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Questions and Answers
Which lattice has the most efficient packing of particles?
fcc/ ccp
Which lattice has the least efficient packing of particles?
sc
What is the coordination number of atoms in a simple cubic lattice?
6
What is the coordination number of atoms in a bcc lattice?
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What is the coordination number of atoms in an fcc lattice?
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What is the packing efficiency of a simple cubic lattice?
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What is the packing efficiency of a bcc lattice?
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What is the packing efficiency of an fcc lattice?
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What is the formula for the number of particles in a given volume?
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What is the formula for the number of unit cells in a given mass of metal?
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Study Notes
Number of Tetrahedral and Octahedral Voids
- Number of tetrahedral voids is 2N, where N is the number of particles.
- Number of octahedral voids is N.
Packing Efficiency
- Packing efficiency is the fraction or percentage of the total space occupied by the spheres (particles).
- It is a measure of how tightly particles are packed together.
- Formula: Packing efficiency = (Volume occupied by particles in unit cell / Total volume of unit cell) × 100
Packing Efficiency in Simple Cubic Lattice
- In simple cubic unit cell, particles are at the corners and touch each other along the edge.
- Radius of sphere (r) = a/2, where a is the length of unit cell edge.
- Volume of sphere = (4/3π)(r³)
- Volume occupied by particles in unit cell = (4/3π)(r³) = πa³/6
- Total volume of unit cell = a³
- Packing efficiency = (πa³/6 / a³) × 100 = 52.4%
Packing Efficiency in Face-Centred Cubic Lattice (FCC or CCP or HCP Lattice)
- Radius of particle (r) = a/√2, where a is the length of unit cell edge.
- Volume of sphere = (4/3π)(r³) = πa³/8
- Volume occupied by particles in unit cell = 4 × πa³/8 = πa³/2
- Total volume of unit cell = a³
- Packing efficiency = (πa³/2 / a³) × 100 = 74%
Comparison of Packing Efficiency in Different Lattices
- Face-centred cubic lattice (FCC or CCP or HCP) has the most efficient packing of particles, with a packing efficiency of 74%.
- Simple cubic lattice has the least efficient packing of particles, with a packing efficiency of 52.4%.
Coordination Number and Packing Efficiency in Various Cubic Systems
- Coordination number is the number of neighbouring spheres that surround a sphere in a lattice.
- Table 1.4 shows the coordination number and packing efficiency in simple cubic, body-centred cubic, and face-centred cubic lattices.
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Description
Learn about the number of tetrahedral and octahedral voids in crystal structures, as well as how to calculate packing efficiency in terms of the volume occupied by particles in a unit cell compared to the total volume of the unit cell.
