Afrenkel defect in a crystal is formed when an atom leaves a normal site and moves to an interstitial site (a space inside the crystal). the energy of formation of the defect is e suppose a crystal has n normal sites and n' interstitial sites (n' is usually similar to n.) (a) (i) show that the multiplicity q of the state in which the crystal has n frenkel defects is given by n'n! ω- (n n)(nn)n [2 marks] (11 write down an expression for the entropy s as a function of n [2 marks] equilibrium is (b) show that, for n < < n, n', the number of frenkel defects at (nn exp-s/2kt) [4 marks] (c) explain briefly why the equilibrium number of vacancies differs from zero when the crystal is at temperature t greater than zero