Kronig-Penny model, how electrons get free of their atom?

[LostConjugate]

I am reading about this for the first time.

The Kronig-Penny model seems to assume the electrons have already escaped their atom and starts out with free electrons between potentials, then proceeds to calculate the energy eigenstates.

Did I miss something here? How do the electron's escape their atom in the first place, they don't seem to have much reason to?

In the limit that the space between atoms goes to infinity this model gives a free particle solution.

 

[alxm]

Well, remember here that they're not 'free' as in an electron in vacuum far, far away from the crystal. The boundary conditions on the model eliminate that possibility.
They're 'free' as in delocalized; free to move about in the crystal - which is of course a different situation.
Of course, whether or not you have any delocalized electrons depends on the barrier height between the atoms, which is a (crude) model of chemical bonding; a chemical bond by definition being an electronic state where (some) electrons are shared between two atoms.

So your barrier height here, i.e. the nature of the bonding between the atoms, is what determines to what extent you have delocalized electrons, and ultimately, whether or not the material is an insulator or conductor.

 

[LostConjugate]

Well, remember here that they're not 'free' as in an electron in vacuum far, far away from the crystal. The boundary conditions on the model eliminate that possibility.
They're 'free' as in delocalized; free to move about in the crystal - which is of course a different situation.
Of course, whether or not you have any delocalized electrons depends on the barrier height between the atoms, which is a (crude) model of chemical bonding; a chemical bond by definition being an electronic state where (some) electrons are shared between two atoms.

So your barrier height here, i.e. the nature of the bonding between the atoms, is what determines to what extent you have delocalized electrons, and ultimately, whether or not the material is an insulator or conductor.

Ok, I was just thinking of a bunch of atoms sitting side by side with no chemical bonding. I think I need to do more reading on the properties of solids to get a better understanding. Thanks!

 

[abid220]

actually, i have also bit confusion in this regards. For example in hexa-boride compound, has, an Octahedra of 6-boron atoms, which are connected to another Octahedra by covalent bond. so In the unit cell, 8-octahedra of boron are lying on corners, which are connected via single covalent bond. In the middle we can put one Rare Earth metal at the center of unit cell. let say, Ca, Sr or Ba, i.e. CaB6, or SrB6, BaB6. So now the Metal ion is surrounded by 8- Octahedra of Borons. So here how can we vissualize the electronic structure, in relation to chemical bonding.