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) \(8: 8\)

Understanding the zinc blende structure is crucial for grasping many fundamental concepts in crystallography and materials science. Zinc blende, the name given to the cubic crystal form of zinc sulfide (ZnS), is a critical structure to study due to its widespread occurrence in semiconductors.

The uniqueness of this structure lies in the way the zinc (Zn) and sulfur (S) atoms are arranged. In the zinc blende form, each Zn atom is bonded to four S atoms, forming a tetrahedron. A similar situation is found with S atoms, each bonded to four Zn atoms. This bonding pattern leads to a highly symmetric, three-dimensional network of tetrahedra interconnected at their corners. The adoption of this configuration minimizes the electrostatic energy, following the principle that opposite charges attract and like charges repel.

Coordination Number in Zinc Blende

One might wonder about the immediate environment of each atom in a crystal—this is described by the coordination number. For both zinc and sulfur in zinc blende, the coordination number is four, meaning that Zn is surrounded by four S atoms and vice versa. This four-fold coordination is indicative of strong covalent bonding, a characteristic important in the electrical and optical properties of materials with this structure.

A face-centered cubic (FCC) lattice is a common arrangement for many elemental metals and compounds, where each corner and the centers of all the faces of the cube have atoms. When delving into lattice structures, it's important not only to consider the positions of the atoms but also the spaces between them. These spaces are known as interstitial sites, and in an FCC lattice, two types are primarily observed: octahedral and tetrahedral holes.

Tetrahedral holes are smaller and have a shape resembling a tetrahedron with atoms at the four corners. Understanding these interstitial sites is key to explaining the zinc blende structure. In zinc blende, Zn atoms occupy half of the tetrahedral holes in the FCC lattice of S atoms. The choice of tetrahedral holes is not arbitrary; it's due to size considerations and electrostatic stabilization resulting from charge interactions between the ions.

Importance of Tetrahedral Holes

These holes play a pivotal role in determining the properties of the crystal. For semiconductors like ZnS, the occupation of tetrahedral holes by the smaller cations (Zn) is what allows the crystal to have its characteristic band structure, directly impacting its electronic properties. The knowledge of such positions is crucial when modifying or doping the crystal to alter its conductivity or to introduce new functionalities.

The ZnS cubic crystal structure is not just one arrangement, but rather it encompasses two polymorphs: zinc blende (sphalerite) and wurtzite. Each of these forms has the same chemical composition, ZnS, but differ in the way the atoms are stacked, influencing physical properties such as optical behavior and hardness.

The zinc blende structure, as discussed previously, is an FCC lattice derivative. It is often used as an example in solid-state physics and materials science because it shows how crystalline solids can be formed by the repetition of a unit cell, which in the case of zinc blende is a cube with sulfur atoms at each corner and a Zn atom within.

Significance of Cubic Crystals

The significance of cubic crystals like ZnS in technologies cannot be understated. The sphere packing and gap filling in these lattices affect everything from how light interacts with the material (making it valuable in optoelectronics) to the material's ability to withstand mechanical stress. A clear understanding of the cubic crystal structure aids in predicting and explaining the behavior of a material under different conditions, thus guiding the design of new materials and devices.