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Unformatted text preview: Study Guide for the E45 Final Examination, Fall 2008 Study Guide E 45 FINAL Examination Friday, December 19, 2008 5 PM — 8 PM Room 0001 Pimentel Hall Policy: Your Final Exam will be a closed book exam. No reference materials will be permitted. No calculators will be permitted. No Blue Books will be permitted. You should bring a supply of sharpened pencils (two colors will be helpful), eraser(s), and a straightedge (not the edge of your calculator). All answers must be written in the spaces provided on the Exam. Students requiring special arrangements must see the instructor before December 12th. The Final counts for 300 points out of the 1000 points on which your course grade will be based. Preparation: Memorization of facts is futile. Understanding of concepts is key. Posted solutions to this year's homework assignments and midterms set the standards of scholarship expected in E45. Use them to calibrate your level of understanding of the concepts covered in class this year. There are four Final Exams in this binder that can be used to prepare for this year ’s Final Exam. It will be obvious from these exams that both breadth and depth of course coverage changes from year to year. Your guide for this year's exam should be your class notes. Patience: Most errors occurring on examinations are committed when students answer what they think is the question, but the actual question is completely different. This most likely comes from familiarity with the “practice” exams from prior years, where the problems might appear to be the same at the outset, but end with a different question. Best practice is to read and understand the question(s) thoroughly before beginning any answer(s). And please follow instructions. When the problem calls for you to “sketch and label,” your answer must show a labeled sketch, not a verbal description, to get full points. Here is a plot summarizing performances since the year 2000. Prior Perfor mance: 167 158 164 175 78 75 2000 61 64 2001 MT01 Average 60 59 2005 60 63 2007 MT02 Average 45 56 2008 FINAL 320 280 240 200 160 120 80 40 0 UNIVERSITY OF C ALIFORN IA College of Engineer ing Department of Materials Science and Engineer ing Professor R. Gronsky Fall Semester 2001 ENGINEERING 45 _____________________________________________________________ (Please PRIN T your Name here… …and your SID nu mber here) Problem # Possibl e Score Initials 1 2 3 4 5 6 Total 50 50 50 50 50 50 300 Please READ Today is T uesday, December 18th, 2001, and this closed book exam is scheduled t o last fr om 5—8 pm, allowing you an aver age of 30 minutes per pr oblem. You must wor k independently, and no text books, r eference mater ials, calculat ors, cr ib sheets, or cell phones are permitted. Due t o the large class size, there can be no questions asked dur ing the exam. If you find err ors or choose t o call out options, please comment in wr iting. Please use only the pages given here. Draw, write, or other wise ent er your answer s using the spaces pr ovided. Final Exam Initia ls: __________ Questi on 1 (10 pts) Bonding, Cry st al St ruct ure and C ry st al Defects Dual Nob el Laureate and American chemist Linus Pa uling defined electronega tivity a s the ability of an a tom to “attra ct electrons to itself.” Expla in, using your und erstanding of the concep ts of chemical bonding, w hy metallic elements tend to ha ve low er values of electronegativity, w hile nonmetallic elements ha ve hig her va lues. See data in the App endix for additional information. a. (10 pts) b. Using your und erstanding of the concep ts of chemical bond ing, exp lain w hy metals ha ve “luster” while ceramics do not. Be sure in your expla nation to includ e the role of visible lig ht in p rod ucing a lustrous app ea rance. Page 2 of 20 Final Exam Initia ls: __________ (20 pts) c. The meta llic sup erconductor w ith the highest critical transition temp erature (Tc = 23K, rep orted in 1974) is d escrib ed as ha ving a n A15 “strukturb ericht,” with atoms at the following p ositions in a cubic lattice. Niobium at 1 1 ,0, ; 4 2 11 , , 0; 24 0, 11 ,; 24 3 1 ,0, ; 4 2 13 13 , , 0 ; a nd 0 , , 24 24 Germa nium at 0,0,0; and 111 ,, 222 Sketch and label a ll Nb and Ge a tom p ositions in both “p erspective” a nd “projection” d raw ing s of a cubic unit cell, using the templates below. z y y x ! perspective projection x ! ! What is the Bra vais lattice? _________________________________ What is the motif? ________________________________________ What is the chemica l formula for this sup ercond uctor? ____________ Page 3 of 20 Final Exam Initia ls: __________ (10 pts) d. Using the attributes of a line direction vector (! ) and Burg ers vector (b) associated with disloca tions in a crysta lline lattice, expla in how a dislocation loop ca n have both edg e and screw chara cter. Label both b and ! in ea ch ca se. dislocation loop slip p lane Now refer to the follow ing d rawing and explain the significance of the la rg e points app earing at the intersection of the two misoriented sub- lattices. What is the na me of this construction? 