Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Ternary Phase Diagrams Sections through ternary phase diagrams
Ternary Phase Diagrams AimsBefore you startIntroductionRepresenting ternary phase diagramsSections through ternary phase diagramsTie lines and tie trianglesApplying the Gibbs phase rule to ternary systemsSolidification of ternary alloys – complete solid solutionSolidification of ternary alloys – one eutectic valleySolidification of ternary alloys – Class I reactionsSolidification of ternary alloys – Class II reactionsSolidification of ternary alloys – Class III reactionsCase Study: Sn-Ag-Cu systemUses of ternary alloysSummaryQuestionsGoing further
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Sections through ternary phase diagrams

Why take sections through Ternary Phase Diagrams?

Space models contain all the temperature-composition information of a system. By looking at just one section of the space model, information is lost.

Some systems are simple enough (like those on the previous page) that interpretation can be done from the space model alone. However, more complex systems are difficult to accurately represent and interpret this way.

It is in these more complex systems that taking sections becomes a vital tool in the interpretation of ternary systems. While there is information loss in taking the section, the simplification of the representation and ease with which sections can be manipulated vastly outweighs this drawback.

Different Sections Taken through Ternary Phase Diagrams

There are a few different kinds of sections commonly used to analyse ternary systems.

Each kind of section provides different information and suffers from different information loss. Interpreting ternary (and higher order systems) often involves a trade-off of information for simplicity.

Isothermal Sections

Isothermal (or horizontal) sections are sections through the space model taken at a constant temperature. They are triangular sections that are parallel to the composition triangle.

Isothermal sections are the most common way to represent information about ternary systems. They show which phase (or phases) are in equilibrium for varying compositions at the given temperature.

Isothermal sections can provide compositional information: the limits of solid solubility, ternary eutectic compositions, compositions of phases in two and three phase regions and more.

However, isothermal sections contain no information about the system at any other temperature. Information about the temperatures at which reactions occur or which phases are stable at different temperatures must be found on different sections.

The animation below shows isothermal sections at various temperatures for three different kinds of ternary system:

Vertical Sections

Vertical sections (sometimes known as isopleths) are sections taken through a ternary phase diagram that are perpendicular to the plane of the composition triangle. They are rectangular with a horizontal composition axis (showing a series of compositions that plot on a straight line in ternary composition space) and a vertical temperature axis.

Vertical sections show the equilibrium phase (or phases) for a restricted set of compositions at varying temperatures.

Vertical sections provide information on the temperatures at which reactions occur. They provide information on the solidus and liquidus temperatures and eutectic and peritectic temperatures.

However, vertical sections do not contain compositional information. Despite looking similar to binary phase diagrams, the composition of phases cannot be read off vertical sections and the lever rule cannot be applied (for more information see Tie Lines and Tie Triangles)

Vertical sections are often taken parallel to one of the binaries (so it corresponds to a constant proportion of one component while the other two vary) or from one component to a point on the opposite binary (so it corresponds to a constant ratio of the other two components). These are simply the most common geometries though; vertical sections can be taken along any line in compositional space.

The animation below shows a vertical section of each type through three different kinds of ternary system:

Increasingly complex ternary systems (such as those containing class II and class III reactions – see Applying the Gibbs Phase Rule to Ternary Systems) give rise to vertical sections that are increasingly difficult to determine and interpret. For real ternary systems (which often have multiple reactions), vertical sections quickly become unwieldy. This is why isothermal sections are preferred for analysis of ternary systems.

Liquidus Projections

A liquidus projection is a two-dimensional projection of the three-dimensional liquidus surface onto the composition triangle.

This is often done using contours - lines linking points on the liquidus surface that are at the same temperature – in the same way that maps use contours to show how the elevation of the area being mapped varies.

The positions of equilibria involving the liquid phase (such are eutectic valleys along which the liquid decomposes into two solids or invariant points where liquids can undergo congruent solidification) are also included on liquidus projections.

Liquidus projections also include labels to indicate which solid is in equilibrium with the liquid in different regions (e.g., \( \rm{L + \alpha} \) and \( \rm{L+\beta} \) regions are labelled).

Liquidus projections are incredibly useful as they contain information on the changes an alloy undergoes upon solidification. It is possible to determine which solid phases form (and in which order) and which reactions occur during the cooling of an alloy. Conversely, it is possible to determine the changes of the alloy upon melting.

hile vital in understanding cooling histories of alloys, liquidus projections have their limitations. They provide no information on solid state reactions or any changes in solid solubility which occur below the liquidus surface.

ther projections (such as solidus and solid solubility surface projections) can be used to provide the information that liquidus projections lack. They are constructed in very similar ways with features of the surface being plotted as well as temperature contours.

The animation below shows the construction of the liquidus projection for a variety of different ternary systems:

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