For a \(68 \mathrm{wt} \% \mathrm{Zn}-32 \mathrm{wt} \% \mathrm{Cu}\) alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: \(1000^{\circ} \mathrm{C}\) \(\left(1830^{\circ} \mathrm{F}\right), 760^{\circ} \mathrm{C}\left(1400^{\circ} \mathrm{F}\right), 600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)\), and \(400^{\circ} \mathrm{C}\left(750^{\circ} \mathrm{F}\right)\). Label all phases and indicate their approximate compositions.

For this problem, we must refer to the Zn-Cu phase diagram to analyze the microstructure of the alloy at different temperatures. This phase diagram can be found in various metallurgy textbooks or through online databases. Please use the phase diagram provided by the source you have in front of you.

Begin by locating the 68 wt% Zn-32 wt% Cu alloy composition on the horizontal axis of the phase diagram. Then, locate the temperatures (1000°C, 760°C, 600°C, and 400°C) on the vertical axis. For each temperature, draw a horizontal line from the temperature graduation to intersect the phase boundaries related to the given alloy composition.

At each intersection point or region, determine which phases are present in the alloy's microstructure. Note the phases for each temperature, as described below: - At 1000°C: One phase-present, known as the α phase with a composition between 38 wt% Zn and 72 wt% Zn. - At 760°C: Two phases present, known as the α phase and the β phase. The α phase composition is between 38 wt% Zn and 52 wt% Zn, and the β phase composition is between 52 wt% Zn and 89 wt% Zn. - At 600°C: Two phases present, known as the α phase and the β phase. The α phase composition is between 38 wt% Zn and 52 wt% Zn, and the β phase composition is between 52 wt% Zn and 89 wt% Zn. - At 400°C: One phase present, known as the β phase with a composition between 52 wt% Zn and 89 wt% Zn.

Based on the phase descriptions in Step 3, create schematic sketches of the alloy microstructure at each temperature: - 1000°C: Sketch a microstructure consisting only of the α phase. Label this phase and indicate its composition range (38 wt%-72 wt% Zn). - 760°C: Sketch a microstructure containing both the α and β phases. Show the α phase as a continuous matrix, and the β phase as embedded particles within the α phase. Label both phases and indicate their composition ranges (α: 38 wt%-52 wt% Zn, β: 52 wt%-89 wt% Zn). - 600°C: Sketch a microstructure containing both the α and β phases, with the β phase becoming more predominant as the temperature decreases. Label both phases and indicate their composition ranges (α: 38 wt%-52 wt% Zn, β: 52 wt%-89 wt% Zn). - 400°C: Sketch a microstructure consisting only of the β phase. Label this phase and indicate its composition range (52 wt%-89 wt% Zn). Remember that these sketches are schematic representations of the microstructure; the actual appearance may vary depending on the specific alloy and cooling conditions.