Chemistry Study Material

Band Theory was developed with some help from the knowledge gained during the quantum revolution in science. In 1928, Felix Bloch had the idea to take the quantum theory and apply it to solids. In 1927, Walter Heitler and Fritz London discovered bands- very closely spaced orbitals with not much difference in energy.  In this image, orbitals are represented by the black horizontal lines, and they are being filled with an increasing number of electrons as their amount increases. Eventually, as more orbitals are added, the space in between them decreases to hardly anything, and as a result, a band is formed where the orbitals have been filled. Different metals will produce different combinations of filled and half filled bands.  Sodium's bands are shown with the rectangles. Filled bands are colored in blue. As you can see, bands may overlap each other (the bands are shown askew to be able to tell the difference between different bands). The lowest unoccupied band is c

Spinel Structure Formulae – (A 2+ )(B 3+ ) 2 O 4  or AB 2 O 4  or AO.B 2 O 3 FCC Packing of anions Partial occupancy of both tetrahedral and octahedral sites i.e.1/8 th  of tetrahedral and ½ of the octahedral sites are occupied. A spinel unit-cell is made up of eight FCC cells  made by oxygen ions in the configuration 2×2×2, so it is a big structure consisting of 32 oxygen atoms,  8 A atoms and 16 B atoms . Depending on how cations occupy different interstices, spinel structure can be Normal or Inverse.         1.7.4.1 Normal Spinel Chemical formula: (A 2+ )(B 3+ )O 4 Examples are many aluminates such as MgAl 2 O 4 , FeAl 2 O 4 , CoAl 2 O 4  and a few ferrites such as ZnFe 2 O 4  and CdFe 2 O 4 . In this structure, all the A 2+  ions occupy the tetrahedral sites and all the B 3+  ions occupy the octahedral sites. Apply bond strength rule to verify the stoichiometry Cations: -  A 2+  -  2 ⁄ 4  ; B 3+  -  3 ⁄ 6 Oxygen valence  = ( 2 ⁄ 4 x1)+ ( 3 ⁄ 6 x

The simple structures come from the arrangement of the anions (though sometimes the cations) in the positions of the spheres in the fcc or hcp lattices, and the cations go into some or all of the octahedral and tetrahedral holes within the lattices. Structures based on face centered cubic lattices The Rock Salt structure This the structure adopted by  Sodium Chloride , NaCl. It is based on the fcc array of the large chloride anions, and the sodium cations occupy all the octahedral holes in the fcc  lattice . However, it could also be seen as an fcc array of sodium ions, with the anions in all the octahedral holes. Each ion is octahedrally coordinated by six counterions, and so this structure has so-called  (6,6)-coordination , where the first number refers to the coordination of the  cation  and the second to the  anion . The structure beyond the first coordination sphere can also be visualized. The Rock Salt, or NaCl, structure The sodium cations (green) occupy the oct