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315 2007 Midterm 2 Solutions

315 2007 Midterm 2 Solutions - [QM Ave?4 —-7/f2fi I...

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Unformatted text preview: [QM Ave;?4«+ —-7/f2fi I _ AW:sz Kzs/ X W4-m§§fsi__xr 3.. . a Mo “/ g» “9 Pr: mar Department of Materials Science and Engineering 750-315 Phase Equilibria and Diffusion of Materials Midterm No. 2 March 2, 2007 Instructions: You are allowed two sides of an 8.5” by 11" sheet with notes and equations. Please Show all work so as to maximize partial credit. Good luck! 1. In lecture, we demonstrated that 1 11m size gold particles should melt 291K below the bulk melting temperature of 1336K. a. Estimate the melting point of 18 nm gold particles. x I; 4 TA; 19 A M) = __%I 2 K m“ e avg/.5 V: 7740/1) ARM I F 29:41)) _ if” 2 1217 : 1:; K 5;: b. If the enthalpy of fusion of gold is 1236 kI/mole and its molar volume is 10.2 cm3 What is its surface energy? V35, 4 nmAT’ qfés L» F Ar/Afimfi : 4421/6/er swig) m'm 273 71.4.0) Mug M i3 13% x" V” ,wa'w“ , _ Io’b'a c. Smrting with a cube of gold 1 centimeter on a side, if we subdivide this cube into cubes 1 nanometer on a side, what will be the surface area? . 3 _ .y " {3}) CyfiiSQ z‘hiéxflf’) i / Z, 75M fifi‘nm. flmlyfié Lf j {alnM @4flwx "fly I; 7 Jun 4M“ 2. The diffusion coefficient for carburization/decarburization of bcc iron (ferrite) is approximated by the equation: 2' EC 2 2 x 10'2 cmZ/s exp [(434.1 kJ/mole)/RT] : ‘4 am"— é.” m _S, Q We; (5:30 C\ a. Based upon the fare-exponential factor and a lattice vibrational frequency of 1.5 x 6‘ 1013/5, estimate the entropy of motion. The lattice parameter is 0.43 nm. A r g I Z , 56:0 =— Z 2 j] p( : fo0—2 ml [(—rC). 8571M R. s {wag} 2x10" ("EA €ff/A5n - ~————-———»~~ -4 _ ‘ _3 L a. 2,5710 CM "a. ) 25(4; Lb—deséfi'fyx‘fl “*3 24”” ‘N b. If a 5 mm thick slab of ferrite with an initial carbon content of 0.09% is held at 700°C in an atmosphere which holds the surface composition at 003%, how far in from the surface would you expect to find the composition to be 0.05% after 1 hour of decarburizing? C 4:, _ H. do : (9,0007 0,0005 : cl, c.6071.) :0, 0005‘ Hem-1 l, {mfg—5) 714-811 X £66 +) — (J = 0' gaQS‘l-v-v 0,9003 fl ; ‘ L r -F x z _ _0,§33 sew %— 2;}; , :‘ Ca I 6" 0-0041: -- aoouj b ( ) a a 211—5... Y= M 1%»): x10"??,rlj{3goop>j :28/X/D—Zm =ZEBI/MM4457’LWK so {ref/1L) c. If instead the same slab (5mm thick, initial composition of 0.09% carbon) is held in a Is 7144‘ vaccum at 700°C (taking the surface composition of both surfaces effectively to zero), Cflfl'flfc" how long would you predict to reduce the overall composition to 0.02% carbon? mun—Tu) Ml 7-D use , f t — 15' Co "_ 5L :0 2 C :- _.8_ {7? C0 C0 7:1 2— (‘5 a‘ L { ‘7.ch a O r: if" = “’0 )1; a K : 44% wk 2:: O'OLOZ’ :U.ZZL 1T Be TzfllllX/‘O £13 '1 Q 0041:, 2’4 /7}: 5.353708 («EL/4,411 3a. if undope disorder, sketch 6 Brouwer di with relevant mas ' 5 o E M Q Q I: m s 5 O ? LAM. 14+ szfl : y+ 15/57 3b. In 15% calcia—doped zirconia—(Zrti)2)a,gs(CaO)o15——at 1000°C the ionic conductivity is measured as 8.57 x 10‘3 Sun. Given that the molecular weight of this composition is 113.15 g/mole and that the density is 5.5 g/cm3, calculate a) the vacancy concentration per cmg’, b) the vacancy diffusivity, and c) the ratio of vacancy diffusivity to oxygen ion diffusivity. _ 4 fide /53 3 Utigémjzfié ‘é'OZSX/OHFU I/N'TS 113.15- —~—7 3/ Ma ="2.42, will/‘4 2,0S _ n. M' 7' “W’afl :Ca F— a”: s. ,, : Cu 0") u I :— 64» +7: 438:1: (a v- m f ‘f vicar/c V v., /R— Z. ( —~— cm: “if ° " C/e 97' .. 