Skip to main content
Engineering LibreTexts

12.6: Experiment

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    The simplest way to construct a phase diagram is by plotting the temperature of a liquid against time as it cools and turns into a solid. As discussed in Interpretation of cooling curves, the solidus and liquidus can be seen on the graphs as the points where the cooling is retarded by the emission of latent heat.


    An experiment can be performed to get a rough idea of a phase diagram by recording cooling curves for alloys of two metals, in various compositions. The alloy chosen for this example is bismuth-tin, both of which metals have low melting points, and so can be heated and cooled more quickly and easily in the lab. So that the experiment could be performed in a reasonable time, 11 compositions were used, from pure bismuth to pure tin in steps of 10%. All the compositions were measured in weight percent.

    Heating apparatus


    (Click on image to view a larger version)

    The apparatus pictured was set up, with the maximum temperature to be attained of around 300°C. The sample in the crucible cooled, and the temperature was recorded at regular intervals. In the case of the results produced here, readings were made every two seconds, using a computer. However, it is adequate to take readings every 15 seconds manually.


    The procedure was repeated for all 11 compositions, and the following results recorded:

    Graph showing the temperature of several tin-bismuth alloys cooling over a period of time

    These lines can be made clearer by spacing them along the time axis, so that the alloys with a higher bismuth content appear further to the right, as shown below.

    Graph showing the temperature of several tin-bismuth alloys cooling over a period of time, lines displaced along the time axis

    From these graphs it is possible to pick out the changes in gradient which allow a simplified phase diagram to be drawn.

    On the diagram with the displaced time-temperature plots, the changed gradients, i.e. the parts where some of the liquid is solidifying, are coloured white. These show the top of the liquidus and the bottom of the solidus.

    If these curves are now straightened out, and the colours kept, with the white representing the solidification, it is possible to construct a basic phase diagram, as was shown for an isomorphous system in Interpretation of cooling curves. This is shown below, where the white line is part of the phase diagram, constructed from the cooling curves, and the thin grey line is the actual phase diagram, found from many experiments over a long period of time.

    Graph comparing phase diagram constructed from cooling curves with that found from many experiments


    It can be seen from the diagram above that the recorded phase diagram is roughly 15°C lower than it should be, and that some of the measurements of the liquidus are not in the expected places. The lowering of the diagram is due to the thermocouple being contained in a glass rod, rather than actually touching the alloy. The occasional unexpected liquidus temperatures are probably due to the compositions being slightly inaccurate.

    It is also worth noting that in this projected phase diagram, it was not possible to draw in a proper solidus on the right hand side, as none of the compositions near pure bismuth showed evidence of a solidus. As such, a dotted line has been plotted as an estimate of where it would go.

    The microstructure of the alloy changes with composition. This can be seen in scanning electron microscope (SEM) images taken from each of the compositions used in the experiment above.

    Interactive Sn-Bi phase diagram and SEM images

    This page titled 12.6: Experiment is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?