A hammer, a battery, and two crystals
Put a piece of copper and a crystal of salt side by side. Both are hard, shiny-looking solids at room temperature. Both are giant lattices of ions held by electrical attraction. Now do two things to each.
First, connect each one to a battery and a bulb. The copper lights the bulb at once. The salt does nothing. Second, hit each one with a hammer. The copper flattens and bends. The salt shatters into pieces.
Two solids that look so alike behave in opposite ways. The difference is not luck, and it is not a list of facts about metals to learn. The last lecture ended with a promise: two features of metallic bonding would explain the properties of metals. The electrons can move, and the bond has no particular direction. This lecture follows each property back to one of those two features.
Electrical conductivity: charge that is free to move
An electric current is a flow of charge. So any material that conducts must contain charged particles that are free to move through it. In a metal, those particles are the delocalised electrons. They already move through the whole lattice. They do not belong to any one ion, so nothing has to be broken to set them free.
When a metal wire is connected to a battery, the battery pushes the electrons. They drift through the lattice, away from the negative terminal and towards the positive terminal. That drift of electrons is the current. (In Physics, the direction of "conventional current" is drawn the other way, from positive to negative. That was decided before anyone knew that electrons carry the charge.)
Now compare salt. Solid sodium chloride is made of Na⁺ and Cl⁻ ions. They are charged, but each one is held in its place in the lattice. Every electron belongs to a particular ion. So nothing can drift, and no current flows. Melt the salt, or dissolve it in water, and the ions themselves can move. Then it conducts. A metal needs no such change. Its delocalised electrons are mobile as a solid and as a liquid, which is why liquid mercury conducts too.
Metals are not all equally good conductors. The table compares several, using copper as the standard.
| Material | Conducts electricity, compared with copper |
|---|---|
| Silver | 1.06 |
| Copper | 1 |
| Aluminium | 0.63 |
| Tungsten | 0.30 |
| Iron | 0.17 |
| Glass | about 10⁻¹⁷ or less |
Data note: worked out from the resistivities at 20 °C in the HyperPhysics table (copper 1.68 × 10⁻⁸ Ω m). Other tables differ slightly.
Even the poorest metal here, iron, conducts at least 10¹⁶ times better than glass: ten thousand million million times. Every metal has a pool of delocalised electrons. Glass has none.
Electrons flow out of one end of a copper wire for hours. Does the wire slowly run out of electrons and become positively charged?
Show the answer
No. The wire is part of a complete circuit. For every electron that leaves one end, another enters the other end from the circuit. The pool of electrons moves along, but its size stays the same. The last lecture showed that a metal is neutral because the charge of its ions is balanced by the delocalised electrons. That balance holds while the current flows. A current is a movement of charge, not a loss of it.
Thermal conductivity: fast carriers of energy
Touch a metal rail and a wooden bench on a cool morning. Both are at the same temperature, but the metal feels colder. This is because the metal carries energy away from your hand much faster than the wood does.
Two things carry heat through a metal. The first is the same in every solid: the particles vibrate, and each one passes some of its vibration to its neighbours. The second belongs to metals. The delocalised electrons pick up energy in the hot region, move quickly through the lattice, and pass that energy on in cooler regions. In most metals, the electrons carry most of the heat.
This explains a pattern you can check in the table above. The metals that conduct electricity best, silver and copper, are also among the best conductors of heat. The same mobile electrons do both jobs. The last lecture met this link in Drude's model of 1900, which explained it partly by a lucky cancelling of errors. The link itself is real. It is why cooking pans often have copper or aluminium bases, and why the metal blocks that cool computer chips are made of these metals.
Malleable and ductile: layers that slide
A material is malleable if it can be hammered or pressed into a new shape without breaking. It is ductile if it can be pulled out into a wire. Most metals are both. To see why, look at what happens when a force pushes one layer of ions over the next.
