hume rothery rules

Metals and alloys. Hume-Rothery rules.
1. Three types of metals.
2. Alloys. Hume-Rothery rules.
3. Electrical resistance of metallic alloys.
4. Applications of metallic alloys.
5. Steels. Super alloys.
6. Electromigration in thin wires.

Three types of metals
Metals share common features that define them as a separate class of materials:
• Good thermal and electrical conductors (Why?).
• Electrical resistance increases with temperature (Why?).
• Specific heat grows linearly with temperature at low (Why?). temperatures. • Good reflectivity in infrared and, for some metals, in visible light
(Why?).
• High molar densities and structures with large number of nearest neighbors(Why?).

Properties of metals are largely defines by their electron structure.

For sp-bonded metals assuming one can assume that the macroscopic properties are the energy of electron gas (see lecture notes of the fall semester).
Energy of an electron gas with Fermi energy EF:
3
3 Nh 2  3π 2 N

U = nEF =
5
10 m  V

∂U 

P = −
Pressure of electron gas:

∂V  S

 ∂ 2U 
2nEF
 ∂P 
 =
= −V 
B = −V 
Bulk modulus:

 ∂V 2 
∂V  S
3


S

This derivation does not include the attraction force between the lattice and the electrons and coulomb repulsion.






sp-bonded metals follow Sommerfeld model.

sp-bonded metals are quite different: Ia –metals are soft, IIa – metals are hard, IIIa and IVa – metals are soft. Most of these metals are good conductors.

Transition metals.

Properties of transition metals strongly depends on the number of d electrons!
Cohesive energy

Bulk modulus.

Melting temperatures and elastic constant follow the same pattern.
The behavior reflects the strength of the d-orbital interactions.

Rare Earth Metals.

f-orbitals are localized and interaction between forbitals of different atoms is weak.
Most of the RE metals are trivalent (exception
Ce4+, Sm2+, Eu2+).

Most