an order-disorder transformation

In many alloys two kinds of atom share one lattice. At high temperature they sit at random — any site is equally likely to hold either species, like a chessboard whose squares have been coloured by coin-toss. Cool it down and the atoms sort themselves out, each species preferring its own set of sites, until the pattern becomes regular — a proper chessboard of alternating colours. That switch from random-mixing to a regular chemical pattern, with no change in the underlying lattice geometry, is an order-disorder transformation.

Beta-brass is the textbook case. It is body-centred-cubic CuZn: above about 454 degrees C, Cu and Zn are randomly spread over all the BCC sites (disordered, A2). Below it, copper atoms migrate to the cube corners and zinc to the cube centres (or vice versa) — the two interpenetrating simple-cubic sublattices each become chemically pure, giving the ordered CsCl-type (B2) structure. Cu3Au does the same on an FCC lattice: gold gathers on the cube corners and copper on the face centres, giving the ordered L1_2 structure below about 390 degrees C. Note this needs atoms to swap places, so it does require some diffusion — but the lattice sites themselves do not move.

Ordering enlarges the true repeat of the chemical pattern, so it creates a superlattice and, with it, new superlattice diffraction spots; it can be gradual (second-order, like beta-brass, where order fades in continuously) or abrupt (first-order, like Cu3Au). Ordering changes properties sharply — ordered alloys are often harder, more brittle, and electrically different — and the degree of order is captured by a single number, the order parameter.