Problem 11 - Chemistry in 30 days

Question

How many nearest neighbours are there in a body-centered cubic packing ? (a) Two (b) four (Q) eight (d) twelve

Step-by-Step Solution

Answer

The correct answer is (Q) eight.

Step 1: Understanding Body-Centered Cubic (BCC) Structure

The body-centered cubic (BCC) structure is a type of crystal structure. In a BCC arrangement, each corner of the cube has one atom (making 8 corner atoms), and there is also one atom in the center of the cube.

Step 2: Identifying Nearest Neighbors

For the atom at the center of the BCC cube, the nearest neighbors are all the corner atoms. Since the cube has 8 corners, the center atom has 8 nearest neighbors. This is because each corner atom is equidistant from the center atom.

Step 3: Understanding Corner Atom Neighbors

Each atom located at the corner of a BCC lattice is equidistant from the center atom of two adjacent cubes. Therefore, each corner atom technically shares 4 neighbors per cube arrangement, but because of the cube sharing, these are counted differently. The key part of this exercise is understanding the center atom's neighbors.

Step 4: Concluding the Solution

The primary focus in determining nearest neighbors is the central atom in the BCC structure. This atom is surrounded by the 8 corner atoms, making 8 nearest neighbors. Hence, the correct answer based on the typical nearest neighbor calculation around the central atom in a BCC structure is eight.

Key Concepts

Nearest Neighbors in Crystal Structures

When we talk about nearest neighbors in crystal structures, we refer to the closest atoms surrounding a central atom. In any structured lattice, such as a body-centered cubic (BCC) setup, understanding nearest neighbors helps us to predict various properties. These properties can include atomic interactions and how the crystal behaves physically.

For a central atom, its nearest neighbors are simply the atoms closest in proximity. Imagine if you're in the middle of a group of friends, the nearest neighbors would be those standing closest to you.

Identifying these neighbors in different crystal structures like BCC, face-centered cubic (FCC), or simple cubic (SC) arrangements helps to establish structural stability. For BCC, all corner atoms surrounding the central atom are its nearest neighbors. This configuration leads to unique bonding and interactions that influence the crystal's characteristics.

BCC Structure

The body-centered cubic (BCC) structure is one of the most common crystal structures. In this configuration, here's what you'll see:

• One atom sits at the center of the cube.
• Eight other atoms sit at each corner of the cube.

This arrangement gives it a distinctive symmetry and spacing.

What makes BCC unique compared to other cubic structures is its higher density which stems from these additional coordinating atoms in the center. Materials with a BCC structure, such as iron at room temperature, often exhibit high strength and resistance to deformation.

The central atom in a BCC structure will touch all the corner atoms, and so, it results in each center atom having 8 nearest neighbors. This number significantly influences the density and bonding conditions of the material displayed.

Crystal Lattice

A crystal lattice is a repeating three-dimensional arrangement of atoms, ions, or molecules. Think of it like a pattern that repeats over and over. This pattern forms the backbone of a solid material. Each point in the lattice represents the position of an atom or a group of atoms within the unit cell.

Lattice structures determine how a crystal will grow. They affect the material's properties like strength, flexibility, and electrical conductivity. Different types of lattices, such as simple cubic, body-centered cubic (BCC), and face-centered cubic (FCC), offer different coordination numbers and geometric designs.

• Simple Cubic: Atoms are simply placed at each corner of the cube.
• BCC: Each cube has an atom at its center adding another layer of organization.
• FCC: Includes an atom at each face of the cube thereby enhancing packing efficiency.

Having a solid grasp of lattice types helps in centralizing ideas and understanding the robustness of material on a molecular level.