A-level Physics (Advancing Physics)/Metals

There are several physical properties of metals you need to know about:

Metals are constructed from positive ions in a sea of electrons. This explains many of their properties.

Electrical Properties

Metals on a microscopic scale consist of positive metal ions in 'sea' of free (delocalised) electrons. The electrons act are able to freely move around the metallic lattice, in and between the ions. Metallic bonding is therefore described as non-directional, in contrast to the directional bonds found between atoms in covalently-bonded materials (e.g. carbon atoms in diamond).

As the delocalised electrons each carry charge and are able to move freely, they are described as 'mobile charge carriers'. Electricity is simply the flow of charged particles, and so the presence of a high number of mobile charge carriers per unit volume in metals means they tend to be very effective conductors. In contrast, ionically-bonded materials involve ions in fixed positions. The ions are charged particles, however as they are immobile they are not described as mobile charge carriers, making ionic substances (eg sodium chloride) unable to carry electric current when solid.

When a current flows through a metal, the delocalised electrons collide with the metal ions, transferring kinetic energy to them, resulting in an increase in the temperature of the metal. As the temperature of the metal increases and its metal ions vibrate more, electrons are more likely to collide with them, meaning the flow of current is resisted. The resistance of a metal therefore increases with temperature.

Similarly, as higher currents involve a faster flow of electrons, they cause more collisions between electrons and metal ions, and so cause the conducting material to increase in temperature. This is exemplified by the UK power grid - electricity is transferred throughout the country at extremely high voltages (typically 275kV or 400kV) but low currents, therefore allowing the electricity to travel at a high power without significant heating occurring in the wires.

Mechanical Properties

This 'sea' of free electrons can also be described as a glue that does not dry. The negatively charged electrons have an electro-static attraction to the positively charged metal ions. This is what holds the entire metal structure together and gives metals their strength, i.e. the ability of the material to resist coming apart.

It also means that metals will change shape without coming apart completely (breaking). This is known as plastic deformation, which is when a material changes permanently (unlike elastic deformation) and also does not fracture (like when a glass fibre is stretched too far). Pure metals are usually incredibly ductile and malleable and can worked into a wide variety of shapes. The sea allows the atoms to move past each other. Atoms can move out of their place on the lattice. Other atoms can then go and fill that place. Entire layers of atoms in a crystal lattice can slip past one another, and the free electrons flowing between will keep them stuck together [see dislocations]. The glue allows movement of atoms without breaking the metallic bond, i.e. the electrostatic attraction between the free-flowing electrons and the positive ions.

Of course, metals do eventually fracture, however, they tend to show necking first.

This could not happen in a material where the strength comes from covalent bonds because the electrons need to be in specific positions. When ionic bonds or covalent bonds are broken, they do not generally go back together. Materials held together entirely by covalent or ionic bonds tend to be very brittle. The bonding in metals is not directional and not permanent. This gives metals their strength and plasticity, their most useful mechanical properties.

List of Mechanical Properties

Stiffness

As the electrostatic attraction between the sea of electrons and metal ions hold the layers quite strongly, metals resist deformation quite well. This is especially true with alloys, where atoms of different sizes prevent the layers slipping past each other.

Ductile

Since the bonding is non-directional and non-permanent, with electrons that are free to move around, atoms can move about and slide past each other. This makes metals relatively ductile.

Toughness

Metals are tough for the same reason as they are ductile: the positive ions can slide past each other while still remaining together. So, instead of breaking apart, they change shape, resulting in increased toughness. This effect is called plasticity. When a tough material breaks the ratio of 'energy used / new surface area created' is very large.

Elasticity

When a metal is stretched, it can return to its original shape because the sea of electrons which bonds the ions together can be stretched as well.

Brittle

The opposite of tough: a material is likely to crack or shatter upon impact or force. It will snap cleanly due to defects and cracks. Metals can be brittle in certain circumstances, and a metal can be made more brittle by alloying or by work hardening.

Malleability

Metals are malleable because their atoms are arranged in flat planes that can slide past each other. Their bonds are non-directional. Metals also contain dislocations which mean that ions in the structure can be moved unilaterally rather than as a whole layer, which takes less energy to do.

Thermal Properties

Metals conduct electricity well for 2 main reasons. Firstly, they are in a lattice. The atoms are arranged both closely and neatly. This means that atoms transmit forces very efficiently through the material, so thermal vibrations pass heat energy along easily. This effect is also observed in ionic lattices and in silicon and diamond which are covalent lattices.

Secondly, the free electrons move more when heated, which is another method of passing heat through the lattice.

Transformation

Diffusive transformation: occur when the planes of atoms in the material move past each other due to the stresses on the object. This transformation is permanent and cannot be recovered from due to energy being absorbed by the structure

Diffusionless transformation: occurs where the bonds between the atoms stretch, allowing the material to deform elastically. An example would be rubber or a shape memory metal/alloy (often referred to as SMA) such as a nickel-titanium alloy. In the shape memory alloy the transformation occurs via the change of phase of the internal structure from martensitic to deformed martensitic, which allows the SMA to have a high percentage strain (up to 8% for some SMA's in comparison to approximately 0.5% for steel). If the material is then heated above a certain temperature the deformed martensite will form austenite, which returns to twinned martensite after cooling.

Arrangement of atoms

Metal atoms form lattices. These are neat ordered rows of atoms that stack together to make layers, which in turn stack neatly to make a 3D structure. The fact metals stay in ordered structures is key to their properties. The neat ordered rows will stretch billions and billions of atoms across. However, they do not go on forever. Metals are usually formed from a molten state. When the liquid solidifies, this happens in many places at once. Therefore many crystals form at once, and the crystals are oriented randomly with respect to one another. Metals are polycrystalline.

How grains affect the mechanical properties is beyond the scope of the A-level course, however, as a rule of thumb, smaller grains mean a higher strength. Single crystal metals can be grown, and they have interesting unique properties related to their geometry. However, this is a difficult and specialised process, but single crystal metals can be used for turbine blades inside aeroplane engines.

Questions

1. Would you expect a metal to have more or less conductivity than a semiconductor? Why?

2. How can the stress-strain graph for a metal be explained in terms of ions in a sea of electrons?

3. As a metal heats up, what happens to its conductivity? Why?

Worked Solutions