3.091SC | Fall 2010 | Undergraduate

Introduction to Solid State Chemistry

Solid Solutions

34. Binary Phase Diagrams: Complete Solubility

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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


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.


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


Lecture Slides (PDF - 2.5MB)

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.


Problems (PDF)

Solutions (PDF)

For Further Study

Supplemental Readings

Carter, Kelley. “Absinthe flows again, more stylish than ever.” USA Today, September 27, 2007.



William Hume-Rothery


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  

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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