Bonds to Bands:  Conduction Properties of Solids.
This page:
Bonding and Conductivity of Metals
Band formation in extended covalent solids
Band Structure
Benzene and Graphite
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 Metallic Solids
Ionic Solids
Covalent Solids
Conduction properties
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Solids can exhibit a wide range of conduction properties, these can be rationalized and interpreted by considering the character of their bonding and structure.
 


 
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Bonding and Conductivity of Metals.

Metals: low electronegativity, extensive delocalization of valence electrons, high coordination numbers, high electronic conductivity.

A metal can be viewed as an infinitely large molecule; using the concepts of Molecular Orbital theory and the LCAO approach the overlap of an infinite number of atomic orbitals leads to the formation of "Crystal Orbitals".
 
 
From the MO treatment of diatomic, triatomic and multiatomic molecules we know that as the number of contributing Atomic Orbitals is increased, the energy separation of the resultant Molecular Orbitals is decreased. 

In this example we show the M.O.'s formed by combining 2, 3, 4, and n, s-type atomic orbitals.  Darker circles represent a "+" lobe, lighter circles "-" lobe.  

The filling of the orbitals is shown for an example containing  a single electron in each A.O. (e.g. the alkalis) 

For a solid with an infinite number of contributing atomic orbitals we form continuous bands with negligeable energy separations between the energy levels within the band. 

The solid is stabilized becuase the electrons can occupy the lower levels of the band.

 

The conduction in metals arises from:
(a) the delocalization of the electron energy levels over the entire solid.
(b) the availability of empty orbitals in a given band permitting movement of the electrons.  Almost no energy is required to promote the electrons to the open level.

While this treatment readily explains the conduction properties of the Group 1 metals which have a single s electron in each atomic orbital and therefore might be expected to form a half filled s band, what about Group 2 (Alkaline earths), where the atomic s orbital is full - shouldn't this lead to a filled s band and therefore no conduction ?

In fact the energy separation of the constituent s and p orbitals are close enough that for the solid the s and p bands overlap.  Therefore the alkaline earths are metallic as they have a partially filled s-p band.  See below.

The highest occupied level in the band is known as the Fermi Level.
 


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Semiconducting and Insulating solids: Band formation in extended covalent solids.
 
For compounds where the separation in energy of the bonding and antibonding orbitals is large, the broadening of the levels in the solid state is insufficient to cause overlap of the resultant bands.  In these cases insulating or semi-conducting behavior will result.

For example, consider the case of diamond where we have seen previously the bonding is closely related to methane
(see Structure of Covalent Solids).

For methane the s overlap of the H(1s) and C(sp3) orbitals produces s bonding and s* antibonding levels with a large energy separation.  A similar situation arises for the s sp3-sp3 overlap between 2 C atoms.  In diamond, the s and s* levels undergo some degree of broadening into bands, however the energy gap between the top of the s band and the bottom of the s* band - the BAND GAP - is large.  The s band is filled by the available electrons (this is called the VALENCE BAND),the s* band is empty (this is the CONDUCTION BAND).  Conduction requires transfer of electrons to the conduction band across the very large band gap. Becuase the gap is so large diamond is an insulator.
 

As the separation of the bonding and antibonding bands decreases the band gap decreases.  It is then possible for the solid to exhibit some degree of conductivity through thermal excitation of the electrons across the energy barrier, these solids are known as SEMI-CONDUCTORS.  Silicon is a well known example.

Silicon has the diamond structure and therefore a similar MO arrangement to diamond.  However in silicon the atom-atom separation (Si-Si = 2·35Å) is longer than the C-C distance in diamond (C-C = 1·54Å).  As a result there is less overlap between the hybrid A.O.'s and the band gap is smaller (band gap in Si = 1.1 eV).
Similarly Ge, below Si in the Group IV, has an even smaller band gap (0.7eV) and longer Ge-Ge bond length (2.45Å).
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Band Structure.

A summary of the band structures of metals, semi-conductors and insulators is given below.
 


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Benzene and Graphite.

The similarity between the bonding in methane and diamond allowed us to interpret the insulating properties of diamond; in a similar way it is possible to interpret the electronic properties of graphite.  The properties of diamond and graphite are very different, diamond is hard, colorless, and an insulator; graphite is a well known lubricant, black, and a conductor.  These differences arise from the different bonding and structure.   The structure of graphite is based on layers of connected six-member rings of carbon atoms - the structure of the layers is very similar to that of benzene, see below.  While the bonding in the layers is very strong, only  weak Van Der Waals forces bond the layers together (thus the effectiveness of graphite as a lubricant).
 
 
Benzene
Layered structure of Graphite
 
The conduction of electrons within the graphite layers can be rationalized using M.O. theory.  Consider benzene: each carbon atom forms sp2 hybrids that overlap to form s and s* M.O.'s.  The remaining pz orbitals overlap to form 6 p molecular orbitals - the nature of the overlap is shown below.  The p M.O.'s  have  4 discrete energy levels.  The separation of the levels is  small compared to the s - s* separation.  In graphite each of the levels is broadened into bands and the p orbitals overlap to form a continuous band.  This band is half filled and graphite exhibits metallic conduction within the layers.
 


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