Unformatted text preview: · ( ~a 2 × ~a 3 ) , 2 π ~a 1 × ~a 2 ~a 1 · ( ~a 2 × ~a 3 ) are the primitive vectors of the reciprocal lattice! b) If V is the volume of the primitive cell of the direct lattice, show that the volume of the primitive cell of the reciprocal lattice is 8 π 3 /V . Problem 3: Facecentered and bodycentered cubic lattices (12 points) The facecentered cubic (fcc) lattice can be deﬁned by the primitive vectors a 2 (1 , 1 , 0) , a 2 (1 , , 1) , a 2 (0 , 1 , 1) where a is the lattice spacing of the conventional cubic unit cell. For the bodycentered cubic (bcc) lattice, a set of primitive vectors is a 2 (1 , 1 ,1) , a 2 (1 , 1 , 1) , a 2 (1 ,1 , 1) . a) Calculate the volumes of the primitive cells and compare them with the volume of the conventional cubic unit cell. What does this tell you about the number of particles in the cubic cell? b) Show that the reciprocal lattice of a fcc lattice is a bcc lattice and vice versa....
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 Spring '11
 ThomasVojta
 Physics, Crystallography, Work, Cubic crystal system, Condensed matter physics, Reciprocal lattice, primitive vectors

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