Materials Science & Engineering

Homework #4 Professor Estrada ENGR 245: Intro to Materials Science & Engineering February 9, 2016 In order to receive full credit, all work MUST be shown and appropriate units must be specified. Working together is encouraged, however, all work that you turn in must be YOUR OWN work. Exercise 1. Derive Bragg’s Law. You should find n? = 2d sin(?). In order to receive full credit, explain the justification for each step. Exercise 2. Calculate the spacing between the (111) plane in BCC Fe. Cite the source you used to look up the lattice constant, a. Exercise 3. Given the following set of experimental data for the number of vacancies (Nv) in copper as function of temperature, plot Nv on a logarithm scale (or the natural log of Nv) as a function of T -1 (i.e., 1/T) for a temperature range of 500K to 1250K. T(K) Nv(cm-3 ) 500 7.23e13 600 1.75e15 700 3.86e16 800 1.094e17 900 8.83e17 1000 2.475e18 1100 6.97e18 Exercise 4. The equilibrium vacancy concentration, Nv, is given by equation 4.1 in the 9th edition of Callister and Rethwisch. Given the density (?) and atomic weight (ACu) of copper are 8.4 g/cm3 and 63.5 g/mol, find the activation energy of vacancy formation in copper (Qv) by fitting equation 4.1 to the experimental data in exercise 3. Show at least three of your fits on the same plot as the data points. 1      

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