Unit Cell Chemistry Simple Cubic, Body Centered Cubic, Face Centered Cubic Crystal Lattice Structu

Summary

This video provides an introduction to three key crystal structures: Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). It explains their atomic arrangements, coordination numbers, and space efficiency. The SC structure has one atom per unit cell with 52% space utilization, while the BCC structure has two atoms per unit cell and occupies 68% of space. The FCC structure is the most efficient, with four atoms per unit cell and 74% space utilization. The video also includes key formulas relating atomic radius, edge length, and volume in each structure.

Takeaways

• 😀 Simple Cubic (SC) structure has one atom per unit cell, with a coordination number of 6.
• 😀 Body-Centered Cubic (BCC) structure contains two atoms per unit cell and has a coordination number of 8.
• 😀 Face-Centered Cubic (FCC) structure contains four atoms per unit cell and has a coordination number of 12.
• 😀 The Simple Cubic (SC) structure uses 52% of the volume for atoms, with 48% empty space.
• 😀 The Body-Centered Cubic (BCC) structure is 68% efficient, meaning 32% of the volume is empty space.
• 😀 The Face-Centered Cubic (FCC) structure is the most efficient, with 74% of its volume occupied by atoms.
• 😀 In the Simple Cubic (SC) structure, the edge length (x) is twice the atomic radius (2r).
• 😀 In the Body-Centered Cubic (BCC) structure, the edge length (x) is 4/√3 times the atomic radius (r).
• 😀 In the Face-Centered Cubic (FCC) structure, the edge length (x) is √8 times the atomic radius (r).
• 😀 The volume of atoms in a unit cell can be calculated by dividing the volume of the atoms by the volume of the cube, resulting in a percentage efficiency.

Q & A

What are the three cubic structures discussed in the video?

The three cubic structures discussed are the simple cubic structure, the body-centered cubic structure, and the face-centered cubic structure.

How many atoms are present in one unit cell of the simple cubic structure?

In the simple cubic structure, there is only one atom per unit cell.

What is the coordination number for the simple cubic structure?

The coordination number for the simple cubic structure is 6, meaning each atom is adjacent to 6 other atoms.

What is the efficiency of space usage in the body-centered cubic structure?

The body-centered cubic structure is 68% efficient, meaning that 68% of the volume of the cube is occupied by atoms, while the remaining 32% is empty space.

What is the coordination number for the face-centered cubic structure?

The coordination number for the face-centered cubic structure is 12, meaning each atom is adjacent to 12 other atoms.

Why is the face-centered cubic structure known as cubic closest packing?

The face-centered cubic structure is known as cubic closest packing because it is the most efficient use of space, with atoms arranged in such a way that they occupy 74% of the cube's volume.

What is the relationship between the edge length (x) and atomic radius (r) in the simple cubic structure?

In the simple cubic structure, the edge length (x) is equal to twice the atomic radius (x = 2r).

How do you calculate the edge length of the body-centered cubic structure in terms of atomic radius?

The edge length (x) for the body-centered cubic structure is given by the formula x = (4/√3) * r, where r is the atomic radius.

What is the formula for the volume of the cube in the simple cubic structure?

The volume of the cube in the simple cubic structure is given by the formula V = x³, where x is the edge length, and x = 2r (twice the atomic radius).

How is the volume occupied by atoms in the simple cubic structure calculated?

To calculate the volume occupied by atoms in the simple cubic structure, divide the volume of the atoms in the unit cell by the volume of the cube. This results in a volume occupancy of approximately 52.36%.