Construct the hypothetical phase diagram for metals \(\mathrm{A}\) and \(\mathrm{B}\) between room temperature \(\left(20^{\circ} \mathrm{C}\right)\) and \(700^{\circ} \mathrm{C}\), given the following information: \- The melting temperature of metal \(\mathrm{A}\) is \(480^{\circ} \mathrm{C}\). \- The maximum solubility of \(B\) in \(A\) is 4 wt \(\%\) B, which occurs at \(420^{\circ} \mathrm{C}\). \- The solubility of \(\mathrm{B}\) in \(\mathrm{A}\) at room temperature is 0 wt \(\%\) B. \- One eutectic occurs at \(420^{\circ} \mathrm{C}\) and \(18 \mathrm{wt} \%\) B-82 wt \(\%\) A. \- A second eutectic occurs at \(475^{\circ} \mathrm{C}\) and \(42 \mathrm{wt} \%\) B- \(58 \mathrm{wt} \% \mathrm{~A}\) \- The intermetallic compound AB exists at a composition of \(30 \mathrm{wt} \% \mathrm{~B}-70 \mathrm{wt} \% \mathrm{~A}\), and melts congruently at \(525^{\circ} \mathrm{C}\). \- The melting temperature of metal B is \(600^{\circ} \mathrm{C} .\) \- The maximum solubility of \(\mathrm{A}\) in \(\mathrm{B}\) is \(13 \mathrm{wt} \% \mathrm{~A}\), which occurs at \(475^{\circ} \mathrm{C}\). \- The solubility of \(\mathrm{A}\) in \(\mathrm{B}\) at room temperature is \(3 \mathrm{wt} \% \mathrm{~A}\)

Step by step solution

01

Prepare the axes of the phase diagram

Begin by drawing a vertical axis labeled "Temperature (°C)" and a horizontal axis labeled "Composition (wt% B)." Mark the temperature axis with increments from 20°C (room temperature) to 700°C, and the composition axis from 0 wt% B to 100 wt% B, with increments every 10 wt% B.

02

Plot individual metal melting points

Mark and label the melting points of metals A and B on the phase diagram. These are given as 480°C for metal A, and 600°C for metal B. Place these points on the temperature axis at their respective positions (0 wt% B for A and 100 wt% B for B).

03

Plot the solubility lines for B in A and A in B

Mark and label the solubility points for B in A (4 wt% B at 420°C) and A in B (13 wt% A at 475°C, which corresponds to 87 wt% B). Draw a line connecting the solubility points for B in A between the room temperature point (0 wt% B) and the given point (4 wt% B at 420°C). Draw another line connecting the solubility points for A in B between the room temperature point (3 wt% A, 97 wt% B) and the given point (87 wt% B at 475°C).

04

Plot eutectic points and intermetallic compound

Mark and label the eutectic points (at 420°C with 18 wt% B and 475°C with 42 wt% B) and the intermetallic compound (30 wt% B, melting congruently at 525°C). Draw a horizontal line at the temperature of the intermetallic compound (525°C) between the solubility lines for B in A and A in B.

05

Draw phase region boundaries

Draw lines or curves to separate the solid, liquid, and eutectic regions of the phase diagram. This includes the liquidus and solidus lines that connect the melting points of A and B with the eutectic points, and the phase region boundary splitting pure B and the solubility of A in B (the composition of the second eutectic). The result should display separate regions for solid A, solid B, eutectic mixtures, the liquid phase, and the intermetallic compound AB.

06

Label phase regions

Clearly label the regions in the phase diagram, including regions for solid A, solid B, liquid, eutectic mixtures, and the intermetallic compound AB. This will clarify the different phases present in the diagram and help interpret the phase behavior of metals A and B at various temperatures and compositions.

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Key Concepts

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

Eutectic Point

The eutectic point is a crucial concept in analyzing phase diagrams because it represents a specific composition and temperature where a mixture of substances melts or solidifies at a single temperature. This phenomenon occurs at the lowest possible melting point for the mixture of the two phases involved. In the context of our hypothetical metals A and B, two eutectic points are identified. One is at 420°C with an 18 wt% B composition, and the other is at 475°C with a 42 wt% B composition. At these points, the metallic mixture transitions from a solid to a liquid at a constant temperature, forming a eutectic mixture that solidifies into a microstructure typically composed of alternating layers or lamellae of the two solid phases.

Understanding eutectic points is essential for manufacturing processes that require precise control over melting and solidifying temperatures of metal alloys, such as in soldering and casting industries.

Solubility Limits

Solubility limits refer to the maximum concentration of one component that can be dissolved in another to form a solid solution at a given temperature. Beyond this limit, additional substance will form a separate phase. The solubility limits are represented in our phase diagram for metal A and B as lines that demarcate the boundaries of the solid solution regions. For instance, at 420°C, the maximum solubility of B in A is defined as 4 wt% B. Similarly, the maximum solubility of A in B at 475°C is 13 wt% A. These solubility limits are crucial for material engineers who must consider the extent to which materials can mix to form solid solutions with desirable properties such as strength and ductility.

Notably, room temperature solubility limits are given as 0 wt% B in A and 3 wt% A in B, highlighting how solubility can be dependent on temperature.

Intermetallic Compounds

Intermetallic compounds are a type of phase that exists at a specific stoichiometric ratio and possess a unique crystalline structure, different from that of the parent metals. In our metal A and B phase diagram, the intermetallic compound AB, with a composition of 30 wt% B and 70 wt% A, has a melting point of 525°C. These compounds often exhibit distinct mechanical and thermal properties, such as high hardness or resistance to corrosion, making them valuable in various applications.

The formation of intermetallic compounds can be desirable or detrimental, depending on the application, and understanding their behavior in a phase diagram assists in predicting their effects on the overall properties of the metal alloy. Engineers can enhance or mitigate their presence accordingly through temperature control and compositional adjustments.

Melting Points

Melting points are the temperatures at which a substance transitions from a solid to a liquid state. On our phase diagram, the melting points of pure metals A and B are 480°C and 600°C, respectively. These points form the basis of the phase diagram construction, as they represent the pure components' thermal behavior before any mixing.

The melting points are of great interest in material science and engineering because they influence material selection and processing conditions. For example, knowing the melting points allows engineers to design processes like alloying and casting to create components with the desired mixture of properties.

Solidus and Liquidus Lines

The solidus and liquidus lines in a phase diagram are the boundaries that separate the solid and liquid phases. The solidus line indicates the temperature below which the alloy is completely solid, while the liquidus line indicates the temperature above which the alloy is completely liquid. In our phase diagram for metals A and B, the solidus and liquidus lines emanate from the melting points of A and B, curving toward the eutectic points.

These lines are pivotal for understanding the solidification process of alloys, as they indicate the conditions under which the mixture will start to solidify upon cooling (liquidus) or will be fully solidified upon heating (solidus). Processes such as annealing, forging, and heat treatments are based on these critical phase boundaries to manipulate material properties such as hardness and malleability, ensuring the desired outcome in a finished product.