MS524 Phase Equilibria and Phase Diagrams DMSE, KAIST December 19, Problem 1 (35 Points) Problem 2 (40 Points)

Transcription

1 MS524 Phase Equilibria and Phase Diagrams DMSE, KAIST December 19, 2005 Final Exam 19:00~midnight Prof. Hyuck Mo Lee Problem 1 (35 Points) Problem 2 (40 Points)

2 Problem 3 (25 Points) 3

3 Fig. 1

4 Fig. 2

5 Fig. 3

6 MS524 Phase Equilibria and Phase Diagrams DMSE, KAIST December 20, 2006 Final Exam 13:00 ~ Prof. Hyuck Mo Lee Problem 1 (40 points) According to Fig. 1, a two liquid region extends from the binary C-B system into the primary field of C. The binary systems are all simple eutectic types, as is the ternary system. A plane projection of the liquidus surface of this system is shown in Fig. 1, where the point denoted by K is the consolute point. Answer the following questions. 1) Draw the C-B binary phase diagram. 2) What are the maximum and minimum temperatures of the only two liquid phase field in the ternary system? 3) What are the maximum and minimum temperatures of the three-phase field including two liquids? Explain. 4) Identify the composition region (range) where the three-phase field including the two liquids is thermodynamically possible. 5) Assume that the alloy denoted by the composition, Y, is now inside a C + liquid region. On further cooling, a new liquid phase is separated from the current liquid. What is the temperature for the liquid-liquid separation? 6) Assume that the alloy denoted by the composition, b, is now inside a two liquid region. On further cooling of the alloy b, a new phase begins to appear from the two liquid. What are this phase and the starting temperature? 7) When the alloy denoted by the composition, c, is cooled, it may be composed of C + liquid. What is the temperature range? Note : In answering Prob. 1, you are recommended to use Fig. 1 directly attached to the exam sheet and submit it together with your answer sheet.

7 Fig. 1

8 Problem 2 (30 points) Part of the Cu-Ag-P system is represented by the liquidus projection in Fig. 2, taking compound Cu 3 P as one of the components. Each of the binary systems contains an eutectic and the ternary system contains an invariant eutectic L Ag + Cu + Cu 3 P. (Solid solubility, which is small at room temperature, is neglected here.) The system includes a group of brazing alloys (in the range 0-15 wt% Ag; wt% Cu; wt% Cu 3 P) used for joining copper alloys. 1) For an alloy containing 50 wt% Cu 3 P and 5 wt% Ag determine : (i) the liquidus temperature : (ii) the percentage of liquid present at the temperature when separation of Cu 3 P begins : (iii) the proportions of the phases present at the stage when the liquid contains 10 wt% Ag and lies on the L Cu + Cu 3 P eutectic valley : and (iv) the percentages of primary phase and of binary and ternary eutectic mixtures respectively present at room temperature. (Assume equilibrium conditions and neglect solid solubility.) 2) Sketch isothermal sections through the system at (i) 800 and (ii) at a temperature above 646 but below the binary eutectic temperatures. (Make assumptions as necessary concerning the liquidus isotherms and neglect solid solubility.)

9 Fig. 2 Ag-Cu-Cu 3 P system. From G. H. Sistaire (1973) Metals Handbook (8 th edition), American Society for Metals, 8, pp. 379.

10 Problem 3 (30 points) Using Fig. 3, draw joins which will create the proper composition triangles for the system. Place arrows on ALL boundary lines in the binary and ternary systems indicating the direction of falling temperature so that temperature maxima on boundary lines may be recognized and so that invariant points may be identified and labeled as eutectics, peritectics, etc. 1) For a composition containing 10% A, 10% B and 80% C, trace the crystallization path, making sure to describe ALL major events as the liquid cools below the temperature of the invariant point. 2) Trace the crystallization path of a composition containing 15% A, 10% B and 75% C. The composition is on the join AC-BC. Make a quantitative calculation just before and just after final crystallization to show exactly what takes place at the invariant point. 3) How much solid and how much liquid coexist when the liquid composition is 30% A, 10% B and 60% C? What is the composition of the solid? Note : In answering Prob. 3, you are recommended to use Fig. 3 directly attached to the exam sheet and submit it together with your answer sheet.

11 Fig. 3

12 MS524 Phase Equilibria and Phase Diagrams DMSE, KAIST December 14, 2009 Final Exam 11:00 ~ Prof. Hyuck Mo Lee Problem 1 (40 points) According to Fig. 1, a two liquid region extends from the binary C-B system into the primary field of C. The binary systems are all simple eutectic types, as is the ternary system. A plane projection of the liquidus surface of this system is shown in Fig. 1, where the point denoted by K is the consolute point. Answer the following questions. (1) Draw the C-B binary phase diagram. (2) What are the maximum and minimum temperatures of the only two liquid phase field in the ternary system? (3) What are the maximum and minimum temperatures of the three-phase field including two liquids, i.e. C+L 1 +L 2? Explain. (4) Draw the composition region (range) where the three-phase field including the two liquids is thermodynamically possible. (5) Assume that the alloy denoted by the composition, Y, is now inside a C + liquid region. On further cooling, a new liquid phase is separated from the current liquid. What is the temperature for the liquid-liquid separation? (6) Assume that the alloy denoted by the composition, b, is now inside a two liquid region. On further cooling of the alloy b, a new phase begins to appear from the two liquid. What are this phase and the starting temperature? (7) When the alloy denoted by the composition, c, is cooled, it may be composed of C + liquid. What is the temperature range? Note : In answering Prob. 1, you are recommended to use Fig. 1 directly attached to the exam sheet and submit it together with your answer sheet.

13 Fig. 1

14 Problem 2 (20 points) The typical Gibbs triangle is shown in Fig. 2. Show why (1) X A /X C is constant on the line oa and (2) X A - X C is constant on the line ob. Fig. 2

15 Problem 3 (40 points) The Y 2 O 3 -SiO 2 -Al 2 O 3 phase diagram is shown in Fig 3. By answering the fo11owing questions you will explore how phase equilibria influence processing of polyphase materials. (1) Identify the ternary invariant points, making a table showing the three solid phases in equilibrium with liquid at each critical point. Identify whether the invariant point is a peritectic or eutectic. In a separate diagram, show the compatibility triangles in this system. (2) Which compounds in this system melt incongruently? (3) Yttrium aluminum garnet (YAG, or Y 3 Al 5 O 12 ) is of interest as a laser host (when doped with rare earths such as Nd) and as an IR-transparent window material. What (approximately) is the melting point of YAG? (4) A small amount of SiO 2 powder (5 wt%) is added to a fine YAG powder, in hopes of densifying the powder compact into a transparent polycrystalline YAG by forming a minor amount of liquid phase during firing. After mixing uniformly, the powder mixture is pressed into a pellet and rapidly heated in a furnace. What is the minimum temperature (approximately) at which a liquid phase might form? What is the corresponding liquid composition? (5) What is the most refractory (highest melting) three-phase composite one can prepare in this ternary system?

16 Fig. 3