SS - Periodicity, crystal systems and unit cells

Question 1

Define a lattice

Answer 1

An infinite array of points where each point has identical surroundings

Question 2

Define a unit cell

Answer 2

A building block which when repeated in all directions gives the lattice

Question 3

Define a lattice point

Answer 3

A single point within a lattice. The separation between lattice points is a, and knowledge of one point and a can build the whole lattice

Question 4

Define a motif

Answer 4

Otherwise known as a basis. A motif/basis represents one or more atoms, ie a molecule or a protein. When a motif is placed on a lattice, a crystal structure is formed

Question 5

Describe how to count atoms in a 2D representation

Answer 5

Question 6

Describe how to count atoms in a 3D representation

Answer 6

Question 7

State the 4 types of unit cells

Answer 7

1. Primitive (P)
2. Body centred (l)
3. Face centred (F)
4. C centred (C)

Question 8

Draw a primitive unit cell

Answer 8

Question 9

Draw a body centred unit cell

Answer 9

Question 10

Draw a face centred unit cell

Answer 10

Question 11

Draw a C centred unit cell

Answer 11

Question 12

How many lattice points does a primitive unit cell have

Answer 12

1

Question 13

How many lattice points does a body centred unit cell have

Answer 13

2

Question 14

How many lattice points does a face centred unit cell have

Answer 14

4

Question 15

How many lattice points does a C centred unit cell have

Answer 15

2

Question 16

Draw a unit cell and label the parameters

Answer 16

Question 17

Define bravais lattices

Answer 17

Combinations of the 7 unit cell shapes and 4 possible lattices give 14 Bravais laticces

Question 18

State the 7 unit cell shapes

Answer 18

1. Cubic
2. Orthorhombic
3. Tetragonal
4. Triclinic
5. Rhombohedral
6. Monoclinic
7. Hexagonal

Question 19

Give the parameters for a cubic unit cell

Answer 19

Question 20

Give the parameters for an orthorhombic unit cell

Answer 20

Question 21

Give the parameters for a tetragonal unit cell

Answer 21

Question 22

Give the parameters for a triclinic unit cell

Answer 22

Question 23

Give the parameters for a rhombohedral unit cell

Answer 23

Question 24

Give the parameters for a monoclinic unit cell

Answer 24

Question 25

Give the parameters for a hexagonal unit cell

Answer 25

Question 26

Describe a crystal structure in terms of Bravais Lattices

Answer 26

Crystal structure = bravais lattice + basis

Question 27

Give the parameters of the hexagonal primitive cell

Answer 27

Question 28

Define the coordination number of an atom and give the coordination numbers for each type of cubic unit cell

Answer 28

The number of atoms bonded to the atom in question gives its coordination number. Ie the number of nearest neighbours.

Question 29

Describe miller indeces

Answer 29

• Miller indices are used to describe planes in crystals, and to distinguish between different surfaces expressed by a crystal.
• Planes diffract X-ray radiation which can be used to determine crystal structures.
• A miller index takes the form (h k l) where h, k and l are integers.
• The plane (h k l) intercepts the a, b and c axis at a/h, b/k, c/l.
• The separation between planes is referred to as d_hkl.
• Note: -2 = 2 bar

Question 30

Give the volume of a cubic unit cell in terms of a

Answer 30

V = a³

Question 31

State the equation for density

Answer 31

p = M/V