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 ? ? ? ? ? ? ? ? 1ln Where a 1 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 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 j 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: H 2 =2H L log K’ = -4620/T - 3.22 1/2 O 2 =O L log K’ = 7030/T - 2.84 H 2 O=2H L +O 2 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 + Cr 2 O 3 ZrO 2 + CaO Cr, (Cr, Al) 2 O 3 , Pt Where (Cr, Al) 2 O 3 is an oxide solid solution and ZrO 2 + 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 P O2 – dependence of n-type electronic conduction in the ZrO 2 -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 + O 2 (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/CO 2 /H 2 /H 2 ) 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 H Fe = 0.5 exp (-6000(cal/mol/)/RT) cm 2 /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. Question No. 20 Contrast the use of the terms ‘scattering’ and ‘diffraction’ as applied to the interaction of xrays or electrons with crystalline materials, distinguishing ciearly between the form of the amplitude distribution obtained. The six circles represent atoms forming part of a two-dimensional lattice with unit cell of side 0.3nm. Calculate the angles for bragg scattering at the horizontal planes for x-rays of wavelength 0.2nm. By summing the individual contributions to the diffracted beam from each of the six atoms, compare the intensities for the two lowest orders of diffraction (a.b. intensity is proportional to (amplitude) 2 ). Question No. 21 Calculate the ideal work of deformation par unit volume in drawing a wire through a die. Express it in terms of the strain in the longitudinal direction. Question No. 22 Structural composites are now used in significant quantities in military aircraft and aports equipment, e.g. skis, tennis rackets. They are almost always more expensive per pound than the material they replace. Give a few examples of specific products or parts using composites and explain why the composite does a better job. If the Hall reduction cell operates with 95% current efficiency, calculate the electrical cost to make one pound of aluminum, assuming that the cost of power is $0.01 K-W-H. What factor limits the rate at which aluminum is made in the Hall cell? M Al = 27 1 pound = 454 gms Question No. 23 Define the following terms: a) Austemper b) Martemper c) Normalize d) Monotectic Reaction e) Rimmed Steel f) Luders bands g) Hot shortness h) Investment casting i) Hall process j) Kroll process Question No. 24 Describe and compare the processes that occur when the martensitic phase of Fe-0.6%C and Fe-0.6C-3%Mo are tempered. Include a comparison of hardness changes. Question No.25 a) Define the discipline of mechanical metallurgy. b) What is meant by a constitutive equation for a material? What is its form for a homogeneous isotropic body (elastic continuum). c) Why is the tensile strength so useful in testing materials? d) Explain in detail what material characteristics determine the energy absorbed in a notched-bar impact test. It measures chiefly what attribute of the material? Question No. 26 What is meant by hardenability in steels? How is hardenability determined? What effects do the following have on hardenability and why. a) Rate of cooling b) Austenite grain size c) Carbon content d) Cobalt addition e) Other alloy additions as chromium or nickel Question No. 27 From mass spectrometry, the following data are obtained for the sulfur vapor species and their equilibrium vapor pressures over pure liquid sulfur: Molecule P(473K)atm P(673K)atm S 2 1.4*10 -6 9.40*10 -3 a) Using the Gibbs-Helmoltz relations, calculate the values of ΔH and ΔS for the reaction. 2S(l) = S 2 (g) b) Calculate the equilibrium P S2 at 800K over a phase in which the sulfur activity (relative to pure liquid sulfur standard state) equals 10 -3 . Question No. 28 a) Draw isothermal sections at temperatures above, at and below a ternary eutectic isotherm (isobaric system). b) What is the fundamental reason for the phase diagram “rule” that in a binary, isobaric, two-component diagram, the metastable extensions of the line separating one and two phase regions must extend into a one phase field? Question No. 29 a) Using the methods of quantitative metallography how would you determine the solubility of Cu in Ag (simple eutectic) at several temperatures below the eutectic? Describe two methods, one using alloys well into the two phase field, and one with alloys near the phase boundary. b) Determine the grain size of the alloy? Give two methods. Question No. 30 Sketch an Ellingham diagram on which you show lines for the formation of the following oxides. Cu 2 O FeO SiO 2 Cr 2 O 3 Al 2 O 3 CO (from C) CO 2 (from CO) H 2 O (from H 2 ) a) Indicate on the graph the location of the oxides that might be reduced with CO/H 2 mixtures. b) Indicate how you would decide whether or not an oxide might be reduced carbothermically. How do you estimate the critical temperature? c) How can you use electrochemical principles to assist carbothermic reduction (Hall cells)? d) How can you take advantage of the stability of volatile halides to promote carbothermic reduction?