22.6° What is the va lue of " a ssociated with this construction? What two-d imensiona l “d efect” is this construction norma lly used to d escrib e? Expla in. 11.3° Page 4 of 20 Final Exam Initia ls: __________ Questi on 2 (30 pts) Phases, Eq uilibria, and Kinetics Construct the P t-Ag eq uilib rium pha se d iagra m on the temp late below using the follow ing information. Lab el all p hase field s and reaction isotherms. a. 1800 1600 1400 T (°C) 1200 1000 800 600 Pt 10 20 30 40 50 60 70 80 90 Weight Percentage Ag Ag • • • • • • • Platinum melts at 1772 °C. Silver melts at 962°C. At 1400°C, an alloy of 70% Pt exhibits equa l fra ctions of a liquid pha se, containing 45% Pt, and a solid # p hase, containing 95 % P t. At 1100°C, an alloy of 70% Ag exhibits equa l fractions of a liquid pha se, containing 85% Ag, and a solid $ pha se, conta ining 55 % Ag. There is a peritectic rea ction isotherm a t 1186°C where $ phase of 42.4% Ag “melts nea rby” to form # pha se of 10.5% Ag and liquid of 66.3% Ag. The solub ility of silver in the # p ha se is only 3% at 600°C and at 1700°C. The solub ility of pla tinum in the $ pha se is 20% at 700°C. Page 5 of 20 Final Exam Initia ls: __________ (20 pts) b. Two different samp les of the same silver- rich a lloy conta ining 20% P t a re subjected to two different thermal treatments, b oth beg inning w ith a solutionizing anneal at 800°C. One samp le is cooled very slow ly to room temp era ture, the other is rapidly quenched to room temp erature, then aged at 300°C for two hours. Sketch in the following pa nels the microstructure tha t w ould evolve in both cases, b eginning w ith the single-pha se p olycrystalline structure shown. Clea rly lab el a ll pha ses using color-coding to cla rify d ifferences. D escrib e the morphologies of all pha ses, ma king sure to d istinguish the cond itions und er which heterog eneous nucleation at g rain bounda ries mig ht be favored. Slow cool Quench and age Page 6 of 20 Final Exam Initia ls: __________ Questi on 3 (10 pts) Prop ert ies of St ruct ural Mat erials The stress-stra in plot shown here was d etermined from a unia xia l tensile test of a w rought magnesium alloy. Lab el clea rly a nd directly on this p lot the follow ing para meters: Yield strength, Ultima te tensile streng th, F racture Strength, M odulus of Elasticity, a nd D uctility. a. Stress Strain (10 pts) b. How w ould you use the above da ta to estimate the “toughness” of this magnesium a lloy? Exp lain your answ er b y first defining “toughness,” then rationa liz ing why your estimate is a valid a nd a cceptable one. Page 7 of 20 Final Exam Initia ls: __________ (10 pts) c. Data ob tained from tw o d ifferent thermosetting polymers a re plotted b elow. 30 Which of these two materials ha s the g rea ter fra cture toug hness, and w hy ? 25 Fracture 20 Stress 15 (MPa) 10 5 Petra-B Petra-C 0.5 1.0 1.5 2.0 Flaw size (mm) If the maximum flaw size that could b e tolera ted in an eng ineering applica tion of these p olymers wa s set a t 1 mm due to the visua l a cuity of the inspector, which of these tw o options would you sp ecify for the applica tion, and why? Page 8 of 20 Final Exam Initia ls: __________ (20 pts) d. Expla in why it is g enerally p referred to use fib er-reinforced composites when they a re load ed und er isostrain, rather than isostress, conditions? R efer to the follow ing plot for illustra tion, and exp lain your answ er. Glass fiber 1000 Stress (MPa) 500 Epoxy matrix 0.01 0.02 Strain Page 9 of 20 Final Exam Initia ls: __________ Questi on 4 (10 pts) Prop ert ies of Elect ronic, Optical and Mag netic Mat erials Use simp le sketches to illustrate the differences betw een cond uctors, semiconductors, and insula tors, ba sed upon their ba nd structures. a. (10 pts) b. Gallium a rsenid e is a compound semiconductor with a structure defined b y a face- centered-cubic Bra vais lattice, a nd a two-atom motif: Ga at 0,0,0 a nd As at 1/ 4, 1/4, 1/4. D raw the contents of the unit cell in b oth p ersp ective and projection view s. z y y x perspective projection x Is stoichiometric Ga As an n- typ e or a p-typ e semicond uctor? Expla in. Page 10 of 20 Final Exam Initia ls: __________ (20 pts) c. Refer to the follow ing schematics of two different typ es of optical fib ers. Note that they a re ob viously d istinguished b y the rela tive dimensions of the “core” and the “cladding.” See da ta in the Appendix for add itiona l informa tion. Answer all q uestions b elow. n x n x Complete the p lots of the ind ex of refra ction (n) vs dista nce across the full diameter of the fib er for the ca se of the “multi- mod e, g rad ed-index” fib er on the left, a nd the “sing le- mod e” fib er on the right. Be p recise, esp ecially w ith the ab scissa . How is an op tical (light) sig nal preserved during tra nsit along the full length of an op tical fib er tra nsmission line? Explain. Now expla in the relationship b etween ind ex of refra ction and w idth of the core in estab lishing sing le mod e vs multi- mod e transmission. Page 11 of 20 Final Exam Initia ls: __________ (10 pts) d. The p rima ry d ifference b etw een ferromagnetic a nd ferrimagnetic materia ls can b e expressed in this wa y: ferromagnetism derives from para llel spin pairing, while ferrimagnetism d erives from antip arallel sp in pairing. Expla in and show with a sketch how these seemingly opposite phenomena result in a net magnetic moment. What is the orig in of the “sp ins” tha t a re paired? Page 12 of 20 Final Exam Initia ls: __________ Questi on 5 (30 pts) Environment al Degrad ation of Materials The d raw ing show n here illustra tes a ga lvanic cell betw een F e and Cu, both immersed in one mola r solutions of their resp ective ca tions, sepa rated b y a semi-p ermeab le memb rane. Note data in the Appendix for add itional information. Identify the anod e, and w rite the anode reaction. a. Identify the ca thod e and w rite the cathod e rea ction. Show the direction of electron tra nsp ort through the conductor connecting the two electrod es, a nd the d irection of ionic transport throug h the electrolytes on both sid es of the separa ting memb rane. What happ ens to the corrosion rea ction when the memb rane is removed? Expla in. What happ ens to the corrosion rea ction when the b ottom end s of the electrod es a re “short- circuited” by physical contact b eneath the fluid level of the electrolyte? Expla