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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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