Question

a) Generally, the crystals are expected to expand by temperature. What are the reasons for this? In which cases, it can be expected to decrease the size of the objects whose temperature increases.
b) Explain the reasons for the formation of the forbidden band.
c) Explain the source of diamagnetism (Paul Langevin 1905).
d) Find the mesh vectors and the angles between the mesh vectors of conventional and primitive brim cells for volume centered cubic (BCC) mesh. Find the volume of the unit cells and obtain the ratio of the volume of the conventional cell to the volume of the primitive cell.

Answer 1

(a) The expansion of crystals due to heating is due to the added kinetic energy to the atoms in the lattice. As more heat is added the vibration of the atoms increases making them to increase distance between the other atoms (due to repulsion between the atoms, increase in vibration of one atom, causes the displacement of other atoms too). This eventually leads to a expanded crystal structure. In some cases due to a particular arrangement of atoms, some materials tends to shrink when heated. One example is ScF3, in this material each flourine has bonds with two other Sc atoms.When the material is heated the flourine atoms oscillates more in the perpendicular direction of the bond making the Sc atom to come closer, This happens in the whole material, and due to that the whole structure shrinks.