Outline the methods used by the Braggs to determine crystal structure

Diffraction occurs when waves bend around obstructions, and interference patterns result when waves interfere. Diffraction can often result in interference patterns when the bent wave (acting as a point source) interferes with the original wave. A diffraction grating uses small obstructions with separations similar to the wavelength of the wave in question placed side by side to produce a predictable interference pattern that is directly linked to the spacing within the diffraction grating. The Braggs realised that the spacing between layers in a crystal lattice were similar to the wavelength of x-rays, and would therefore act as a diffraction grating. Further, they realised that from the interference pattern they obtained they could calculate the spacing between the lattice layers. The Braggs used an x-ray tube as their x-ray source, and the x-rays travelled through a hole in a shield which acted as a collimator to produce a tightly focussed beam of x-rays. The waves then reflected through a crystal target which acted as a diffraction grating, and then the x-rays travelled to a sensor to analyse the interference pattern. From this they could calculate lattice separation distance, which was of great importance to science and understanding crystal structures.

Remember- The Braggs used diffraction and interference patterns with x-rays to calculate the spacing between crystal lattice layers.

Identify that metals possess a crystal lattice structure

Metals, like many other molecules, have a crystal lattice structure in their solid state. This means that they exist as a 3-dimensional grid of atoms arranged into layers. It is a repeating structure where each atom occupies a well-defined equilibrium distance from its neighbours. In the case of metals, free electrons exist in between lattice layers and conduct electricity.

figure 11

Describe conduction in metals as a free movement of electrons unimpeded by the lattice

A metal has free electrons that exist in the space between metal ions in the lattice. This means that they exist in a more-or-less empty space containing no lattice ions, leaving them free to travel without being impeded by the lattice. However, collisions between the electron and the lattice still occur, as do collisions between electrons and other electrons. When an electric field or potential is applied to a metal, the metal conducts because the electrons move freely between the lattice layers.

Remember- Conduction occurs when electrons travel through the metal lattice, thereby moving charge.

Identify that resistance in metals is increased by the presence of impurities and the scattering of electrons by lattice vibrations

In order to conduct electricity, electrons must travel through the space between lattice layers. Resistance is low when the electrons are free to travel unimpeded, and resistance is high when the passage of electrons is obstructed. Impurities in a metal distort the lattice structure and electrons collide with the impurity, increasing resistance. Similarly, vibrations in the lattice (often caused by heating) destabilize the structure and make it harder for electrons to flow, increasing resistance.

figure 12

Remember- Impurities and lattice vibrations increase resistance.

Describe the occurrence in superconductors below their critical temperature of a population of electrons unaffected by electrical resistance

Phonons are a particular type of quantum particle. They represent quantised vibration states within a crystal structure. It is not necessary to know precisely what they are, only the role that they play in the formation of Cooper pairs.

Superconductors are materials that exhibit no resistance. They only occur at low temperatures because at higher temperatures electron pairs are not capable of forming. In a superconductor, lattice vibrations are eliminated due to the low temperature. As an electron travels through the lattice, it attracts lattice ions causing a lattice distortion- a small region of positive space that attracts another electron. The two electrons then exchange phonons and bind, forming a Cooper pair of electrons which behaves as a single particle. Because the two electrons are interacting with each other they interact less with the lattice, and so travel through it very easily with very little resistance. So below the critical temperature, when a material becomes a superconductor pairs of electrons form that are unaffected by electrical resistance.

Remember- Superconductivity occurs at low temperatures when electrons swap phonons to form Cooper pairs that interact far less with the lattice, resulting in superconductivity.

Process information to identify some of the metals, metal alloys, and com- pounds that have been identified as exhibiting the property of superconductivity and their critical temperatures

You shouldn’t need to remember this list, since in a test they will most likely give you a table of data to use in an answer. However, it will be useful to remember one or two values from this table so you can add them to any answer to show depth of knowledge. Also make sure you remember that 138K is the maximum temperature for superconductivity as of 2009 (though it probably isn’t necessary to remember the exact material).

