Q1(a). Frenkel disorder in silver bromide
(i) Does the Frenkel disorder in AgBr create vacancies of Ag⁺, vacancies of Br⁻ or both? Explain. The ionic radii are 1.15 Å for Ag⁺ and 1.96 Å for Br⁻. (ii) Calculate the temperature at which the fraction of Frenkel defects in a crystal of AgBr exceeds 1 part per billion. The enthalpy of Frenkel defect formation, ΔHf, has the value of 1.16 eV/defect, and the entropic prefactor, A, has a value of 3.091.
Answer in brief
A silver ion leaves its normal site for an interstitial site; taking 1.16 eV as the formation enthalpy of one vacancy–interstitial pair, the threshold is approximately 308 K.
Key points
- The smaller Ag⁺ ion occupies an interstice more readily than the larger Br⁻ ion, so cation vacancies and cation interstitials form together; bromide vacancies are not involved.
- The crystal retains its Ag:Br ratio and electrical neutrality: AgAg → V′_Ag + Ag•ᵢ.
- For dilute Frenkel pairs, f = A exp[−ΔHf/(2kBT)]; at the threshold T = 1.16(1.602 × 10⁻¹⁹)/[2(1.38 × 10⁻²³) ln(3.091/10⁻⁹)] = 308.1 K.
- Therefore f > 10⁻⁹ for T > 308.1 K; the factor 2 follows from the two independently placed members of a Frenkel pair.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
CoversFrenkel defectAgBrpoint defectsinterstitial silver iondefect concentration
All parts of Question 1
- 1(a) Frenkel disorder in silver bromide8 marks
- 1(b) Changing the enthalpy reference8 marks
- 1(c) C–F and C–I potential-energy curves8 marks
- 1(d) Desilverisation of lead8 marks
- 1(e) Equilibrium constant of a Zn–Ag cell8 marks