CHM 401

 

The Solid State

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

Amorphous Solids: x-rays scatter broadly and diffusively which implies no long range order

Closest packed structures

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.