This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 xyplane. 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 nearestneighbor 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 xyplane 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 )...
View
Full
Document
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.
 Winter '12
 Kotakoski

Click to edit the document details