PX3012The Solid State

Course coordinator:Dr. J. Skakle

CM3020Solid State Chemistry

Course coordinator:Dr. J. Feldmann

SOLID STATECrystals

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

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

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

Crystals are everywhere!

More crystals

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)

?

Group discussionKepler 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.

Definitions1. 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 - , ,

Seven unit cell shapes• Cubic a=b=c ===90°• Tetragonal a=bc===90°• Orthorhombic abc ===90°• Monoclinic abc ==90°, 90°• Triclinic abc 90°• Hexagonal a=bc==90°, =120°• Rhombohedral a=b=c ==90°

Think about the shapes that these define - look at the models provided.

2D example - rocksalt (sodium chloride, NaCl)

We define lattice points ; these are points with identical environments

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

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

- or if you don’t start from an atom

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

In 2D, this IS a unit cellIn 3D, it is NOT

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

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!]

SummarySummary

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