How many atoms are there in a simple cubic unit cell? in a bcc unit cell? in a f

Question

How many atoms are there in a simple cubic unit cell? in a bcc unit cell? in a fcc unit cell? in the unit cell characterizing the diamond lattice? b) In terms of the lattice constant a, what is the distance between nearest-neighbor atoms in a simple cubic lattice? Assuming a cubic crystal system, make a sketch of the following planes. a) (001), b) (111) c) (123), d) (110), e) (010), f) (111), g) (221) h) (010) Assuming a cubic crystal system, use an appropriately directed arrow to identify each of the following directions a) [010], b) [101], c) [001], d) [111], e) [001]. f) [110], g) [010], h) [123] As shown in Fig. 1. a crystalline plane has intercepts of 1a, 3a, and 2a on the x, y, and z axes, respectively. A is the cubic cell side length a) What is the Miller index notation for the plane? b) What is the Miller index notation for the direction normal lo the plane? Assuming the crystal Structure to be cubic, determine the Miller indices for (a) the plane and (b) the vector pictured in Fig. 2 A crystalline lattice is characterized by the cubic unit cell pictured in Fig 3. The cell has a single atom positioned at the center of the cube. a) What is the name of the lattice generated by the given unit cell? b) Determine the number of atoms per unit volume in the crystal in terms of the lattice constant, a. c) Suppose the crystal has a (110) surface plane. Determine the number of atoms per unit area whose centers lie on the (110) plane. d) A direction vector is drawn through the center of the atom in the unit cell. Specify the Miller indices of the direction vector. Sketch the plane and direction vector characterized by (011) and [011] Give a cubic lattice, indicate how many equivalent planes or equivalent directions arc associated with each of the following designations: a) {100} b) {110} c) {111} d) e) f)

Explanation / Answer

1(a) for simple cubic

n= number of atom=8*1/8=1.

For FCC, n=number of atom=8*1/8+6/2=4

For BCC, n= 8*1/8+1=2

For diamond, n=8*1/8+6/2+4=8

1(b) r= nearest neighbour distance in simple cubic=a

=

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