Magnetic Breakdown in a dislocated lattice

The network model of electron orbits coupled by magnetic breakdown is extended to a two dimensional metal containing dislocations. It is shown that the network is still likely to be a valid representation, but the phase lengths of the arms are altered, and a very low dislocation density (about one per electron orbit) is enough to produce almost complete randomization. The Bloch-like quasi-particles that can travel in straight lines on a perfect network are now heavily scattered, and it is preferable to think of electrons performing a random walk on the arms of the network, although the justification for this procedure is somewhat doubtful. A simpler alternative to Falicov & Sievert’s method is presented for calculating the electrical conductivity of a random-phase network, and is extended to cases where randomness affects only some of the phases, as is believed to be the situation in real metals like zinc and magnesium.