Question

The coordination number of \(\mathrm{Zn}^{2+}\) and \(\mathrm{S}^{2}\) ions in the zinc blende (ZnS) type structure is (a) \(6: 8\) (b) \(4: 4\) (c) \(4: 8\) (d) \(8: 8\)

Short answer

The coordination number is \(4:4\) for ZnS structure.

Step-by-step solution

Understanding the Concept

The coordination number in a crystal structure refers to the number of nearest neighbor atoms or ions immediately surrounding a central atom or ion. In the zinc blende (ZnS) structure, both \(\mathrm{Zn}^{2+}\) and \(\mathrm{S}^{2-}\) ions form a face-centered cubic lattice.

Identify the Coordination Number

In zinc blende, the structure is based on a cubic lattice, but each ion is tetrahedrally coordinated. This means that each \(\mathrm{Zn}^{2+}\) ion is surrounded by four \(\mathrm{S}^{2-}\) ions and vice versa.

Analyzing the Options

We need to match the correct coordination numbers from the given options. From our understanding, each ion in zinc blende has a coordination number of 4.

Key concepts

Zinc Blende Structure

The Zinc Blende structure is a highly relevant and frequently studied type of crystal structure, especially in inorganic chemistry and materials science. Zinc blende, also known as sphalerite, is the crystalline form of zinc sulfide (ZnS). The characteristic feature of this structure is that it combines both ionic and covalent bonding attributes, showcasing an interesting interplay between the two.
In the zinc blende structure, each zinc ion (\(\mathrm{Zn}^{2+}\)) is surrounded by four sulfide ions (\(\mathrm{S}^{2-}\)), resulting in a tetrahedral arrangement. Conversely, each sulfide ion is similarly surrounded by four zinc ions. This mutual surround creates its stability and distinctive properties. Such a formation reduces the spatial extent of repulsion between like charges, leading to a balanced, stable structure.

• This tetrahedral coordination forms due to electron cloud overlaps that lend stability to the crystal.
• It is worth noting that many other binary semiconductors, such as GaAs and InP, also form this type of structure, making it significant beyond just ZnS itself.

Face-Centered Cubic Lattice

The Face-Centered Cubic (FCC) lattice is crucial in describing the arrangement of ions in complex structures such as zinc blende. An FCC lattice is a type of crystal structure where each cube in the lattice has atoms located at each corner and in the center of each face of the cube.
This arrangement is one reason why materials with an FCC lattice, like zinc blende, have high packing efficiencies and are densely packed. In terms of coordination, the FCC lattice in zinc blende refers to the overarching framework in which the tetrahedral coordination of ions fits, rather than the direct face-centered arrangement of atoms.

• FCC structures are highly symmetrical, leading to isotropic properties which are identical in all directions.
• It reveals a high degree of efficient space utilization, contributing to its commonality in metals and ionic compounds.

Understand the FCC context in relation to zinc blende helps appreciate why it is commonly used to explain complex crystal structures and properties.

Tetrahedral Coordination

Tetrahedral coordination is a pivotal concept in understanding the bonding and structure within the zinc blende crystal. In tetrahedral coordination, a central atom or ion is surrounded by four atoms or ions at the corners of a tetrahedron. This is a common configuration found in many minerals and compounds, such as zinc blende.
The geometry of tetrahedral coordination leads to specific angles and distances between atoms, which directly impacts the physical and chemical properties of the material. For instance, in zinc blende, the equal sharing of electrons between neighboring zinc and sulfur ions results in its semiconductor properties.

• Tetrahedral coordination leads to bond angles of approximately 109.5°, which is crucial for maintaining structural integrity.
• It aids in achieving maximum separation of charges, creating a balanced and symmetrical distribution of ions.

This type of coordination is not unique to zinc blende; it is also prevalent in many organic compounds in addition to other inorganic structures.

Crystal Structure

Crystal structure is the three-dimensional arrangement of atoms, ions, or molecules in a crystalline material. Understanding the crystal structure of a compound gives valuable insights into its properties, including its density, durability, and electrical conductivity.
For example, the zinc blende structure defines a cubic crystal system with a distinct repetition pattern at an atomic or ionic level, creating a solid but specific form of matter. The periodicity and symmetry intrinsic to these structures also aid in understanding phenomena such as diffraction and electron band structures in solid-state physics.

• Knowledge of crystal structures helps predict how a material might form and behave under different conditions.
• It is crucial for the design of new materials, especially semiconductors and superalloys.

The study of crystal structures isn't just foundational for material science; it's pertinent to numerous fields, ranging from physics to nanotechnology.