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Homework Problem Set 1 Solutions Ohring 1.2, 1.8, 1.9, 1.14 1.2 Au (FCC) and W (BCC) both have density = 19.3 g/cm^3 and atomic weights 197.0 for Au and 183.9 for W. a) Calculate lattice parameter for each. Density / Atomic Weight = mol/cm^3, convert to atoms / cm^3. FCC has 4 atoms/unit cell, BCC Inverse of u.c./cm^3 is volume of unit cell in cm^3. Converet to Å^3 and take cube root. Answ mol/cm3 atoms/cm3 uc/cm3 cm3/uc Au: 0.098 5.90E+22 1.47E+22 6.78E-23 W: 0.105 6.32E+22 3.16E+22 3.16E-23 b) Assume hard spheres and calculate ratio of diameters. FCC, d110 = 2 atomic diameter; BCC d111 = 2 atomic diameters. atomic d110 d111 diameter Ratio Au:W Au: 5.766 7.062 2.883 1.053 W: 4.473 5.478 2.739 1.8 80 at% Ga - As melt is equilibrium cooled from 1200°C to 0°C. a) Perform phase analysis of crucible contents, phases present, compositions, % phase present at these tempe Composition Composition Phase #1 Phase #2 #1 #2 % Phase 1 1200°C Liquid na 80% Ga na 100 1000°C Liquid GaAs 88% Ga 50% Ga 79% 600°C Liquid GaAs 98% Ga 50% Ga 63% 200°C Liquid GaAs 99%+ 50% Ga 60% 30°C Liquid GaAs 99%+ 50% Ga 60% 29°C (Ga) GaAs 100%Ga 50% Ga 60% b) Sketch the temperature-time cooling response Temp 1200 1100 1000 Assumes heat withdrawn at 900 constant rate. Assumes heat withdrawn at constant rate. 800 700 600 500 400 300 200 100 0 time c) Do a phase analysis for 80at% As at these temperatures: Composition Composition Phase #1 Phase #2 #1 #2 % Phase 1 1000°C GaAs Liquid 50at% As 87at%As 19% 800°C GaAs (As) 50at% As 100 at%As 40% 600°C GaAs (As) 50at% As 100 at%As 40% 1.9 Diffuse P from a constant source of 1020 atoms/cm3 into a p-type Si wafer with 1016 B atoms/cm3.DP = 10-12 cm How far from the surface is the junction depth (where Cn=Cp)? Boundary conditions: Cn(x,0)=0, Cn(∞,t) = 0, and C(0,t) = 1020 The erfc curve shows C/C0 = 10-4 when X/√(4Dt) = ~2.8 X(cm) = 2.8*√(4Dt) 0.000336 cm = 3.36 1.14 Bimetallic strip with αA>αB, strip is clamped as a cantilever beam. a) Show how the strip will deform when heated uniformly Metal A will expand more than metal B, so A is in compressio , B in tension. The strip will curl to B A b) Despite my sketch, the beam will have a constant radius of curvature. c) The strain will be elastic until the thermal mismatch stress exceeds the yield point of one of the metals. Ohring 2.3, 2.10, 2.12, 2.17 2.3 Consider a vacuum system with a gate valve between the chamber and the pummp. a) A sample is introduced at 760 torr while pumps are at 10-6 torr. What is the sealing force on the 15 cm diam F=ΔPA, ΔP=760 torr = 1.013*105N/m2. A= Pi*D2/4 = 0.0177m2. F(N): 1790 b) What is the sealing force once the chamber has been roughed to 10-2 torr? F=ΔPA, ΔP=0.01 torr = 1.33N/m2. A= 0.0177m2. F(N): 0.024 2.10 V= 30 l, P = 10-6 torr, P rises to 10-5 in 3 minutes. a) Calculate the leakage rate. R(torr-liters/s)= ΔP*V/Δt R(t-l/s): 1.50E-06 b) What will be the ultimate pressure, P0, if pump speed, S, is 40 l/s? Ultimate pressure achieved when rate in = rate out. Rate in = 1.5E-6 torr-l/sec, rate out = P 0*S P0 (torr): 3.75E-08 3 6 3 2.12 V= 1 m (=10 cm ), static P0 = 10-7 torr, S = 200 l/s, Gas flow (f) = 100 cm3/min (STP) (= 1.67e-3 l/s). a) What is P0 when gas is flowing? Time to fill chamber with pump valve closed, Δt = V/f = 104 sec, Rin = ΔP·V/Δt = ΔP·f, Rout= P0· P0(torr): 6.35E-03 b) What conditions are necessary to maintain this process at 10-3 torr? Reduce flow or increase