- 33. Unary Phase Diagrams
- 34. Binary Phase Diagrams: Complete Solubility
- 35. Binary Phase Diagrams: Limited Solubility
- Self-Assessment
Looking for something specific in this course? The compiles links to most course resources in a single page.
Solid Solutions
Session Overview
| Modules | Solid Solutions |
| Concepts | introduction to phase diagrams, basic definitions of phase, component, and equilibrium, one-component phase diagrams |
| Keywords | stability, pressure, temperature, vapor, liquid, solid, phase, equilibrium, component, triple point, melting, boiling, glass transition temperature, polymorph, sublimation, supercritical |
| Chemical Substances | water (H2O), zirconia (ZrO2), snowflake obsidian, aluminum (Al), silicon (Si), carbon dioxide (CO2), nitrogen (N), bismuth (Bi), sulfur (S), oxygen (O), argon (Ar), “dry ice”, carbon (C), mercury (Hg) |
| Applications | failure analysis, cooking food at altitude and in pressure cooker, automobile engine cooling, ice skating, artificial diamonds, coffee decaffeination |
Prerequisites
Before starting this session, you should be familiar with:
- The Bonding and Molecules module, in particular Session 12: Intermolecular Forces
Looking Ahead
This is the first of three sessions on solid solutions and phase diagrams. Proceed to the next session, Session 34.
Learning Objectives
After completing this session, you should be able to:
- Summarize the purpose of a phase diagram.
- Give a detailed interpretation of the phase diagram of water.
- Given a set of material properties data, draw the phase diagram.
- Given a phase diagram, describe some properties of the material, e.g. the relative densities of its solid and liquid forms.
Reading
Archived Lecture Notes #10 (PDF), Part A
| Book Chapters | Topics |
|---|---|
| [Saylor] 11.6, “Critical Temperature and Pressure.” | Supercritical fluids; molten salts and ionic liquids |
| [Saylor] 11.7, “Phase Diagrams.” | General features of phase diagrams; phase diagrams of water and carbon dioxide |
Lecture Video
Resources
Lecture Summary
Phase stability is the basis for the solid state of matter. Knowledge of phase stability enables applications like:
- conducting failure analysis – recognizing phase “signatures” in the material
- cooking at altitude – adapting to different pressure/temperature relationships
- automobile engine cooling – exploiting pressure and chemical composition to control the coolant’s boiling point (a phase transition temperature)
Prof. Sadoway introduces phase diagrams as “stability maps” and “archives of pressure/temperature relationships.”
This lecture defines and gives examples of phase, one phase and two phase systems, equilibrium, component, and triple point. A detailed discussion of the most familiar one phase system, water, is followed by comparisons of the phase diagrams of aluminum and silicon.
Prof. Sadoway does some live demonstrations for the class:
- various objects are immersed in liquid nitrogen, going below their glass transition temperature
- properties of liquid oxygen
- sublimation of solid frozen CO2, aka ‘dry ice’
The phase diagram of zirconia illustrates the concept of changing a material’s composition to produce desired behaviors at particular temperature/pressure conditions. The phase diagram of carbon illustrates how artificial diamonds are made. Bisumth and sulfur phase diagrams – “phase diagrams from hell” – have many regions. Returning to water, Prof. Sadoway discusses the unusual phases of ice at very high pressures and very low temperatures.
As a final application note, the lecture ends with a quick summary of coffee decaffeination as a process employing sophisticated manipulation of phase transitions.
Homework
More phase diagram homework problems will be provided for the next two sessions.
For Further Study
Culture
Queen. “‘Under Pressure’ (Live at Wembley).” June 16, 2009. YouTube. Accessed November 18, 2010. http://www.youtube.com/watch?v=SJCTgtDU-74.
Alexander Calder, Mercury Fountain, 1937. Fundació Joan Miró. Barcelona, Spain.
