Valency and the Partially Filled Band

A feature common to both bismuth and copper oxides is the availability of three consecutive oxidation states Cu1, Cu11, Cum and 

All of these oxidation states are well known to chemists, with the exception of Biiv. We know that s1 cations such as BiIV are unstable when concentrated. Thus, we do not normally find discrete compounds where bismuth is entirely in the tetravalent state. However, we do find BiIV in dilute systems, both insulating and metallic systems (3). 

The mixed valency situation may be equally well described in terms of bands. The band to be considered in the case of bismuth is the Bi6s-02p band. The band in the case of copper is the Cu3d y2 -02p band. Both of these are d bands. For the lowest oxidation state (Cu1 or Bira), these bands are filled for the highest oxidation state (Cu111 or Biv), these bands are empty. According to simple band structure considerations, we would expect metallic properties for any partial filling of these o bands in bismuth and copper oxides. While metallic properties are indeed observed for most of the intermediate 

There are two competing mechanisms to produce an insulating state for the half-filled o band. One is through valency disproportionation, and this is the case for BaBiOs, i.e., 2BiIV — Bira + Biv. If BiIV had not disproportionated in BaBiOj, we would expect this compound to be metallic because it would have a half-filled band. Many have been confused by this disproportionation description because of confusion about the meaning of valent states as opposed to real charges. We will come back to the subject later. 

La2Cu04. The metallic compounds (a) are hypothetical materials without disproportionation or magnetic interactions which cause band splitting (b) when the o band is half filled. Both p-type (c) and n-type (d) conductors are shown. 

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