Why some solids are electrical conductors

[Kawakaze]

Homework Statement

Describe what influence the periodic structure of a crystalline solid has on the energy distribution of the free electrons, and hence explain, in general terms, why some solids are electrical conductors and some are insulators.

Homework Equations

The Attempt at a Solution

Im assuming the question can be partly answered with band theory. What I don't understand is what bearing the crystalline structure has. Please note this is for an assessment, so no direct answer please. Band theory refers to the sub-shells and the energy gaps between them, can I have a hint on how the crystalline structure may affect this? Is it something to do with bonding, ionic or covelant and how can this even factor in something like a pure metal sample? Thanks =)

 

[Dickfore]

Bloch's Theorem.

 

[Kawakaze]

Hi Dick, thanks for the answer, unfortunately that isn't in my course material at all. Maybe a little higher than the level I am doing. I did have a read of it, and it does mention the same two models i am aware of, namely the nearly free electron model and the tightly bound electron model. I still cannot see how this all fits together though. Maybe another hint please? =)

 

[Dickfore]

What course are you taking and what is the course material you are using?

Have you ever met some of these terms:

1. Direct Lattice
2. Reciprocal Lattice
3. First Brillouin Zone
4. Born von Karman Periodic Boundary Conditions
5. Density of States

Essentially, the free-electron (+hole) model is a fairly good approximation when analyzing the electric properties of solids. But, instead of using plane waves as the stationary states for the electron, the corresponding basis is spanned by the above-mentioned Bloch states. Two main effects arise from this modification:

1. The energy levels are split into bands of allowed and forbidden intervals;
2. The electrons (and holes) acquire an effective mass (which might be a second - rank tensor quantity) which has a profound effect on the density of states