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           UNIVERSITI SAINS MALAYSIA  First Semester Examination Academic Session 2010/2011  November 2010  EBB 512/3 – Phase Diagram and Phase Equilibra  Duration : 3 hours    Please ensure that this examination paper contains ELEVEN printed pages and TWO pages APPENDIX before you begin the examination.  This paper consists of SEVEN questions.  Instruction: Answer FIVE questions.  If candidate answers more than five questions only the first five questions answered in the answer script would be examined.  The answers to all questions must start on a new page.  All questions must be answered in English.           …2/-    [EBB 512] - 2 -    1. Considering a binary solution containing A and B, based on quasi-chemical model show that for an ideal solution the following relationship is true  EAB  = (EAA + EAB)/2  where: EAA is the bond energy for A-A bonds EBB is the bond energy for B-B bond EAB is the bond energy for A-B bons.  Define clearly other terms used in the derivation. Explain what is/are the characteristic of the solution when EAB < (EAA + EBB)/2 and EAB > (EAA + EBB)/2. (100 marks)  2. For the following questions please refer to Figure 1 for your answer.  [Figure 1 in Appendix should be submitted together with the answer script].                …3/-   [EBB 512] - 3 -    [a] Label all the two-phase fields on the SiO2 – Al2O3 phase diagram. (15 marks)  [b] Identify the invariant reactions in the SiO2-Al2O3 system. (15 marks)  [c] Because of their high-temperature stability and their resistance to hot environments the include liquids and gases,ceramic materials are used as refractories.  The SiO2-Al2O3 system forms the basis for the production of a class of materials used in the refractories industry.  A starting material that is readily available is kaolinite, Al2O3.2SiO2.2H2O.  If kaolinite is heated to 1500oC and held until it has been equilibrated, what phases will be present,what are their compositions and how much of each phase is present? (35 marks)  [d] What is the maximum use temperature for a refractory made from kaolinite? (15 marks)  [e] How much Al2O3 must be added to kaolinite in order to significantly increase its maximum use temperature? (20 marks)         …4/-   [EBB 512] - 4 -    3. [a] Based  on the  free energy  curves given in Figure 2,  sketch the  possible  phase diagram of this binary system.                  Figure 2 (35 marks)           …5/-   [EBB 512] - 5 -    [b] Calculate the phase present, compositions and the amount (in weight percent) for the microstructure at 1000oC for a spinel (MgO.Al2O3) refractory with 1 wt% excess MgO (i.e 1 g MgO per 99 g MgO.Al2O3).  Refer Figure 3.                     Figure 3 (45 marks)  [c] Briefly explain why upon solidification an alloy of eutectic composition forms a microstructure consisting of alternating layers of two solid phases. (20 marks) …6/-   [EBB 512] - 6 -    4. [a] A  partially   stabilized   zirconia   (for  a  novel  structural   application)   is  desired to have an equal weight fractions of tetragonal and cubic zirconia at an operating temperature of 1500oC.  Calculate the proper CaO content (in weight %) for this structural ceramic.  Refer Figure 4.                        Figure 4 (35 marks)   …7/-   [EBB 512] - 7 -    [b] A solder batch is made by melting together 64 g of a 40:60 Pb-Sn alloy with 53 g of a 60:40 alloy.  Calculate the amounts of D and E phase that would be present in the overall alloy, assuming it is slowly cooled to room temperature, 25oC.  Refer Figure 5.                   