in. What happ ens to the corrosion rea ction when the electrolyte is d ra ined a nd repla ced w ith fresh wa ter? Exp lain. Page 13 of 20 Final Exam Initia ls: __________ (10 pts) b. Corrosion ca n a lso occur b y the following ga seous red uction rea ction O2 + 2H2O + 4e # 4OH " " in a n “oxyg en concentra tion cell.” Consid er now how this mod el rela tes to a brass comp onent that is pa rtia lly immersed in salt water. Identify the anod e, and w rite the a nod e reaction. Identify the ca thod e and w rite the cathod e reaction. What is corrod ing ? Expla in. (10 pts) c. Expla in the p rinciple behind corrosion p rotection using a “sacrificial” anode, b y describ ing how to p rotect steel oil tankers against corrosion on the hig h sea s using z inc meta l. W hat sp ecifica lly is done w ith the Zn to make it p rotect the steel ta nker hull? Be sp ecific. Page 14 of 20 Final Exam Initia ls: __________ Questi on 6 (10 pts) Mat erials Selection and Design A matched set of eutectoid steel b ea ring housings wa s heat- trea ted in a ba tch process. After the housing s w ere simulta neously extra cted from the furna ce and quenched, the furnace wa s switched off to save energ y. One of the housings wa s soon decla red °C “lost,” but eventually found, two 800 days la ter, unfortunately still ! 727° lying in the now- cool furna ce. 700 How w ould you expect the microstructure of the orphan bea ring housing to d iffer from the other housing s? Expla in. 600 500 400 300 200 100 0.1 215° a. coarse pearlite fine pearlite upper bainite ! " + Fe3C lower bainite martensite sec 1 10 min 102 103 hour 104 day 105 time (sec) Is there any way to salvag e the orphan housing, instead of send ing it ba ck for re-melt? Expla in. (10 pts) b. A cera mic oxid e of composition Li2O•Al2O3•4SiO2 (ca lled #-spod umene) is molten above 1550 °C, and undergoes a p recipitation reaction at approximately 1050°C, g enerating a crystalline phase within a n a morphous matrix. Use this information to d esign a process for ma king a strong electrica l insulator with a complex g eometry via the “g lass- cera mics” route. Show a schematic tempera ture-time p lot to illustra te your answ er. Page 15 of 20 Final Exam Initia ls: __________ (10 pts) c. An alterna tive method for producing cera mic ma teria ls in comp lex shap es is called “sintering .” Expla in wha t is mea nt b y sintering , calling out specifica lly the forma tion of a g reen compact on the wa y to the final sintered product for use as an orthop edic implant. How ca n porosity be controlled d uring sintering to match the natura l p ore structure of cortical b one? (10 pts) d. The choice of materials for a ny engineering applica tion should a lways be based up on their life- cycle, including the ea se w ith which they can b e recycled beyond their origina l p rod uct applica tion. Comment on the issue of recycling for the following eng ineering ma terials used in consumer app lia nces: polymers (thermosetting vs thermopla stic); composites ( fib er vs aggrega te); and monolithic metallic a lloys. Page 16 of 20 Final Exam Initia ls: __________ (10 pts) e. A M EMS (microelectromechanical system) a rray calls for a piezoelectric actuator mad e from ba rium tita nate, a compound tha t exists in two polymorphic forms. Above the critical temp erature ( Tc) of 120°C, Ba TiO3 ha s the cubic structure show n here in a [001] projection. Below 120°C, the equilib rium structure is tetragonal, and is associated with a spontaneous polarization, making it a ferroelectric material. Expla in how p iez oelectric a ctuation is a chieved using Ba TiO3. What is the crystal structure ( cubic or tetragona l) of the a ctive component, and wha t ca uses the actua tion? Page 17 of 20 Final Exam Initia ls: __________ Appendi x Work sheet, Not es Page 18 of 20 Final Exam Initia ls: __________ Appendi x Periodic Table, Relevant Phase Diag rams 1537° 1495° 0.11 0.52 0.16 "-Fe #-Fe (Austenite) 2.11 L 1400 1394° 1200 1148° 4.30 T (°C) 910° 800 600 400 200 0 !-Fe (Ferrite) Fe3C (Cementite) 0.021 0.77 727° 1000 Fe 1.0 2.0 3.0 4.0 5.0 6.0 6.67 wt % C L L + Al2O3 T SiO2 + L L + mullite Al2O3 + mullite SiO2 + mullite SiO2 Al2O3 Page 19 of 20 Final Exam Initia ls: __________ Appendi x Dat a Table I: Relative Elect ronegati vity of Selected Elements Element Electronegati vity Fe Cu Au C O F 1.8 1.9 2.4 2.5 3.5 4.0 Table II: Gal vanic Series i n Sea water Material Noble (Cathodic) (Anodic) Active Pt Au Graphite Titanium Ag Stainless steel Nickel Bronz e C op p e r Bra ss Sn Pb Pb-Sn sold er Fe 2024 aluminum a lloy Cd Al Zn Mg Table III: Refracti ve Index for Optical Materials Average Refractive Index (n) Material Quartz (SiO 2) Corundum (Al2O 3) Periclase (MgO ) Silica Glass (SiOx) Borosilicate Glass Soda-L ime-Silica Glass 1.55 1.76 1.74 1.46 1.47 1.51 Page 20 of 20 Professor R. Gronsky UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science & Engineering Fall Semester, 2005 N ame : ( P le a s e p r i n t) ENGINEERING 45 FINAL EXAM Monday, December 19, 2005, 5:00 PM — 8:00 PM INST RUCTIONS GR ADING Problem # 1 2 3 Possible Points 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 300 Your Score LATTICE seating.................. Please be seated with occupied seats to your front and back, vacant seats to your left and right. CLOSED BOOK format...... All you need are writing instruments and a straightedge. Please store out of sight all books, reference materials, calculators, PDAs, cell phones (OFF), and iPods. 4 5 6 7 8 NO DISRUPTION rule......... Questions cause too much of a disturbance in a crowded examination room. Include any concerns or alternative interpretations in your written answers. 9 10 11 12 13 14 PROFESSIONAL protocol... Engineers do not cheat on the job; there will be no cheating on this examination. 