Phase diagram materials microstructure

Phase diagrams arc condensed presentations of a large amount of information. They provide quantitative information on the phases present under given conditions of alloy composition and temperature and, to the experienced metallurgist, a guide to the distribution of the phases in the microstructure of the alloy. They also dictate what alterations in phase constitution will occur w ith changing conditions, whether these be alteration of alloy composition, temperature, pressure or atmosphere in equilibrium with the material. 

Like its nonconservative counterpart seen in the Allen-Cahn equation, the Cahn-Hilliard equation is aimed at describing the evolution of field variables used to describe microstructures. In the present setting, a particularly fertile example (of which there are many) of the use of this equation occurs in the context of phase separation. Recall that the Cahn-Hilliard equation describes a system with a conserved field variable. What we have in mind is the type of two-phase microstructures described in chap. 10 where the phase diagram demands the coexistence of the host matrix material and some associated precipitates. The Cahn-Hilliard equation describes the temporal evolution of such microstructures. 

The importance of knowing the phase diagram in a particular system cannot be overemphasized. It is the roadmap without which it is very difficult to interpret and predict microstructure distribution and evolution, which in turn have a profound effect on the ultimate properties of a material. 

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