The primitive, body-centred and face-centred cubic unit cells

Summary

This video explores the structure of crystalline solids, focusing on how particles like atoms, ions, or molecules arrange in a regular array. It explains unit cells, the smallest portions that define crystal structures, and discusses the three types of cubic unit cells: simple, body-centered, and face-centered. Each cell type differs in particle arrangement and coordination number. The video highlights how stacking these unit cells leads to different packing efficiencies, which explains why certain crystal structures, like those of sodium chloride and zinc sulfide, are more common in nature due to their efficient space utilization.

Takeaways

• 🔍 The particles in a crystal, such as atoms, ions, or molecules, are arranged in a regular, close-packed array.
• 🧱 A unit cell is the smallest portion of a crystal that defines its structure, and repeating unit cells form the entire crystal.
• 🔲 Simple cubic unit cells have particles only at the corners, and the particles touch along the edges but not along the diagonals.
• 🧩 Each simple cubic unit cell contains one complete particle when considering particle portions from neighboring unit cells.
• 🔢 In a simple cubic structure, each particle has six nearest neighbors – one above, below, left, right, front, and back.
• 💠 Body-centered cubic unit cells have particles at each corner and one particle in the center, providing a total of two particles per unit cell.
• 🔺 In a body-centered cubic structure, each particle has eight nearest neighbors due to the particle in the center touching the corner particles.
• 🏛 Face-centered cubic unit cells have particles at each corner and in the center of each face, resulting in a total of four particles per unit cell.
• 🔗 The face-centered cubic structure gives each particle 12 nearest neighbors, four above, below, and around.
• 🌐 Cubic closest packing, based on the face-centered cubic structure, is the most efficient stacking, occupying 74% of available volume.

Q & A

What is a unit cell in a crystal structure?

A unit cell is the smallest portion of a crystal structure that defines its overall structure. By stacking unit cells in all three directions, the entire crystal structure is formed.

What are the three types of cubic unit cells discussed in the script?

The three types of cubic unit cells are: simple cubic, body-centered cubic (BCC), and face-centered cubic (FCC).

How do particles in a simple cubic unit cell interact?

In a simple cubic unit cell, particles are located at the corners of the cube. They touch along the edges of the cube but not diagonally across the faces or through the body of the cube.

What is the coordination number in a simple cubic unit cell?

The coordination number in a simple cubic unit cell is 6, meaning each particle has six nearest neighbors: one above, one below, one to the left, one to the right, one in front, and one in back.

What distinguishes a body-centered cubic (BCC) unit cell from a simple cubic unit cell?

A body-centered cubic (BCC) unit cell has particles at each corner and one particle in the center of the cube. In contrast, the simple cubic unit cell only has particles at the corners.

What is the coordination number in a body-centered cubic (BCC) unit cell?

In a body-centered cubic (BCC) unit cell, the coordination number is 8, meaning each particle has four nearest neighbors above and four below it.

What is the particle arrangement in a face-centered cubic (FCC) unit cell?

In a face-centered cubic (FCC) unit cell, particles are located at each corner of the cube and in the center of each face, but there is no particle in the center of the cube.

What is the coordination number in a face-centered cubic (FCC) unit cell?

The coordination number in a face-centered cubic (FCC) unit cell is 12, meaning each particle has 12 nearest neighbors: four around it, four above, and four below.

Why is the simple cubic unit cell rarely found in nature?

The simple cubic unit cell is rarely found in nature because it uses space inefficiently, with only 52% of the available volume occupied by particles. More efficient structures like body-centered cubic (BCC) and face-centered cubic (FCC) are more common.

What structure does sodium chloride (NaCl) adopt, and how are the ions arranged?

Sodium chloride (NaCl) adopts the rock salt structure, where face-centered cubic arrays of chloride ions and sodium ions interpenetrate. The smaller sodium ions fit into the spaces between the larger chloride ions.