pumping speed. Much easier to reduce gas flow. f= P0·S/ΔP. f (sccm): 15.8 2.17 1000 liter chamber with eight 0.635 cm diameter scrrews with 0.0794 cm of space at the bottom of a blind hol a) What chamber pressure would be associatedwith this volume of gas? Calculate moles of ideal gas in the trapped volume at atmospheric pressure, then calculate P for V (cm3): 0.2012 N(moles): 0.0082 b) Describe the gauges you would use to monitor pressure bursts from these virtual leaks. Would you recomme Expect pressure bursts in the range of 10-2 torr, so use a thermocouple gauge. An analog gauge might give a better feel for the 'burst' nature of the leak, in any case a chart o Monty 1.1, 1.2 1.1 Design an experiment to study the proportion of unpopped kernal of popcorn. Complete steps 1-3 of the guide 1.Recognition and statement of the problem. Not all kernals of popcorn pop. Would like to develop process that maximizes popping without d 2. Selection of the response variable(s) a. Number of kernals unpopped - assume microwave process, bags all have same number of ke b. Whether or not there are any burned kernals or a burned smell. 3. Choice of factors levels and ranges Variable Range Levels Oven Power 700 - 1600 w 700, 1100 W Power Setting 10 - 100 % 50, 100 % Time at Power on - 20+ min 0 1,3 min Popcorn Brand Categoric A, B Are there any major sources of variatiion that would be difficult to control? Incoming material variation in size and quality, water content of kernals, size of kernals. 1.2 Investigate the factors that potentially affect cooking rice. What is response variable, how would you measure? Taste, texture, moisture Panel of judges, weight, microscope x-section List potential sources of variation grain size, average and variability water content of dry rice amount of water in pot amount of rice in pot amount of heat input time additives prewash Complete the first three steps of the guidelines 1.Recognition and statement of the problem. Want to cook rice to the right texture and taste reliably 2. Selection of the response variable(s) Taste Texture Variability 3. Choice of factors levels and ranges Variable Range Levels Time 0 - 60 min 20 - 30 min Heat Input Lo - Hi Lo, Med Lo Type of Rice Various Basmati, Regular s 197.0 for Au and 183.9 for W. ^3. FCC has 4 atoms/unit cell, BCC has 2. Divide atoms/cm^3 by atoms/uc to get uc/cm^3. to Å^3 and take cube root. Answer is lattice parameter. Å3/uc a (Å) 67.80 4.077 31.65 3.163 d110 = √(a² +a²) d111 = √(a² +d1102) % phase present at these temperatures: h 1016 B atoms/cm3.DP = 10-12 cm2/s and t=1 hour. This is the error function condition, and we need the length x when C/C0 = 1016/1020 = 10-4. μm B in tension. The strip will curl towards metal B. d point of one of the metals. e sealing force on the 15 cm diameter valve plate. 1.5E-6 torr-l/sec, rate out = P 0*S. 3 /min (STP) (= 1.67e-3 l/s). c, Rin = ΔP·V/Δt = ΔP·f, Rout= P0·S, So P0= ΔP·f/S. e gas flow. f= P0·S/ΔP. space at the bottom of a blind hole. eric pressure, then calculate P for that N and the chamber V. R(t-l)/(mole·K): 62.3637 P(torr): 0.153 virtual leaks. Would you recommend digital gauge readouts? mocouple gauge. of the leak, in any case a chart output would be certain to captre the events. Complete steps 1-3 of the guidelines for designing experiments. hat maximizes popping without degrading taste. bags all have same number of kernals. of kernals, size of kernals.

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