Question No. 1 A liquid Ni-Al alloy sphere is levitated with an induction coil in an excellent vacuum chamber at 500 C. Stirring of the droplet is intense so that the melt composition is uniform at any time. If the sphere has a radius of one cm and an initial Al mole fraction of 1%. Derive an expression which should describe the Al content of the droplet at any time. Identify any properties or parameters required State your assumptions If the vacuum were poor, a smoke(or fog) would be observed around the droplet. Explain the mechanism of smoke(or fog) formation Is the rate of Al loss higher in the excellent vacuum or upon the formation of smoke? Why Question No. 2 Discuss the use of statistical mechanics for the calculation of thermodynamic properties such as entropy, internal energy, and free energy. Illustrate your answer by reference to a simple diatomic cule Question No. 3 (a)(i) Demonstrate that the variation of the chemical potential of a component in a mixture with applied pressure at constant temperature is given by the partial molar volume of the component in the mixture le (ii) Convert the preceding expression to find an expression for aIn ai aP Where ar is the activity of component I with respect to pure 1 (b)For a particular binary system (many alloy systems exhibit this behavior) "retrograde solubility"is established as shown in the accompanying sketch. Note that the solubility of in a is a minimum at Tr, the "retrograde temperature". Sketch Gibbs energy-composition curves for the binary system at Tr and slightly below Tr. Can you draw any conclusions about the relative stability of 8 at lower temperatures
Question No. 1 A liquid Ni-Al alloy sphere is levitated with an induction coil in an excellent vacuum chamber at 1500 C. Stirring of the droplet is intense so that the melt composition is uniform at any time. If the sphere has a radius of one cm and an initial Al mole fraction of 1%. Derive an expression which should describe the Al content of the droplet at any time. Identify any properties or parameters required. State your assumptions. If the vacuum were poor, a smoke (or fog) would be observed around the droplet. Explain the mechanism of smoke (or fog) formation. Is the rate of Al loss higher in the excellent vacuum or upon the formation of smoke? Why? Question No. 2 Discuss the use of statistical mechanics for the calculation of thermodynamic properties such as entropy, internal energy, and free energy. Illustrate your answer by reference to a simple diatomic molecule. Question No. 3 (a) (i) Demonstrate that the variation of the chemical potential of a component in a mixture with applied pressure at constant temperature is given by the partial molar volume of the component in the mixture.1.e. 1 1 VT P u ⎟ = ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ (ii) Convert the preceding expression to find an expression for: T P a ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ ln 1 Where a1 is the activity of component 1 with respect to pure 1. (b) For a particular binary system (many alloy systems exhibit this behavior) “retrograde solubility” is established as shown in the accompanying sketch. Note that the solubility ofε in α is a minimum at Tr, the “retrograde temperature”. Sketch Gibbs energy-composition curves for the binary system at Tr and slightly below Tr. Can you draw any conclusions about the relative stability of ε at lower temperatures?
(c)Describe in detail a procedure, with supporting equations, to do each of the following (i) Calculate the enthalpy of fusion of a metal from melting point lowering data(liquids line on a binary T-X phase diagram) (ii) Calculate the activity of component B from the measured equilibrium partial pressure of con ent A over A-b mixtures Question No 4 he high-temperature electrical conductivity of the mixed conducting compound MX are required Describe an experimental program to establish the electrical conductivity behavior of MX. Offer tentative (or alternative) interpretations for your proposed experiments involving some point defect model Question No 5 Discuss the electrochemical theory for metallic corrosion as proposed by Wagner and Traud Illustrate your answer with schematic current-voltage curves for the partial anodic and cathodic processes. Your answer should include a discussion of the relationship between the corrosion potential and the equilibrium and kinetic properties of the individual reactions Question No 6 (a) Describe the characteristics and functions of fluxes and slag used in metal refining (b) Present a rational definition of the "basicity"of slags in terms of relative oxide ion activity and illustrate its use in connection with predicting the desulphurizing potential of a particular (c)Sketch, in detail, the saturation boundaries of Fe-Al-O melts (1600 C). Show clearly the molten oxide, hercynite, and alumina lines and all interesting features of these boundaries Explain how the features are determined by the magnitude of the solute interaction(Al-O)in (d)During the reduction of a solid metal oxide in hydrogen(or carbon monoxide) what kinetic factors determine whether the reduction will proceed in a topochemical or diffuse manner? Under what circumstances is the reduced metal likely to form with a filamentary morphology Calculate the potentials of the hydrogen electrode and the oxygen electrode at pH=7. 