










Basic concepts/terms.
Crystalline solids: highly regular arrangement of atoms, ions, molecules
 periodic (repeating)
Amorphous solids: no repeating pattern, only short range order, extensively
disordered  non crystalline (e.g. glasses)
We will focus on Crystalline solids :
 how do we describe them ?  lattices
Crystallinity  have a repeating unit = unit cell what types exist ?  metallic, ionic, extended covalent (or network), molecular. how can we study their structures ?  many ways, for example xray diffraction.
To define repeating unit use concept of a lattice
A lattice is "an infinite 1,2, or 3D regular arrangement of points, each of which has identical surroundings".
Any periodic pattern can be described by placing lattice points at equivalent positions within each unit of the pattern.
To recover original pattern we add the motif to each lattice point.
(return to top)
1D lattices. The regular pattern
of wagons below can be described by placing a lattice point at the same
place in each wagon. The arrangement of dots is the lattice, which
has a given repeat distance. The motif is the wagon. The pattern
is recovered by stamping the motif on each lattice point.
2D patterns: Planar lattices.
Consider each of the patterns below  what is the lattice and unit cell
?
Place lattice points at equivalent positions in the pattern, find smallest
repeat unit that by translation, can cover all space.
All of these patterns have the same Planar Lattice.(square),
but each has a different motif.
Crystal structures repeat in 3 dimensions. The motif can be single atoms or groups of atoms. Again we assign lattice points to the atomic structure and produce a Space Lattice.
There are 7 unique unitcell shapes that can fill all 3D space. These are the 7 Crystal systems.
We define the size of the unit cell using lattice parameters
(sometimes called lattice constants, or cell parameters). These are
3 vectors, a, b, c. The angles between these vectors are given by
a (angle between b and c), b
(angle between a and c), and g (angle between
a and b).
Although there are only 7 crystal systems or shapes, there are 14 different crystal lattices, called Bravais Lattices. (3 different cubic types, 2 different tetragonal types, 4 different orthorhombic types, 2 different monoclinic types, 1 rhombohedral, 1 hexagonal, 1 triclinic). See below.
Real crystals always possess one of these lattice types, but different crystalline compounds that have the same lattice can have different motifs and different lattice parameters (these depend upon the chemical formula and the sizes of the atoms in the unit cell). We will only concern ourselves with the cubic lattices, though we will refer to the hexagonal lattice in passing.
3 types; Simple cubic (also called primitive cubic), lattice points only at corners.
Body Centered Cubic (BCC), lattice points at corners and in middle of cube.
Face Centered Cubic (FCC) lattice points at the corners and in the middle of each face.
Faces :  these lattice points are shared by 2 cells, each one is "worth" 1/2 to each cell.
Body :  this is the sole possesion of that cell, worth 1.
Total number lattice points: primitive cubic = 8(1/8)
= 1; FCC = 6x1/2 + 8(1/8) = 4; BCC = 8(1/8)
+ 1 = 2.
Now that we know how to describe crystalline solids, let us examine different types according to the nature of their bonding. We will begin with metallic solids, followed by ionic solids, and extended covalent or framework solids.