who is MATTER? what do we do? how to contact us? external links

Materials Science on CD-ROM version 2.1


List of topics


Online manual

Download demo


Product Endorsements



Materials Science on CD-ROM User Guide

Introduction to Phase Diagrams

Version 2.1

Andrew Green, MATTER
Trevor Myers, UMIST/University of Manchester

Assumed Pre-knowledge

This module has been designed as a basic introduction to many of the concepts associated with phase diagrams. As such, little or no pre-knowledge of phase diagrams is assumed.

Before developing the software, a series of interviews with a range of 1st year UK materials science students was conducted with the aim of identifying the major areas of conceptual difficulty in the area of phase diagrams. The main results of these interviews are summarised as follows:

  • The concept of time was often associated with equilibrium phase diagrams, in that equilibrium alloy constitution, microstructure, etc. were described as varying with time, rather than with temperature. This is an understandable, albeit undesirable misconception, which probably results from the study of microstructural change in alloys during cooling.
  • Nearly half the students had difficulty in distinguishing between the terms phase and phase region (on a diagram).
  • Common misuse of the terms component (usually denoted by capital letters, A, B,...) and phase (denoted by Greek letters a, b,...).
  • Inability to define the terms constitution, equilibrium, phase satisfactorily.

In designing the software, deliberate attempts have been made to divorce the concept of time from that of equilibrium constitution. On page 9 of the section Thermal Analysis, a series of cooling curves (temperature - time axes) are ‘collapsed’ into vertical lines so that only the transformation temperatures remain - it is stressed that time is no longer a consideration.

One of the relative advantages of interactive computer-based learning software over textbooks is the ability to hyperlink text to a glossary such that definitions of important terms can be accessed immediately. This accessibility can only be beneficial in encouraging a more precise usage of scientific terminology amongst students.

Module Structure

The module comprises 4 main sections:

Construction of Phase Diagrams from Thermal Analysis Data

This section starts with an introduction of cooling curves for single and dual component alloy systems. The experimental measurement of melting points for pure components from the arrest is illustrated. Although the concept of undercooling is introduced, it is not considered in detail in this particular module. A short exercise is then provided to check that the student has understood some of the terminology used up to this point.

For binary alloys, the concept of solidification over a temperature range is introduced, together with definitions of liquidus and solidus temperatures.

Having studied a single cooling curve for a hypothetical alloy solidifying to give a solid solution, the user is then shown a series of cooling curves for a range of alloy compositions. A graphical 'animation' then shows how the temperature data from these curves is extracted to construct the equilibrium phase diagram. It is also stressed that equilibrium phase diagrams are, by definition, independent of time.

Alloy Constitution

The user is reminded of the three parameters required to define the constitution of an alloy:

  • Phases present
  • Composition of each phase
  • Proportion of each phase

A portion of a phase diagram for a hypothetical alloy solidifying to a solid solution is used throughout this section. The main region of interest is in the liquid + solid phase field. An animation sequence is used to explain how the equilibrium phases for any given composition and temperature are read from the phase diagram. The Cu-Zn phase diagram is used as an example of a real (and more complex) alloy system to let the user check that they understand this.

Returning to the hypothetical phase diagram, the use of tie lines to measure the equilibrium composition of the liquid and solid phases for any given composition and temperature is introduced. The user is able to see how the compositions of each phase changes with temperature by moving a slider button up and down a temperature scale.

Lastly, measurement of the equilibrium proportions of each phase is considered. A graphical construction is used to demonstrate how the proportion of liquid decreases as the temperature is lowered from the liquidus to the solidus. The lever rule is then explained in both graphical and mathematical terms.

Again, the user is asked to interact with the phase diagram to see how the proportions of each phase vary with temperature.

In order to check the student’s understanding of the material covered in this section, an exercise is provided whereby the user is asked to select any point in the liquid + solid phase field. They are then asked to calculate the compositions and proportions of each phase at this point and to compare their results with the computed values.

Simple Alloy Systems

This section looks at an example of an alloy system (Cu-Ni) whose components are completely miscible in the solid state.

The user is reminded of the necessary conditions for this to occur, i.e. similar crystal structure, atomic size and valency. A detailed description of the Hume-Rothery rules is not given here.

The concept of solid solubility is illustrated by a 2D animation showing different atoms diffusing at random within a close packed lattice. The user is allowed to change the proportion of each component.

An exercise is set in which the user is asked to identify the melting temperatures of the pure components, Cu and Ni from the phase diagram. Next, an alloy containing 50 weight % Ni is considered, and the user is asked to find the following, by means of graphical interaction:

  • The liquidus temperature
  • The liquid and solid compositions, just below this temperature.
  • The solidus temperature
  • The liquid and solid compositions, just above this temperature.

The section is completed by explaining the development of microstructure during solidification and its relationship to the equilibrium phase diagram.

Eutectic Alloy Systems

This section starts by explaining that most alloy systems do not exhibit complete solid solubility and that two solid phases often exist together in equilibrium. The Ag-Cu system is used as the main example in this section.

The different phase regions of the Ag-Cu system are explained. An exercise is provided to check that the user can identify the eutectic temperature and composition from the diagram, and also to test that they can differentiate between phase (liquid, a, b) and phase region (a, b, a+ b, a+liquid, b+liquid, liquid). An open-format question asks the student to write down the phase transformations for a range of Ag-Cu compositions.

A multiple-choice exercise checks if the user can describe the constitution of 6 Ag-Cu alloys at various temperatures. This is followed by a look at cooling curves for this type of system. A hyperlink allows a comparison with the simpler type of alloy system described in sections 1 and 3.

The remainder of the section concentrates on the relationship between microstructure and phase diagram. The development of microstructures during cooling is simulated for alloys of eutectic, hypoeutectic, hypereutectic and off-eutectic composition.


The student is referred to the following resources in this module:

Ashby, M.F., and Jones, D.R.H., Engineering Materials 2, Pergamon, 1986

Barrett, C.S. and Massalski, T.B., Structure of Metals, McGraw-Hill, 1980

Cottrell, A.H., An Introduction to Metallurgy, Edward Arnold, 1975

Hansen, M. and Anderko, K., Constitution of Binary Alloys, McGraw-Hill, 1958

Rollason, E.C., Metallurgy for Engineers, Edward Arnold, 1973


The University of Liverpool
Copyright of The University of Liverpool 2000