E1 Phases and Composition

Topic

The overall chemical composition of this multicomponent alloy, together with the corresponding phase diagram, determines—via the lever rule—the proportions in which the alpha and beta phases coexist at equilibrium: within the diagram's two-phase region, the distances between the alloy's overall composition and the compositions of the two individual phases dictate, through the lever rule, the fraction of each phase present. If the alloy's overall composition lies closer to the alpha phase composition on the phase diagram, the lever rule dictates a higher fraction of the alpha phase and, consequently, a lower fraction of the beta phase.

This coexistence of alpha and beta phases consistently satisfies the alloy's overall mass balance: the total mass of each constituent element—distributed between the two phases according to their respective compositions and the fractions assigned by the lever rule—must exactly equal the total mass of that element in the alloy's overall composition. If the fraction of one phase changes while the alloy's overall composition remains constant, the composition of the other phase must adjust accordingly to maintain this overall mass balance.

The number of variables that can be freely adjusted—specifically, the composition of each phase and the system temperature—without altering the number of coexisting equilibrium phases is limited by Gibbs' phase rule (applied here at constant pressure): the more phases coexisting simultaneously in the alloy, the fewer degrees of freedom remain to vary composition and temperature without causing a phase to appear or disappear. The fact that this alloy—within a specific region of its phase diagram—exhibits multiple coexisting phases means, according to Gibbs' phase rule, that there are fewer degrees of freedom available in that region.

Consequently, this model—starting with the overall composition and the initial alpha and beta phase fractions—feeds into three other models within the set: the one detailing the binary phase diagram (from which only the lever rule is utilized here), the one describing diffusion between these phases, and the one describing the alloy's solidification from the liquid state. Since this model allows the phases present in the alloy and their respective fractions to be determined from composition and temperature—without requiring direct observation—another distinct model in the set (describing X-ray diffraction on the metal) can experimentally measure them and, using Bragg's law, identify which of those phases are actually present.

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