problems_section_8[1] - Problems – Microstructural...

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Problems – Microstructural Development 1. Suppose a thin film (50 nm thick) of nickel is deposited on the end of a very long copper bar. If this bar is heated to 0.8 of the melting temperature of Cu, draw schematic plots of the Ni concentration as a function of distance from the end of the bar for t=0, t = infinity, and two intermediate times. Note that no calculations are needed for this problem. You simply need to think about how nickel diffuses into copper and how the composition profiles change with time. 2. Sketch the microstructure corresponding to a sample of 1080 plain-carbon steel after slowly cooling to room temperature. Draw a straight line anywhere across this sketch and plot the carbon concentration as a function of position along this line. Suppose the sample is heated to T=900 o C. Sketch the carbon concentration as a function of position along this same line for three subsequent times including t=infinity. No calculations are needed. 3. A) A Cu rod 1 cm in diameter and 20 cm long rod is joined at one end to an identical rod of Ni to form a rod 40 cm long with a perfectly sharp interface in the middle. Suppose this couple is heated to 1000 o C and held there for several hours. Sketch profiles of Cu concentration across the interface for t=0 and for three subsequent times. No calculations are needed, simply a well- labeled sketch. B) Suppose an identical couple is made from rods of pure lead and pure tin and heated to 175 o C. Draw a similar set of composition profiles. You should refer to the Cu-Ni and Pb-Sn phase diagrams. 4. Referring to the Fe-Fe 3 C phase diagram, suppose the microstructure of a 0.6 wt% C steel (a 1060 steel) at room temperature is described by the sketch below. (A) Sketch (no calculations needed) on a well-labeled graph the carbon composition as a function of position along the line z-z’; (B) Suppose this steel is heated to 1000 o C. Sketch the carbon concentration along line z- z’ after the steel equilibrates at this new temperature. 5. Suppose a thin film of pure Boron 1 m m thick is sandwiched between thick wafers of Si, each 1mm thick and then annealed at T=1200 o C. Sketch a series of three or more curves, including one at time t=0, describing the Boron concentration in this system as a function of time (no calculations are needed here). Z Z’ C B position 0.5 - 0.5
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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 10 18 atoms/cm 3 . The furnace is held at 1100 o C where the Al diffusivity in Si is 4x10 -13 cm 2 /sec. (A) sketch a series of composition profiles that describe the Al concentration as a function of depth into the silicon for t=0 and for two times thereafter. (B) Using the erf solution to Fick’s Second Law, calculate the depth at which the Al concentration is 10 17 atoms/cm 3 after 7 hours in the furnace. (C) Suppose the furnace temperature is lowered to 1000 o C with everything else remaining the same. Will the depth at which the Al concentration is 10 17
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This note was uploaded on 10/03/2009 for the course E e 344l taught by Professor Libera during the Spring '09 term at Stevens.

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problems_section_8[1] - Problems – Microstructural...

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