(a) The phase diagram of the binary system, neodymium-scandium (Nd-Sc) is given below. There are two polymorphs in the solid state: α which is hexagonal close packed (HCP) and β which is body-centered cubic (BCC).

Identify all phases present at points 1, 2, and 3.

Point 1:

Liquid

Vapor

β-phase

Sc-rich β-phase

Nd-rich β-phase

α-phase

Sc-rich α-phase

Nd-rich α-phase
Point 2:

Liquid

Vapor

β-phase

α-phase
Point 3:

Liquid

Vapor

β-phase

Sc-rich β-phase

Nd-rich β-phase

α-phase

Sc-rich α-phase

Nd-rich α-phase
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(b) Are there any examples of a three-phase equilibrium in this phase diagram?

Yes, there is a eutectic at 700 degrees C and 60 at. % Sc.

Yes, there is a eutectoid at 800 degrees C and 22 at. % Sc.

Yes, there is a peritectic at 800 degrees C and 22 at. % Sc.

No, there are no three-phase equilibrium points in this diagram.
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(c) At point 3, calculate the phase fraction of the phase richest in Nd.

unanswered

Pls show your work

To determine the phase fraction of the phase richest in Nd at point 3, we would need the composition of the mixture at that point. If you can provide the composition (in terms of atomic percentages or molar fractions) at point 3, I can help you calculate the phase fraction.

To identify the phases present at points 1, 2, and 3 in the neodymium-scandium (Nd-Sc) binary system, we need to refer to the given phase diagram. Let's go through each point one by one:

(a) Point 1:
In the diagram, we see that point 1 lies in the β-phase region. So, the phases present at point 1 are the β-phase, Sc-rich β-phase, and Nd-rich β-phase. Other phases such as the liquid, vapor, α-phase, Sc-rich α-phase, and Nd-rich α-phase are not present at this point.

(b) Point 2:
With reference to the diagram, we can see that point 2 falls within the two-phase region of the β-phase and α-phase. Therefore, the phases present at point 2 are the β-phase and α-phase. The liquid and vapor phases are not present here.

(c) Point 3:
To calculate the phase fraction at point 3, we need more information such as the composition of the alloy at that point. However, based on the phase diagram, we can see that point 3 falls within the α-phase region. Therefore, the phases present at point 3 are the β-phase, Sc-rich β-phase, Nd-rich β-phase, α-phase, Sc-rich α-phase, and Nd-rich α-phase. The liquid and vapor phases are not present here.

Now let's move on to the second part of the question:

(b) Are there any examples of a three-phase equilibrium in this phase diagram?
According to the phase diagram, there are no three-phase equilibrium points indicated. Therefore, the correct answer would be: No, there are no three-phase equilibrium points in this diagram.

I hope this helps you understand the identification of phases and the absence of three-phase equilibrium in the neodymium-scandium binary system's phase diagram. If you have any further questions, feel free to ask!