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NaCl Structure (Rock Salt)

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NaCl (Halite)
The classic rock salt structure with Na+ and Cl- ions in a 6:6 coordination forming a cubic lattice.
Sodium chloride crystallizes in the rock salt structure, one of the most common ionic structures. Both Na+ and Cl- ions form interpenetrating face-centered cubic (fcc) lattices. Each Na+ is octahedrally coordinated by 6 Cl- ions, and vice versa. The structure belongs to space group Fm3̄m with 4 formula units per unit cell. The radius ratio (rNa+/rCl-) of approximately 0.52 falls perfectly within the predicted range for octahedral coordination (0.414-0.732). This structure type is adopted by many alkali halides and serves as a prototype for understanding ionic solids.

Problem 1

Question: In NaCl structure, how many formula units of NaCl are present per unit cell?

Solution

Calculation:

Na⁺ ions: 12 (edges) × (1/4) + 1 (center) = 4

Cl⁻ ions: 8 (corners) × (1/8) + 6 (faces) × (1/2) = 4

Formula units = 4 NaCl per unit cell

Problem 2

Question: If r(Na⁺) = 1.02 Å and r(Cl⁻) = 1.81 Å, calculate the edge length of the NaCl unit cell.

[In rock salt structure: a = 2(r₊ + r₋)]

Solution

Calculation:

a = 2(r₊ + r₋)

a = 2(1.02 + 1.81)

a = 2(2.83)

a = 5.66 Å

Problem 3

Question: What is the coordination number of both Na⁺ and Cl⁻ in the rock salt structure?

Solution

Answer:

Coordination number of Na⁺ = 6 (octahedral coordination by 6 Cl⁻)

Coordination number of Cl⁻ = 6 (octahedral coordination by 6 Na⁺)

The coordination ratio is 6:6

Challenging Numerical Problem

Question: Sodium chloride (NaCl) crystallizes in a rock salt structure with a unit cell edge length of 5.64 Å. The density of NaCl is 2.165 g/cm³.

(a) Calculate the number of NaCl formula units per unit cell and verify it matches the theoretical value for rock salt structure.

(b) If a Schottky defect is introduced where 0.1% of the Na+ and Cl- ion pairs are missing from the lattice, calculate the density of the defective crystal.

(c) Calculate the coordination number that would result if the crystal underwent a phase transition where the edge length increased by 15% while maintaining the same structure type. Would this coordination be stable based on radius ratio rules?

[Given: Atomic mass Na = 23 u, Cl = 35.5 u, NA = 6.022 × 10²³ mol⁻¹, rNa+ = 1.02 Å, rCl- = 1.81 Å]

Solution

(a) Number of formula units per unit cell:

Using the density formula: ρ = (Z × M)/(a³ × NA)

Where: M = molar mass of NaCl = 23 + 35.5 = 58.5 g/mol

a = 5.64 Å = 5.64 × 10⁻⁸ cm, ρ = 2.165 g/cm³

Rearranging: Z = (ρ × a³ × NA)/M

Z = (2.165 × (5.64 × 10⁻⁸)³ × 6.022 × 10²³)/58.5

Z = (2.165 × 179.41 × 10⁻²⁴ × 6.022 × 10²³)/58.5

Z = 233.89/58.5 = 4 formula units

This matches the theoretical value for rock salt structure (4 NaCl units per unit cell).

(b) Density with Schottky defect:

Schottky defect: Both cation and anion vacancies created, ions leave the crystal

0.1% of ion pairs missing = 0.001 × 4 = 0.004 formula units removed

Effective Z = 4 - 0.004 = 3.996 formula units

Volume remains constant (a³ remains same)

New density: ρ' = (Z' × M)/(a³ × NA)

ρ' = (3.996/4) × 2.165 = 0.999 × 2.165

ρ' = 2.163 g/cm³

Density decreases by 0.1% (same as defect percentage)

(c) Coordination after expansion:

New edge length: a' = 1.15 × 5.64 = 6.486 Å

In rock salt structure: 2(rNa+ + rCl-) = a (ions touch along edge)

Original: 2(rNa+ + rCl-) = 2(1.02 + 1.81) = 5.66 Å ≈ 5.64 Å ✓

After expansion, nearest neighbor distance increases

The coordination number remains 6 (octahedral) as the structure type is maintained

However, checking stability with radius ratio:

rNa+/rCl- = 1.02/1.81 = 0.564

For octahedral coordination: 0.414 < r⁺/r⁻ < 0.732 ✓

The structure would remain stable as the radius ratio still falls within the octahedral range, though the increased lattice parameter would reduce lattice energy and stability.

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