lecture_17_07b

lecture_17_07b - 08/29/08 Physics 13 - Fall 04 - G.R....

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Unformatted text preview: 08/29/08 Physics 13 - Fall 04 - G.R. Goldstein 1 Solids Crystal structure (slow cooling vs. amorphous from fast cooling) Polycrystalline (~ 1 mm) vs. single crystal Symmetry - determined by atomic bonds and sizes NaCl : face centered cubic - fcc Na + alternates with Cl- in every other node 08/29/08 Physics 13 - Fall 04 - G.R. Goldstein 2 Giants Causeway - Belfast, Ireland The Causeway proper is a mass of basalt columns packed tightly together formed 60 million years ago by volcanic activity. The tops of the columns form stepping stones that lead from the cliff foot and disappear under the sea. Altogether there are 40,000 of these stone columns, mostly hexagonal but some with four, five, seven and eight sides. The tallest are about 40 feet high, and the solidified lava in the cliffs is 90 feet thick in places. http://www.giantscausewayofficialguide.com/geology.htm For more information 08/29/08 Physics 13 - Fall 04 - G.R. Goldstein 3 Na Cl crystal Na + and Cl- in fcc crystal. Equilibrium spacing or size. r =0.281 nm (larger than Single molecule 0.236 nm) How is stable configuration found? Consider potential energy experienced by one ion due to Coulomb forces from all neighboring ions and repulsion due to exclusion. 08/29/08 Physics 13 - Fall 04 - G.R. Goldstein 4 Crystal stability Potential energy of single ion - let r be variable spacing Attraction: U attraction ( r ) = - a k EM e 2 r Madelung constant (geometrical): a = + 6- 12 2 + 8 3- ... =1.7476 for nearest neighbors, next nearest neighbors, next - to- next nearest neighbors, ... , in nearest neighbors, ....
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lecture_17_07b - 08/29/08 Physics 13 - Fall 04 - G.R....

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