Figure 5 (35 marks)        …8/-   [EBB 512] - 8 -    [c] For an iron-carbon alloy of composition 5wt%C-95wt%Fe , draw sketches of microstructure that would be observed for conditions of very slow cooling at the following temperatures: (i) 1175oC (ii) 1145oC and (iii) 700oC.  Refer Figure 6.                     Figure 6 (30 marks)      …9/-   [EBB 512] - 9 -    5. [a] When a phase  transformation occurs such as a liquid phase transforming  to a solid below its melting temperature, what are the two steps involved in the process.  Briefly describe each. (30 marks)  [b] The expression X = 1-exp[-(kt)n] is a powerful empirical function that is useful in describing the kinetics of diffusional transformations.  In the equation, X is the fraction transformed, k is a rate constant having units of reciprocal time, t is time and n is a unitless constant.  Sketch the behavior of this function over a range times that demonstrated why this expression is useful for describing microstructural changes like recrystallisation,or the decomposition of austenite to form pearlite. (25 marks)  [c] Figure 7 are IT or time-temperature transformation diagrams for a hypoeuctectoid, eutectoid and hypereutectoid alloy. (i) Which diagram is associated with a composition that is hypoeutectoid,eutectoid and hypereutectoid, and why?  [Figure 7 in Appendix should be submitted together with the answer script]. (ii) Label the regions on each diagram. (iii) If a thin specimen of alloy II is quenched instantaneously from 900oC to 550oC, held for 1 second, and quenched to room temperature,what phases will be present in the microstructure. (45 marks)       …10/-   [EBB 512] - 10 -    6. A ternary Ag-Cu-Cu3P system is represented in the following Figure 8.  Each of the binary systems contains a eutectic and the ternary system contains an invariant eutectic: L ↔ Ag + Cu + Cu3P.  Solid solubility, which is small at room temperature, is neglected here.  For an alloy containing 50 wt% Cu3P and 5 wt% Ag, determine: (i) The percentage of liquid present at the temperature where separation of Cu3P begins. (ii) The proportion of the phases present at the stage when the liquid contains 10 wt% Ag and lies on the L ↔ Ag + Cu + Cu3P valley. (iii) The percentage of primary phase, and of binary and ternary eutectic mixtures respectively present at room temperature (assume equilibrium conditions and neglect solid solubility).                 Figure 8 (20 marks)  …11/-   [EBB 512] - 11 -    7. [a] Elaborate  on  the  following  cases.  In each case,  which phase  diagram  would you refer to?  Discuss what would be the purpose of using the phase diagram you mentioned and the result that you will get out of the diagram. (i) Study of the IMC formation of lead-free Sn-Ag-Cu solder reflow on Ni-P/gold substrate and effect of alloying elements (Fe, Sb, Bi and In). (ii) Study of composition (and possible adjustment in composition) of slag from iron making process (EAF slag or blast furnace slag).  The slag contains mainly CaO, SiO2 and Al2O3 plus some remaining iron oxides. (iii) Formulation of a ceramic whiteware body (typical combination of clay, flux and filler). (12 marks)  [b] Figure 9 is the phase diagram of the ABC system.  Discuss solidification paths for the compositions p, q and r indicated on the diagram.             Figure 9: Phase diagram of ABC system (8 marks) - oooOooo –   [EBB 512] - 12 -   APPENDIX (Figure 1)                                   [EBB 512] - 13 -   APPENDIX (Figure 7)                             IT diagrams for three plain carbon steels: a hypoeutectoid, a hypereutectoid, and a eutectoid 