4 ‘ 43 D4).- : “TIL—I, E XFH/O ngwfifldf/yffigfl [>st by; XV; g, 12: Error Function Table 2 “ _,2 erf(x):fi o 6 dz 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 0 1 2 3 Hundrede digit of x 4 5 6 7 8 _7 9 0.00000 0.11246 0.22270 0.32863 0.42839 0.52050 0.60386 0.67780 0.74210 0.79691 0.84270 0.88021 0.91031 0.93401 0.95229 0.9661 1 0.97635 0.98379 0.98909 0.99279 0.99532 0.99702 0.99814 0.99886 0.99931 0.99959 0.99976 0.99987 0.99992 0.99996 0.99998 0.99999 0.99999 0.01128 0. 12362 0.23352 0.33891 0.43797 0.52924 0.61 168 0.68467 0.74800 0.80188 0.84681 0.88353 0.91296 0.93606 0.95385 0.96728 0.97721 0.98441 0.98952 0.99309 0.99552 0.9971 5 0.99822 0.99891 0.99935 0.99961 0.99978 0.99987 0.99993 0.99996 0.99998 0.99999 0.99999 0.02256 0.13476 0.24430 0.34913 0.44747 0.53790 0.61941 0.69143 0.75381 0.80677 0.85084 0.88679 0.91553 0.93807 0.95538 0.96841 0.97804 0.98500 0.98994 0.99338 0.99572 0.99728 0.99831 0.99897 0.99938 0.99963 0.99979 0.99988 0.99993 0.99996 0.99998 0.99999 0.99999 0.033 84 0.14587 0.25502 0.35928 0.45689 0.54646 0.62705 0.69810 0.75952 0.81 156 0.85478 0.8 8997 0.91805 0.94002 0.95686 0.96952 0.97884 0.98558 0.99035 0.99366 0.99591 0.9974] 0.99839 0.99902 0.99941 0.99965 0.99980 0.99989 0.99994 0.99997 0.99998 0.99999 1.00000 0.04511 0.15695 0.26570 0.3 6936 0.46623 0.55494 0.63459 0.70468 0.76514 0.81627 0.85865 0.89308 0.92051 0.94191 0.95830 0.97059 0.97962 0.9 8613 0.99074 0.99392 0.99609 0.99753 0.99846 0.99906 0.99944 0.99967 0.99981 0.99989 0.99994 0.99997 0.99998 0.99999 1.00000 0.05637 0.1 6800 0.27633 0.37938 0.47548 0.56332 0.64203 0.7 1116 0.77067 0.82089 0.86244 0.89612 0.92290 0.94376 0.95970 0.97162 0.98038 0.98667 0.991 11 0.99418 0.99626 0.99764 0.99854 0.99911 0.99947 0.99969 0.99982 0.99990 0.99994 0.99997 0.99998 0.99999 1.00000 0.06762 0.17901 0.28690 0.38933 0.48466 0.57162 0.64938 0.71754 0.77610 0.82542 0.86614 0.89910 0.92524 0.94556 0.96105 0.97263 0.98110 0.98719 0.99147 0.99443 0.99642 0.99775 0.99861 0.99915 0.99950 0.99971 0.99983 0.99991 0.99995 0.99997 0.99998 0.99999 1.00000 0.07886 0.18999 0.29742 0.39921 0.49375 0.57932 0.65663 0.72382 0.78144 0.82987 0.86977 0.90200 0.92751 0.94731 0.96237 0.97360 0.98181 0.98769 0.99182 0.99466 0.99658 0.99785 0.99367 0.99920 0.99952 0.99972 0.99934 0.99991 0.99995 0.99997 0.99999 0.99999 1.00000 0.09008 0.20094 0.30788 0.40901 0.50275 0.5 8792 0.66378 0.73001 0.78669 0.83423 0.87333 0.90484 0.92973 0.94902 0.96365 0.97455 0.98249 0.98817 0.99216 0.99489 0.99673 0.99795 0.99874 0.99924 0.99955 0.99974 0.99985 0.99992 0.99995 0.99997 0.99999 0.99999 1.00000 0.10128 0.21 184 0.31828 0.41874 0.51 167 0.59594 0.67084 0.73610 0.79184 0.83851 0.87680 0.90761 0.93190 0.95067 0.96490 0.97546 0.98315 0.98864 0.99248 0.99511 0.99688 0.99805 0.99880 0.99928 0.99957 0.99975 0.99986 0.99992 0.99996 0.99998 0.99999 0.99999 1 .00000 ECE 3610 Engineering Probability & Statistics 3-1 ...
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