PROBLEMS -

1: In a drawing of a hexagonal prism, indicate the following planes and directions (1210), (1012), (1011), [110], [111], [021]. Show cell axes.

2: The unit cells of several orthorhombic crystals are described below. What is the Bravais lattice of each and how do you know? Do not change axes. (In solving this kind of problem, examining the given atom positions for the existence or nonexistence of centering translations is generally more helpful than making a drawing of the structure.)

a) Two atoms of the same kind per unit cell located at 0 ½ 0, ½ 0 ½.

b) Four atoms of the same kind per unit cell located at 0 0 z, 0 ½ z, 0 ½ (½ +z), 0 0 (½ + z)

c) Four atoms of the same kind per unit cell located at x y z, x^- y^- z, (½ + x) (½ - y)z^-, (½ - x) (½  + y) z^-.

d) Two atoms of one kind A located at ½ 0 0, 0 ½ ½; and two atoms of another kind B located at 0 0 ½, ½ ½ 0.

3: Draw a standard (111) projection of a cubic crystal, showing all poles of the form {100}, {110}, {111} and the important zone circles between them.

4: Draw a standard (001) projection of white tin (tetragonal, c/a = 0.545), showing all poles of the form {001}, {100}, {110}, {011}, {111} and the important zone circles between them.

5: Lutetium has a hexagonal structure with lattice parameters a = 3.516 Å and 570 Å. Plot the h0l plane of the reciprocal lattice of this material.

6: Aluminum silicate (mullite) Al₆Si₂O₁₃ has an orthorhombic Bravais lattice and lattice parameters a = 7.5456 Å, b = 7.6898 Å and c = 2.8842 Å. Assuming that the Bravais lattice is simple orthorhombic, in one diagram plot the h0l net of the reciprocal lattice, and in a second diagram plot the 0kl net of the reciprocal lattice.