Material Critical temperature (K)
Zinc 0.85
Aluminium 1.175
Mercury 4.15
Lead 7.196
Tin 7.72
AuBa2Ca3Cu4O11 99
Ba2Ca2Cu3O8.33 138

Discuss the BCS theory

If asked a question like this in an exam, ensure you describe the BCS theory before discussing it. 

The BCS theory of superconductivity is simply the idea that lattice distortions at low temperatures lead to the formation of Cooper pairs. This theory is extremely successful at explaining supercon- ductivity in Type 1 superconductors (substances that have a critical temperature below 30K) as it is almost 50 years old now, and still used. It provided a concrete framework on which to model superconductivity that was vital to understanding how it works. However, it is unable to explain superconductivity in Type 2 superconductors- the ceramic variety that can be superconductors at far higher temperatures. This is because the model predicts 30K as being the maximum temperature at which Cooper pairs are able to form. So while it is extremely important to understanding Type 1 superconductors, it does little to explain Type 2 and so is an incomplete theory.

Remember- The BCS theory explains Type 1 superconductivity but cannot explain Type 2 semicon- ductors.

Discuss the advantages of using superconductors and identify limitations to their use

There are many advantages to using superconductors. These are mainly that they operate with very little loss and so are extremely efficient, and also that they generate no waste heat because they are perfect conductors. They are capable of generating very strong magnetic fields per unit of weight, useful for MRI scanners, and could be used to make very efficient motors, generators and batteries. There are two key limitations to superconductors, however. Firstly, it is very difficult to cool superconductors to below their critical temperatures- they require a constant supply of liquid nitrogen at the moment (given the low temperatures currently needed to achieve superconductivity), and secondly it is very hard to shape ceramic superconductors as they are not ductile, making it difficult to turn superconductors into wires

Remember- Superconductors increase efficiency and can reduce size and weight, but are difficult to manufacture and require cooling.

Analyse information to explain why a magnet is able to hover above a super-
conducting material that has reached the temperature at which it is superconducting

A magnet is able to hover over a superconducting material for two reasons- firstly because magnetic fields are excluded from the superconductor, forcing the magnet to be repelled from the supercon- ductor thus causing it to rise up (this is the Meissner effect), and secondly due to the phenomenon of quantum pinning which stops the magnet from moving horizontally off the superconductor.

The Meissner effect is separate to the induction of eddy currents which would theoretically perfectly oppose the magnetic field of a magnet. This is shown to be true because if a magnet is placed on a superconductor as it is being cooled, it will jump into the air as the superconductor becomes superconducting- this shows it is not an induction phenomenon as change in magnetic flux is required to induce eddy currents. Therefore the levitation occurs due to the exclusion of magnetic fields from the superconductor.

figure 13

Remember- A magnet can float above a superconductor due to the Meissner effect.

Perform an investigation to demonstrate magnetic levitation

In this experiment, we had a ceramic superconducting disk in a Petri dish and a small magnetic cube. We poured liquid nitrogen onto the superconducting disk (and into the dish) to lower it below its critical temperature, making it superconductive. When we used insulated plastic tongs to place the magnet just above the disk, the magnet floated. Nudging it with the tongs caused it to rotate. Eventually, the magnet fell as the disk warmed up and lost its superconductivity. In our second trial, we left the magnet on the disk before pouring liquid nitrogen. As the disk cooled, the magnet suddenly floated upwards off the disk. This showed that the Meissner effect is due to the exclusion of magnetic fields from superconductors, rather than the formation of perfect eddy currents due to changes in flux (because for eddy currents to form there must be an initial change in flux to create them. In the experiment the magnet rose upwards by itself. In fact, the movement of the magnet upwards would have ordinarily induced eddy currents that would drag the magnet down. So this is compelling evidence that the levitation of the magnet is due to the exclusion of the field and not due to eddy currents).

