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Wurtzite Structure (ZnS)

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Wurtzite (ZnS)
A hexagonal polymorph of zinc sulfide where Zn2+ and S2- ions are in 4:4 tetrahedral coordination.
Wurtzite is the hexagonal form of ZnS with a structure based on hexagonal close-packing of sulfur atoms. Zinc atoms occupy half of the tetrahedral holes in an ordered manner, specifically alternating tetrahedral sites. Each Zn2+ is tetrahedrally coordinated by 4 S2- ions and vice versa. The structure belongs to space group P6₃mc with 2 formula units per unit cell. Unlike zincblende (the cubic polymorph), wurtzite has an ABAB stacking sequence and lacks a center of symmetry, making it piezoelectric. The structure is adopted by many II-VI semiconductors including ZnO, CdS, and AlN.

Problem 1

Question: In the wurtzite (ZnS) structure, sulfide ions form HCP arrangement. What fraction of tetrahedral holes are occupied by Zn²⁺ ions?

Solution

Calculation:

In HCP, number of tetrahedral holes = 2 × number of atoms in HCP

For ZnS (1:1 ratio), number of Zn²⁺ = number of S²⁻

Fraction occupied = (number of S²⁻)/(2 × number of S²⁻) = 1/2

Fraction occupied = 1/2 or 50%

Problem 2

Question: What is the coordination number of Zn²⁺ and S²⁻ in the wurtzite structure?

Solution

Answer:

Coordination number of Zn²⁺ = 4 (tetrahedral coordination by 4 S²⁻)

Coordination number of S²⁻ = 4 (tetrahedral coordination by 4 Zn²⁺)

The coordination ratio is 4:4

Problem 3

Question: What is the main difference between wurtzite and zinc blende structures?

Solution

Answer:

Wurtzite: Hexagonal structure with HCP arrangement (ABAB stacking)

Zinc blende: Cubic structure with FCC arrangement (ABCABC stacking)

Both have 4:4 coordination, but differ in their stacking sequence and crystal symmetry.

Wurtzite is also polar (non-centrosymmetric) while zinc blende is not.

Numerical Problem

Question: In the wurtzite structure of ZnS, the sulfur atoms form a hexagonal close-packed (hcp) arrangement, and zinc atoms occupy half of the tetrahedral holes.

(a) If there are 100 sulfur atoms in a wurtzite crystal, how many tetrahedral holes are present in total?

(b) How many of these tetrahedral holes are occupied by zinc atoms?

(c) What is the coordination number of Zn2+ and S2- in wurtzite structure?

[Given: In a close-packed structure, number of tetrahedral holes = 2 × number of atoms forming the close-packed structure]

Solution

(a) Total number of tetrahedral holes:

Given: Number of sulfur atoms = 100

In a close-packed structure (hcp in this case):

Number of tetrahedral holes = 2 × number of atoms in close-packed arrangement

Number of tetrahedral holes = 2 × 100

Number of tetrahedral holes = 200

(b) Number of tetrahedral holes occupied by Zn:

In wurtzite structure, zinc atoms occupy half of the tetrahedral holes

Number of Zn atoms = (1/2) × total tetrahedral holes

Number of Zn atoms = (1/2) × 200

Number of Zn atoms = 100

Note: This gives the stoichiometry ZnS (1:1 ratio), which matches the formula. We have 100 Zn atoms and 100 S atoms.

(c) Coordination numbers:

Coordination number of Zn2+ = 4

Each Zn2+ ion is surrounded by 4 S2- ions in tetrahedral arrangement

Coordination number of S2- = 4

Each S2- ion is surrounded by 4 Zn2+ ions in tetrahedral arrangement

Explanation: In wurtzite, both ions have tetrahedral coordination (4:4), which is characteristic of covalent bonding. This is different from ionic structures like NaCl which have octahedral coordination (6:6). The tetrahedral coordination in wurtzite reflects the significant covalent character in the Zn-S bond.

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