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Hilary Term – 30 lectures/tutorials – 5 credits (I Shvets)

Part I: Crystal Structure
Part II: Thermal & Electronic Properties

Learning Outcomes
On successful completion of this module, students should be able to:

  • Describe crystal structure in terms of translational and rotational symmetry, conventional unit cell, and Miller indices
  • Demonstrate the relationship between direct lattice and reciprocal lattice
  • Calculate crystal structure parameters from experimental diffraction data
  • Describe the main characteristics of the vibrational dispersion curves and the electronic band structure of crystalline metals, semiconductors and insulators
  • Apply the free electron and nearly free electron models to the quantitative analysis of the transport properties of real metals
  • Provide a quantitative interpretation of the heat capacity of insulators and metals, including temperature dependence


Part I: Crystal Structure
Crystal systems, Bravais lattices, unit cell parameters, translational and rotational symmetry elements, point groups, space groups, Miller indices. The reciprocal lattice. X-ray and neutron scattering. Laue conditions, Bragg's Law. Diffraction patterns and their interpretation. Crystal field explained using the example of 3d electronic wavefunctions. Crystal defects. Points defects. Variation of the crystal field caused by point defects. Jahn-Teller effect. One-dimensional defects: dislocations. Energetics and thermodynamics of defects. Equilibrium density of point defects.

Part II: Thermal & Electronic Properties
Plane waves in free space and in crystals, Bloch functions, Brillouin zones and diffraction in crystals, crystal binding. Atom dynamics in crystals. Electron dynamics in crystals, Free electron model, Nearly free electron model. Real metals, semiconductors and insulators. Electron and hole concepts. Thermal and electric conductivities. Lattice and electronic contributions to heat capacity. Umklapp processes and anharmonic effects.






Continuous Assessment