21-Mat-B10 Properties and Processing of Micro- and Nanomaterials · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — 12-Mtl-B10, Advanced Electronic Materials — December 2018, 3 hours. Six questions; Question 6 (40 marks) is mandatory and any 4 of the remaining 5 questions (15 marks each) complete the paper. All six are answered below.
Reference texts: S.O. Kasap, Principles of Electronic Materials and Devices; W.D. Callister, Materials Science and Engineering: An Introduction.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Below its critical temperature Tc and below a critical field Hc(T), a superconductor actively expels an applied magnetic field from its interior, developing surface (screening) currents that cancel the field everywhere inside the bulk — it becomes a perfect diamagnet (bulk B = 0), not merely a perfect conductor. This distinguishes true superconductivity from a hypothetical zero-resistance normal metal: a perfect conductor would simply trap whatever flux was present at the moment it became resistance-free, while a superconductor actively expels flux that was already present before cooling through Tc. The effect is what levitates a magnet above a superconducting disk and is the basis of practical flux-exclusion applications such as magnetic shielding.
The Bardeen–Cooper–Schrieffer (BCS) theory explains conventional superconductivity as arising from electrons forming weakly bound pairs, called Cooper pairs, mediated by lattice (phonon) interactions: one electron slightly distorts the positive-ion lattice as it passes, and that distortion attracts a second electron, producing a net attractive interaction that overcomes the electrons' mutual Coulomb repulsion. Below Tc, essentially all conduction electrons near the Fermi surface condense into these paired states, separated from unpaired excited states by an energy gap (a few meV); because scattering a Cooper pair requires breaking it (costing at least the gap energy), the pairs move through the lattice without dissipating energy, giving zero DC resistance.
The Seebeck effect is the generation of an electromotive force (EMF) in a conductor subjected to a temperature gradient: the hot end's charge carriers have higher average thermal energy and diffuse toward the cold end faster than the reverse flow, building up a charge separation (and hence a voltage) that opposes further net diffusion at equilibrium, V = SΔT, where S is the material's Seebeck coefficient. A thermocouple exploits this by joining two DISSIMILAR conductors (different S values) at a junction held at the temperature to be measured, with the free ends held at a known reference temperature; because the two legs develop different Seebeck voltages for the same ΔT, the net measurable voltage across the open ends is proportional to the junction temperature difference, which is how a thermocouple converts a temperature into a directly readable voltage.