Remember- The exclusion of the magnetic field from the superconductor caused the magnet to levitate.

Gather and process information to describe how superconductors and the effects of magnetic fields have been applied to develop a maglev train

Note that this dotpoint is not only about how superconductors are used in maglev trains, but also how superconductors make maglev trains possible. Often questions will require to you to examine the benefits of using superconductors for maglev trains, in addition to outlining how they are used.

A maglev train relies on superconductors for operation, because superconductors are extremely light, extremely strong magnets, making them well suited to levitate a heavy load such as the train. Superconductors are used in two areas- to levitate the maglev train, and to propel the train. The tracks and the train both have superconductors. Superconductors on the train consist of a looped superconductor on either side of the train. The superconductor is charged with electric current when it is made, and because it is looped (physically, with one end joined to the other), the current flows continuously. This sets up a strong, constant magnetic field. Superconducting electromagnets on the track, positioned above and below the train’s magnetic loops, repel the train from the bottom, and attract the train from the top, causing the train to float. The track magnets are mounted on the vertical sides of the track. Additional superconducting electromagnets on the track serve to propel the train. These electromagnets are situated all along the side of the track. Magnets in front of the train attract the train’s magnets, while magnets on the track behind the train repel the train. By constantly changing the polarity of the track magnets, the train is attracted and repelled in the same direction constantly, causing the maglev train to move rapidly along the track. Superconductors are vital to the development of maglev trains, because permanent magnets would be too heavy to generate the same field strength, and conventional electromagnets would lose too much energy as waste heat due to electrical resistance.

Remember- Superconductors are used in maglev trains because they are light and can produce the incredibly strong magnetic fields required to levitate and propel a train.

Process information to discuss possible applications of superconductivity and the effects of those applications on computers, generators and motors, and trans- mission of electricity through power grids

Superconductors offer great potential in a variety of fields, offering increased performance and ef- ficiency compared to conventional conductors. However, there are still two major obstacles that impede the use of superconductors in virtually all their applications. Firstly, superconductors must be extremely cold, necessitating liquid nitrogen cooling. In some cases this is merely inconvenient, such as in a maglev train, but in applications such as computers, it is extremely difficult and unwieldy to use liquid nitrogen as a coolant, although it has been accomplished by some computer enthusiasts. Secondly, at present type-2 superconductors, (the only realistic option for real-world applications be- cause they only require liquid nitrogen cooling, as opposed to type-1 superconductors with lower critical temperatures), are ceramic compounds that are not ductile. This makes it extremely difficult to use in electrical circuits that rely on ductility to produce a long wire to transfer electricity. Because they are not ductile, they would also be difficult materials to use in computer processors.

However, once these obstacles are overcome, using superconductors in place of standard conductors would bring tremendous benefits. In computers, a great deal of energy is wasted as heat. Further, heating makes it difficult for processors to operate properly, as it changes the properties of the silicon presently used. By using a superconductor, there will be little, if any, waste heat produced, resulting in a processor that can function at far faster speeds. Further, by replacing transistors with superconducting quantum switches (SQUID, or superconducting quantum interference device), the processor can operate faster still. In motors and generators, they can be used to operate at high currents with no losses and no heat production, resulting in extremely efficient motors and generators. According to V = IR, current output will be maximised when there is low resistance, showing that a superconductor will improve current output. Finally, in terms of transmission, a great deal of energy is wasted in the transmission of electricity through conversion to heat in wires. By using superconducting wires, energy loss through the electricity grid will be eliminated, resulting in greater efficiency, with possible impacts such as reduced cost of power, or a reduced need for additional electricity generation capacity. A superconducting electricity grid was successfully trialled in America 4 years ago, and is presently used in parts of the New York grid.

Remember- Superconductors can be used in generators, computer chips and electricity grids, al- though at present there are challenges that need to be resolved first.