In a metal, every ion is a positive ion, and every ion is attracted by the pool of electrons around it. When a layer slides, the ions arrive in new positions. But the new neighbours are still positive ions in the same pool of electrons. The electrons simply flow into the new gaps. The attraction never had a direction, so there is no particular bond to break. The metal changes shape and stays in one piece.
In an ionic crystal, the lattice alternates: positive ion, negative ion, positive ion. Each ion's neighbours have the opposite charge. Slide one layer by one ion's width, and the pattern lines up the wrong way. Positive ions now sit next to positive ions, and negative next to negative. Like charges repel strongly, and the crystal splits apart.
Try both below, and a third case: a metal with a few larger atoms mixed in.
Choose a material. Then push the top layer to the right with the slider, and watch what happens to the ions and their neighbours.
What happens when the top layer is pushed sideways by one ion's width:
- Pure metal: the layer slides. Every positive ion is still surrounded by delocalised electrons, so the attraction is the same as before. The metal bends.
- Ionic crystal: after one ion's width, each Na⁺ sits next to an Na⁺, and each Cl⁻ next to a Cl⁻, as in the figure. Like charges repel, and the crystal splits.
- Alloy: a larger atom in the lower layer sticks up into the path of the top layer. The layer moves only about 0.3 of an ion's width before it catches. More force is needed, so the alloy is harder.
What did you see? In the pure metal, the top layer slid as far as you liked, and every ion stayed surrounded by electrons. In the ionic crystal, one ion's width of sliding put like charges face to face. In the mixed metal, the layer could hardly move at all, because the larger atom stuck out into its path.
That is it. That is the whole idea. Bending a metal means sliding layers, and the electron pool lets them slide. Shattering a salt means sliding layers too, but its fixed pattern of charges turns that slide into repulsion.
Delocalised electrons that can move explain electrical and thermal conductivity.
A bond with no particular direction lets layers of ions slide, which explains why metals are malleable and ductile.
Alloys: why steel is stronger than iron
The last lecture left one question open: how strong iron is as a material, and why steel is stronger still. The explorer has just answered it.
An alloy is a mixture of a metal with other elements. Steel is iron with a small amount of carbon. Bronze is copper with tin. Brass is copper with zinc. In each case, atoms of a different size sit among the metal ions. A different-sized atom spoils the regular layers. When a force pushes a layer, the layer catches on the odd-sized atoms and cannot slide easily. So more force is needed to change the shape. The alloy is harder and stronger than the pure metal, though usually less malleable.
Notice what has not changed. The metallic bonding is no stronger in an alloy. What has changed is the arrangement: the layers are no longer smooth. This is a different reason from the one for high melting points, and an exam answer must not mix them up.
Pure gold is a good example of why this matters. It is so soft that a ring of pure gold scratches and bends easily. So most gold jewellery is an alloy, mixed with copper or silver to make it harder.
Melting points and lustre
Most metals have high melting and boiling points, because the attraction between the ions and the pool of electrons acts through the whole giant lattice. The last lecture explained why it varies: more delocalised electrons per atom, a higher charge and smaller ions all make the attraction stronger. Sodium melts at 97.8 °C. Tungsten melts at 3422 °C, the highest melting point of any element.
Metals are also shiny, a property called lustre. When light falls on a metal, the delocalised electrons near the surface absorb it and give it out again almost at once. Because the electrons can absorb every colour of visible light, they send every colour back, so most metals look silvery-white. Copper and gold are the well-known exceptions. They absorb some of the blue end of the spectrum, so the light they reflect looks reddish or yellow. For gold, detailed calculations show that Einstein's theory of relativity is part of the reason, as it was for mercury's low melting point in the last lecture. Without relativity, gold would be expected to look silvery.
Worked examples
Explain, in terms of bonding, why copper is used for electrical wiring.
Conducts. Copper has metallic bonding: a lattice of positive copper ions in a pool of delocalised electrons. When a potential difference is applied, the delocalised electrons move through the lattice and carry charge. So copper conducts electricity. The table shows that only silver conducts better, and silver costs far more.
