Q1(a). Zinc blende and wurtzite: radius-ratio rationale
Zinc blende and wurtzite are two different naturally occurring minerals, having same cation/anion in unary composition, but crystallizes in two different forms. Rationalize the observation with radius of cation (74 pm or 88 pm) and anion (184 pm).
Answer in brief
Both ratios fall at or near the tetrahedral range, so both minerals are 4:4 coordinated ZnS. They differ only in the stacking of the close-packed S²⁻ layers: ABC (cubic) in blende, AB (hexagonal) in wurtzite.
Key points
- tetrahedral hole 0.225–0.414; octahedral hole 0.414–0.732. 74/184=0.402 lies just inside the tetrahedral range; 88/184=0.478 lies just above its limit.
- S²⁻ forms a close-packed array; Zn²⁺ fills half the tetrahedral holes. Every Zn has 4 S and every S has 4 Zn.
- S layers stacked ABCABC (ccp, fcc cell, 4 ZnS per cell). Wurtzite: S layers stacked ABAB (hcp, 2 ZnS per cell).
- the Madelung constants (1.638 and 1.641) and lattice energies differ by less than 1%. A cation near the tetrahedral/octahedral boundary (0.48) with covalent, polarising character gives very little energetic preference, so the…
The full model answer
Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.
- Radius ratio: tetrahedral hole 0.225–0.414; octahedral hole 0.414–0.732. 74/184=0.402 lies just inside the tetrahedral range; 88/184=0.478 lies just above its limit.
- Common unit: S²⁻ forms a close-packed array; Zn²⁺ fills half the tetrahedral holes. Every Zn has 4 S and every S has 4 Zn.
- Blende: S layers stacked ABCABC (ccp, fcc cell, 4 ZnS per cell). Wurtzite: S layers stacked ABAB (hcp, 2 ZnS per cell).
- Why two forms: the Madelung constants (1.638 and 1.641) and lattice energies differ by less than 1%. A cation near the tetrahedral/octahedral boundary (0.48) with covalent, polarising character gives very little energetic preference, so the stacking depends on temperature and growth: blende is the low-temperature form, wurtzite is stable above about 1020°C.
the same two types are met by CdS, ZnO (wurtzite) and CuCl, GaAs (blende); a larger cation pushes the structure towards CN 6 (NaCl type), as in CdO.
Coversstructure of ZnSZinc blende and wurtziteradius-ratio rationale
All parts of Question 1
- 1(a) Zinc blende and wurtzite: radius-ratio rationale5 marks
- 1(b) Spin-forbidden bands in 4d and 5d complexes5 marks
- 1(c) Phosphate buffer at pH 7.405 marks
- 1(d) Onset of AgCl precipitation5 marks
- 1(e) Iodometry and iodimetry5 marks
- 1(f) Masking agents in the estimation of Ca²⁺5 marks
- 1(g) First-row metal in EAN-obeying organometallics5 marks
- 1(h) Radioactive displacement: ²¹⁰Pb and ²²⁶Ra5 marks
- 1(i) Electronic spectra of Eu³⁺ and Am³⁺ complexes5 marks
- 1(j) Urea required to precipitate Fe³⁺ as Fe(OH)₃5 marks