1, and 14 The standard reduction potential for the oxygen electrode is +0. 401 volts for the reaction occurring in aqueous alkaline solutions. (All pertinent reactions and relationships must be included (a)Using completely classical ideas, derive Ohms law and an expression for the electrical conductivity in terms of electronic parameters such as electronic charge, mass, etc (b) Repeat the derivation in(a), but now use the concept of a Fermi distribution as in a simple quantum approach. Compare the results of (a)and(b) (c) Assume that different electron scattering mechanisms act independently, so that the scattering probabilities are additive. Also, define a mean time between two successive scattering events
(c) Describe in detail a procedure, with supporting equations, to do each of the following: (i) Calculate the enthalpy of fusion of a metal from melting point lowering data (liquids line on a binary T-X phase diagram) (ii) Calculate the activity of component B from the measured equilibrium partial pressure of component A over A-B mixtures. Question No. 4 The high-temperature electrical conductivity of the mixed conducting compound MX are required. Describe an experimental program to establish the electrical conductivity behavior of MX. Offer tentative (or alternative) interpretations for your proposed experiments involving some point defect model. Question No. 5 Discuss the electrochemical theory for metallic corrosion as proposed by Wagner and Traud. Illustrate your answer with schematic current-voltage curves for the partial anodic and cathodic processes. Your answer should include a discussion of the relationship between the corrosion potential and the equilibrium and kinetic properties of the individual reactions. Question No. 6 (a) Describe the characteristics and functions of fluxes and slag used in metal refining. (b) Present a rational definition of the “basicity” of slags in terms of relative oxide ion activity and illustrate its use in connection with predicting the desulphurizing potential of a particular slag. (c) Sketch, in detail, the saturation boundaries of Fe-Al-O melts (~1600 C). Show clearly the molten oxide, hercynite, and alumina lines and all interesting features of these boundaries. Explain how the features are determined by the magnitude of the solute interaction (Al-O) in iron. (d) During the reduction of a solid metal oxide in hydrogen (or carbon monoxide) what kinetic factors determine whether the reduction will proceed in a topochemical or diffuse manner? Under what circumstances is the reduced metal likely to form with a filamentary morphology? Question No. 7 Calculate the potentials of the hydrogen electrode and the oxygen electrode at pH=7.1, and 14. The standard reduction potential for the oxygen electrode is +0.401 volts for the reaction occurring in aqueous alkaline solutions. (All pertinent reactions and relationships must be included.) Question No. 8 (a) Using completely classical ideas, derive Ohm’s law and an expression for the electrical conductivity in terms of electronic parameters such as electronic charge, mass, etc. (b) Repeat the derivation in (a), but now use the concept of a Fermi distribution as in a simple quantum approach. Compare the results of (a) and (b). (c) Assume that different electron scattering mechanisms act independently, so that the scattering probabilities are additive. Also, define a mean time between two successive scattering events
for a given electron as T for a given mechanism j. Use the information to deduce Matthiessen's rule, which expresses the total electrical resistivity in terms of the resistivity due to thermal effects, pt(scattering from phonons)and the resistivity due to solutes, pi Questions No 9 Nearly pure liquid copper contains 1X10 weight H and 8X10 wt %O. Initially the solidification is dendritic with the H and o rejected to interdendritic spaces (a) At what fraction of solid will pores begin to form? (b) What will be the final volume fraction of voids present in this casting? (c) What gas or gases will comprise the voids? Assume compete diffusion of H and o in the liquid and solid over distances of the dendrite spacing. The ratio of solid solubility