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Classifying the Invariant Points: Drawing Phase Diagrams

There are two fundamental ways that invariant points can arise:1

  1. When two two-phase regions join at a temperature and become one two-phase region:
    Eutectic
    $ (\alpha +$   liquid$ ) + ($liquid$ + \beta) \ensuremath{\rightleftharpoons}(\alpha + \beta)$
    Eutectoid
    $ (\alpha + \gamma) + (\gamma + \beta) \ensuremath{\rightleftharpoons}(\alpha + \beta)$

    Figure: Eutectic-type (EV-TYPE at MASSACHVSETTS INSTITVTE OF TECHNOLOGY) invariant points.
    \begin{figure}\resizebox{6in}{!} {\epsfig{file=figures/e-type.eps}} \end{figure}


  2. When one two-phase region splits into two two-phase regions:
    Peritectic
    $ (\alpha +$   liquid$ ) \ensuremath{\rightleftharpoons}($liquid$ + \beta) + (\alpha + \beta)$
    Peritectoid
    $ (\alpha + \gamma) \ensuremath{\rightleftharpoons}(\gamma + \beta) + (\alpha + \beta)$

Figure 30-15: Peritic-type invariant points.
\begin{figure}\resizebox{6in}{!} {\epsfig{file=figures/p-type.eps}} \end{figure}

The invariant points determine the topology of the phase diagram:

Figure 30-16: Construct the rest of the Eutectic-type phase diagram by connecting the lines to the appropriate melting points.
\begin{figure}\resizebox{6in}{!} {\epsfig{file=figures/e-draw.eps}} \end{figure}

Figure 30-17: Construct the rest of Peritectic-type phase diagram, on the left a rule for all phase diagrams is illustrated--the ``lines'' must metastably ``stick'' into the opposite two phase region.
\begin{figure}\resizebox{6in}{!} {\epsfig{file=figures/p-draw.eps}} \end{figure}

These diagrams can be combined and drawn:

Figure 30-18: Construct the lens over peritectoid phase diagram.
\begin{figure}\resizebox{6in}{!} {\epsfig{file=figures/22-6A.eps}} \end{figure}

Figure 30-19: Construct the peritectic over eutectic phase diagram.
\begin{figure}\resizebox{6in}{!} {\epsfig{file=figures/22-6B.eps}} \end{figure}

In all cases, you should be able to predict how the phase fractions and equilibrium compositions change as you reduce the temperature at equilibrium.


next up previous
Next: About this document ... Up: Lecture_30_web Previous: A Menagerie of Binary
W. Craig Carter 2002-12-03