Other OCW and OER Content
| Content | Provider | Level | Notes |
|---|---|---|---|
| 3.012 Fundamentals of Material Science | MIT OpenCourseWare | Undergraduate (second-year) | See Thermodynamics lectures 15-16 on single-component phase diagrams, plus associated recitation and assignment content |
Session Overview
| Modules | Solid Solutions |
| Concepts | two-component phase diagrams, complete solubility (Type 1), limited solubility of both components in each other (Type 2), lever rule |
| Keywords | pressure, temperature, composition, isomorphism, slush, lenticular, coexistence curve, liquidus, solidus, tie line, lever rule, metallurgy, phase separation, syncline, consolute temperature, miscibility gap, cosolvation |
| Chemical Substances | solutions of Cu-Ni, NiO-MgO, Au-Ni, hexane–nitrobenzene, KCl-NaCl |
| Applications | metal refining, metal recycling, ouzo, absinthe, cognac |
Prerequisites
Before starting this session, you should be familiar with:
Looking Ahead
Binary phase diagrams are introduced in this session, and completed in Session 35.
Learning Objectives
After completing this session, you should be able to:
- Compare binary and unary phase diagrams.
- Show where liquidus, solidus, and the miscibility gap are represented in a binary phase diagram.
- Create a binary phase diagram from temperature and composition data.
- Derive phase and composition information from a Type 1 or Type 2 binary phase diagram.
Reading
Archived Lecture Notes #10 (PDF), Part B and #10 Supplement (PDF)
| Book Chapters | Topics |
|---|---|
| [JS] 9.1, “The Phase Rule.” | Discussion of phase, component, and state; Gibbs phase rule; unary (one-component) phase diagram |
| [JS] 9.2, “The Phase Diagram.” | Binary phase diagrams; complete solid solutions; eutectic diagrams with no solid and limited solid solutions |
Lecture Video
Resources
Lecture Summary
This lecture begins with quick review of the prior session: unary phase diagrams, the phase diagram of water, and the concepts of equilibrium, triple point, and supercriticality.
This session introduces two-phase or binary phase diagrams, in which pressure, temperature, and composition can vary. Since 3.091 focuses on the solid state, and the solid state is relatively insensitive to pressure, this complex topic can be simplified to the temperature versus composition relationships.
Prof. Sadoway classifies binary phase diagrams into three types, varying by bonding (which determines solubility). This is his own system, not found in textbooks. Type 1 and 2 are covered in this lecture, while Type 3 is covered in the next session.
Type 1: The solution exhibits complete solubility as solids and liquids, and change of state is present. The two components have identical crystal structures, similar atomic volumes, and minimal difference in electronegativity. For metals, British scientist William Hume-Rothery proposed this classification as a set of rules about 75 years ago.
Isomorphism create a “lens” shaped or lenticular phase diagram. Prof. Sadoway defines the key terms liquidus and solidus, and then gives some binary phase diagram examples for Type 1 solutions of Cu-Ni, NiO-MgO, and Au-Ni. The lever rule determines the relative percentages of solid and liquid phases with different compositions that coexist at a given temperature, and gives metallurgists an essential tool for controlling processes like refining and recycling.
Type 2: The solution exhibits partial or limited solubility of both components in each other. There is no change of state (it is always solid or always liquid). This type has a characteristic synclinal coexistence curve. Prof. Sadoway defines consolute temperature, describes the miscibility gap, and then demonstrates the visual effect of the miscibility gap in a mixture of water and the liquor ouzo.
The lecture ends with a discussion of the history and chemistry of absinthe. This transparent green liquor is traditionally mixed with water in a 1:5 ratio, a solution that shows a miscibility gap effect as in the ouzo demonstration.
Homework
For Further Study
Supplemental Readings
Carter, Kelley. “Absinthe flows again, more stylish than ever.” USA Today, September 27, 2007.
People
Culture
The Manchurian Candidate. Directed by John Frankenheimer. MGM, 1962.
Moulin Rouge! Directed by Baz Luhrmann. 20th Century Fox, 2001.
Other OCW and OER Content
| Content | Provider | Level | Notes |
|---|---|---|---|
| 3.012 Fundamentals of Material Science | MIT OpenCourseWare | Undergraduate (second-year) | See Thermodynamics lectures 17-19 on multi-phase and binary phase diagrams, plus associated recitations and assignment content |
| Phase Diagrams and Solidification, Solid Solutions | DoITPoMS | Undergraduate |
Session Overview
| Modules | Solid Solutions |
| Concepts | two-component phase diagrams: limited solid solubility (Type 3) |
| Keywords | binary phase diagram, liquidus, solidus, metallurgy, lenticular, syncline, eutectic, solvus, alpha and beta structures, lamellar structure |
| Chemical Substances | solutions of ethylene glycol – water, chloride salt – water, cubic zirconia, aluminum-magnesium, lead-tin, aluminum-copper, aluminum-magnesium, iron-sulfur, ethanol-water |
| Applications | automobile antifreeze/coolant, deicing, manufacturing aluminum beverage cans, metallurgical failure analysis, aircraft metals, champagne |
Prerequisites
Before starting this session, you should be familiar with:
Learning Objectives
After completing this session, you should be able to:
- Describe how a Type 3 binary phase diagram is a hybrid of Type 1 and Type 2 diagrams.