of H to that of the liquid is 1: 3. The o negligible solid solubility. Neglect effects of surface energy and metallo-static head. The casting solidifies at ambient pressure. The melting point of copper is 1083C Solubility data are H2=2H1 logK'=-4620/T-322 logK=7030-2.84 H20=2HL+O2 logK=-10640/-3.09 Question No. 10 An austenitic stainless steel pump was severely corroded by concentrated sulfuric acid containing solids in suspension. a study was made in which a disc specimen was rotated at different velocities in the above environment. Under static conditions the potential of the specimen was found to be +200 mV positive to a solid calomel reference electrode. The electrode potential became more positive as the specimen was rotated at a peripheral velocity from 0 to 8 ft/sec. Negligible corrosion was observed in this range of velocities. When the velocity was increased from 8 to 12 ft/sec the potential changed to -200 mV and the rate of metal loss increased gradually to a ratio of several thousand mils per year. Upon reducing the velocity to 8 ft per second the potential of the stainless again returned to 200 mV. Describe in detail the causes of the shifts in electrode potential and metal removal as a function of velocity over the entire velocity range from zero to 12 fu/sec Question No. 1l Open-circuit galvanic cell measurements are made for the following cell at 1000C Pt, Cr +Cr,O3 ZrO+ Cao Cr, (Cr, Al)O3, Pt Where(Cr, Al)O3 is an oxide solid solution and Zro Cao is an exclusive oxide electrolyte (a) Write the half-cell reactions for this cell (b) Interpret the cell emf in term of the thermodynamic properties of the phases involved (c) If the cell voltage is measured over a range of temperature. What is the interpretation of the temperature dependence of the cell voltage? (d) Suppoes the electrolyte exhibite some(non-negligible) electronic conduction. How will the cell voltage be affected ( i) For reversible electrodes? (ii For non-reversible electrodes?
for a given electron as Tj for a given mechanism j. Use the information to deduce Matthiessen’s rule, which expresses the total electrical resistivity in terms of the resistivity due to thermal effects, ρ t (scattering from phonons) and the resistivity due to solutes, ρ i. Questions No. 9 Nearly pure liquid copper contains 1×10-4 weight % H and 8×10-4 wt % O. Initially the solidification is dendritic with the H and O rejected to interdendritic spaces. (a) At what fraction of solid will pores begin to form? (b) What will be the final volume fraction of voids present in this casting? (c) What gas or gases will comprise the voids? Assume compete diffusion of H and O in the liquid and solid over distances of the dendrite spacing. The ratio of solid solubility of H to that of the liquid is 1:3. The O negligible solid solubility. Neglect effects of surface energy and metallo-static head. The casting solidifies at ambient pressure. The melting point of copper is 1083C. Solubility data are: H2=2HL log K’ = -4620/T - 3.22 1/2O2=OL log K’ = 7030/T - 2.84 H2O=2HL+O2 log K’ = -10640/T - 3.09 Question No. 10 An austenitic stainless steel pump was severely corroded by concentrated sulfuric acid containing solids in suspension. A study was made in which a disc specimen was rotated at different velocities in the above environment. Under static conditions the potential of the specimen was found to be +200 mV positive to a solid calomel reference electrode. The electrode potential became more positive as the specimen was rotated at a peripheral velocity from 0 to 8 ft/sec. Negligible corrosion was observed in this range of velocities. When the velocity was increased from 8 to 12 ft/sec the potential changed to -200 mV and the rate of metal loss increased gradually to a ratio of several thousand mils per year. Upon reducing the velocity to 8 ft per second the potential of the stainless again returned to 200 mV. Describe in detail the causes of the shifts in electrode potential and metal removal as a function of velocity over the entire velocity range from zero to 12 ft/sec. Question No. 11 Open-circuit galvanic cell measurements are made for the following cell at 1000C: Pt, Cr + Cr2O3 ZrO2 + CaO Cr, (Cr, Al)2O3, Pt Where (Cr, Al)2O3 is an oxide solid solution and ZrO2 + CaO is an exclusive oxide ion conducting electrolyte. (a) Write the half-cell reactions for this cell. (b) Interpret the cell emf in term of the thermodynamic properties of the phases involved. (c) If the cell voltage is measured over a range of temperature. What is the interpretation of the temperature dependence of the cell voltage? (d) Suppoes the electrolyte exhibite some (non-negligible) electronic conduction. How will the cell voltage be affected: (i) For reversible electrodes? (ii) For non-reversible electrodes?
