SolutionHW4-new - ME311 MATERIALS ENGINEERING SPRING 2012...

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ME311 MATERIALS ENGINEERING SPRING 2012 HOMEWORK #4 PROBLEM 1: The measured density of a sample of Iron is 7.87 g/cm 3 . If the lattice parameter of this sample is 0.2866 nm, calculate the percentage of vacancies in this sample. Hint: In the absence of vacancies, bcc iron has 2 atoms/unit cell. Consider that the density is mass/volume. SOLUTION: The density of Iron can be calculated by In order for this expression to be correct, one should determine the number of atoms/unit cell, which can be calculated from the equation above. This gives a value of 1.998 atoms/unit cell. Because there should be 2 atoms/unit cell in a perfect BCC iron crystal, the difference must be due to the presence of vacancies. Thus the percentage of vacancies is given by %vacancies= (2-1.998)/2 *100 =0.1 % PROBLEM 2: You are an engineer working in a nuclear plant. In order to select the appropriate material for the reactor you perform a series of experiments to determine the equilibrium mole fraction of vacancies as a function of the working temperature. The results from your experiments are shown in the table below. Based on the data you have generated, determine a) the entropy/mole of vacancies, b) the enthalpy of vacancy formation /mole of vacancies and c) the equilibrium mole fraction of vacancies at 400 C. 27 C 227 C 427 C 627 C X v 3.13E-13 6.99E-8 1.37E-5 2.57E-4 Work with the following units (Temperature in degrees Kelvin, Energy in Joules and the molar gas constant R in Joules/mol.K).
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Hint: Using the expression that relates the equilibrium mole fraction of vacancies with temperature, first remove the exponential terms to obtain an equation of a straight line.
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