exercise_2 - Molecular Dynamics Simulations 2011 Exercise...

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Unformatted text preview: Molecular Dynamics Simulations 2011 Exercise 2: Suggested solutions Eero Holmstr om September 21, 2011 1. Lets first construct the orthorhombic unit cell of the HCP structure with side vectors a 1 , a 2 , and a 3 . From Fig. 1 we get the unit vectors in the xy-plane. Let a = a 1 = a 2 . We see that a 1 = a tan / 3 = 3 a (1) and trivially that a 2 = a . Also, a 3 = a 3 = radicalbig 8 / 3 a . Now, to make the (111) planes of the HCP lattice and the FCC lattice match, we set a to the nearest-neighbor distance of FCC, a = a / 2, where a is the side of the conventional FCC unit cell. Finally we have a 1 = radicalbig 3 / 2 a , a 2 = a / 2, and a 3 = 2 a / 3. We still need the basis, i.e. locations of the atoms in the unit cell. In the units of the othorhombic unit cell given above they are (000) , ( 1 2 1 2 0) , (0 1 3 1 2 ) , ( 1 2 5 6 1 2 ). Now, from the solutions of the previous exercise, for the FCC lattice with the xy-plane in the (111) plane we have b 1 = a / 2 , b 2 = radicalbig 3 / 2 a , and b 3 = 3 a . The basis here is (000) , ( 1 2 1 2 0) , (0 1 3 1 3 )...
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This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.

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exercise_2 - Molecular Dynamics Simulations 2011 Exercise...

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