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) Write down the reason why good conductors are used in mirror construction.
d) Show S_dia = S_bas × S_fcc for the structure factors; S_dia, S_bas, S_fcc which are diamond crystal, the base of the diamond, and for FCC respectfully.

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. 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.