On a binary phase diagram, a tie line represents what?

• A. A vertical line at fixed composition.
• B. A line showing diffusion path across phases.
• C. A curved line representing a solubility limit.
• D. A horizontal line at a fixed temperature representing the coexistence of two phases, with endpoints giving their compositions.

Answer: (D)

In a binary phase diagram, when two phases coexist at a given temperature, their compositions are fixed. A tie line is that horizontal line at that temperature that connects the composition of the first phase to the composition of the second phase. Each end of the line marks the exact composition of one phase in equilibrium with the other. The overall alloy composition lies somewhere along that line, and the lever rule uses the distances to the ends to determine how much of each phase is present. This horizontal tie line is distinct from the solubility boundary, which is a curved curve showing the limit of complete solid solution rather than the compositions of the coexisting phases.