EBB 512/3 – PHASE DIAGRAM AND PHASE EQUILIBRA NOV 2010.

PPKBSM, Pusat Pengajian Kejuruteraan Bahan dan Sumber Mineral

   UNIVERSITI SAINS MALAYSIA  First Semester Examination Academic Session 2009/2010  November 2009  EBB 512/3 - Phase Diagram and Phase Equilibra  Duration : 3 hours    Please ensure that this examination paper contains TEN  printed pages before you begin the examination. This paper consists of SEVEN questions.  Instruction: Answer FIVE  questions.  If candidate answers more than five questions only the first five questions answered in the answer script would be examined. The answers to all questions must start on a new page.  All questions must be answered in English.              …2/-   [EBB 512] - 2 -    1. [a] Considering a binary solution containing A and B, show that the heat of formation ΔHM  based on quasi-chemical model is given by ΔHM = PAB(EAB -(EAA + EAB )/2) Where ΔHM P = enthalpy of mixing xy E = no.of bonds of each type xy  = bond energy of each type State any assumptions made for the derivation. (10 marks)  [b] Shown in Figure 1 is the diagram of free energy of mixing of liquid and solid solutions of the A-B binary system at temperature T1  (i) Is it true that T1< Tm(A) and T1< Tm(B)?  Tm is the melting point of I. (ii) The diagram shown occurs when the heat of mixing, HM is positive.  Prove that HM(solid) >HM (liquid). Sketch the expected phase diagram based on the free energy diagram and indicate the stable phases. (10 marks)             …3/- Figure 1   [EBB 512] - 3 -                         Figure 2  2. Refer Figure 2 Be-W phase diagram for the following questions:  [a] List the composition and temperature of ALL the invariant points, congruent points and what kind of reaction it is. (6 marks)  [b] For the temperature 2000o(4 marks) C, use the Be-W binary phase diagram to sketch the Gibbs free energy curves as function of at% W needed to make up the phase diagram at this temperature.  Be sure to note the important composition points on your graph. …4/-   [EBB 512] - 4 -    [c] Based on the phase diagram, what can you deduce about the elements W and Be relative to one another?  Explain your reasoning. (4 marks)  [d] For the alloy composition of 80at% W, determine the phases present, their compositions and relative amounts, and sketch the microstructure at the following temperatures (i) 2500oC and (ii) 2090o(6 marks) C.  3. [a] An important structural ceramic is partially stabilized zirconia (PSZ) which has a composition lying in the two-phase ZrO2-cubic ZrO2 (ss) region.  By referring to Figure 3 calculate the amount of each phase present in a           10 mol% CaO PSZ at 500o(6 marks) C.  [b] In a test laboratory, quatitative x-ray diffraction determines that a refractory brick has 25 wt% alumina phase and 75 wt% mullite solid solution.  What is the overall SiO2(9 marks)  content (in wt%) of this material.  Refer Figure 4 for your answer.  [c] Briefly explain why a proeutectoid phase forms along austenite grain boundaries (5 marks)           …5/-   [EBB 512] - 5 -                             Figure 3         …6/-   [EBB 512] - 6 -                           Figure 4           …7/-   [EBB 512] - 7 -    4. [a] Name the two stages involved in the formation of particles of new phases.  Briefly describe each. (6 marks)  [b] A theoretical expression for the rate of pearlite growth from austenite is  Ŕ= Ce-Q/RT(TE-T) 2 where C is a constant.  Q is the activation energy for carbon diffusion in austenite, R is the gas constant, and T an absolute temperature below the equilibrium transformation temperature TE.  Derive an expression for the temperature TM corresponding to the maximum growth rate, that is the 'knee' of the transformation curve.  If TE = 1900K and Q = 42 kJ/mol calculate TM. (6 marks)  5. [a] In 10 kg of an iron-carbon alloy and at a temperature just below the eutectoid temperature, the mass of total cementite is 0.76 kg.  (i) What is the proeutectoid phase in this alloy?  Why?  (ii) Calculate the mass fraction of pearlite at a temperature just below the eutectoid.  Refer Figure 5. (8 marks)  [b] Briefly describe the phenomenon of coring and why it occurs.  Cite one undesirable consequence of coring. (4 marks)           …8/-   [EBB 512] - 8 -    [c] For an iron-carbon alloy of composition 5 wt% C - 95 wt% Fe, make schematic sketches of the microstructure that would be observed for conditons of very slow cooling at the following temperatures (i) 1175oC (ii) 1145oC and 700o(8 marks) C.  Label the phases and indicate their composition.  Refer Figure 5.                           Figure 5  …9/-   [EBB 512] - 9 -    6. [a] Explain, with the help of appropriate diagram(s), how a ternary phase diagram is constructed. (6 marks)  [b] Discuss how a ternary phase diagram is related to the binary phase diagram.  When does a ternary phase diagram become useful? (4 marks)  [c] In relation with the above, elaborate on the following cases.  In each case, which phase diagram would the student refers to?  And what would be the purpose of using the phase diagram you mentioned (or the result that you will get out of the diagram)?: (i) A student is doing a research project on the effect of certain alloying elements on a metal (say, effect of adding Cerium, Bi and In to Sn-Ag-Cu solder alloy). (ii) Another student is studying the optimum heat treatment route to homogenize TiAl-Nb alloys microstructure. (iii) Another student is trying to fabricate a ceramic body consisting of Forsterite-Anorthite-Silica, and study the effect of different composition on microstructure. (10 marks)  7. [a] Shown in Figure 6 is the phase diagram of the SiO2-CaO-Al2O3(10 marks)  system*.  Discuss solidification paths for the compositions p, q and r indicated on the diagram.         …10/-   [EBB 512] - 10 -    [b] In the system ABC, a ternary alloy containing 40% B and 8% C undergoes a eutectic reaction L  α + β over a temperature range 550 - 500°C as part of its solidification sequence.  The compositions of the phases coexisting in equilibrium at 540°C and 510°C are as follow:   α β L 540o 85%A, 10%B, 5%C C 5%A, 93%B, 2%C 55%A, 30%B, 15%C 510o 82%A, 11%B, 7%C C 6%A, 89%B, 5%C 48%A, 32%B, 20%C  Calculate: (i) The proportions by weight of α and β phases present in the alloy at 540°C. (ii) The ratio of the proportions of liquid phase present at 540°C and 510°C. (10 marks)                     - oooOooo - Figure 6 - Phase diagram of SiO2-CaO-Al2O3   [EBB 512]     APPENDIX 1                                   [EBB 512]    APPENDIX 2   [EBB 512]    APPENDIX 3   [EBB 512]     APPENDIX 4 

EBB 512/3 - PHASE DIAGRAM AND PHASE EQUILIBRA NOV 2009.

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EBB 512/3 – PHASE DIAGRAM AND PHASE EQUILIBRA NOV 2010.

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