# HW7-new - ME311 MATERIALS ENGINEERING SPRING 2012...

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ME311 MATERIALS ENGINEERING SPRING 2012 HOMEWORK #7 DUE DATE: April 5, before class PROBLEM 1: Estimate the number of spherical clusters in 1mm 3 of copper at its melting point that contain a) 10 atoms and b) 60 atoms. The atomic volume of liquid copper is 1.6x10 -29 m 3 , γ SL is 0.177 J/m 2 , k =1.38x10 –23 J/K and T m is 1356 K. Hint: Consider that at the melting temperature, the free energies per unit volume of the liquid and the solid are the same. PROBLEM 2: Copper (FCC crystal structure) is normally alloyed with additional elements in order to increase its strength. For an alloy with a composition of Cu (75 wt%) and Ag (25 wt%) (check the Cu-Ag phase diagram), when the first solid nucleates from the liquid, spherical clusters of radius r form with interfaces having an interfacial energy of 250 mJ/m 2 . Assuming that the latent heat of melting, L T is 4.8x10 8 J/m 3 , determine the critical radius for nucleation if the sample is cooled from the single-phase liquid region to a temperature of 900 C. PROBLEM 3:

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HW7-new - ME311 MATERIALS ENGINEERING SPRING 2012...

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