2. Crystal structure

Question 1

What is the crystal lattice?

Answer 1

An origin and all other equivalent sites in a crystal where the arrangement of atoms around these points is identical to the arrangement of atoms around the origin point.

Question 2

What are lattice vectors?

Answer 2

The two shortest vectors from the origin to the nearest neighbours for a crystal lattice, usually named a and b.

Question 3

What is a lattice translation vector?

Answer 3

A vector that can be used to map out the entire crystal lattice using two lattice vectors (i.e. any point in the lattice can be reached by a lattice translation vector, T).

Question 4

Give the equation for a lattice translation vector

Answer 4

T = lattice translation vector
u, v = integers
a, b = lattice vectors

Question 5

What is the basis of a crystal?

Answer 5

The position of the atoms relative to each lattice point.

Question 6

Give the equation for the basis vector

Answer 6

r = basis vector
x, y = integers
a, b = lattice vectors

Question 7

What two components make up the crystal structure

Answer 7

Lattice & Basis

Question 8

Give the equation for the translation vector of a 3D crystal

Answer 8

T = lattice translation vector
u, v, w = integers
a, b, c = lattice vectors

Question 9

What is a unit cell?

Answer 9

An arrangement of points in space, such that the arrangement of points about a given point is exactly the same as the arrangement of points about any other point.

Question 10

What is a primitive unit cell?

Answer 10

A unit cell that only has one lattice point in the crystal.

Question 11

What are the 4 types of Bravais lattice covered in this course?

Answer 11

• Simple cubic (sc)
• Body-centred cubic (bcc)
• Face-centred cubic (fcc)
• Hexagonal (hex)

Question 12

Describe the shape of a simple cubic Bravais lattice

Answer 12

Question 13

Describe the shape of a body-centred cubic Bravais lattice

Answer 13

Question 14

Describe the shape of a face-centred cubic Bravais lattice

Answer 14

Question 15

Describe the shape of a hexagonal Bravais lattice

Answer 15

Question 16

Which type of Bravais lattice is primitive?

Answer 16

Simple cubic (sc)

Question 17

What lattice structure does NaCl have?

Answer 17

Rocksalt structure: fcc with a basis of Na atoms and a basis of Cl atoms

Question 18

What lattice structure does silicon have?

Answer 18

Two interpenetrating fcc lattices

Question 19

What lattice structure does GaAs have?

Answer 19

Zinc blende structure: fcc with a two-atom basis (interpenetrating)

Question 20

What lattice structure does gold have?

Answer 20

fcc: single atom basis

Question 21

What lattice structure does titanium have?

Answer 21

hcp (hexagonal close-packed): two-atom basis

Question 22

What is the packing fraction?

Answer 22

A measure of how much volume is taken up by actual atoms within a crystal, also known as the packing efficiency.

Question 23

Give the equation for the packing fraction

Answer 23

Volume occupied by atoms (in the unit cell) / Total volume (of the unit cell)

Question 24

How is the plane through a crystal determined?

Answer 24

Find the intercepts of the a, b, and c vectors.

Question 25

How is the Miller index of a crystal plane determined?

Answer 25

1. Find the intercepts of the a, b, and c vectors.
2. Take the reciprocals of each intercept.
3. Reduce the values to the smallest integers with the same ratio.
4. This is the Miller index (hkl).

Question 26

Give examples of the Miller Indices of cubic crystals

Answer 26

The hat over an index represents a negative plane.

Question 27

How does the Miller-Bravais system work for hexagonal crystals?

Answer 27

a1 is associated with h
a2 is associated with k
a3 is associated with i (and is redundant)
c is associated with l

Question 28

How can planes within crystals become surfaces?

Answer 28

By cleaving the crystal to expose the surface.

Question 29

Cubic crystals have a ______ indices while hexagonal crystals have a ______-_______ indices.

Answer 29

Miller
Miller-Bravais