Packing Efficiency of Metal Crystal in Simple Cubic Lattice
The steps below are used to achieve Simple Cubic Lattice’s Packing Efficiency of Metal Crystal:
Step 1: Radius of sphere
In a simple cubic unit cell, spheres or particles are at the corners and touch along the edge. Below is an diagram of the face of a simple cubic unit cell.
It is evident that,
a=2r or r = a/2 …(Equation 1)
Where, r is the radius of atom and a is the length of unit cell edge.
Step 2: Volume of sphere:
Volume of a sphere = (4/3π)(r3)
Substitution for r from equation 1 gives,
∴ Volume of one particle = (4/3π)(a/2)3
∴ Volume of one particle = πa3 / 6 …(Equation 2)
Step 3: Total volume of particles:
Simple cubic unit cells only contain one particle.
∴ Volume occupied by particle in unit cell = πa3 / 6
Step 4: Packing Efficiency:
We have,
Packing efficiency = (Volume occupied by particles in unit cell / Total volume of unit cell) × 100
∴ Packing efficiency = ((πa3 / 6) / a3) × 100
∴ Packing efficiency = 100π / 6
∴ Packing efficiency = (100 × 3.142) / 6
∴ Packing efficiency = 52.36 %
Therefore, in a simple cubic lattice, particles take up 52.36 % of space whereas void volume, or the remaining 47.64 %, is empty space.
Packing Efficiency of Unit Cell
A crystal lattice is made up of a relatively large number of unit cells, each of which contains one constituent particle at each lattice point. A three-dimensional structure with one or more atoms can be thought of as the unit cell. Regardless of the packing method, there are always some empty spaces in the unit cell. so the question is, What Is Unit Cell Packing Efficiency? The packing fraction of the unit cell is the percentage of empty spaces in the unit cell that is filled with particles. In this article, we shall learn about packing efficiency.
Table of Content
- Packing Efficiency
- Packing Efficiency Formula
- Packing Fraction Formula
- Packing Efficiency of Metal Crystal in Simple Cubic Lattice
- Packing Efficiency of Metal Crystal in Body-centered Cubic Lattice
- Packing Efficiency of Metal Crystal in Face-centered Cubic Lattice
- Unit Cell Packing Efficiency
- Solved Examples of Packing Efficiency
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