Ag-Pb Alloy System: Understanding Phase Diagrams
Ag-Pb Alloy System: Phase Diagram Explained
The lead-silver (Ag-Pb) system exemplifies a simple eutectic system. Silver and lead are miscible in all proportions and do not react chemically. When molten silver and lead are mixed together, a single homogeneous solution is formed. The system consists of the following phases:
- Solid silver (Ag)
- Solid lead (Pb)
- Solution of molten silver and lead
- Vapor
Since pressure has a negligible effect on equilibrium, the system can be represented by a temperature and concentration diagram at constant atmospheric pressure. As the gaseous phase is practically absent, one variable in the phase rule is neglected, and the condensed phase rule, F = C – P + 1, will be applicable.
Diagram Components
The phase diagram of the silver-lead system consists of:
- Areas (AOB, ADOA, BOEB, Area below DOE)
- Curves (AO and BO)
- Eutectic point O
Area AOB
This area consists of only one phase (liquid solution). Applying the reduced phase rule equation, the degree of freedom is two. Hence, the system is bivariant, and both temperature and composition are required to completely define the system.
F = C – P + 1, where P = 1, C = 2, thus F = 2 – 1 + 1 = 2 (Bivariant System).
Area ADOA
This area contains two phases: solid Ag and a solution containing Pb and Ag. C = 2, P = 2.
F = C – P + 1, thus F = 2 – 2 + 1 = 1 (Univariant System).
Area BOEB
It represents the phases solid Pb and a solution containing Pb and Ag. C = 2 (Pb and Ag), P = 2 (liquid + solid phase).
F = C – P + 1, thus F = 2 – 2 + 1 = 1 (Univariant System).
Area Below DOE
This area represents a solid mixture of Pb or Ag with the eutectic. The number of phases is 2 (either Ag or Pb + eutectic), and the system is univariant.
C = 2, P = 2, thus F = C – P + 1 = 2 – 2 + 1 = 1.
Eutectic Point ‘O’
The two curves AO and BO intersect at point O at a temperature of 303°C. Point O is known as the eutectic point. At this point, three phases—solid Ag, solid Pb, and the melt—are in equilibrium. Applying the phase rule equation, we get F = C – P + 1, thus F = 2 – 3 + 1 = 0 (Non-variant system).
Thus, the system at this point is non-variant. Both temperature (303°C) and composition (Ag 2.6% and Pb 97.4%) are fixed at this point.
Curves
Curve AO
It shows the effect on the freezing point of Ag upon the addition of lead in small quantities. The curve starts from A (961°C), the melting point of Ag, where pure Ag co-exists as solid and liquid (vapor being neglected). Along this curve, solid Ag and solution coexist; hence, according to the reduced phase rule equation:
C = 2, P = 2, thus F = C – P + 1 = 2 – 2 + 1 = 1 (Univariant System).
The point O (303°C) corresponds to a fixed composition of 2.6% Ag and 97.4% Pb and is known as the eutectic composition. Upon cooling, the whole mass crystallizes out as such.
Curve BO
It represents the effect on the freezing point of Pb upon the gradual addition of a small amount of Ag to it. Point B is the melting point of pure lead (327°C).
Along BO, the melting point gradually falls upon the addition of Ag until the lowest point O is reached.
At this point, the solution gets saturated with respect to Ag, and the melting point of lead does not fall any further.
On cooling, the whole mass (having eutectic composition) crystallizes out. The system is univariant.
C = 2, P = 2, thus F = C – P + 1 = 2 – 2 + 1 = 1 (Univariant System).