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SolutionHW5-new

# SolutionHW5-new - ME311 MATERIALS ENGINEERING SPRING 2012...

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ME311 MATERIALS ENGINEERING SPRING 2012 HOMEWORK #5 PROBLEM 1: You are given the task of purchasing a Microscope with the highest resolution possible. Among the instruments shown in the Table below, which microscope would you select? What is the best resolution for each radiation used? Assume the numerical aperture of the lens, NA=1. Microscope Radiation Used A X-rays B Ultraviolet C Green Light D Electrons E Red Light SOLUTION The resolution of the microscope is given by where λ is the wavelength and NA is the numerical aperture of the lens. Therefore, we get: Microscope Radiation Used λ (m) d (Å) A X-rays 10 -8 -10 -11 0.06 B Ultraviolet 10 -7 -10 -8 61 C Green Light 5.1×10 -7 3121 D Electrons 2.5×10 -12 0.015 E Red Light 4×10 -7 2448 and the best resolution obtained is for the microscope using electrons.

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PROBLEM 2: The diffusivity of lithium in silicon is 10 -5 cm 2 /sec at 1376 K and 10 -6 cm 2 /sec at 968 K. What are the values of for the enthalpy and the pre-exponential term for diffusion of lithium in silicon? Hint: Using the expression that relates the Diffusion coefficient with temperature, first remove the exponential terms to obtain an equation of a straight line. Subsequently, use a graphical form to answer the above questions. SOLUTION Let T1= 1376 K and T2= 968 K Thus G*=(2.3*8.314)/3x10 -4 = 63740 J/mole To evaluate the pre-exponential term, we simply use the value of D at either 1376 or 968. Thus, we can write PROBLEM 3: Consider a diffusion couple setup between pure tungsten and a tungsten alloy containing 1 at% thorium. After several minutes of exposure at 2000 C, a transition zone of 0.01 cm thickness is established. What is the flux of thorium atoms at this time if the pre- exponential term has a value of 1 cm 2 /s and the activation energy for diffusion has a value of 120,000 cal/mole? Hint: Calculate the concentration in terms of number of atoms per cubic centimeter. SOLUTION The lattice parameter of BCC tungsten is about 3.165 A. Thus, the number of tungsten atoms/cm3 is
In the tungsten-1at% thorium alloy, the number of thorium atoms is In the pure tungsten, the number of thorium atoms is zero. Thus the concentration gradient is given by On this basis we can now calculate the flux according to the equation Since the concentration gradient has been determined, we just need to calculate the

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SolutionHW5-new - ME311 MATERIALS ENGINEERING SPRING 2012...

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