(Kroll process). Question No. 31 How may the yield strength of a pure metal be increased without the addition of alloying elements? Using simple arguments, discuss the mechanism(s) responsible for the increase in strength. Question No. 32 Sketch a schematic Charpy curve typical of low alloy ferritic steels. Show both energy absorbtion and fracture appearance versus test temperature. Sketch the same curves for a precipitation hardened aluminum alloy. How and why do the curves differ? Question No. 33 A sphere of densely compacted NiO is reduced in pure H 2 with the formation of a porous nickel product having the same external radius R0 as the original sphere. Suppose that the system exhibits “mixed control” by gaseous transport through the product layer and a chemical reaction at the reaction interface. Derive expressions to describe the progress of the reaction as a function of time. Define all the necessary physical properties and rate constants carefully. State all assumptions. If you obtained a graph of sample weight versus time in the laboratory, how would you analyse the data to teat your model; i.e. what type of coordinates would you cry in a modified graph? Question No. 34 Neutron diffraction shows that hydrogen dissolves in the octahedral sites of fcc palladium. Assuming only nearest neighbor interaction between the hydrogen atoms in solution, relate the pressure of hydrogen to the equilibrium amount of hydrogen in solid solution in palladium. The rotational partition function is 2 2 2 8 h AkTπ , the translational (Pf) = 2 3 2 2 2 V h mkT ? ? ? ? ? ? ? ? π and the vibrational (Pf) = ? ? ? ? ? ? ?? ? ? ? ? ? ? ? kT hv kT hv exp1 2 exp . Use the canonical ensemble or the grand canonical ensemble. Compute the critical temperature. Tc, and composition cθ , for phase separation. Sketch the pressure-composition isotherm for T>Tc; T=Tc and T<Tc. What is the sign of the interaction parameter W HH for phase separation? Question No. 35 Consider the solidification of an alloy of composition Co indicated on the phase diagram below: Where m L = slope of the liquidus and K = equilibrium distribution coefficient = C S /C L (a) Using the phase diagram data and assuming steady state growth conditions, no mixing and equilibrium partitioning, develop the stability relation for planar front growth. (b) For the one-dimensional case, present schematic temperature vs. position and composition vs. position diagrams for the stable plane front condition. (c) Prepare a temperature-position diagram which shows constitutional supercooling. Question No. 36 The following questions should be answered with rigor. (a) Is it correct to say that the Gibbs energy of a system always decreases as it undergoes change? Why? Present a statement consistent with thermodynamics. (b) Is it correct to say that the activity of a component must be the same in two mutually equilibrated phases? Why? Formulate an acceptable statement. (c) Can the entropy of an adiabatic system decrease? If so, indicate how you would observe (measure) the entropy change. (d) Can CP be less than CV for a stable system? Support your answer. (e) Is it necessary to have an atomistic model to apply thermodynamic arguments? Must all atomistic models be consistent with thermodynamics. Question No. 37 Two slabs of Fe-C alloy containing 0.8 wt% C are decarburized in flowing pure hydrogen at 850C and at 1000C For the steady-state condition prior to completion of the decarburization: (a) Carefully draw schematic concentration profiles for carbon for reaction at 850C and at 1000C. (b) What consideration(s) are used to decide these profiles? (c) Write an equation for the carbon concentration profile at 1000C. (d) Would a cylinder of alloy yield the same depth of decarburization at a given time as the slab? Why? Question No. 38 For many substances, m f T HΔ 2 cal/degree mole (Richard’s rule). (a) Estimate the free energy of solidification for pure copper at its maximum undercooling, = 236C. max TΔ (b) Assuming homogeneous nucleation occurs at the maximum undercooling condition, indicate how one could calculate the liquid-solid surface energy of copper. Question No. 39 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. 40 (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 + O 2 (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/CO 2 /H 2 /H 2 ) with unit carbon activity. Explain these results.