PROBLEM SET 5

PROBLEM SET 5 - BAND STRUCTURE AND CONDUCTIVITY IN SOLIDS...

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MSE 110 - U of A Band structure: metallic conductors BAND STRUCTURE AND CONDUCTIVITY IN SOLIDS • The band in alkali metals is formed from overlap of outer shell s orbitals • The band in alkaline earth metals is formed by overlap of the bands formed by s orbitals and by p orbitals • The transition metals have partially filled d and f band. • Because the band is partially filled conductivity and reflectivity are high. . E Electronic Energy Band Structure
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MSE 110 - U of A Band structure of ionic solids: BAND STRUCTURE AND CONDUCTIVITY IN SOLIDS • In ionic solids the cation donates its electron to the anion to satisfy the octet rule (complete the p orbitals of the anion). • The Na atoms transfer electrons to the Cl atoms which form the full valence band while Na atoms form th eempty conduction band . • Because of the strong electronegativity difference in ionic solids, the band gap between the valence and conduction band is very large. So, electrons cannot be excited across the gap by thermal energy and conductivity is very, very low. The material is an insulator. Electronic Energy Band Structure Eg Eg > 4 eV
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MSE 110 - U of A Band structure of covalent solids: BAND STRUCTURE AND CONDUCTIVITY IN SOLIDS • Each atom combine 4 sp3 hybridized orbitals to form the bonding (valence) and anti-bonding (conduction) band. • Group IV elements contribute their 4 outer electrons to the valence band and fill it. The conduction band is empty. • These two bands are separated by a small gap Eg. 1 2 3 4 Band Structure Valence Conduction Eg Thermally excited electrons in conduction band
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MSE 110 - U of A Problem 1 What type of band structure does CrCo possess? [answer A, B, C] AM e t a l l i c B Insulating C Semiconducting Ans: Cr and Co have similar electronegativities so no electron transfer will occur. Also, they both have partially filled d orbitals that will overlap to form a partially filled energy band. A partially filled band is consistent with the energy band structure or a metal. The answer is A.
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MSE 110 - U of A Problem 2 What type of band structure does MgF 2 possess? [answer A, B, C] AM e t a l l i c B Insulating C Semiconducting Ans: Mg and F have a large difference in electronegativity. The Mg ions will give up their electrons to the F ions to complete their outer shells by filling the p orbitals. The filled p orbitals will overlap to create a filled valence band and the empty s orbitals from the Mg cations will overlap to create an empty conduction band. Because of the strong difference in electronegativity, the band gap will be large.
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PROBLEM SET 5 - BAND STRUCTURE AND CONDUCTIVITY IN SOLIDS...

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