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Chapter 5 Introduction to Order-Disorder Transitions In the previous chapter, two new types of nanometer rod-shaped precipitates wereobserved; they were named QP and QC and seemed to be precursors of the stable Q-Al Cu Mg Si . Before a complete TEM and HREM study of these phases, subject of the next5 2 8 7chapter, an introduction to ordering mechanisms is required. Order-disorder transitions will beintroduced in the global framework of phase transitions (solid-liquid-gas, ferro-paramagnetic, ferro-para electric, superfluids, polymers), without enlarging the presentation tocritical phenomena. Most of the approach presented in this chapter is based on the simple followingthermodynamic concept: for a closed system in thermal equilibrium, the transition is aconsequence of a compromise: the energy tends to order and the entropy associated to thetemperature tends to break the order. Different classifications of phase transitions will bepresented in section 5.1. Phenomenological Landau’s approach by thermodynamics will betreated in section 5.2. A more general approach by using statistical mechanics on an Isingmodel, as well as Monte Carlo simulations, will be treated in section 5.3. It will help us tointroduce the order parameters and approximate methods such as the Bragg-Williams method.Since we are interested in disordered nano-precipitates present in a matrix, the mostappropriate ...