midterm1-solutions

midterm1-solutions - E45 First Exam October 7, 2009 8 CL...

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Unformatted text preview: E45 First Exam October 7, 2009 8 CL TMUE’ Point Values of Problems 1. 14 2. 16 3. 25 4. 25 5. 20 Z= atomic number R= gas constant = 1-98? cal/mole-K 0K = 273°C Formulae for E45 Exam #1 o = FIAO s = (l. — lo)r’lo ET = ln_(l.llo) 0 2 Es v -= 4,45}. %RA = {(A0 — Arm} 100% E = -A}'r + Bfr" ET = Ind/10) A = (Zle)(Zze)f4‘ztso Young’s Modulus ~ dzEfdrz X = C(IE — AE) %ionic = {I-exp[-(0.25)(XA - X3)2]}x100 (th) {hkl} [ijk] <ijk> APF = (Vol of atoms in unt cell)f(vol of unit cell) LD = (# of atoms centered on direction vector);’(length of direction vector) PD = (# of atoms centered on plane)! (area of plane) dth = 8.3012 + 18 + 12)”2 NV = chp(-QvaT) Wu 2 (C0 _ CByICu— CB) 1. The engineering stress-strain curve of an unknown metal was measured by a tensile test and is presented in the following ﬁgure. The linear region terminates at a strain of 0.005 and the curve exhibits a slope of zero at a strain of 0.20. (D ms Engineering Stress 0 ID i ® 01' Engineering Strain (a) Identify the following regions and parameters on the diagram: elastic region; plastic region; 0.2% offset yield stress; ultimate tensile stress (b) A second identical sample is subjected to the same tensile test except the test is stOpped when the stress reaches the ultimate tensile strength. The gauge length of the cylindrical sample is 5 cm and the sample’s diameter is 0.5 cm. Calculate the gauge length of the sample after it is removed from the tensile test machine. A0,: skulh — Blaslti Ski-tibia All 2 (0.20—- 0,935,,“ = 0.97:9.“ heel gem-3t: lemul'k“ 59M swan?» ': 5.9chm- 1th @®®@ 2. The energy versus distance of atomic separation of two unknown solids is presented in the following ﬁgure. (3) Which solid, A or B, has the higher melting temperature? 9 (b) Which solid has the higher coefﬁcient of thermal expansion? (c) Which solid has the higher modulus of elasticity? ll (d) Based on the shapes of the two curves is it possible to identify the type of primary bonding (metallic, ionic, covalent) exhibited by the solids? N0- Energy 3. The most densely packed plane in the body centered cubic crystal (bcc) structure is {1 10}. The most densely packed direction in bcc is <1 I 1>. (3) Sketch the (110) and the [I 1 l] in the unit cube presented below. (b) For the bcc structure, calculate the number of atoms per unit area on 110. { } a fr; ﬁcm‘neﬂ Wm col (aloe "ml" M Tu 1th (c) For the bee structure, calculate the number of atoms per unit length in <1 11>. Hus. «k WW“ ’1’“? ‘ I {5 ‘ﬂgibm dank (‘9an @ meax MSI‘H 1: /2_ (2) + 1- : Z Mlun3<w> /v\J—{'Q Wok Ihghvg (“be 41¢.ng 4. ldentify the second element, X, in each of the three Al-X phase diagrams. Veg: brieﬂx, explain your reasoning. Element CﬂStﬂl Structure Al Ge Zn Si Al fcc 0.182nm diamond cubic 0.152nm hep 0.153nm diamond cubic 0.146nm %X-> \$©AV: 7 JAN-hm . c' beech Table 4 50 _ 6. mm a. 5:01.!“ fh‘oe Jeajrm atomic radius priming: valence Electronegativig: 1.82 2.01 1.65 1.90 Numbers correspond to atom percent of element X 2.8 30 %X— > e a m cab-wt?” W ioU'i’fx Shank! aria”. @ 51M Ga Ma v'dlﬂqigV61—4M‘Lr‘e swimmith bondd, WLLLii-‘M staged: {and /v' @ Z so 2“ Simon. fl seine} t .' f»; ("M-V; \$43“? ins-2n 1‘5 (Sinai exh; far is m chub? WM“ "‘1 r}: She-Ltd dig SCIUC MAL. i5 lager S“ M 6'“: a-S'Ge tin Inf-(i7 {L[ {a iarjer- 5mm” “not was dots/H 441cm imr- 5. Elements A and B form a binary eutectic phase diagram. (a)Using the following information construct the A—B phase diagram. The melting points of A and B are 700°C and 600°C, respectively. Pure A and pure B form the a and [3 phases, respectively. The maximum solubility of B in (1 is 20 atomic percent (afo). The maximum solubility of A in B is 30 21/0. The eutectic composition is 40%8 and the eutectic temperature is 500°C. At 400°C: the solubility of B in or. is 10 a/0; the solubility of A in B is 15 aIO. Show on your diagram each of the previous pieces of information. k@ (b) At equilibrium, what phases are present at 400°C in an alloy that contains 30%B? Calculate the relative amounts of each phase that is present at 400°C. Sr = a £3: , 0.??53 0i 35110 H” as? 1mg roam , ‘50in _. 20 - far role?— 2 ESE-r10 ...
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This note was uploaded on 02/12/2011 for the course E 45 taught by Professor Gronsky during the Fall '08 term at University of California, Berkeley.

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midterm1-solutions - E45 First Exam October 7, 2009 8 CL...

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