Ductile. The metallic bond has no particular direction. When copper is pulled through a die to make wire, layers of ions slide past each other while staying in the pool of electrons. So copper can be drawn into long, thin wires without breaking.
Notice the shape of the answer. Each property is linked to the particles (ions and delocalised electrons) and to what they do. The key word for conductivity is "delocalised". "Free electrons" alone does not say why they are free.
In an old-style filament bulb, a thin wire glows white-hot. Different sources give its working temperature as about 2500 °C to 3000 °C. Why was tungsten chosen?
First, the filament must not melt. Iron melts at 1538 °C and copper at about 1085 °C, so both would melt long before the filament reached working temperature. Tungsten melts at 3422 °C. Only a few metals melt above about 3000 °C (rhenium 3186 °C, osmium 3033 °C, tantalum 3017 °C), and tungsten is the highest of all.
Second, why is tungsten's melting point so high? Its atoms have six outer electrons (in the 5d and 6s subshells), and several of them join the pool of delocalised electrons. Many delocalised electrons, held by small, highly charged ions, give very strong metallic bonding throughout the lattice.
Third, the filament is a very fine wire. Like other metals, tungsten is ductile enough to be drawn out, so a long filament can be coiled into a small bulb. So the choice rests on both features of metallic bonding: strong attraction for the high melting point, and sliding layers for the wire.
A saucepan has an aluminium body and a plastic handle. Explain both choices in terms of structure and bonding.
The body. Aluminium has metallic bonding. Its delocalised electrons pick up energy where the pan touches the flame and carry it quickly through the metal, so heat spreads to the food. Aluminium is also malleable: its layers of ions slide, so a flat sheet can be pressed into the shape of a pan without cracking.
The handle. A plastic is made of molecules held by covalent bonds. Every electron belongs to a particular bond, so there are no delocalised electrons to carry energy. Heat passes only through the slow vibrations of the molecules, so the handle stays cool enough to hold.
Check the reasoning: the one difference between the body and the handle, mobile electrons or none, explains the one difference in behaviour.
Here is a common exam question, answered by a student. Find the line that goes wrong.
The question: "Explain why solid copper conducts electricity but solid sodium chloride does not." Exactly one line of this answer is wrong. Tap it.
A student's answer. Line 5 is wrong.
- Line 1. Copper has metallic bonding: positive copper ions in a lattice, surrounded by delocalised electrons. Correct.
- Line 2. When a potential difference is applied, the delocalised electrons move through the lattice towards the positive terminal. Correct.
- Line 3. This flow of charge is an electric current, so copper conducts. Correct.
- Line 4. Sodium chloride is a giant ionic lattice of Na⁺ and Cl⁻ ions. Correct.
- Line 5. Its electrons are also delocalised, but the ions hold them back so they cannot flow. Wrong: an ionic solid has no delocalised electrons. Every electron belongs to a particular ion, and the ions are fixed in place.
- Line 6. When sodium chloride melts or dissolves, its ions are free to move, so it conducts. Correct.
Three classic mistakes
In a solid metal, the positive ions stay in the lattice. Only the delocalised electrons drift. Moving ions carry the current in molten or dissolved ionic compounds, not in metals.
Alloys are harder because atoms of a different size make the layers irregular, so the layers cannot slide easily. Write about layers and sliding, not about the strength of the bond.
"Electrons are free to move" describes the result. "The outer electrons are delocalised, so they are free to move through the lattice" gives the cause. Examiners look for the cause.
Work each one on paper first. Open a hint only when you are stuck.
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Liquid mercury conducts electricity. Molten sodium chloride also conducts. Explain what carries the charge in each.
Hint 1
Mercury is a metal. Sodium chloride is ionic.
Hint 2
Which charged particles are free to move in each liquid?
Full answer
In mercury, the delocalised electrons carry the charge, as in any metal, solid or liquid. In molten sodium chloride, there are no delocalised electrons. The charge is carried by the Na⁺ and Cl⁻ ions, which are free to move once the lattice has melted. Check: solid mercury would still conduct, but solid sodium chloride does not.