(e) Derive an expression for the Po2- dependence of n-type electronic conduction in the ZrO2-CaO solid electrolyte Question No. 12 (a)Present on the same graph plots of velocity of sustained crack growth for a sharp tipped crack as a function of applied mode I stress intensity for steel specimens failing (i) Intergranular cleavage (ii) Ductile rupture by hole growth (b) Can the above cracking processes be described in terms of the J-integral? (c)Describe the mode of crack initiation and the fraction of life spent in crack initiation for the high-cycle-fatigue failure in (1) Pure, Single-crystal copper igh-strength alloy steel Question No. 13 Briefly discuss the following terms which are frequently encountered in corrosion science: (i) active dissolution, (ii) passivity,(iii) transpassive dissolution, and (iv)cathodic polarizatio Illustrate your answer by reference to the schematic polarization curve for a metal or alloy which exhibits the above phenomenon, and indicate briefly the mechanisms involved in these processes (a) In an oil refinery the metal cap at the top of a "flare " can corrode rapidly at 600C although the hotter portions of the pipe are less attacked.(A flare"is a small chimney uded for burning waste process gases.) How can you explain this higher corrosion rate at lower temperatures? (b)A"heat wheel"for the recovery of waste heat is a paddle-type wheel which rotates slowly with one half heated by exiting hot waste combustion product gases while the other half (previously heated) is being cooled by heating cool incoming air. The worst corrosion occurs where the wheel is coolest(about 70C)and in contact with the humid waste gases Explain the corrosive stack and recommend corrective action (c) At very high temperatures, platinum evaporates in air as P+ O2 (vapor). Deposition of a porous ceramic coating on the metal reduces drastically the rate of oxidation-evaporation Explain this result. ( d)A common laboratory test for the tendency of a high-temperature Fe-Ni-Cr-Si alloy to suffer carburization in highly reduced gases with unit carbon activity is to pack the alloy in an enclosure with carbon and argon But this test provides much too severe carburization attack compared to service in a process gas of CO/CO2/H2/H2)with unit carbon activity Explain these results Question No 15 Your employer(a petrochemical company) has a large steel pressure vessel (wall 0.3 m thick) which has contained high pressure hydrogen at temperatures of 400C for a year. Your problem is to calculate the time the vessel should be held at temperature with, the hydrogen pressure removed So that 90% of the hydrogen can diffuse out. (The aim is to avoid hydrogen cracking on cooling
(e) Derive an expression for the PO2 – dependence of n-type electronic conduction in the ZrO2-CaO solid electrolyte. Question No. 12 (a) Present on the same graph plots of velocity of sustained crack growth for a sharp tipped crack as a function of applied mode I stress intensity for steel specimens failing. (i) Intergranular cleavage (ii) Ductile rupture by hole growth (b) Can the above cracking processes be described in terms of the J-integral? (c) Describe the mode of crack initiation and the fraction of life spent in crack initiation for the high-cycle-fatigue failure in (i) Pure, Single-crystal copper (ii) High-strength alloy steel Question No. 13 Briefly discuss the following terms which are frequently encountered in corrosion science: (i) active dissolution, (ii) passivity, (iii) transpassive dissolution, and (iv) cathodic polarization. Illustrate your answer by reference to the schematic polarization curve for a metal or alloy which exhibits the above phenomenon, and indicate briefly the mechanisms involved in these processes. Question No. 14 (a) In an oil refinery the metal cap at the top of a “flare” can corrode rapidly at 600C although the hotter portions of the pipe are less attacked. (A “flare” is a small chimney uded for burning waste process gases.) How can you explain this higher corrosion rate at lower temperatures? (b) A “heat wheel” for the recovery of waste heat is a paddle-type wheel which rotates slowly with one half heated by exiting hot waste combustion product gases while the other half (previously heated) is being cooled by heating cool incoming air. The worst corrosion occurs where the wheel is coolest (about 70C) and in contact with the humid waste gases. Explain the corrosive stack and recommend corrective action. (c) At very high temperatures, platinum evaporates in air as P + O2(vapor). Deposition of a porous ceramic coating on the metal reduces drastically the rate of oxidation-evaporation. Explain this result. (d) A common laboratory test for the tendency of a high-temperature Fe-Ni-Cr-Si alloy to suffer carburization in highly reduced gases with unit carbon activity is to pack the alloy in an enclosure with carbon and argon. But this test provides much too severe carburization attack compared to service in a process gas of CO/CO2/H2/H2) with unit carbon activity. Explain these results. Question No. 15 Your employer (a petrochemical company) has a large steel pressure vessel (wall 0.3 m thick) which has contained high pressure hydrogen at temperatures of 400C for a year. Your problem is to calculate the time the vessel should be held at temperature with, the hydrogen pressure removed. So that 90% of the hydrogen can diffuse out. (The aim is to avoid hydrogen cracking on cooling.)
