Coordination Number = CN = the number of nearest neighbors
Td = tetrahedral holes (4 nearest neighbors, CN = 4)
Oh = octahedral holes (6 nearest neighbors, CN = 6)
In solids, atoms or molecules are near each other to the point of "touching" (high density)
In the simplest case, a solid can be thought of as an array of spheres put together in some arrangement (spherical symmetry certainly is a good assumption for metals, perhaps poorer for molecular solids)
The packing of spheres can fit into one of two extremes:
Crystalline Solids : x-rays diffract sharply which implies regular order on the scale of nm
spheres pack into a regular, repeatable fashion called the crystal lattice
the smallest repeat unit in the lattice is called the unit cell
the unit cells fit together snugly like bricks in a wall-this is translational symmetry
Amorphous Solids: x-rays scatter broadly and diffusively which implies no long range order
Closest packed structures
spheres pack together closely but there is no translational symmetry
no regular order to the unit cells (there still may be short range order)
like the pile of bricks before being laid into a wall
ABAB (hexagonally closest packed, hcp)
Coordination Number = CN = the number of nearest neighbors
Td = tetrahedral holes (4 nearest neighbors, CN = 4)
Oh = octahedral holes (6 nearest neighbors, CN = 6)
ABCABC (cubic closest packed, ccp or face centered cubic, fcc)
fcc still has CN = 12, still 26% void volume, the unit cell has 4 spheres in it.
Closest packed structures are the most efficient way to pack spheres but are not required or even the most common.
Other common structures:
body centered cubic (bcc):
spheres only "touch" along the body diagonal of the cubic unit cell
CN = 8, 2 spheres per unit cell, ~32% void volume
primitive cubic:
spheres only touch along cell edges, CN = 6, void volume ~48%
1 sphere per unit cell
The structure of metals often changes as a function of temperature - phase transitions occur - this is called polymorphism or polytypism
Alloys are form by mixing different types of metals together:
Substitutional alloys: one metal replaces another metal at some lattice sites. This requires that both types of metals be roughly the same size.
Interstitial alloys: the new atoms are introduced into the hole sites (called interstices) of the host lattice. The new atoms can occupy either Td or Oh holes.
