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DoITPoMS Teaching & Learning Packages Ternary Phase Diagrams Solidification of ternary alloys – Class III reactions
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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Solidification of ternary alloys – Class III reactions

The ternary system below has a ternary peritectic invariant point. Associated with this point is a ternary peritectic (or class III) reaction:

\[\rm{ L + \alpha + \beta \rightleftharpoons \gamma} \]

Two of the bounding binaries have binary peritectic points while the third has a binary eutectic point. A eutectic valley runs from the eutectic point to the invariant point and two peritectic valleys run from the invariant point to the binary peritectic points.

Figure 24: A ternary system with a ternary peritectic point. Adapted from https://commons.wikimedia.org/wiki/File:Space_diagram_of_a_three-component_system.jpg

This system has three single-phase regions (\(\rm{ \alpha, \beta} \) and \( \rm{\gamma} \)), three two-phase solid regions (\( \rm{\alpha + \beta, \alpha + \gamma, \beta + \gamma} \)), one three-phase solid region (\(\rm{ \alpha + \beta + \gamma} \)), three two-phase solid and liquid regions (\(\rm{ L + \alpha, L + \beta, L + \gamma} \)), three three-phase regions (\(\rm{ L + \alpha + \beta, L + \beta + \gamma, L + \alpha + \gamma} \)) and a single phase liquid region.

Notably, three of the four three-phase regions lie below the invariant point (\( \rm{\alpha + \beta + \gamma, L + \beta + \gamma} \) and \( \rm{L + \alpha + \gamma} \)). This is distinct from the class I and class II cases where one and two three-phase regions lie below the invariant point, respectively.

There are five kinds of solidification routes worth considering in this system:

  • Alloys that do not pass through a three-phase region on cooling
  • Alloys that pass through a three-phase region above the invariant point but not through the invariant point
  • Alloys that pass through a three-phase region below the invariant point but not through the invariant point
  • Alloys that pass through the invariant point and are fully solid below the invariant point
  • Alloys that go through the invariant reaction and are not fully solid below the invariant point.

The kind of solidification route an alloy takes can be determined by observing where the composition lies at the invariant temperature.

An example isothermal section from a system with a class III reaction at the invariant temperature is shown below:

Figure 25: The invariant reaction plane for a ternary system with a class III reaction.

The invariant reaction plane shows four phases in equilibrium. This is shown as a tie triangle (\(\rm{ L + \alpha + \beta} \)) with the composition of \(\rm{ \gamma} \) plotted inside the triangle. The invariant point is at the composition of the liquid at the invariant temperature.

The position of the composition of \( \rm{\gamma} \) (the solid phase formed in the peritectic reaction) within the \(\rm{ L + \alpha + \beta} \) tie triangle (the reactants) is characteristic of class III reactions.

Any point within the \(\rm{ L + \alpha + \beta} \) tie triangle (including the composition of \(\rm{ \gamma} \)) can be described as proportions of each phase. Combining \(\rm{ L, \alpha} \) and \( \rm{\beta} \) in the reaction can make \( \rm{\gamma} \) without violating the conservation of matter.

Figure 26: Isothermal section at the invariant temperature for a system with a class II reaction showing only single-phase solid fields.

At the invariant temperature, maximum solubility of unlike atoms in single phase solids occurs for \( \rm{\alpha} \) and \( \rm{\beta} \). If an alloy plots in a single-phase field at this temperature, it will cool without passing through a three-phase region. This cooling is analogous to an alloy cooling through a two-phase solid + liquid region in a system with complete solid solubility. Compositions plotting in the single-phase liquid region will also solidify in this way, passing into the \(\rm{ L + \gamma} \) region then into the \(\rm{ \gamma} \) region. This case has been discussed on the previous two pages in more detail.

Figure 27: Isothermal section at the invariant temperature for a system with a class III reaction showing only the \( \rm{\alpha + \gamma} \) field.

If an alloy plots in the \( \rm{\alpha + \beta} \) field, then it will pass through a three-phase region above the invariant temperature (due to the monovariant eutectic reaction) but not the invariant point. These alloys will precipitate out either \(\rm{ \alpha} \) or \(\rm{ \beta} \) until the composition of the liquid lies on the eutectic valley, at which point coprecipitation of \(\rm{ \alpha} \) and \( \rm{\beta} \) will occur until the system is fully solid.

Figure 28: Isothermal section at the invariant temperature for a system with a class III reaction showing only the solid + liquid fields.

If an alloy plots in either of the liquid + solid regions, it will undergo one of the monovariant peritectic reactions. These alloys will pass through one of the three-phase regions below the invariant point. Their solidification will begin with the precipitation of \(\rm{ \alpha} \) or \( \rm{\beta} \) (depending on which primary solid field the composition lies in). The alloys will then undergo one of the monovariant peritectic reactions where the primary solid reacts with the liquid to produce \( \rm{\gamma} \) until the liquid is exhausted and the system is fully solid – a mixture of the primary solid (\(\rm{ \alpha} \) or \(\rm{ \beta} \)) and \( \rm{\gamma} \).

If an alloy plots in the four-phase region it will undergo the ternary peritectic reaction. As there are three reactants in this reaction, it can terminate when any of these reactants are exhausted.

Figure 29: Isothermal section at the invariant temperature for a system with a class III reaction showing only the \( \rm{\alpha + \beta + \gamma} \) tie triangle.

If the alloy plots in the \(\rm{ \alpha + \beta + \gamma} \) tie triangle, the liquid will be exhausted first, and the system will be fully solid once the invariant is complete.

Figure 30: Isothermal section at the invariant temperature for a system with a class III reaction showing only the \( \rm{L + \beta + \gamma} \) tie triangle.

If the alloy plots in the \(\rm{ L + \beta + \gamma} \) tie triangle, \(\rm{ \alpha} \) will be exhausted first and there will be liquid remaining after the invariant reaction. The system will solidify via the \(\rm{ L + \beta} \) peritectic reaction (as there is no \(\rm{ \alpha} \) present for the \(\rm{ L + \alpha} \) peritectic).

Figure 31: Isothermal section at the invariant temperature for a system with a class III reaction showing only the \( \rm{L + \alpha + \gamma} \) tie triangle.

If the alloy plots in the \(\rm{ L + \alpha + \gamma} \) tie triangle, \(\rm{ \beta} \) will be exhausted first and there will be liquid remaining after the invariant reaction. The system will solidify via the \(\rm{ L + \alpha} \) peritectic reaction.

Alloy R in the diagram below will undergo the ternary peritectic reaction but will complete solidification by the \(\rm{ L + \beta \rightarrow \gamma} \) reaction:

Figure 32: Composition of alloy R plotted onto a ternary system with a class III reaction. Adapted from https://commons.wikimedia.org/wiki/File:Space_diagram_of_a_three-component_system.jpg

The solidification of alloy R is described below:

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