Over the past few units we've learned quite a bit about "perfect" crystal structures in materials structure (metals, ionic/covalent ceramics) as well as the complex structures that can arise in large assemblies of molecular chains (polymers). We've covered deviations from perfect materials in terms of point defect structure, and we've described how atoms move through regular crystalline assemblies via diffusion.

In all of these examples (with few exceptions), we are essentially talking about a materials of a single phase. For example: the NaCl salt crystal we introduced in Section 5.12 is just that: a single, solid chunk of $\ce{NaCl}$ salt. It's properties are essentially uniform anywhere within that chunk of salt. When we talked about molecular solids like ice, we showed that the $\ce{H2O}$ formed a single, regular repeating structure (a pattern which is ultimately reflected at the macroscopic scale (in snowflakes). We introduced metal crystals mainly by highlighting their crystal structures: FCC, BCC, SC, etc.

Indeed, even when we began exploring what happens when "atoms" interact via the Lennard-Jones potentials we found they formed regular, periodic arrays. However, it was always the same pattern: a close-packed two-dimentional hexagonal array. We never saw some region of hexagonal structure and another of cubic or oblique. That is, our Lennard-Jones simulation yielded single structure - or a single phase (Section 5.3).

In this chapter, we'll explore phase behavior. Can we change this structures by changing the environment of a material? Can we use our understanding of phase behavior to help us design materials? Let's see.

Heating of Iron

Iron has broad and varied use in society, but one of those uses is in piano wire. Piano wires (which are made of an alloy of iron and carbon) is held in tension between posts. When struck by a hammer, they vibrate with a certain pitch - depending on their mass, tension, and length. Piano players may notice this - a change of a few degrees $^{\circ}\text{C}$ can lead to an audible change in pitch. This behavior is related to something we already know about - thermal expansion and the interatomic potential.

However, if you take the piano wire out of the piano and really heat it up - to about $900 ^{\circ}\text{C}$ - something interesting happens. Watch the video by University of Utah Materials Science and Engineer Professor Taylor Sparks in Section 10.2.3 and complete exercise Exercise 10.2.1. Note - he's explaining what happens... you can listen to his explanation, or you can turn off the volume and trying to figure out what's going on by yourself. You might want to view the video directly on YouTube because it's tough to see embedded here.

The Mixing of Two Metals

Above, we looked at the behavior of iron as a function of temperature, and saw evidence of some interesting change in crystal structure. What if we mix two types of materials together? What might we see? Let's try:

In its pure form, indium is a silvery, ductile metal which possesses a body-centered tetragonal crystal structure. It's used most in consumer electronics, and the majority of of the world's indium goes into devices with touch screens.

Gallium is a silver-blue metal with an orthorhombic crystal structure. It's famous because it has a melting temperature of about $30 ^{\circ}\text{C}$, and so it would melt if you held it in your hand. Like indium, it's used in electronics - about 95% of all gallium produced goes into the production of the important semiconductor GaAs for use in solar cells, light-emitting diodes, and integrated circuits.

Both these materials are solid at room temperature - but what happens if we mix them? Watch this happening via simple physical contact in Video 10.2.1, and answer the questions in Exercise 10.2.2.

Phase Behavior Exploration Summary

In the example of heating iron, we see something unexpected, which is due to a change in crystal structure. In the example of mixing indium and gallium, we also see something that is perhaps unexpectes: when we put the two metals in contact with each other, we get a new state of matter (or phase of matter) - a liquid! Those of you with chemistry backgrounds might think that there's a chemical reaction producing a new compound that his liquid at room temperature. However, a quick search turns up no chemical compounds for the In-Ga, that is - there's no record of something like $\ce{In2Ga}$ or $\ce{In3Ga2}$. So, we don't have a chemical reaction, but something is certainly changing as we start with two solids and yield a liquid.

This change in phase is central to the field of materials science. In the example above, it's clearly important to know that if we have an application in which solid In and Ga touch at room temperature, we get a liquid. There are many addition phase behaviors that are important in different applications. So, it is clearly important that we somehow be able to predict when a phenomena like that in Video 10.2.1 occurs.

The reason these changes occur is deeply steeped in thermodynamics. In this course, we won't delve into the specifics, but if you continue your studies in materials science (or chemistry/chemical engineering, for that matter) you'll learn about how mixtures of different elements or chemicals can yield this type of "phase behavior".

At this point - we simply need two clear observations from the experiments above:

1. If we increase the temperature of a material, we can change its structure.
2. If we mix a material with another (i.e., change the composition of the material), we can change its structure.

This implies that we could make a map of the structures we observe for materials if we change (i.e.) their temperatures and compositions. We can make a diagram, or a map of these structures as a function of temperature. We call this map a phase diagram, and it is one of the most important tools of an materials scientist or engineer.

Outcomes

At the end of this module students should be able to:

• Use language and terms central to describing phase equilibria and microstructure, including language specific to Fe-C phase diagrams.
• Interpret phase diagrams to determine (at a specific temperature and composition):
  • Phases present.
  • Composition of phases.
  • Phase fractions
  • Equilibrium microstructure
• Formulate processing sequences that would yield specific phase mixtures and microstructures (and be able to sketch the resulting microstructures).
• Identify critical features of phase diagrams, including melting/freezing points, solubility limits, and phase boundaries.
• Identify invariant points and invariant reactions that occur at and near the points.
• Evaluate how phase behavior and microstructural changes influence certain properties - including plasticity and electrical conduction.

Outline

The outline for this chapter is as follows:

• Section 10.3- What's a Phase?: If we want to talk about phase behavior, we'll first need to define what a phase is.
• Section 10.4- Unary Phase Diagrams: The first type of phase diagram we'll introduce is familiar to most folks who have taken high school or first-year university chemistry. It is a single component phase diagram, typically plotted as temperature vs pressure.
• • Section 10.4- Binary Phase Diagrams: The second type of phase diagram we'll introduce is the binary phase diagram, in which two distinct chemical