hw 7 - [010] [110] ME311 MATERIALS ENGINEERING SPRING 2011...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: [010] [110] ME311 MATERIALS ENGINEERING SPRING 2011 HOMEWORK #7 DUE DATE: March 25, 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 , 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. SOLUTION At the equilibrium melting temperature T m we have In addition, at the equilibrium melting temperature , so that For a cluster containing n c atoms with an atomic volume we have . Therefore the expression for G r becomes Substituting = 1.6 10-29 m 3 and = 0.177 Jm-2 gives . For 1 mm 3 , n = 6.25 10 19 atoms . Therefore when n c = 10 atoms, n r = 9 10 13 clusters mm-3 ; and when n c = 60 atoms, n r = 3 clusters mm-3 . 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 (80 wt%) and Ag (20 wt%) (check the Cu-Ag phase diagram), when the first solid nucleates from the liquid,...
View Full Document

Page1 / 7

hw 7 - [010] [110] ME311 MATERIALS ENGINEERING SPRING 2011...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online