Construct the hypothetical phase diagram for metals \(A\) and \(B\) between temperatures of \(600^{\circ} \mathrm{C}\) and \(1000^{\circ} \mathrm{C}\) given the following information: \- The melting temperature of metal \(A\) is \(940^{\circ} \mathrm{C} .\) \- The solubility of \(\mathrm{B}\) in \(\mathrm{A}\) is negligible at all temperatures. \- The melting temperature of metal \(\mathrm{B}\) is \(830^{\circ} \mathrm{C}\). \- The maximum solubility of \(\mathrm{A}\) in \(\mathrm{B}\) is 12 wt \(\%\) A, which occurs at \(700^{\circ} \mathrm{C}\). \- At \(600^{\circ} \mathrm{C}\), the solubility of \(\mathrm{A}\) in \(\mathrm{B}\) is \(8 \mathrm{wt} \% \mathrm{~A}\). \- One eutectic occurs at \(700^{\circ} \mathrm{C}\) and \(75 \mathrm{wt} \%\) B- \(25 \mathrm{wt} \% \mathrm{~A}\) \- A second eutectic occurs at \(730^{\circ} \mathrm{C}\) and 60 \(\mathrm{wt} \% \mathrm{~B}-40 \mathrm{wt} \% \mathrm{~A}\). \- A third eutectic occurs at \(755^{\circ} \mathrm{C}\) and 40 \(\mathrm{wt} \%\) B-60 wt \(\% \mathrm{~A}\). \- One congruent melting point occurs at \(780^{\circ} \mathrm{C}\) and \(51 \mathrm{wt} \%\) B-49 wt \(\% \mathrm{~A}\). \- A second congruent melting point occurs at \(755^{\circ} \mathrm{C}\) and \(67 \mathrm{wt} \%\) B-33 wt \(\% \mathrm{~A}\). \- The intermetallic compound \(\mathrm{AB}\) exists at \(51 \mathrm{wt} \%\) B-49 wt \% A. \- The intermetallic compound \(\mathrm{AB}_{2}\) exists at \(67 \mathrm{wt} \%\) B-33 wt \(\% \mathrm{~A}\).

Step by step solution

01

Set up a temperature vs. composition graph

Before we begin constructing the phase diagram, we need to set up a graph where the x-axis represents the composition (weight percentage of A and B) and the y-axis represents the temperature (in °C). The x-axis should range from 0 wt% A (100 wt% B) to 100 wt% A (0 wt% B), and the y-axis should range from 600°C to 1000°C.

02

Plot melting points

Next, plot the melting points of metal A and metal B on the graph. The melting point of metal A (940°C) should be plotted at 100 wt% A (0 wt% B), and the melting point of metal B (830°C) should be plotted at 0 wt% A (100 wt% B).

03

Plot solubility data

Now, plot the solubility data given for A in B. At 600°C, the solubility of A is 8 wt%, so plot a point at 8 wt% A and 600°C. At 700°C, the maximum solubility of A in B is 12 wt%, so plot a point at 12 wt% A and 700°C. Since the solubility of B in A is negligible at all temperatures, we don't need to plot any points for B in A.

04

Plot eutectic points

We are given three eutectic points. Plot each of them on the graph: - First eutectic: 700°C and 75 wt% B-25 wt% A - Second eutectic: 730°C and 60 wt% B-40 wt% A - Third eutectic: 755°C and 40 wt% B-60 wt% A

05

Plot congruent melting points

There are two congruent melting points given. Plot them on the graph: - First congruent melting point: 780°C and 51 wt% B-49 wt% A - Second congruent melting point: 755°C and 67 wt% B-33 wt% A

06

Plot intermetallic compounds

Two intermetallic compounds are provided. Plot their points on the graph: - Intermetallic compound AB: 51 wt% B-49 wt% A - Intermetallic compound AB2: 67 wt% B-33 wt% A

07

Connect the points

Now that all the points are plotted, connect them on the graph to form the phase boundaries, solidus lines, and liquidus lines. Don't forget to extend the lines all the way to the vertical edges of the graph. Connect the solidus lines for the solubility of A in B (Step 3) and the other points to form distinct regions corresponding to the different phases and phase combinations that exist in different temperature and composition ranges.

08

Label the regions

Finally, label each region on the graph as solid A, solid B, solid AB, solid AB2, liquid A, liquid B, etc. The final phase diagram should show how the phases change as a function of temperature and composition between the two metals A and B.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Eutectic Points

A eutectic point in a phase diagram represents a specific composition at which a mixture of two or more substances melts or solidifies at a single temperature, which is the lowest possible for that specific ratio of substances. It's a key feature in binary phase diagrams and indicates the temperature and composition where a liquid phase transforms directly into two or more solid phases, or vice versa.

For example, in the exercise given, three eutectic points are highlighted - each occurring at a unique combination of temperature and composition of metals A and B. When constructing the phase diagram, plotting these eutectic points is crucial as they mark the intersections where two solubility lines meet, creating invariant points. The eutectic reactions can be summarized as a liquid transforming into solid phases of different compositions. For instance, the first eutectic occurs at 700°C and 75 wt% B (25 wt% A), indicating the temperature at which a liquid mixture of that composition will solidify into separate phases of A and B.

Congruent Melting Points

Congruent melting points are characteristic points on a phase diagram where a compound melts or solidifies at a single, definite temperature and composition without any change in composition. Essentially, at this point, a solid phase transitions directly into a liquid of the same composition, or vice versa. This phenomenon contrasts with the eutectic point, where a liquid transforms into solids of different compositions.

In the hypothetical phase diagram for metals A and B, we identify the congruent melting points for specific intermetallic compounds that form between A and B. During the phase diagram construction, congruent melting points are plotted and connected to form what are commonly referred to as congruent melting lines. These lines shape the phase diagram and help to define regions of solid and liquid phases. The exercise identifies two congruent melting points at different temperatures and compositions, reflecting the presence of stable intermetallic compounds with singular melting points.

Intermetallic Compounds

Intermetallic compounds are complex structures formed by two or more metallic elements, which exhibit specific stoichiometry and often distinct crystal structures. They are typically characterized by their rigidity, brittleness, and high melting points. In phase diagrams, these compounds often show up as vertical lines or narrow regions, reflecting the precise compositions at which they exist.

Since intermetallic compounds have a defined composition, such as AB or AB2, they are represented by single points on a temperature-composition phase diagram if they melt congruently. If they exhibit a range of compositions, they will appear as a line or a small area. In our exercise, two intermetallic compounds, AB and AB2, are identified. Their importance in the phase diagram stems from their structural and functional properties that can be exploited in various industrial applications. These points are plotted and connected to guide the bound between the different solid phases and the single phase regions.

Solubility Data

Solubility data reflects the maximum amount of one component that can be dissolved in another to form a solution at a particular temperature. In the context of a phase diagram, this data helps to map out the solid solution regions, where one metal is dissolved in another, forming a single-phase solid solution. The solubility limit is depicted as a curve on the phase diagram, often referred to as the solvus line.

When constructing the hypothetical phase diagram for metals A and B, the solubility data provides critical points that must be plotted. For instance, the solubility of metal A in metal B at 600°C and 700°C forms the basis for delineating the solid solution regions and the remaining phases of the diagram. Understanding solubility trends is important for material scientists and engineers, as these have direct implications for alloy design and processing conditions, like heat treatments.