RANDOM-WALKS ON 3-DIMENSIONAL LATTICES WITH THE COORDINATION NUMBER 4

The octahedral interstices (oct.b) and the tetrahedra) interstices (tet.b) in the hotly–centred–cubic lattico each form three–dimenxional lattices with the coordination number four. Random walk calculations are made for the two lattices. The number of visits to the origin (P(0; 1)), the return probability, and the correlation factor for tracer diffusion via the vacancy mechanism, have been compared with those for the diamond lattice, which has the same coordination number. An expression is derived for the electrical resistance between two points in a resistor network isomorphous with a crystal lattice. © 1979 Taylor & Francis Group, LLC.