ss_8 - l_—__"____'—_ I 23. Recrystallization...

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Unformatted text preview: l_—__"____'—_ I 23. Recrystallization is a thermally activated process which can be characterized by an Arrhenius-type relation. Suppose an aluminum alloy is cold work to a 75% reduction in cross- sectional area. The alloy fully recrystallizes in 100 hours at T=256°C and in 10 hours at T=283 °C. (a) Calculate the activation energy for this recrystallization process. (b) Calculate the temperature at which the alloy could be fully recrystallized in 1 hour. (0) Sketch a plot describing changes in hardness during the 1-hour recrystallization anneal. (d) How does the dislocation density change within the alloy during the 1-hour recrystallization anneal? C + Ev. I :95 R: o W be; \00 NA <;Z"\ ® \0 ans €54 ‘C‘Z / thgkhflzf L5 ‘8 ()an Ewttpb‘t ML WT NDWS N memumw that/sass, N1 652.2052 mm was Mcka $.3me NAM \p N22,; Muwm Em" W Rimhvfizw uth Efi‘fifl“ m Wc. Eu 5 WT Wast M— N we» fish. 0?» M mg, m L, 3205 «mm News; {M o amt M- 7. '5 ..-r W A (.9 LauT‘CH. C :MPvD/N‘JC/ U 1 W621: \Cz It. I“ Vflofi“: Rh“ 0‘; { r—“wf—fi— - - — ——-1. ‘ 6. Consider the diffusion of aluminum into an initially pure wafer of silicon 1 mm thick. An Al- containing gaseous atmosphere in a furnace fixes the surface concentration of Al on the wafer at 1018 atoms/cm3. The furnace is held at name where the Al diffusivity in Si is 4x10'13 cmzlsec. (A) sketch a series of composition profiles that describe the Al concentration as a function of depth into the silicon for F0 and for two times thereafter. (B) Using the erf solution to Fick’s Second Law, calculate the depth at which the Al concentration is 1017 atoms/cm3 after 7 hours in the furnace. (C) Suppose the furnace temperature is lowered to 1000°C with everything else remaining the same. Will the depth at which the Al concentration is 1017 atoms/cm3 be more or less than that in (b) at 1100°C? Briefly justify your answer. 6;) 1" CM "Ct C; 0 nave-x 1.- I V‘ 1 ® \0\ ,0 3 . \68‘0 ' J” ‘ w M '34 \ oww 0" fm— —' _ — "—1 12. The surface of a single crystal silicon wafer is to be doped with phosphorus. The wafer initially contains no phosphorus. It is 500 microns thick. It is held in a furnace at T=1100°C with a phosphorus-containing atmosphere which fixes the surface concentration of P to be 4 ppm (parts per million). free surface of Si wafer exposed to P containing atmosphere at x=0 Phosphorus—containing atmosphere bottom of Si wafer at x=500ttm = 0.5mm T=1100°C=1373K E 4.0 Gvfima Con-all?de , g FstbcD WW” 3" ' g 3.0 wt, ‘s Kama? O- "3 a 2.0 § . g 1.0 0 £14 0.5 1.0 1.5 2.0 Depth into the Si wafer (pm) a. Calculate the time required at T=1100°C for the phosphorus concentration at a depth of lum from the fi‘ee surface to reach 0.5 ppm. The diffusivity of P in Si at 1100°C is 3.0x10'17 mzlsec. b. On the graph above, qualitatively sketch the concentration of phosphorus as a function of depth for times F0 < t1 < t2. NOTE: qualitative here means you don’t need to calculate anything. Just sketch approximately the shape of the curves for the three different times. 13. The temperature dependence of the diffusion coeficient characteristic of carbon in ferritic (BCC) Fe is described by the diagram below. (a) Calculate the activation energy for C diffusion in BCC Fe. (b) Carbon is an interstitial alloying element in steel. Does its diffiisivity depend on the Fe vacancy concentration? Briefly explain your answer. pd C? 00 yd C? ._. O p—L I H 4:. Diffusivity, m2/ sec p...‘ Q 5 0.00075 0.0001 0.0015 l/T (K) 7. (15 pts.) The temperature dependence of the diffusion coefficient charactenstic of carbon in ferritic (BCC) Fe is described by the diagram below. _' _ . ' ' (a) Caicuiate the activation energy for C diffusion in 800 Fe. (13) Ali else being equal, wouitt youegfipectthe diffusivity of Chromium in 800 Fe to be higher, lower, or the same as that eff-carbon in 806 Fe? Briefly explain your answer. ' b ‘335‘5 ‘ \fitzi‘“L “we/M gu—l E De Diffusivity, 312/330 m» w ~ m 32.2, a.» ~ “ml 2 meme $7 0:: VB (N fieskc game» \‘n e mfise‘t‘x‘mmwm %LW?W 999* we bimemx‘t‘i \‘e Memorieer 9»? Page — 6 93;. QM ’ C kg i t ' - hm write/aw:ng he: * ...
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ss_8 - l_—__&amp;quot;____'—_ I 23. Recrystallization...

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