Maps of Phase Equilibrium - Binary Phase Diagrams

Now, instead of showing phase diagrams with pressure on the $y$-axis and temperature on the $x$-axis, let's instead think about what might happen when we hold pressure constant (at 1 atm), but allow the composition of our mixture change. So, we'll continue water, but instead of just considering water, we'll add another chemical component. One of the most tangible systems is to consider the two-component system of water $\ce{H2O}$ and sucrose ($\ce{C_{12}H_{22}O_{11}}$, or table sugar).

Why is this so nice to consider? Most of us have had a cup of tea, and we've added sugar to that tea to sweeten it. If you like sweet, you've noticed you can add a lot of sugar to water and it goes into solution (we call water-sugar solutions syrups). If you are from some parts of the United States, you might even have grown up drinking Sweet Tea - which can be up to about 20% sugar by weight (or 20 wt% sugar). Amazingly, if you want, you could make your Sweet Tea much, much sweeter than this. Let's use this system to demonstrate our first binary or two-component phase diagram.

The most common binary phase diagram you'll encounter plots composition ($C$, often, but sometimes $x$ or $\chi$) on the $x$-axis and temperature ($T$) on the $y$-axis. These diagrams are sometimes called $T$-$X$ phase diagrams. In Figure 10.5.1 we show a region of the temperature-composition phase diagram for the sugar-water system. Temperature is conventionally measured in degrees Celsius or Kelvin. Composition is the measure of the relative amounts of the constituent chemical components, and is typically reported in weight percent (wt%, the fraction of the total weight due to one of the components) or mol/atomic percent (mol%/at%, the fraction of the total moles or atoms due to one of the components). These are different measures, of course, if the chemical components weight different amounts. For example, if you have a Pb-Sn alloy which is 50 at% Sn (half the atoms are Sn, half are Pb), it is only 37 wt% Sn because Pb is much heavier than Sn.

Let's investigate the new phase diagram in Figure 10.5.1. Again, we're plotting composition on the $x$-axis, shown in weight percent. Since we only have two components, we can choose which composition to plot and the other composition is known. In Figure 10.5.1 we're explicit, shoing both components in wt%. Sugar increases in concentration from the left size of the diagram to the right, and water decreases in concentration. At the left extremum of the diagram, we have pure water. At the right extremum we have pure sugar. In between we have a mixture.

Let's consider we start with pure water at $60 ^{\circ}\text{C}$ and start adding sugar. We know what phase diagrams tell us: with a composition and a temperature we know the the equilibrium phases present in the mixture. As we increase the wt% of sugar we form a sweeter and sweeter water-sugar solution. The phase field here is labeled and tells us that the phase will be liquid about 70 wt% sugar, at which point we encounter a phase boundary. In this diagram, the phase boundary denotes the solubility limit of sugar in water. If we try to add more than 70 wt% sugar into the solution, we'll find that we cannot: we have reached the solubility limit. Any additional sugar will not be dissolved, it will remain as a solid.

This is communicated by the phase field labeled on the right. Once we've added enough sugar to the mixture to cross the solubility limit we now have a two-phase mixture: a mixture containing a liquid phase (a sugar-rich syrup) and a solid-phase (crystalline sugar).

Note - we're using common language that you may have encountered in a chemistry course to describe these phase mixtures. Solutions, solubility limits, composition, and so on. In materials science, we'll continue to use this language as we move to materials-relevant systems such as alloys, polymer mixtures, and ceramic systems.

As we can see, this is a very useful tool. We can determine, precisely, how much sugar we can add to a beverage and maintain a single-phase liquid solution! So let's practice in @ref().