Maps of Phase Equilibrium- Intermediate Phase Diagrams

The phase diagrams we've shown on previous pages (isomorphous and eutectic) are the simple exceptions to what we see in real life. These more complicated phase diagrams are called intermediate phase diagrams because they have new phases at intermediate compositions - i.e., not just at the compositional extrema of the phase diagrams.

Figure 10.9.1 shows common one, the Cu-Zn phase diagram - this is the phase diagram for brass of various types. Low Zn content of about 30 wt% Zn in brass is called "cartridge brass" because it was (and still is) used for ammunition cartridges. This type of brass is typically single-phase (denoted $\alpha$ phase) and is relatively soft and malleable. On the other side of the phsae diagram is metallic zinc, denoted the $\eta$ phase. In between - in the intermediate ranges - we have naval brasses - which are around 40 wt% Zn and posses the strengthening $\beta^{\prime}$ BCC phase. (Note, when shown in phase diagrams the prime does not indicate a "primary" phase. It usually indicates that the structure is related to, but somehow different from, the unprimed phase.) These brasses are sometimes called duplex brasses. There are also $\gamma$ brasses (containing high zinc content) and the $\gamma$ phase and white brasses which have zinc contents above 50 wt% and contain $\gamma$, $\epsilon$, or $\eta$ phases. Use of white brass is uncommon outside of decorative uses and some marine/industrial applications.

There are a number of new features here - some of you may observe new "invariant" points - we'll discuss them soon. However, note that you can use everything you know already regarding 1. phase identification, 2. tie lines, and 3. the lever rule to solve for phases present, phase composition, and phase fraction.

Some phase diagrams have a very special feature that can, at first, be a bit confusing. Let's look at the Mb-Pb phase diagram in Figure 10.9.2. This phase diagram contains a line compound which is a phase (in this case $\ce{Mg2Pb}$ at 81 wt% Pb (or exactly 33 at% Pb) which only exists at a single composition. This means that the compound cannot accommodate any off-stoichiometric composition and remain phase pure. In short, the phase diagram tells us that if we add Mg to $\ce{Mg2Pb}$, we'll form a new phase ($\alpha$ phase below about $466 ^{\circ}\text{C}$), and if we add Pb we'll precipitate the $\beta$ phase below $249 ^{\circ}\text{C}$.

An interesting feature of this phase diagram is that if you maintain a stoichiometry of $\ce{Mg2Pb}$ and heat the specimen to $550 ^{\circ}\text{C}$, you go through a surprisingly simple phase transition: melting $\ce{Mg2Pb} \rightarrow L$. Regardless, you can navigate this phase diagram the same way you would any other, and will do so in your problem sets.

Phase diagrams exist for all materials classes - no just just metals. Figure 10.9.3 shows a phase diagram with $\ce{ZrO2}$ on the left side, where we increase the fraction of $\ce{CaO}$. We only plot up to equal portions $\ce{CaO}$ and $\ce{ZrO2}$, at which we form the compound $\ce{CaZrO3}$. Again - from very simiplar features with a eutectic at high temperature and various phases forming. One think to note about this phase diagram is that has lots of dashed lines instead of solid lines for phase boundaries. When you see this, it means that the exact positions of these phase boundaries have high uncertainties. This may be due to difficulties in measuring these structures at high temperatures, difficulty in controlling compositions, or disinterest from the academic community of finding the exact position of the line (as it may be of no scientific or technological importance).

Invariant Reaction Points

In each of these more complicated phase diagrams, above, you may have noticed points on the diagrams that look something like a eutectic - i.e., points that imply three-phase equilibrium, but perhaps look a bit different: we don't have a phase transition from a liquid solution to two solids $\ell_{\mathrm{s}} \rightarrow S_1 + S_2$ upon cooling.

These other points are also invariant points, but have different reactions. If you practice, they're easy to identify. Below we list some of the most common (and the only ones you'll encounter here):

• Eutectic Reaction Points in which, upon cooling through the point, you have a reaction only of $\ell_{\mathrm{s}} \rightarrow S_1 + S_2$. Eutectic means "easy melting". You can find these by navigating along a liquidus line and finding a minimum in which the liquid solution will transition two a two-phase region upon cooling.
• Eutectoid Reaction Points in which, upon cooling through the point, you have a reaction of a solid to two new solids, $S_1 + S_2 \rightarrow S_3$. Eutectoid is like a eutectic, but not quite (and there is no melting): which is why it contains the word "oid", which denotes resemblance (android, for example) These features look topologically like eutectics on phase diagrams.
• Peritectic Reaction Points in which, upon cooling through the point, you have a reaction in which two phases, one liquid and one solid, convert to a single, new solid phase: $\ell_{s} + S_1 \rightarrow S_2$. The perm "peri" means "covered" or "sorrounded" and "tectic" means melting, and it has to do with the kinetics of solidification, but is something we won't cover here. These features always borders a liquid phase region, so they'll exist near the top of the phase diagram.
• Pertectoid Reaction Points in which, upon cooling through the point, you have a reaction in which two phases, both solids, convert to a single new solid phase $S_1 + S_2 \rightarrow S_3$. Again, the term "oid" tells us that it is like a peritectic, however in this case no liquid phase is involved in the reaction.

These reactions are enumerated and shown schematically in @ref().

Remember, you can always simply check! Draw a vertical line through a point you think might have a pure invariant reaction, write the reaction that occurs, and match it to the list above!

Other Important Reactions

There are two other reactions we'll commonly encounter in phase diagrams that you'll need to be able to identify.

• Freezing(Melting) in which a liquid phase converts into a solid phase upon cooling $\ell_{\mathrm{s}} \rightarrow S_1$.
• Polymorphic Transition in which a single solid phase transitions into a single, new solid phase: $S_1 \rightarrow S_2$.

Let's practice looking at some of these in Exercise 10.9.1.

Supplemental Video