(a) The phase diagram of the binary system, neodymium-scandium ( Nd-Sc ) is given below. There are two polymorphs in the solid state: alpha which is hexagonal close packed (HCP) and beta which is body-centered cubic (BCC).
Identify all phases present at points 1, 2, and 3.
Point 1:
Liquid
Vapor
beta-phase
Sc-rich beta -phase
Nd-rich beta-phase
alpha-phase
Sc-rich alpha-phase
Nd-rich alpha-phase
Point 2:
Liquid
Vapor
beta-phase
alpha-phase
Point 3:
Liquid
Vapor
beta-phase
Sc-rich beta -phase
Nd-rich beta-phase
alpha-phase
Sc-rich alpha-phase
Nd-rich alpha-phase
(b) Are there any examples of a three-phase equilibrium in this phase diagram?
i)Yes, there is a eutectic at 700 degrees C and 60 at. % Sc.
ii)Yes, there is a eutectoid at 800 degrees C and 22 at. % Sc.
iii)Yes, there is a peritectic at 800 degrees C and 22 at. % Sc.
iv)No, there are no three-phase equilibrium points in this diagram.
(c) At point 3, calculate the phase fraction of the phase richest in Nd
(a)
Point 1: Liquid, beta-phase
Point 2: alpha-phase
Point 3: Sc-rich alpha-phase, Nd-rich alpha-phase
(b)
iv)No, there are no three-phase equilibrium points in this diagram.
(c)
0.2631
Thank you
thank you bery much
how you clacula the number c?
@an apply the lever rule.
To identify the phases present at points 1, 2, and 3 in the binary system Nd-Sc, we can refer to the given phase diagram. In the phase diagram, different phases are represented by different regions or areas.
Point 1:
To determine the phases present at point 1, we locate the point on the phase diagram. Based on the diagram, the phases present at point 1 are: liquid, vapor, beta-phase, Sc-rich beta-phase, Nd-rich beta-phase, alpha-phase, Sc-rich alpha-phase, and Nd-rich alpha-phase.
Point 2:
Similarly, for point 2, the phases present are: liquid, vapor, beta-phase, and alpha-phase.
Point 3:
For point 3, the phases present are: liquid, vapor, beta-phase, Sc-rich beta-phase, Nd-rich beta-phase, alpha-phase, Sc-rich alpha-phase, and Nd-rich alpha-phase.
Moving on to part (b), we need to determine if there are any examples of a three-phase equilibrium in this phase diagram.
A three-phase equilibrium occurs when three different phases coexist at a specific temperature and composition. We can identify such equilibria by studying the points on the phase diagram.
Based on the given options:
i) Yes, there is a eutectic at 700 degrees C and 60 at. % Sc.
ii) Yes, there is a eutectoid at 800 degrees C and 22 at. % Sc.
iii) Yes, there is a peritectic at 800 degrees C and 22 at. % Sc.
iv) No, there are no three-phase equilibrium points in this diagram.
Since options i) and iii) mention specific temperature and composition conditions where three phases coexist, these options indicate the presence of three-phase equilibria. Therefore, the correct answer is either i) or iii) or both.
Finally, in part (c), we are asked to calculate the phase fraction of the phase richest in Nd at point 3.
To calculate the phase fraction, we need to know the composition of each phase present at point 3. Unfortunately, the composition information is not provided in the question. Therefore, it is not possible to calculate the phase fraction of the phase richest in Nd at point 3 without additional data.
In summary, the phases present at points 1, 2, and 3 are identified based on the phase diagram. There are examples of three-phase equilibria in this diagram, as indicated by options i) and iii). However, without composition data, it is not possible to calculate the phase fraction at point 3.