Question

1. (7 points) Consider a face-centered cubic (fcc) lattice: (a) (2 points) Draw a 3D primitive unit cell structure (b) (2 points) Sketch the placement of atoms on a (100) plane. Express distances between atoms on the plane in terms of lattice constant (a). (c) (1 point) How many atoms are there per primitive unit cell? (d) (1 point) How many nearest neighbor atoms are there for each atom? (e) (1 point) Assume a lattice constant of Inm. Determine the number of atoms/em

Answer 1

Solution: Face-centered Cubic (FCC) lattice: (a) 3D primitive unit ceu structure (12 Distance between atoms on the plane in terms of lattice constant a (c) A face centered cubic unit cell has 4 almos por unit cen. The no. of almos per present at corners per unit = 8 corner & I atom per ceu atoms o unit ceu 1 - The no. of atoms present at faces per unt = cen 6 faces & I atomper - 3 - Total no. of atoms per unit cell = 1+ 3 2 unit cell = 4 (d) In face-centered cubic unit cell, each atom touches 12 near neighbors and therefore has a co-ordinate no. of 12. Four spheres are present in the layer above, four spheres are in the layer below and four spheres in the layer of the constituent particle. e civent a = 10m Volume of unit cell = a ² = ( 123 = 110m) 3 = (10 g) = 10273 No. of atom in unit cell - Volume of un't ceux density man of one atom

For a better understanding of 3D structure refer image;

QO00

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