3.091SC | Fall 2010 | Undergraduate

Introduction to Solid State Chemistry

Solid Solutions

33. Unary Phase Diagrams

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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


Before starting this session, you should be familiar with:

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.


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


Lecture Slides (PDF - 3.0MB)

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.


Problems (PDF)

Solutions (PDF)

More phase diagram homework problems will be provided for the next two sessions.

For Further Study


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

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Course Introduction
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Recitation Videos
Problem Sets
Exam Materials