15 TOTAL Do n o t o p e n u n t i l “START” i s a n n o u n c e d . E 45 F INAL '05 In i t i a l s: 1. (20 points) Atomic Bonding (a) (10 points) Your friend is a wealthy venture capitalist who just received a proposal to fund a project at the $1M level, and because of the technical nature of the proposal, she has called you in for advice. The author of the proposal claims that the next great innovation in automotive design is a new class of "nanowindows" that "bend and not break", protecting the occupants in the event of a head-on collision, "a thousand times better than tempered glass." The windows would be made of "ductile titanium" using an innovative new self-assembly nanotechnology method that "has already been proven for titanium" but needs development for window applications. Using your knowledge of atomic bonding, what would you advise regarding the feasibility of titanium nanowindows, and why? (b) (10 points) Linus Pauling1 proposed an equation to estimate the fraction (F) of ionic character of a single bond between atoms A and B having electronegativities xA and xB respectively, with the following form Based upon this formula, the fraction of ionic character in the single H—C bond is 4%, and in the single H—O bond is 39%. Using your knowledge of atomic bonding, how would you rationalize the difference in properties between polyethylene ([-C2H4-]n) and water (H2O) at room temperature, incorporating F into your reasoning. F = 1 − e− 4 (xA −xB ) . 1 2 1 L. Pauling, Nature of the Chemical Bond, 3rd. Ed., Cornell University Press, (1960). Pro ble m 1 o f 15 E 45 F INAL '05 In i t i a l s: 2. (20 points) Crystal Structure Alloys of Au and Cu exhibit a range of ordered structures, one of which is designated L10 in Strukturbericht notation, where L is reserved for "superlattices." The specific alloy with this structure is the AuCu type I superlattice. It has tetragonal symmetry, with a = 0.398 nm and c = 0.372 nm. Gold atoms reside at 0,0,0 and ½, ½, 0; Cu atoms at 0, ½, ½, and ½, 0, ½. (a) (10 points) Sketch the unit cell and its c-axis projection, labeling the positions of all atoms in the projection. (b) (10 points) Now show and clearly label on another sketch how this crystal structure can be described by a simple tetragonal Bravais lattice. Specify the motif appropriate to this choice of lattice. Pro ble m 2 o f 15 E 45 F INAL '05 In i t i a l s: 3. (20 points) Lattice Planes Use the appropriate Miller index notation or Miller-Bravais notation to identify the following lattice planes (a, b, and d) or symmetry-related sets of lattice planes (c and e). Answers must be written in the boxes provided. z z z y y y x x x (a) (4 points): (b) (4 points): (c) (4 points): c c a3 a3 a2 a2 a1 (d) (4 points): a1 (e) (4 points): Pro ble m 3 o f 15 E 45 F INAL '05 In i t i a l s: 4. (20 points) Lattice Directions Use the appropriate three-index notation for cubic systems or four-index notation for hexagonal systems to identify the following lattice directions (a, b, and d) or symmetry-related sets of directions (c and e). Answers must be written in the boxes provided. z z z y y y x x x (a) (4 points): (b) (4 points): (c) (4 points): c c a3 a3 a2 a2 a1 (d) (4 points): a1 (e) (4 points): Pro ble m 4 o f 15 E 45 F INAL '05 In i t i a l s: 5. (20 points) Crystal Defects (a) (10 points) Point defects can "cluster" to form line defects, such as in the example illustrated here. A perfect crystal (i) is an idealization; in reality, all crystals have a finite vacancy concentration (ii). With sufficient thermal activation, vacancies can diffuse and condense onto a single plane (iii), lowering the energy of the crystal by reducing the total number of unsatisfied bonds. As the atoms on either side of this vacancy cluster relax, the structural configuration of a "dislocation loop" becomes evident (iv), with extra half planes (⊥) bordering the loop from above and below in this cross-sectional view. Imagine now that the dislocation loop is subjected to an external loading condition that exceeds the critical resolved shear stress for dislocation motion. Using your knowledge of dislocation slip systems, show and explain what happens to this dislocation loop. i ii iii iv (b) (10 points) By extension of the model above, line defects can "cluster" to form planar defects. Show with a sketch and explain how a planar defect might result from the condensation of dislocations. In your explanation, cite the driving force for such dislocation behavior. Pro ble m 5 o f 15 E 45 F INAL '05 In i t i a l s: 6. (20 points) Phase Equilibria Bronze is an alloy of copper and tin that is often cast (directly solidified in molds of complex shapes) for hydraulic valves. The phase diagram [Metals Handbook, 8th Ed., American Society for Metals, Metals Park, Ohio, (1973)] shows that it is a relatively complex system because of a preponderance of peritectic reactions. (a) (10 points) Describe the equilibrium solidification of a 50:50 alloy when cast as a liquid at 800°C, including all phases present as each reaction isotherm is crossed, finishing at room temperature. T (°C) 1100 1000 900 800 700 600 500 400 300 200 100 189° 799° at % Sn 10 20 30 40 50 60 70 80 90 1085° L 756° ! " 586° 520° # ' $ 640° & 415° 350° % 186° 232° %’ !-Sn 0 Cu 10 20 30 40 50 60 70 80 90 Sn wt % Sn (b) (10 points) An alloy of 24.6 wt%Sn (the eutectoid composition) is cooled from the β single phase field, crossing the eutectoid reaction isotherm at 586°C to produce the lamellar α + γ eutectoid decomposition product as shown in the sketch below (high magnification of a single grain boundary region). Note that the α phase appears dark in this image, and it is the minor volume fraction phase as expected from the lever rule. From this initial microstructure, consider what happens when the alloy is further cooled through the two eutectoid isotherms at 520°C and 350°C on the way to room temperature. Sketch on this same template the room temperature microstructure, retaining the same contrast (dark) for the α phase. Pro ble m 6 o f 15 E 45 F INAL '05 In i t i a l s: 7. (20 points) Heat Treatment Note the TTT curve shown here and the phase diagram for an Fe-C alloy (to 6.67 wt.