice alternates cations and anions. Sliding one layer by one ion brings like charges into contact. The resulting strong repulsion pushes the layers apart, and the crystal cleaves along that plane. Hence ionic solids are brittle.

(c) In magnesium metal the charge carriers are the delocalized electrons, which drift through a stationary lattice of cations. In molten magnesium chloride the charge carriers are the ions themselves, \( \mathrm{Mg^{2+}} \) and \( \mathrm{Cl^{-}} \), which are free to move only because the lattice has been melted.

The observable difference: passing a current through the ionic melt decomposes it — magnesium is deposited at the cathode and chlorine gas released at the anode — because the ions are discharged when they arrive. Passing a current through magnesium metal changes nothing chemically, since only electrons move and no substance is transported. (A second acceptable difference: the metal conducts as a solid, whereas the ionic compound must be melted or dissolved first.)

(d) Calcium, in the s-block, delocalizes only its two 4s electrons. Chromium is a transition element, \( [\mathrm{Ar}]\,4s^1\,3d^5 \), and because the 3d and 4s sublevels are close in energy it can delocalize d-electrons as well — contributing far more electrons per atom to the sea. The \( \mathrm{Cr} \) cation is also considerably smaller than \( \mathrm{Ca^{2+}} \), because nuclear charge has increased across the period while the added electrons went into an inner sublevel and shield poorly. Higher electron density and a smaller, more highly charged cation give much stronger metallic bonding, hence the far higher melting point.

Check it. Every metallic-bonding explanation should mention three things: the number of delocalized electrons per atom, the charge on the cation and its radius. If your answer names fewer than two of them, it is probably incomplete. Sanity check (a) against the data: sodium melts below the boiling point of water, magnesium above the melting point of glass — a factor of six in temperature is far too large to come from ionic radius alone, so the doubled charge has to be doing most of the work, and your answer should say so.
Explaining malleability by saying “the bonds are weak”. They are not — iron is malleable and melts at 1538 °C. Malleability has nothing to do with bond strength and everything to do with bond directionality: because the attraction acts equally in all directions and the electrons are mobile, the lattice can be rearranged without any bond ever being broken. Answers that confuse strength with directionality also tend to get the ionic contrast backwards.

📝Practise

Work through these on paper, then reveal the answer.

1. Define the metallic bond and state two properties of metals it explains, giving the explanation in each case.
Definition: the metallic bond is the electrostatic attraction between a lattice of positive metal ions and the delocalized electrons that surround them. Any two of the following, with reasons: electrical conductivity — the delocalized electrons are free to move through the structure, so they drift under an applied potential difference and carry a current, even in the solid; thermal conductivity — the same mobile electrons transfer kinetic energy rapidly from a hot region to a cold one; malleability and ductility — the bonding is non-directional, so layers of cations slide past one another into equivalent positions while the electron sea moves with them, leaving the attraction intact; high melting point — the attraction extends throughout a giant lattice, so a great deal of energy is needed to separate the particles.
2. Explain the trend in melting points down group 1: Li 181 °C, Na 98 °C, K 63 °C, Rb 39 °C, Cs 29 °C.
Every group 1 metal delocalizes exactly one electron per atom and forms a 1+ cation, so the charge factor is constant all the way down and cannot explain the trend. What changes is ionic radius: descending the group, each element has an additional occupied main energy level, so the cations are progressively larger. The delocalized electrons are therefore further from the positive nuclei, and there is more shielding by inner shells, so the electrostatic attraction between the cations and the electron sea weakens. Less energy is needed to overcome it, and the melting point falls steadily. The same reasoning predicts the falling hardness and density trends and the increasing reactivity of the group.
3. Aluminium is used for overhead power cables and for aircraft bodies. Relate each use to a specific property, and to the bonding that produces it.
Power cables require high electrical conductivity, which aluminium has because each atom contributes three delocalized electrons to the electron sea, giving a high density of mobile charge carriers. Cables must also be ductile, so they can be drawn into long wires — possible because metallic bonding is non-directional and layers of cations slide without the attraction being lost. Cables must be light, since they hang between pylons under their own weight, and aluminium has a low density; copper conducts better but is roughly three times denser, which is why aluminium wins here despite the lower conductivity. Aircraft bodies require a high strength-to-weight ratio (low density with strong metallic bonding, usually improved further by alloying — see S2.4), malleability so that panels can be pressed into shape, and corrosion resistance, which aluminium gets from the tough impermeable oxide layer that forms immediately on its surface.
4. Compare the electrical conductivity of sodium metal, solid sodium chloride and molten sodium chloride, explaining each case.
Sodium metal: conducts. It contains delocalized electrons that are free to move throughout the lattice, so a current flows and the metal is chemically unchanged by it. Solid sodium chloride: does not conduct. It contains charged particles — \( \mathrm{Na^{+}} \) and \( \mathrm{Cl^{-}} \) — but they are held in fixed positions in the ionic lattice by strong electrostatic attractions and cannot move, and there are no free electrons. Molten sodium chloride: conducts. Melting has broken down the lattice, so the ions are now mobile and migrate to the electrodes. This third case is electrolysis: the ions are discharged on arrival, so the compound is decomposed, which does not happen when a metal conducts. The general rule is that conduction requires charged particles that are free to move, and the two ways of satisfying it — mobile electrons or mobile ions — have quite different consequences.
5. AHL Explain why the melting points of the d-block elements are all high but vary comparatively little across the period, whereas melting points rise steeply from sodium to aluminium.
All the d-block metals have high melting points because 3d and 4s are close in energy, so d-electrons as well as s-electrons are delocalized. That gives a high electron density in the sea and, with relatively small cations, very strong metallic bonding. The reason the variation across the d-block is small is that successive electrons are added to an inner 3d sublevel. Those electrons shield the outer 4s electrons quite effectively, so the effective nuclear charge and the atomic radius change only slightly from one d-block element to the next, and the number of electrons actually contributed to the delocalized sea is similar throughout. From Na to Al, by contrast, the electrons are added to the outer main energy level, and the number delocalized per atom goes 1, 2, 3 while the ionic radius falls sharply — three large changes in three steps, so the melting point rises steeply.
6. Mercury is a liquid at room temperature, and caesium melts at 29 °C. Suggest, using the metallic bonding model, what these two facts have in common and where the model reaches its limits.
What they have in common is weak metallic bonding. Caesium is straightforward on the model: it has a 1+ cation, contributes only one delocalized electron per atom, and has the largest cation of any stable group 1 metal, so the attraction between the cations and the electron sea is as weak as metallic bonding gets, and very little energy is needed to break the lattice down. Mercury is not so easily explained. It is a d-block element, so the simple model predicts strong bonding and a high melting point, yet it melts at −39 °C. The honest answer at this level is that mercury’s \( 6s^2 \) electrons are held unusually tightly — a relativistic effect associated with very heavy nuclei — so they are poorly delocalized and each atom contributes little to the electron sea. This is a good example of the nature-of-science point that all models have limitations: the charge-and-radius account works well across the s- and p-block and for most of the d-block, but it does not predict every case, and the exceptions are where more sophisticated theory is needed.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET — Conductivity, which contrasts what moves in a metal with what moves in an electrolyte, the distinction this sub-topic is mostly tested on.
  • The Royal Society of Chemistry periodic table — melting points, densities and atomic radii for every element, so you can test the charge-and-radius argument against real data rather than taking it on trust.
  • The RSC’s Chemistry World archive on relativistic effects in heavy elements, if the mercury question in the practice set interested you.