CsCl Structure - Cesium Chloride

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CsCl (Cesium Chloride)

A simple cubic structure where Cs⁺ ions are in 8:8 coordination with Cl^- ions at the body center.

The CsCl structure is often mistaken for body-centered cubic but is actually a simple cubic structure with two interpenetrating simple cubic lattices. Cesium ions occupy cube corners while chloride ions sit at the body center (or vice versa), resulting in 8-fold cubic coordination for both ions. The structure belongs to space group Pm3̄m with 1 formula unit per unit cell. The large radius ratio (r_Cs+/r_Cl- ≈ 0.93) exceeds the limit for octahedral coordination (0.732) and favors this 8-coordinate structure. Many binary compounds with similar-sized ions adopt this structure, including CsBr, CsI, TlCl, and some intermetallic compounds like CuZn.

Problem 1

Question: How many formula units of CsCl are present per unit cell in the cesium chloride structure?

Solution

Calculation:

Cs⁺ at body center: 1 (completely inside)

Cl⁻ at corners: 8 × (1/8) = 1

Formula units = 1 CsCl per unit cell

Problem 2

Question: If r(Cs⁺) = 1.67 Å and r(Cl⁻) = 1.81 Å, calculate the edge length of the CsCl unit cell.

[In CsCl structure: body diagonal = 2(r₊ + r₋) and body diagonal = a√3]

Solution

Calculation:

Body diagonal = a√3 = 2(r₊ + r₋)

a√3 = 2(1.67 + 1.81)

a√3 = 2(3.48)

a√3 = 6.96

a = 6.96/√3 = 6.96/1.732

a = 4.02 Å

Problem 3

Question: What is the coordination number in the CsCl structure and why does CsCl adopt this structure instead of rock salt?

Solution

Answer:

Coordination number = 8:8 (each Cs⁺ surrounded by 8 Cl⁻ and vice versa)

Reason: The radius ratio r(Cs⁺)/r(Cl⁻) = 1.67/1.81 = 0.92

Since 0.732 < 0.92 < 1.0, the structure favors 8-coordination.

Cs⁺ is large enough to accommodate 8 Cl⁻ ions around it in cubic geometry.

Numerical Problem

Question: In the CsCl structure, Cs⁺ ions occupy the corners of a cube and Cl^- ion is at the body center (or vice versa).

(a) How many Cs⁺ ions are effectively present per unit cell? (Remember: each corner atom is shared by 8 unit cells)

(b) How many Cl^- ions are effectively present per unit cell? (A body-centered atom belongs entirely to one unit cell)

Solution

(a) Number of Cs⁺ ions per unit cell:

Cs⁺ ions are located at the 8 corners of the cube

Each corner atom is shared by 8 adjacent unit cells

Contribution of each corner atom = 1/8

Number of Cs⁺ ions = 8 corners × (1/8)

Number of Cs⁺ ions = 1

(b) Number of Cl^- ions per unit cell:

Cl^- ion is located at the body center of the cube

A body-centered atom belongs entirely to one unit cell

Contribution of body-centered atom = 1

Number of Cl^- ions = 1

Verification: Cs : Cl = 1 : 1, which matches the formula CsCl ✓

(c) Coordination number of Cs⁺:

If we place a Cs⁺ ion at one corner, the nearest Cl^- ions are at the body centers of all cubes sharing that corner

Each corner is shared by 8 cubes, and each cube has 1 Cl^- at its body center

Therefore, each Cs⁺ is surrounded by 8 Cl^- ions

Coordination number of Cs⁺ = 8

Note: Similarly, each Cl^- is also surrounded by 8 Cs⁺ ions at the corners of its cube. So the coordination number is 8:8, which is characteristic of the CsCl structure.

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CsCl Structure (Cesium Chloride)

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Problem 1

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Problem 2

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Problem 3

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Numerical Problem

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