The following data is given D mol//RT)cm2/s Plate thickness 0.3 m vessel diameter 3m T=400C throughout the plat (b) Give a numerical estimate of the time to diffuse 90% of the gas out of the metal (c) Outline how a more exact calculation of the transient could be made Why do interstitials generally produce greater hardening than substitutional solute atoms? How does the effect vary in different crystal structures? Question No. 17 a binary alloy is solution treated. Quenched to and aged at a temperature at which continuous precipitation of a stable phase takes place. In this system the precipitates nucleate homogeneously and growth is controlled by long range diffusion, for which the invariant field approximation is applicable. Discuss the characteristics of the transformation from the very beginning of the aging time to very long times. Consider the nature of the precipitate, the number of precipitates and their average sizes. uestion No Discuss the tress needed to operate a frank-Read source with one end intersecting a free surface What approximations did you make? If the Burgers vector is inclined at an angle of 30 to the surface, what would be the configuration of the dislocation with no stress applied Question No. 19 (a) The basic symmetry elements used in crystallography are rotations, inversions, reflections, and translations. There are also combinations such as rotation-inversion rotation-translation (screw axis), and reflection-translation(glide plane). Give one example of each, using simple sketches of stereograms(stereographic projections showing equivalent points) (b) Let the Z-axis be along the [110] direction of a BCC crystal. Sketch a stereogram to show the equivalent points consistent with the presence of this axis only (i.e, ignore all other symmetry elements present). Then use matrix methods to prove that these are the only equivalent points present for this case (c)The(110) plane is one of the mirror planes in cubic crystals. Write down the relations between the coordinates of any selected point in the lattice and the corresponding point obtained by reflection. From this, obtain the matrix for the reflection involving(110)as the mirror plane That two reflections bring one back to the original point. You may translate coordinates if this the(200)pla (d) Provide the appropriate Miller indices for the point a-f, for the given standard projection of a cubic crystal. A right hand coordinate system is used
The following data is given: DH Fe = 0.5 exp (-6000(cal/mol/)/RT) cm2 /s Plate thickness 0.3 m, vessel diameter 3m. T=400C throughout the plate. (a) Skatch the concentration profile through the wall at t=0 (b) Give a numerical estimate of the time to diffuse 90% of the gas out of the metal. (c) Outline how a more exact calculation of the transient could be made. Question No. 16 Why do interstitials generally produce greater hardening than substitutional solute atoms? How does the effect vary in different crystal structures? Question No. 17 A binary alloy is solution treated. Quenched to and aged at a temperature at which continuous precipitation of a stable phase takes place. In this system the precipitates nucleate homogeneously and growth is controlled by long range diffusion, for which the invariant field approximation is applicable. Discuss the characteristics of the transformation from the very beginning of the aging time to very long times. Consider the nature of the precipitate, the number of precipitates and their average sizes. Question No. 18 Discuss the tress needed to operate a Frank-Read source with one end intersecting a free surface. What approximations did you make? If the Burgers vector is inclined at an angle of 30 to the surface, what would be the configuration of the dislocation with no stress applied? Question No. 19 (a) The basic symmetry elements used in crystallography are rotations, inversions, reflections, and translations. There are also combinations such as rotation-inversion, rotation-translation (screw axis), and reflection-translation (glide plane). Give one example of each, using simple sketches of stereograms (stereographic projections showing equivalent points). (b) Let the Z-axis be along the [110] direction of a BCC crystal. Sketch a stereogram to show the equivalent points consistent with the presence of this axis only (i.e., ignore all other symmetry elements present). Then use matrix methods to prove that these are the only equivalent points present for this case. (c) The (110) plane is one of the mirror planes in cubic crystals. Write down the relations between the coordinates of any selected point in the lattice and the corresponding point obtained by reflection. From this, obtain the matrix for the reflection involving (110) as the mirror plane. That two reflections bring one back to the original point. You may translate coordinates if this is helpful. Repeat procedure for the (200) plane. (d) Provide the appropriate Miller indices for the point a-f, for the given standard projection of a cubic crystal. A right hand coordinate system is used