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Pure aluminium is soft. Aircraft are made from aluminium alloys containing small amounts of other metals, such as copper. Explain why the alloy is stronger, using a description of the particles.
Hint 1
What do the copper atoms do to the regular layers of aluminium ions?
Hint 2
Think about the third case in the explorer.
Full answer
In pure aluminium, the ions form regular layers that slide over each other easily, so the metal is soft. In the alloy, copper atoms of a different size sit among the aluminium ions. They make the layers irregular, so a layer catches on them and cannot slide easily. More force is needed to change the shape, so the alloy is stronger. The metallic bonding is not stronger; the layers are just harder to move.
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Gold leaf for decoration is beaten to about 0.1 micrometres (0.1 × 10⁻⁴ cm) thick. Gold has a density of 19.3 g/cm³. What area could 1 g of gold cover at this thickness? Which property of metals makes this possible?
Hint 1
First find the volume of 1 g of gold: volume = mass ÷ density.
Hint 2
Then area = volume ÷ thickness. Work in cm, then convert: 1 m² = 10 000 cm².
Full answer
Volume = 1 ÷ 19.3 ≈ 0.0518 cm³. Area = 0.0518 ÷ (0.1 × 10⁻⁴) ≈ 5180 cm² ≈ 0.52 m². So 1 g covers about half a square metre. Check: 0.52 m² × 0.1 µm = 5180 cm² × 10⁻⁵ cm ≈ 0.052 cm³, which is 1 g of gold. This is malleability taken to an extreme: layers of gold ions slide again and again without the metal breaking.
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Overhead power cables are often made of aluminium rather than copper. Aluminium conducts 0.63 times as well as copper (see the table). For the same length and the same resistance, an aluminium cable needs a cross-section 2.65 ÷ 1.68 ≈ 1.58 times larger. The densities are aluminium 2.70 g/cm³ and copper 8.96 g/cm³. Compare the masses of the two cables, and suggest why aluminium is chosen.
Hint 1
For the same length, mass is proportional to cross-section × density.
Hint 2
Mass ratio = 1.58 × (2.70 ÷ 8.96).
Full answer
Mass of aluminium ÷ mass of copper = 1.58 × 2.70 ÷ 8.96 ≈ 0.48. So the aluminium cable is thicker but weighs only about half as much as a copper cable that does the same job. Cables hang between towers, so a lighter cable needs fewer or lighter towers. Aluminium is also cheaper than copper. Both cables work for the same reason: delocalised electrons in a metallic lattice. Check: 1.58 × 2.70 = 4.27, and 4.27 ÷ 8.96 ≈ 0.48 ✓.
Every property in this lecture came from two features of one model: electrons that can move, and a bond with no particular direction. Conductivity, heat transfer, bending, wire-drawing, the hardness of alloys and the shine of a metal surface all follow from them. This is what a good model in science does. It is not a list of facts. It is one picture from which the facts can be worked out, even facts you have never been told.
The next topic tests the picture from the other side. Diamond and graphite are giant lattices of a single element, like a metal, but held by covalent bonds. Diamond has no mobile electrons at all and does not conduct. Graphite, surprisingly, does. The reason is a small pool of delocalised electrons of its own.
- Metals conduct electricity because their delocalised electrons can move through the lattice and carry charge, in the solid and in the liquid.
- Metals conduct heat well because the delocalised electrons carry energy quickly from hot regions to cooler ones, as well as through vibrations of the ions.
- Metals are malleable and ductile because the metallic bond has no particular direction, so layers of ions can slide without the metal breaking.
- Ionic crystals shatter because sliding a layer brings ions of the same charge next to each other, and they repel.
- Alloys are harder than pure metals because atoms of a different size make the layers irregular, so the layers cannot slide easily.
- Most metals are shiny because the delocalised electrons absorb and give out light of every visible colour.