# physics - 1 Consider a metal with a vacancy formation...

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1. Consider a metal with a vacancy formation energy of 0.8 eV/atom. If the material is originally at 1031 K, calculate the temperature rise (in K) needed to increase the vacancy fraction by a factor of 3.5: i. 1.1 ii. 143 iii. 167 iv. 440 v. 551 K K T K T T K atom eV atom eV K K atom eV atom eV K X v 167 ~ 7 . 166 1031 7 . 1197 7 . 1197 * . / 10 62 . 8 / 8 . 0 exp 10 232 . 1 5 . 3 : get to 3.5 by multiply 10 232 . 1 1031 . / 10 62 . 8 / 8 . 0 exp 1031 at 5 4 4 5 2. A hypothetical element is polymorphic, and undergoes a phase transition (change in structure) from body centered cubic (BCC) to hexagonal close packed (HCP) at 500 o C, as it is heated. What is the ratio of the density of the BCC phase to that in the HCP phase for this element? The volume of an HCP unit cell is given by c R 2 3 6 , where R is the radius of an atom of the element and c is the long axis of the HCP unit cell. Assume the HCP unit cell is ideal, meaning c/a = 1.633. a) 0.459 b) 0.500 c) 0.740 d) 0.919 e) 1.088 Just divide the APF’s: 0.68/0.74 = 0.919. Can also do it the long way if you wish. e) 3. Which of the following defects is/are equilibrium defects:

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4. a) Sketch a diagram to illustrate the dependence of the attractive, repulsive and net forces on the inter-atomic separation for two isolated atoms. Clearly mark the bond length on your diagram. b) Sketch a diagram to illustrate the dependence of the attractive, repulsive and net potential energy on the inter-atomic separation for two isolated atoms. Clearly mark the bond length and bond energy on your diagram.

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