For an alloy of composition \(74 \mathrm{wt} \% \mathrm{Zn}-26\) \(\mathrm{wt} \% \mathrm{Cu}\), cite the phases present and their compositions at the following temperatures: \(850^{\circ} \mathrm{C}, 750^{\circ} \mathrm{C}, 680^{\circ} \mathrm{C}, 600^{\circ} \mathrm{C}\), and \(500^{\circ} \mathrm{C}\).

The lever rule is a helpful tool in materials science for determining the proportion of different phases in a two-component system. Imagine a see-saw, where the fulcrum represents the overall composition of the alloy, and the seats represent the compositions of the individual phases. By balancing the see-saw using the weight percentages of each phase, we can find out exactly how much of each phase is present at a given temperature.

For example, in our given exercise for the temperature at 750°C, the presence of both liquid and alpha phases in the alloy is indicated. Using the lever rule, you can determine the specific amounts of each phase from the phase diagram. The calculations involve drawing a tie-line or isotherm at 750°C and using the distances from the overall composition to the phase boundary compositions to set up a ratio. This ratio directly reflects the amounts of the individual phases present in the alloy at that temperature.

Alloy composition is fundamental information when inspecting a phase diagram since it determines the phases present and their proportions. An alloy is a mixture of two or more elements, where the main component is a metal. In the exercise, we are looking at a zinc-copper (Zn-Cu) alloy with a particular composition of 74 weight percent zinc and 26 weight percent copper.

This proportion greatly affects the material properties and behavior under different conditions. For example, at 850°C, the alloy's composition corresponds to a single liquid phase. However, as the temperature decreases, the composition intersects different phase regions on the phase diagram, resulting in changes of phases present like from liquid to alpha, then to alpha plus beta, and finally to a solid beta phase at 500°C.

Phase transitions occur when an alloy changes from one phase to another due to alterations in conditions such as temperature or pressure. Each transition between phases implies a transformation in the structure and properties of the material. In our exercise, the Zn-Cu alloy exhibits several phase transitions as it cools from a high temperature.

At 850°C, it starts in a liquid state. Upon cooling to 750°C, it transitions to a mixed phase of liquid and alpha. When reaching 680°C, it becomes entirely alpha, and as it cools further to 600°C, a beta phase begins to emerge alongside the alpha. Eventually, at 500°C, the alloy is completely in the beta phase. Each phase has distinct mechanical and physical characteristics, which are crucial for the applications of the alloy.

A binary phase diagram is a graphical representation that shows the phases present in an alloy system with two components at various temperatures and compositions. The Zn-Cu diagram in our exercise is a classic example, where the x-axis represents the composition ranging from pure zinc to pure copper, and the y-axis denotes the temperature.

Beneath the surface of this seemingly simple graph lies a treasure trove of information. It tells us about melting points, solidus and liquidus lines, and the solubility limits of phases. For instance, the diagram provides clear regions indicating whether the composition at a specific temperature will be a single solid phase, a mix of solid phases, or if the alloy will be molten. Understanding how to read this diagram is pivotal for materials engineers and scientists in predicting material behavior and designing alloys for various applications.