How do you read the lead–silver phase diagram and what happens at its eutectic point?

In one line

The Pb–Ag system is a two-component simple eutectic system whose temperature–composition diagram shows two freezing-point curves meeting at the eutectic point (303 °C, 2.6% Ag), the lowest temperature at which a liquid alloy can exist.

Explained simply

Pure silver melts at 961 °C and pure lead at 327 °C. Adding a little lead to molten silver lowers its freezing point, just as salt lowers the freezing point of water. Adding silver to lead does the same for lead. The two falling curves meet at one special mixture that freezes at the lowest temperature of all: the eutectic ("easily melted").

How it works

Diagram: x-axis = composition (100% Ag on one side → 100% Pb on the other), y-axis = temperature. Using F′ = C − P + 1 with C = 2:

1. Point A (961 °C): melting point of pure Ag. Point B (327 °C): melting point of pure Pb. (For a pure metal C = 1, so F′ = 1 − 2 + 1 = 0.)
2. Curve AO: freezing-point curve of Ag. Along it, solid Ag ⇌ melt. P = 2, F′ = 1.
3. Curve BO: freezing-point curve of Pb. Along it, solid Pb ⇌ melt. P = 2, F′ = 1.
4. Point O, eutectic: 303 °C, 2.6% Ag + 97.4% Pb. Solid Ag + solid Pb + melt coexist. P = 3, F′ = 0 (invariant).
5. Area above AOB: single liquid phase (melt). F′ = 2.
6. Area AOC (below AO): solid Ag + melt. Area BOD (below BO): solid Pb + melt. P = 2, F′ = 1.
7. Below the eutectic line COD: completely solid; solid Ag + eutectic on the Ag-rich side, solid Pb + eutectic on the Pb-rich side.

Key formula

\( F' = C - P + 1 \), with C = 2.

A eutectic system is a two-component system in which the components are completely miscible as liquids, do not form compounds or solid solutions, and the mixture of a particular composition has the lowest melting point.

Quick example

Cooling a melt with 50% Ag: on reaching curve AO, pure solid Ag starts separating. The melt becomes richer in Pb and moves down AO until it reaches O (2.6% Ag) at 303 °C, where the remaining liquid solidifies as the eutectic mixture at constant temperature.

Common mistakes

• Calling the eutectic a compound. It is an intimate mixture of two solids with a fixed composition and melting point.
• Getting eutectic data wrong: it is 303 °C and 2.6% Ag (97.4% Pb).
• Using F = C − P + 2 and stating F = 1 at the eutectic.

How MU asks it

"Draw and explain the phase diagram of the Pb–Ag system" (5–6 marks), frequently combined with Pattinson's process. For full marks: a neat labelled diagram with temperatures and compositions, the reduced rule, a table or list of each point, curve and area with phases and F′, and the definition of eutectic.