# Copper-Zinc Alloy: Phase Equilibrium Analysis ## Given - **ε phase composition:** 80 wt% Zn, 20 wt% Cu - **Liquid phase composition:** 95 wt% Zn, 5 wt% Cu ## Question Is it possible, **at equilibrium**, for a Cu-Zn alloy to consist of: - An **ε phase** (80 wt% Zn), **and** - A **liquid phase** (95 wt% Zn)? If **yes**, what is the approximate temperature? If **no**, explain why. --- ## Step-by-Step Analysis ### 1. Reference: Cu-Zn Phase Diagram - The Cu-Zn (Brass) phase diagram shows various solid phases (α, β, γ, δ, ε) and the liquid (L) phase. - The ε phase appears at **high Zn concentrations** (typically 79–85 wt% Zn). - **Liquid phase** exists at **high temperatures** (above the solidus line). ### 2. Two-Phase Equilibrium Regions - At equilibrium, **two phases** can coexist **only in the two-phase regions** on the phase diagram (*e.g.,* L + ε). - The **compositions of these coexisting phases** at a given temperature are found by drawing a **horizontal tie-line** at that temperature in the two-phase region. ### 3. Does a Tie-Line Connect 80% Zn (ε) and 95% Zn (L)? - Examine the **L + ε region** on the phase diagram: - **ε phase**: ~79–85 wt% Zn - **Liquid phase**: Exists at higher Zn, but as temperature increases, the liquid phase composition shifts **even higher in Zn content**. - At the **L + ε region**, the **liquid phase** in equilibrium with ε **never reaches as high as 95 wt% Zn**. - At the ε phase boundary (~80 wt% Zn), the liquid in equilibrium is **much lower than 95 wt% Zn**. - At 95 wt% Zn, the only phase present is **liquid**. ### 4. Conclusion - **No**, it is **not possible** for an alloy to have, at equilibrium, both: - ε phase at 80 wt% Zn - Liquid phase at 95 wt% Zn - **Reason:** The **tie-line in the L + ε region** of the Cu-Zn phase diagram **never connects these two compositions**. At 95 wt% Zn, only liquid exists; at 80 wt% Zn, the liquid in equilibrium has a lower Zn content. --- ## Summary Table | Phase | Zn Content (wt%) | Exists at equilibrium with... | |-----------------|------------------|------------------------------| | ε | ~79–85 | Liquid (but not at 95% Zn) | | Liquid (in L+ε) | <~90 | ε phase | | Liquid (95% Zn) | 95 | Only liquid | --- ## References - [Cu-Zn Phase Diagram (Image)](https://www.researchgate.net/figure/The-Zn-Cu-equilibrium-phase-diagram-5_fig1_284719652) - "Materials Science and Engineering: An Introduction" (Callister), Cu-Zn phase diagram section --- **In summary:** It is **not possible** for a copper-zinc alloy to consist of ε phase at 80 wt% Zn and liquid at 95 wt% Zn at equilibrium. **No tie-line connects these two compositions** in the two-phase region of the equilibrium phase diagram.