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

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 shouldn’t occur. Empty space not allowed

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°

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 cell In 3D, it is NOT

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

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