% C). T (°C) 1100 1000 900 800 700 600 500 400 300 200 100 0 0.1 Ms 1 sec 1 min 1 hour 2 3 T (°C) 1600 1500 " + Fe3C 727°C Coarse pearlite " 1538° 1495° # 1400 1394° 1300 1200 1100 1000 900 800 700 0.02 0.77 " 600 500 400 300 200 910° 727° ! 2.11 1148° L 1227° 4.30 6.67 "+ ! + Fe3C !+ Fine pearlite Bainite Fe 6.67 Cementite 3 C 1 day 100 0 Fe 1 2 3 4 wt % C 5 6 Fe3C 1 10 10 10 time (seconds) 10 4 10 5 (a) (10 points) What alloy composition does this TTT curve represent? Explain (what are your clues?), and locate it as a vertical line on the phase diagram. (b) (10 points) Can you devise a sequence of isothermal heat treatments for this steel that would generate a microstructure consisting of only proeutectoid cementite and martensite? Explain, and show the cooling path(s) directly on this TTT curve. T (°C) 1100 1000 900 800 700 600 500 400 300 200 100 0 0.1 Ms 1 sec 1 min 1 hour 1 day " 727°C Coarse pearlite " + Fe3C "+ ! + Fe3C !+ Fine pearlite Bainite Fe 3 C 1 10 102 103 time (seconds) 104 105 Pro ble m 7 o f 15 E 45 F INAL '05 In i t i a l s: 8. (20 points) Mechanical Properties Consider the following stress-strain curve for an aluminum alloy. (a) (10 points) Show directly on this plot the region of the curve corresponding to "elastic" behavior in the Al alloy sample. Explain any uncertainties. Stress UTS YS Fracture What is occurring atomistically over this portion of the curve? Explain. 0.002 Strain (b) (10 points) Explain what is meant by this statement: "Uniform strain of the sample occurs up to the maximum tensile load." In your response, explain what you think "uniform strain" means, and why it is limited in this way, noting as well what happens when the sample continues to strain beyond its maximum tensile load. Pro ble m 8 o f 15 E 45 F INAL '05 In i t i a l s: 9. (20 points) Ceramics and Glasses (a) (10 points) A glass-ceramic labware vessel is fabricated according to the temperature-time processing path shown here. Note that there are two primary phases to the process known as "formation," in which the part takes on its final macroscopic shape, and "crystallization," in which the part assumes its final microstructure. Explain both of these phases, citing specifically what happens at each of the horizontal plateaus during the processing cycle and why they occur at the temperatures indicated. Formation Crystallization Tm Temperature !Tm !Tm time (b) (10 points) Although the process above begins with melting, it is not always feasible to form ceramic materials into complex shapes by melt-processing. The most popular alternative is known as sintering. Particles (powders) of ceramic feed stock are compacted and heated to approximately ⅓ to ½ of the melting point, usually under pressure, and after sufficient time, a solid product results. Unfortunately, the result is not always 100% dense, due to trapped porosity, as shown (dark areas) in the micrograph of sintered SiC at right. Using your understanding of diffusion processes in solids with particular attention to microstructure, comment on how such porosity might be reduced. Is it possible to achieve 100% density? Explain. Pro ble m 9 o f 15 E 45 F INAL '05 In i t i a l s: 10. (20 points) Polymers (a) (10 points) There are a number of thermoplastic polyesters, such as the fiber known by the trade name Dacron™, the film known by the trade name Mylar™, or PET (polyethylene-terephthalate), which is the polymer backing used in magnetic recording tape. These polyesters are based upon the mer shown here. H HO C H H C H OH HO C O C HO O Is polyester the result of addition polymerization or condensation polymerization? Explain, showing how the mer above is adapted (sketch the result) for expression as a polymer with any arbitrary degree of polymerization, n. (b) (10 points) Polymers can crystallize, too, which means that they can be described by a lattice and motif, and crystalline polymers most readily form from the ordered arrangement of simple backbone chains, such as pure polyethylene. However, when side groups are attached to the backbone (such as CH3, making polypropylene), crystallization is more difficult. Moreover, the arrangement of the side groups also matters. Isotactic polypropylene (CH3 groups are regularly arranged on the same side of the backbone chain) can be 90% crystalline, but atactic polypropylene (CH3 groups are irregularly arranged on either side of the backbone chain) can be 0% crystalline. In general, as the side groups become larger and more irregularly arranged, crystallinity decreases, while rigidity and melting point increases. Explain, citing the effect of side groups in both deformation behavior and melting behavior. Pro ble m 10 o f 15 E 45 F INAL '05 In i t i a l s: 11. (20 points) Composites (a) (10 points) Property averaging for fiber reinforced composites parses into two limiting cases, one knows as isostrain, the other isostress. Explain these differences from the perspective of loading condition and effectiveness of the fiber reinforcement phase. Property XC 0 0.5 vf 1 (b) (10 points) There are two fundamentally different design philosophies employed in the development and utilization of fiber-reinforced composites at high stress levels. One applies to composites having a compliant matrix phase, such as polymer-matrix composites or metal-matrix composites, and it