- Derive phase and composition information from a Type 3 binary phase diagram.
Reading
Archived Lecture Notes #10 (PDF), Part B and #10 Supplement (PDF)
| Book Chapters | Topics |
|---|---|
| [JS] 9.1, “The Phase Rule.” | Discussion of phase, component, and state; Gibbs phase rule; unary (one-component) phase diagram |
| [JS] 9.2, “The Phase Diagram.” | Binary phase diagrams; complete solid solutions; eutectic diagrams with no solid and limited solid solutions |
Lecture Video
Resources
About this Video
This lecture begins with a quick review of Type 1 and Type 2 binary phase diagrams from the previous lecture.
This class introduces Type 3 binary phase diagrams, characterized by partial solubility of components A and B, a change of state, and freezing point depression of both components. It’s a hybrid of the Type 1 lenticular (lens) curve and Type 2 syncline curve. The eutectic is the lowest melting point on the diagram; it is a triple point where all three phases exist in equilibrium.
Prof. Sadoway presents some examples of Type 3 phase diagrams:
- ethylene glycol – water solution for automobile antifreeze/coolant;
- chloride salts – water mix for sidewalk and road deicing;
- cubic zirconia and how a jeweler can distinguish it from diamond;
- aluminum-magnesium alloy for easily-manufactured beverage cans;
- lead-tin mix for electronics soldering, with an extensive discussion of the alpha, beta, and lamellar microstructures that form while cooling;
- aluminum-copper for strength, e.g. airplane wings, constrasting with easily manufactured beverage cans;
- brief discussions of aluminum-magnesium and iron-sulfur solutions.
While considering these phase diagrams, he also describes the origins of the Fahrenheit temperature scale; and returns to how a material’s metallurgical microstructure is used for failure analysis (a topic introduced in Session 33).
Champagne manufacturing illustrates an ingenious use of solution chemistry as shown in binary phase diagrams.
The last few minutes of lecture are a preview of the final exam expectations and policies, some of Prof. Sadoway’s personal observations on the course, and a final champagne toast.
Congratulations! You’ve completed the final lecture.
Homework
For Further Study
People
Nicole Barbe Ponsardin (Madame Ponsardin Cliquot)
Other OCW and OER Content
| Content | Provider | Level | Notes |
|---|---|---|---|
| 3.012 Fundamentals of Material Science | MIT OpenCourseWare | Undergraduate (second-year) | See Thermodynamics lectures 17-19 on multi-phase and binary phase diagrams, plus associated recitation and assignment content |
| Phase Diagrams and Solidification, Solid Solutions | DoITPoMS | Undergraduate |
This self-assessment page completes the Solid Solutions module, and covers material from the following sessions.
- Session 33: Unary Phase Diagrams
- Session 34: Binary Phase Diagrams: Complete Solubility
- Session 35: Binary Phase Diagrams: Limited Solubility
On this page are a simple weekly quiz and solutions; relevant exam problems and solutions from the 2009 class; help session videos that review selected solutions to the exam problems; and supplemental exam problems and solutions for further study.
Weekly Quiz and Solutions
This short quiz is given approximately once for every three lecture sessions. You should work through the quiz problems in preparation for the exam problems.
Exam Problems and Solutions
These exam problems are intended for you to demonstrate your personal mastery of the material, and should be done alone, closed-book, with just a calculator, the two permitted reference tables (periodic table, physical constants), and one 8 1/2" x 11" aid sheet of your own creation.
After you’ve taken the exam, watch the help session videos below for insights into how to approach some of the exam problems.
Exam Help Session Videos
In these videos, 3.091 teaching assistants review some of the exam problems, demonstrating their approach to solutions, and noting some common mistakes made by students.
Supplemental Exam Problems and Solutions
These additional exam problems from prior years’ classes are offered for further study.
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