Physical Chemistry notes

1. PX3012
The Solid State
Course coordinator:
Dr. J. Skakle
CM3020
Solid State Chemistry
Course coordinator:
Dr. J. Feldmann

2. SOLID STATE
Crystals
 Crystal structure basics
 unit cells
 symmetry
 lattices
 Some important crystal structures and properties
 close packed structures
 octahedral and tetrahedral holes
 basic structures
 ferroelectricity
 Diffraction
 how and why - derivation

3. Objectives
By the end of this section you should:
• be able to identify a unit cell in a symmetrical
pattern
• know that there are 7 possible unit cell shapes
• be able to define cubic, tetragonal,
orthorhombic and hexagonal unit cell shapes

4. Why Solids?
 most elements solid at room temperature
 atoms in ~fixed position
“simple” case - crystalline solid
 Crystal Structure
Why study crystal structures?
 description of solid
 comparison with other similar materials -
classification
 correlation with physical properties

5. Crystals are everywhere!

6. More crystals

7. Early ideas
• Crystals are solid - but solids are not
necessarily crystalline
• Crystals have symmetry (Kepler) and long
range order
• Spheres and small shapes can be packed to
produces regular shapes (Hooke, Hauy)
?

8. Group discussion
Kepler wondered why snowflakes have 6 corners,
never 5 or 7. By considering the packing of
polygons in 2 dimensions, demonstrate why
pentagons and heptagons shouldn’t occur.

9. Definitions
1. The unit cell
“The smallest repeat unit of a crystal structure, in 3D,
which shows the full symmetry of the structure”
The unit cell is a
box with:
• 3 sides - a, b, c
• 3 angles - , , 

10.  Seven unit cell shapes
• Cubic a=b=c ===90°
• Tetragonal a=bc ===90°
• Orthorhombic abc ===90°
• Monoclinic abc ==90°,   90°
• Triclinic abc     90°
• Hexagonal a=bc ==90°, =120°
• Rhombohedral a=b=c ==90°
Think about the shapes that these define - look at the
models provided.

11. 2D example - rocksalt
(sodium chloride, NaCl)
We define lattice points ; these are points
with identical environments

12. Choice of origin is arbitrary - lattice points need not be
atoms - but unit cell size should always be the same.

13. This is also a unit cell -
it doesn’t matter if you start from Na or Cl

14. - or if you don’t start from an atom

15. This is NOT a unit cell even though they are all the
same - empty space is not allowed!

16. In 2D, this IS a unit cell
In 3D, it is NOT

17. All M.C. Escher works (c) Cordon Art-Baarn-the Netherlands.
All rights reserved.

18. Examples
The sheets at the end of handout 1 show examples of
periodic patterns. On each, mark on a unit cell.
[remembering that there are a number of different
(correct) answers!]

19. Summary
 Unit cells must link up - cannot have gaps
between adjacent cells
 All unit cells must be identical
 Unit cells must show the full symmetry of
the structure  next section