stipulates that the interfacial bonding between the fibers and the matrix should be "perfect," or relatively very strong. The other applies to composites with a brittle matrix, such as ceramic-matrix composites, and it stipulates that the interfacial bonding between the fibers and the matrix should be "imperfect," or relatively weak. Explain these differences, comparing and contrasting the effects of these two design philosophies on the fracture toughness behavior of the composite in both cases, citing the relevant microstructural origins of the observed or anticipated differences. Pro ble m 11 o f 15 E 45 F INAL '05 In i t i a l s: 12. (20 points) Electronic Properties (a) (10 points) Consider that metal B is a much better conductor than metal A, and the two must be alloyed for an engineering application as an electrical spring contact. What happens to the electrical properties when the two metals are alloyed? Complete the plot of electrical resistivity as a function of composition for the resultant A-B alloy begun here. Explain your result. ! (ohm-m) 0 50 xB 100 (b) (10 points) Barium titanite (BaTiO3) is a ferroelectric below 120°C, the temperature at which with a cubic to tetragonal phase transformation occurs, as shown schematically for a single unit cell (Ba2+ at the corners, O2- at the face centers, Ti4+ at the body center) below. T > 120°C T< 120°C In modern engineering applications, "perovskite alloys" of PbTiO3 and PbZrO3 known as lead zirconate titanate or PZT, with transformation temperatures near 200°C, are specially processed to maximize their "piezoelectric" performance. The process is called "poling" and it begins with the candidate ferroelectric perovskite powders immersed in a strong electric field while compacted and sintered. Explain how this electrical poling treatment works, and how it results in piezoelectric behavior. Pro ble m 12 o f 15 E 45 F INAL '05 In i t i a l s: 13. (20 points) Semiconductors (a) (10 points) Explain, using the following schematic of an energy band diagram, the effect of adding boron (Group III) and phosphorus (Group V) together, in small dopant concentrations, to silicon. Assuming the resultant material has a uniform distribution of both dopants, would the resulting material still be a semiconductor? If so, would it be intrinsic or extrinsic? Explain. bottom of conduction band E = Eg top of valence band E=0 (b) (10 points) The plot of ln (conductivity) as a function of (1/T) for the above doped semiconductor is shown here. What can be concluded from this plot? What does the change in slope indicate? Can any quantitative information be extracted from the slope or the change in slope? Explain. ln ! 1/T Pro ble m 13 o f 15 E 45 F INAL '05 In i t i a l s: 14. (20 points) Magnetic and Optical Properties (a) (10 points) On the axes shown to the right draw two superimposed B-H loops, comparing and contrasting a "hard" magnetic material with a "soft" magnetic material, the latter having precisely half the remanent induction of the hard magnet. Label both hard and soft magnets, and label the remanent induction and the coercivity in both cases. B H (b) (10 points) In the search for ever-higher magnetic recording bit densities, the trend to date has been to seek materials with increasingly higher coercivity. Explain this trend. Why do you suppose higher coercivity is attractive for this engineering application? Can you imagine higher coercivity in magnetic recording media being unattractive for any reason? Explain. Pro ble m 14 o f 15 E 45 F INAL '05 In i t i a l s: 15. (20 points) Environmental Degradation (a) (10 points) The galvanic couple at right consists of equivalent volumes of iron and copper connected electrically by aluminum wiring and immersed in a saline solution. Describe the resultant process of galvanic corrosion. What is the anode reaction? What is the cathode reaction? What is corroding? C o pp e r I ro n (b) (10 points) The illustration at right shows a segment of a copper cooling coil inside of an aluminum housing that comprises a portion of a refrigeration unit. Moisture condensation drips from the copper coils onto the aluminum shelf below and causes noticeable corrosion pitting, despite the absence of a continuous electrolyte path between the dissimilar metals. The process is well known in the engineering profession, and has been called by many different names, including ion-exchange, charge-exchange, cementation, or immersion plating. Based upon your knowledge of galvanic corrosion, how would you explain what is happening here. Pro ble m 15 o f 15 UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science & Engineering Professor R. Gronsky Fall Semester, 2007 Please clearly PRINT your full NAME in this box. E 45 FINAL EXAMINATION Wednesday, December 19, 2007 5:00 PM — 8:00 PM Instr uctions LATTICE seating CLOSED BOOK format Please be seated with vacant seats to your left and right. Only writing instruments (pencils, pens, erasers) and a straightedge are permitted. Store ALL other materials out of sight. Silence your cell phones. No questions are allowed during the exam. Problem # 1 2 3 4 5 6 TOTAL Grading Possible Points 50 50 50 50 50 50 300 Your Score NO DISRUPTION rule Do not open until “START” is announced. Fall Semester 2007 Initials: __________ 1. (50 points) Selection & Design of Engineering Materials The micrograph shown to the right is from a conventional lowmelting-temperature lead-tin solder used to make electrical connections in microelectronic circuits. (a) (10 points) Apply some reverse engineering to identify the light phase and the dark phase in this micrograph. Be specific and articulate your reasoning. 5 μm 400 300 Light phase = Dark phase = °C 200 100 0 Pb 10 (b) (10 points) Show with a vertical line directly on the phase diagram at right the nominal composition of this solder. 