Superconducting metals and X-ray crystallography

Nature of science:

Importance of theories—superconducting materials, with zero electrical resistance below a certain temperature, provide a good example of theories needing to be modified to fit new data. It is important to understand the basic scientific principles behind modern instruments. (2.2)

• Superconductors are materials that offer no resistance to electric currents below a critical temperature.
• The Meissner effect is the ability of a superconductor to create a mirror image magnetic field of an external field, thus expelling it.
• Resistance in metallic conductors is caused by collisions between electrons and positive ions of the lattice.
• The Bardeen–Cooper–Schrieffer (BCS) theory explains that below the critical temperature electrons in superconductors form Cooper pairs which move freely through the superconductor.
• Type 1 superconductors have sharp transitions to superconductivity whereas Type 2 superconductors have more gradual transitions.
• X-ray diffraction can be used to analyse structures of metallic and ionic compounds.
• Crystal lattices contain simple repeating unit cells.
• Atoms on faces and edges of unit cells are shared.
• The number of nearest neighbours of an atom/ion is its coordination number.

• Analytical techniques have applications in forensics, mineral exploration, medicine and elsewhere. How does the unequal access to advanced technology affect world economies?

Theory of knowledge:

• X-ray diffraction has allowed us to probe the world beyond the biological limits of our senses. How reliable is our knowledge of the microscopic world compared to what we know at the macroscopic level?

Utilization:

• Syllabus and cross-curricular links:
• Topic 2.2—Pauli exclusion principle
• Topic 3.2—atomic radius and periodicity
• Topic 21.1—X-ray crystallography
• Physics topic 4.2—travelling waves

Aims:

• Aim 7: Animations and simulations would be very useful to explain superconductivity and X-ray crystallography.

• Analysis of resistance versus temperature data for Type 1 and Type 2 superconductors.
• Explanation of superconductivity in terms of Cooper pairs moving through a positive ion lattice.
• Deduction or construction of unit cell structures from crystal structure information.
• Application of the Bragg equation, , in metallic structures.
• Determination of the density of a pure metal from its atomic radii and crystal packing structure.

Guidance:

• Only a simple explanation of BCS theory with Cooper pairs is required. At low temperatures the positive ions in the lattice are distorted slightly by a passing electron. A second electron is attracted to this slight positive deformation and a coupling of these two electrons occurs.
• Operating principles of X-ray crystallography are not required.
• Only pure metals with simple cubic cells, body centred cubic cells (BCC) and face centred cubic cells (FCC) should be covered.
• Perovskite crystalline structures of many superconductors can be analysed by X-ray crystallography but these will not be assessed.
• Bragg's equation will only be applied to simple cubic structures.