Question

In \(\mathrm{NaCl}\), the chloride ions occupy the place in a fashion of: (a) bcc (b) \(\mathrm{fcc}\) (c) both (d) none

Short answer

The chloride ions occupy a face-centered cubic (fcc) arrangement.

Step-by-step solution

Understand the Crystal Structure

Sodium chloride, also known as NaCl or table salt, forms a crystal structure where each ion is surrounded by oppositely charged ions. The basic structure is known as face-centered cubic (fcc) lattice.

Identify the Ion Positions

In the NaCl crystal structure, both sodium and chloride ions occupy a face-centered cubic lattice. Each ion in the fcc lattice is surrounded by six ions of the opposite type.

Compare with Options

Among the given options, we are looking for the configuration that matches the description of chloride ion placement in a face-centered cubic manner.

Conclusion

Given the analysis, the chloride ions in NaCl indeed occupy the face-centered cubic positions.

Key concepts

Face-Centered Cubic Lattice

The face-centered cubic (fcc) lattice is one of the most common structural arrangements in solid state chemistry. In this lattice, each cube has atoms at its corners and one atom at the center of each of its faces.
This arrangement offers a high packing efficiency, meaning more atoms are packed together in a given space. In an fcc lattice:

• There are a total of 14 spheres per unit cell: 8 corner spheres shared by eight unit cells and 6 face centers shared by two unit cells.
• The repeating pattern ensures that each atom is equidistant from its nearest neighbors, creating a stable structure.
• The coordination number for atoms in a face-centered cubic lattice is 12, indicating that each atom touches 12 others, making this one of the most tightly packed lattice structures.

Understanding this arrangement helps in grasping the foundation of many crystal structures including NaCl.

NaCl Crystal Structure

Sodium chloride, or NaCl, commonly known as table salt, possesses a crystal structure that is a fascinating manifestation of the face-centered cubic (fcc) lattice. In this structure, each chloride ion is surrounded by six sodium ions and vice versa. Here’s how the NaCl structure works:

• Chloride ions form a three-dimensional grid in an fcc arrangement.
• Sodium ions fill the octahedral holes created by the chloride lattice.
• This leads to each ion having a coordination number of 6, as each is surrounded by six ions of the opposite kind.

The NaCl structure is significant because it exemplifies how ionic compounds form stable structures in solid state chemistry, balancing attractive forces between oppositely charged ions.

Crystal Lattice

A crystal lattice is a systematic, three-dimensional arrangement of atoms, ions, or molecules in a crystalline solid. Each point in the lattice represents a repeated arrangement of the constituent particles, contributing to its overall geometry and symmetry. Key features of a crystal lattice include:

• Unit cell: The smallest repeating unit in the lattice that, when stacked together with identical units, creates the entire crystal structure. The characteristics of the unit cell, such as its geometry and dimensions, define the larger structure's repeating pattern.
• Lattice constants: These are the parameters that define the dimensions of the unit cell and influence the physical properties of the crystal.
• Lattice types: Different types can exist, such as simple cubic, body-centered cubic (bcc), and face-centered cubic (fcc), each with unique packing patterns and coordination numbers.

Understanding how a crystal lattice is structured aids in unlocking the behavior of various materials, influencing their mechanical, optical, and electrical properties.