13° 327.502° L+! ! 19 183° L 61.9 231.9681° L+" " 97.5 !+" ! Sn 20 30 40 50 60 wt % Sn 70 80 90 Sn Reference: Metals Handbook, 8th Edition, Volume 8, Metallography, Structures and Phase Diagrams, American Society for Metals, Metals Park, Ohio (1973) E45 Final Examination page 2 of 19 Fall Semester 2007 Initials: __________ (c) (10 points) In an attempt to develop an environmentallyfriendly lead-free solder, you investigate the ASM Metals Handbook to locate phase diagrams such as the one at right and discover that it might be possible to replace lead with gold. 1100 What nominal composition might you select as a candidate lead-free solder and why? 1000 900 800 700 600 500 400 °C 300 200 100 309° 231.9681° 0.3 10 252° 217° 280° 80 418° 86.2 490° 95.8 1064.43° L (Au) ! Sn " # $ % 0 Sn 10 Show your choice with a vertical line directly on the phase diagram at right. 20 30 40 50 60 wt % Au 70 80 90 Au Reference: Metals Handbook, 8th Edition, Volume 8, Metallography, Structures and Phase Diagrams, American Society for Metals, Metals Park, Ohio (1973) E45 Final Examination page 3 of 19 Fall Semester 2007 Initials: __________ (d) (10 points) Consider the challenge of selecting an electronic packaging material to mount the components of a laptop computer. The packaging must isolate all of the integrated circuits, solder connections, and supporting components without shorting, and must withstand the elevated temperature associated with a lithium-ion battery power source. Using the data at right, specify the BEST choice for this application, and justify your answer. Polymer ρ (Ω•m) κ (J/s•m•K) epoxy phenolic cellulose acetate polyester polyvinyl chloride nylon 66 acrylic polyethylene 1×105 1×109 1×1010 1×1010 1×1012 5×1012 5×1012 5×1013 2×1014 2×1015 2×1015 2×1016 0.52 0.22 0.26 0.19 0.14 2.9 0.21 0.33 0.12 0.19 2.2 0.24 (e) (10 points) In the spirit of environmental friendliness, how would your choice change if you added the requirement that the polymer be recyclable? Explain. polystyrene polycarbonate polypropylene PTFE E45 Final Examination page 4 of 19 Fall Semester 2007 Initials: __________ 2. (50 points) Mechanical Proper ties of Materials Stress ("), ksi Consider the results of standard uniaxial tensile tests on three different engineering materials, a ductile cast iron (3.65 wt% C, 2.5 wt% Si), a type 304 stainless steel (0.08 wt% C, 18 wt% Cr, 8 wt% Ni), and an AZ31B magnesium alloy (3 wt% Al) shown at right. (a) (10 points) How is the modulus of elasticity determined? Show directly on the curve at right and reconcile your approach with the tabulated value for cast iron. 120 100 80 60 40 20 0 304 stainless steel cast iron AZ31B magnesium 0 10 20 30 40 Strain (!), % elongation at failure (b) (10 points) How is the yield strength determined? Show directly on the curve at right and reconcile your approach with the tabulated value for stainless steel. Alloy E (psi) YS (ksi) UTS (ksi) Iron Mg-Al Steel 24×106 6.5×106 28×106 84 32 30 108 42 75 9% 15% 40% E45 Final Examination page 5 of 19 Fall Semester 2007 Initials: __________ (c) (10 points) How is the elongation at failure determined? Show directly on the curve at right and reconcile your approach with the tabulated value for the magnesium alloy. 120 100 cast iron Stress ("), ksi 80 60 40 20 0 304 stainless steel AZ31B magnesium 0 10 20 30 40 Strain (!), % (d) (10 points) Which of the three materials tested above demonstrates the highest toughness? Explain. elongation at failure Alloy E (psi) YS (ksi) UTS (ksi) Iron Mg-Al Steel 24×106 6.5×106 28×106 84 32 30 108 42 75 9% 15% 40% E45 Final Examination page 6 of 19 Fall Semester 2007 Initials: __________ (e) (10 points) When a material is tested for its "fracture toughness" the standard uniaxial tensile test is not used. Why? What is being tested to assess "fracture toughness" as distinct from "toughness." Qualitest™ Basic Pendulum Impact (BPI) Tester. www.qualitest-inc.com Reference: http:// E45 Final Examination page 7 of 19 Fall Semester 2007 Initials: __________ 3. (50 points) Electronic Proper ties of Materials (a) (10 points) Sketch in the labeled spaces below the relative locations of the valence band edge and conduction band edge for a typical metal, a typical semiconductor, and a typical insulator. Metal Semiconductor Insulator (b) (10 points) Explain why elemental silicon can be doped with antimony to make it an extrinsic semiconductor. How is the band structure altered? E45 Final Examination page 8 of 19 Fall Semester 2007 Initials: __________ (c) (10 points) On the axes shown to the right draw a B-H loop characteristic of a "hard" magnetic material. Label the remanent induction and the coercivity directly on the plot. B H B (d) (10 points) What is meant by the "hysteresis loss" associated with energizing an electromagnet, and how it is determined from a B-H plot? Sketch another B-H loop on the right to indicate a transformer core magnet that has low hysteresis loss. H E45 Final Examination page 9 of 19 Fall Semester 2007 Initials: __________ (e) (10 points) In its August 7, 2007 issue, Fortune Magazine announced Corning's latest breakthrough in optical fiber technology called ClearCurve™ for use in fiber to the home (FTTH) transmission of telecommunications signals (the above figure is from this article). What is the role of the "core" and the "cladding" shown in this figure? Comment on whether you think this is a step-index, graded-index, or single mode optical fiber design. Why? E45 Final Examination page 10 of 19 Fall Semester 2007 Initials: __________ 4. (50 points) Chemical Proper ties of Materials H C H C C N H H C H C C H H C C C C C H H H Engineering applications of ABS resins take advantage of the properties