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

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

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 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 shouldnt occur.

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 -,,

Seven unit cell shapes Cubica=b=c = = =90° Tetragonala=b c = = =90° Orthorhombica b c = = =90° Monoclinica b c = =90°, 90° Triclinica b c 90° Hexagonala=b c = =90°, =120° Rhombohedrala=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 doesnt matter if you start from Na or Cl

- or if you dont 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 cell In 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!]

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