Three-phase equilibria and reactions

The eutectic reaction. In many metallic and ceramic binary systems it is possible for two crystalline phases and a liquid to coexist. The modified Phase Rule reveals that this unique condition is invariant; that is, the temperature and all phase compositions have fixed values. Figure 3.16 shows the phase diagram for the lead–tin system. It will be seen that solid solubility is limited for each of the two component metals, with α and β representing primary solid solutions of different crystal structure. A straight line, the eutectic horizontal, passes through three phase compositions (αₑ, Lₑ and βₑ) at the temperature Tₑ. As will become clear when ternary systems are discussed, this line is a collapsed three-phase triangle: at any point on this line, three phases are in equilibrium. During slow cooling or heating, when the average composition of an alloy lies between its limits, αₑ and βₑ, a eutectic reaction takes place in accordance with the equation Lₑ↔αₑ+βₑ. The sharply-defined minimum in the liquidus, the eutectic (easy-melting) point, is a typical feature of the reaction.

Consider the freezing of a melt, average composition 37Pb–63Sn. At the temperature Tₑ of approximately 180°C, it freezes abruptly to form a mechanical mixture of two solid phases, i.e. Liquid Lₑ → αₑ+βₑ. From the Lever Rule, the α/β mass ratio is approximately 9:11. As the temperature falls further, slow cooling will allow the compositions of the two phases to follow their respective solvus lines. Tie-lines across this (α+β) field will provide the mass ratio for any temperature. In contrast, a hypoeutectic alloy melt, say of composition 70Pb–30Sn, will form primary crystals of α over a range of temperature until Tₑ is reached. Successive tie-lines across the (α+Liquid) field show that the crystals and the liquid become enriched in tin as the temperature falls. When the liquid composition reaches the eutectic value Lₑ, all of the remaining liquid transforms into a two-phase mixture, as before. However, for this alloy, the final structure will comprise primary grains of α in a eutectic matrix of α and β. Similarly, one may deduce that the structure of a solidified hyper-eutectic alloy containing 30Pb–70Sn will consist of a few primary β grains in a eutectic matrix of α and β.

Low-lead or low-tin alloys, with average compositions beyond the two ends of the eutectic horizontal, freeze by transforming completely over a small range of temperature into a primary phase. When the temperature ‘crosses’ the relevant solvus, this primary phase becomes unstable and a small amount of second phase precipitates. Final proportions of the two phases can be obtained by superimposing a tie-line on the central two-phase field: there will be no signs of a eutectic mixture in the microstructure.

5. Open the brackets and put the predicate in the correct form, translate the sentences:

The modified Phase Rule reveals that this unique condition (to be) invariant.

Solid solubility (to be) limited for each of the two component metals.

The sharply-defined minimum in the liquidus, the eutectic (easy-melting) point, (to be) a typical feature of the reaction.

4. Tie-lines across this (α+β) field (to provide) the mass ratio for any temperature.

Low-lead or low-tin alloys, with average compositions beyond the two ends of the eutectic horizontal, (to freeze) by transforming completely over a small range of temperature into a primary phase.

6. When the temperature ‘crosses’ the relevant solvus, this primary phase (to become) unstable and a small amount of second phase precipitates.

6. Join the halves of the sentences in the columns:

It will be seen that solid solubility is	passes through three phase compositions.
A straight line	be obtained by superimposing a tie-line on the central two-phase field.
Final proportions of the two phases can	a typical feature of the reaction.
The sharply-defined minimum in the liquidus, the eutectic (easy-melting) point, is	limited for each of the two component metals.

 

7. Answer the questions:

What is called “the eutectic reaction”?

Is it possible for two crystalline phases and a liquid to coexist in many metallic and ceramic binary systems?

3. What does successive tie-lines across the (α+Liquid) field show?

What will the final structure of the alloy comprise?

Do low-lead or low-tin alloys freeze by transforming completely into a primary phase?