of their constituents. Acrylonitrile promotes thermal and chemical stability, butadiene provides toughness and impact resistance, and styrene imparts rigidity and ease of fabrication. By adjusting the relative molecular weights of these three building blocks, ABS resins can be produced with a wide range of properties. H Acrylonitrile (graft) H C H H C H C H C H Butadiene (chain) Styrene (graft) (a) (10 points) Why is ABS known as a "graft copolymer" instead of a "block copolymer?" Panasonic™ mini-DVD camera has an injection molded ABS housing. E45 Final Examination page 11 of 19 Fall Semester 2007 Initials: __________ (b) (10 points) Sketch the atomic configuration of a representative ABS polymer chain. H C H H C C N H H C H C C H H C C C C C H H H Acrylonitrile (graft) H C H H C H C H C H Butadiene (chain) Styrene (graft) E45 Final Examination page 12 of 19 Fall Semester 2007 Initials: __________ (c) (10 points) In the schematic to the right both electrodes are pure iron, and they are immersed in the same saline solution. Nitrogen gas is injected into one beaker, and oxygen gas is injected into the other. Which side is the anode? and what is the anode reaction? N2 Salt Bridge O2 (d) (10 points) What is the cathode reaction in the same cell? (e) (10 points) What is the role of the "salt bridge" in this cell? E45 Final Examination page 13 of 19 Fall Semester 2007 Initials: __________ 5. (50 points) Microstr ucture of Materials (a) (10 points) Sketch and label the microstructure of a eutectoid steel showing pearlite that nucleated at "prior austenite grain boundaries." T (°C) 1600 1500 1538° 1495° # 1400 1394° 1300 1200 1100 1000 900 800 700 0.02 0.77 " 600 500 400 910° 727° ! 2.11 1148° L 1227° 4.30 6.67 (b) (10 points) The following TTT plot pertains to a steel of what specific carbon concentration? Show it by a vertical line directly on the phase diagram at right. 900 800 700 600 T (°C) 500 400 300 200 100 0 0.1 Ms 1 sec 1 min 1 hour 1 day 727°C ! +" Coarse pearlite " 6.67 Cementite 300 200 100 3 4 5 6 Fe3C wt % C Reference: Metals Handbook, 8th Edition, Volume 8, Metallography, Structures and Phase Diagrams, American Society for Metals, Metals Park, Ohio (1973) Fe 105 0 1 2 "+ ! + Fe3C !+ Fine pearlite Bainite Fe 3 C 1 10 102 103 time (seconds) 104 E45 Final Examination page 14 of 19 Fall Semester 2007 Initials: __________ (c) (10 points) Sketch the microstructure of an Al-9.9 wt% Li alloy solidified from 650°C and label all phases. 800 718° 700 660.37° 600 500 600° 4.0 9.9 20.4 " 25.0 521° 34.0 L 46.8 T (°C) 400 300 200 100 0 Al 10 20 30 40 (Al) ! 179° 180.5° (Li) (d) (10 points) A ceramic alloy of MgO with 60 mol% Al203 is cooled quickly from 1500°C to room temperature, then aged at 500°C for several hours. Sketch the final microstructure and label all phases. 50 60 70 80 90 Li wt. % Li Reference: Metals Handbook, 8th Edition, Volume 8, Metallography, Structures and Phase Diagrams, American Society for Metals, Metals Park, Ohio (1973) T (°C) 3000 L 2500 2000 Spinel 1500 Periclase Alumina 1000 MgO 10 20 30 40 50 60 70 80 90 Mole % Al2O3 Al2O3 E45 Final Examination page 15 of 19 Fall Semester 2007 Initials: __________ (e) (10 points) The following x-ray diffraction pattern was recorded from a Cu alloy. The structure factor rules for FCC allow all reflections of the type hkl when the indices are either all even (0 counts as even) or all odd. Each reflection hkl arises from scattering by the family of planes (hkl) in the crystal according to Bragg's law, nλ = 2dhkl sin θ where n is the index of the diffraction event (assume n = 1 for all of the peaks seen here). Your technician claims to have recorded the first four (4) FCC peaks during this experimental run. Do you agree? Explain, rationalizing your answer on the basis of Bragg's Law and the structure factor rules. Reference: CrystalMaker software, http://www.crystalmaker.com/ E45 Final Examination page 16 of 19 Fall Semester 2007 Initials: __________ 6. (50 points) Defects in Materials Tin is a group IV element that occurs in a two allotropes, α-Sn or gray tin (cubic) below 13.2°C, and β-Sn or white tin (tetragonal) above 13.2°C. The transformation from white tin to gray tin in cold temperatures is known as "tin pest" because the β phase nucleates at the surface of the α phase as a powdery product that easily detaches. White tin has the A5 Strukturbericht symbol, with lattice parameters a = 0.583 nm and c = 0.318 nm. In the unit cell, Sn atoms are located at: 0,0,0; ½, ½, ½; 0, ½, ¼; and ½, 0, ¾. z y x y (a) (10 points) Draw all Sn atoms within the unit cell templates shown at right, indicating their locations both in perspective and in a c-axis projection with elevation labels (bottom x-y plane is location "0"). x E45 Final Examination page 17 of 19 Fall Semester 2007 Initials: __________ (b) (10 points) Now identify all members of the (020) family of planes within the same unit cell in both perspective and projection (use new templates to the right) and indicate all vacancies in these planes. z y x (c) (10 points) Now draw the vector connecting the two atoms that comprise the motif of the A5 structure and specify its direction using [uvw] indices. y x E45 Final Examination page 18 of 19 Fall Semester 2007 Initials: __________ (d) (10 points) On the drawing at right, construct a Burgers circuit in an FSRH convention to deduce the Burgers vector of the edge dislocation in the center of this image. Specify its magnitude and direction in proper vector notation, assuming that this is an FCC stacking sequence. P/2 [1¯ 11] [011] (e) (10 points) Sketch the slip plane of this dislocation directly on the drawing and specify its Miller indices. P/2 E45 Final Examination page 19 of 19 ...
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