Question

Pls explain me the 2D structures of NaCl, CsCl, ZnS as per exam view.

Answer 1

SINCE YOU HAVE NOT MENTIONED WHICH EXAM POINT OF VIEW, IM EXPLAINING IT IN IIT-JEE POINT OF VIEW, WHICH WILL COVER ALL OTHER EXAM SYLLABUS AS WELL.

NaCl
The sodium chloride structure is composed of Na⁺ and Cl^- ions.
The number of sodium ions is equal to that of Cl^- ions. The radii of Na⁺ and Cl^- ions 95 pm and 181 pm giving the radius ratio of 0.524
The radius ratio of 0.524 for NaCl suggest an octahedral void.
Chloride ions (In a typical unit cell) are arranged in cubic close packing (ccp). In this arrangement, Cl^- ions are present at the corners and at the centre of each face of the cube. This arrangement is also regarded as face centred cubic arrangement (fcc).
The sodium ions are present in all the octahedral holes.
Since, the number of octahedral holes in ccp structure is equal to the number of anions, every octahedral hole is occupied by Na⁺ ions. So that the formula of sodium chloride is NaCl i.e. stoichiometry of NaCl is 1:1.
Since there are six octahedral holes around each chloride ions, each Cl^- ion is surrounded by 6 Na⁺ions. Similarly each Na⁺ ion is surrounded by 6 Cl^- ions. Therefore, the coordination number of Cl^- as well as of Na⁺ ions is six. This is called 6:6 coordination.
It should be noted that Na⁺ ions to exactly fit the octahedral holes, the radius ratio r_NA⁺ / r_Cr should be equal to 0.414. However, the actual radius ratio (r_NA⁺ / r_Cr = 0.524) exceeds this value. Therefore to accommodate large Na⁺ ions, the Cl^- ions move apart slightly i.e. they do not touch each other and form an expanded face centred lattice.
number of NaCl units per unit cell is 4.

CsCl
The caesium chloride crystal is composed of equal number of caesium (Cs⁺) and Chloride Cl^-ions. The radii of two ions (Cs⁺ = 169 pm and Cl^- = 181 pm) led to radius ratio of r_CS⁺ to r_Cl^– as 0.93 which suggest a body centred cubic structure having a cubic hole
R_CS⁺ to R_Cl^– = 169 / 181 = 0.93
The chloride ion form the simple cubic arrangement and the caesium ions occupy the cubic interstitial holes. In other words Cl^- ions are at the corners of a cube whereas Cs⁺ ion is at the centre of the cube or vice versa
Each Cs⁺ ion is surrounded by 8 Cl^- ions and each Cl^- ion in surrounded by 8 Cs⁺ ions. Thus the Co – ordination number of each ion is eight.
For exact fitting of Cs⁺ ions in the cubic voids the ratio r_CS⁺ / r_Cl^– should be equal to 0.732. However, actually the ratio is slightly larger (0.93). Therefore packing of Cl^- ions slightly open up to accommodate Cs⁺ ions.
Number of CsCl units per unit cell is 1
Relation between radius of cation and anion and edge length of the cube, r_CS to r_Cl = a√3/2
Other common examples of this type of structure are CsBr, CsI, TlCl, TlBr

ZnS
The zinc sulphide crystals are composed of equal number of Zn⁺² and S^2- ions.
The radii of the two ions (Zn⁺² = 74 pm and S^-2 = 184 pm) led to the radius (r⁺ / r^–) as 0.40 which suggests a tetrahedral arrangement.
r_Zn⁺² / r_S^–2 = 0.40
The Zinc ions are arranged in ccp arrangement, i.e. sulphide ions are present at the corners and the centres of each face of the cube
Zinc ions occupy tetrahedral hole. Only half of the tetrahedral holes are occupied by Zn⁺² so that the formula of the zinc sulphide is ZnS i.e. the stoichiometry of the compound is 1:1 (Only alternate tetrahedral holes are occupied by Zn⁺²)
Since the void is tetrahedral, each zinc ion is surrounded by four sulphide ions and each sulphide ion is surrounded tetrahedrally by four zinc ions. Thus zinc sulphide has 4:4 Co – ordination.
For exact fitting of Zn^{+2 in the tetrahedral holes, formed by close packing of S-2} ions, the ratio Zn⁺²/S^-2 should be 0.225. Actually this ratio is slightly large (0.40) There are four Zn⁺² ions and four S^-2 ions per unit cell as calculated below:
No. of S^-2 ions = 8(at corners) × 1/8 + 6(at face centres) × 1/2 = 4
No. of Zn⁺² ions = 4(within the body) × 1 = 4
Thus, the number of ZnS units per unit cell is equal to 4. Some more examples of ionic solids having Zinc blende structures are CuC, CuBr, CuI, AgI, beryllium sulphide.