Advanced Topic 281 of 1102 States of Matter & Solutions
Packing Efficiency
The fraction of a unit cell's volume occupied by atoms.
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In-depth explanation of Packing Efficiency
Packing efficiency is the fraction of the volume of a unit cell that is occupied by atoms, representing how tightly they fill space. It is calculated as the number of atoms per cell multiplied by the volume of one sphere, (4/3)πr³, divided by the volume of the cell, a³. The values are about 52.4 percent for simple cubic, 68 percent for body-centred cubic, and 74 percent for both face-centred cubic and hexagonal close packing. Higher packing efficiency generally means higher density for a given atomic mass and size. It is a key idea for predicting density and void spaces in metals and ionic solids.
Going deeper: Packing Efficiency
Key ideas: Formula: efficiency = Z x (4/3) pi r^3 / a^3. Values: sc 52.4, bcc 68.0, fcc and hcp 74.05 percent. Void fraction is 1 minus this value. Random close packing of spheres gives about 64 percent, and the Kepler conjecture proved 74 percent is the maximum for regular arrangements.
Common mistakes and connections: A frequent mistake is using wrong edge-radius relations: a = 2r for sc, 4r/sqrt(3) for bcc, 4r/sqrt(2) for fcc. Another is thinking high packing means a hard metal; they are not strictly related. For compounds with two ion sizes, use ion radii in the contact relation. Links to unit cell, density and voids.
Visualization of Packing Efficiency
Packing efficiency is the fraction of cell volume filled by atoms: 52% simple cubic, 68% BCC and 74% for the close-packed FCC and HCP structures. The interactive lesson shows this as a live animation or chart.
Worked example and use case
Copper crystallizes in face-centred cubic packing, and its high packing efficiency helps explain its density of about 8.96 g/cm³.
Frequently asked questions about Packing Efficiency
What is Packing Efficiency?
The fraction of a unit cell's volume occupied by atoms.
Is Packing Efficiency a beginner, intermediate or advanced topic?
Packing Efficiency is a advanced topic in States of Matter & Solutions. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Packing Efficiency?
Study these earlier topics in States of Matter & Solutions first: Body-Centered Cubic, Face-Centered Cubic, Hexagonal Close Packing.
What comes after Packing Efficiency?
The next topics in States of Matter & Solutions are Tetrahedral and Octahedral Voids and Crystal Systems.
Can I practise Packing Efficiency with quizzes?
Yes. The interactive lesson includes a self-check question on Packing Efficiency, and the States of Matter & Solutions quiz draws on every topic in this area.
Where Packing Efficiency fits in States of Matter & Solutions
Packing Efficiency is topic 62 of 109 in States of Matter & Solutions.