E5 Ceramic Phase Diagram

Topic

This model focuses on the phase equilibrium of a multicomponent ceramic system—such as the one formed by silicon dioxide and aluminum oxide. Its most distinctive feature is that, unlike what frequently occurs in metallic systems, this type of system often exhibits a peritectic reaction rather than a simple eutectic reaction. Since the peritectic reaction is the most common behavior in multicomponent ceramic systems, it is necessary to explain how it differs from the simple eutectic reaction before proceeding.

In a simple eutectic reaction, the liquid transforms directly upon cooling into two distinct solid phases that form simultaneously. In a peritectic reaction, by contrast, the liquid reacts with a previously formed solid phase, and a distinct solid phase emerges from the interaction between the liquid and that pre-existing solid. Because the multicomponent ceramic system reacts in this latter manner, the system's final solid phase depends on both the remaining liquid and the solid phase that formed initially.

The fact that the ceramic system exhibits this specific peritectic reaction—and not another—at a given point on the phase diagram is due to the system's free energy of mixing, modeled as a regular solution. This free energy of mixing governs the exact position of the invariant equilibrium lines on the diagram (including the aforementioned peritectic line) via a Clausius-Clapeyron-type relationship; this relationship links the shift of an interphase equilibrium line with temperature changes to the heat and volume changes exchanged by the phases during the transformation. Because this free energy of mixing determines the position of these lines, the exact location of the peritectic reaction on the diagram is not arbitrary but is derived directly from the mixture's thermodynamic properties. However, this phase equilibrium condition does not depend solely on the nominal free energy of mixing; the chemical activity of each component—which deviates from its nominal concentration when the mixture does not behave as an ideal solution—modifies the exact phase equilibrium condition. The fact that a component's chemical activity differs from its nominal concentration causes the equilibrium condition to shift relative to what the nominal concentration alone would predict.

Once this phase equilibrium condition is established, the lever rule quantifies—for a given composition and temperature—the fraction of the ceramic system corresponding to each of the phases present; this fraction is determined by the distance between the system's overall composition and the composition of each phase within the diagram's two-phase region. If the system's overall composition is closer to the composition of one phase, that phase's fraction is greater; if it is closer to the other, the fraction of that other phase is greater. For this calculation, the model reuses the same lever rule employed for the same purpose in the equivalent model for metallic systems.

Thus, this model—based on the phase equilibrium of the multicomponent ceramic system introduced at the start—determines both the peritectic reaction characterizing the system and the fraction of each phase present within it: the former is determined by the free energy of mixing and the chemical activity governing the equilibrium condition, while the latter is determined by the lever rule adopted from the equivalent model for metallic systems.

ID:4388