Atomic Packing Factor Calculator

Calculate Crystal Structure Efficiency

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Common Structures APF Calculator

Calculate APF for common crystal structures.

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Custom APF Calculator

Calculate APF for any unit cell configuration.

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Understanding Atomic Packing Factor

What is APF?

Atomic Packing Factor (APF) is the ratio of the volume occupied by atoms to the total volume of the unit cell. It measures how efficiently atoms are packed in a crystal structure.

APF = (Volume of atoms in unit cell) / (Total volume of unit cell)

Common Crystal Structures

Standard APF values:

  • Simple Cubic (SC): 0.52 or 52%
  • Body-Centered Cubic (BCC): 0.68 or 68%
  • Face-Centered Cubic (FCC): 0.74 or 74%
  • Hexagonal Close-Packed (HCP): 0.74 or 74%

Factors Affecting APF

APF depends on:

  • Crystal structure type
  • Atomic radius
  • Unit cell dimensions
  • Number of atoms per cell
  • Atomic coordination number

Applications

APF is important in:

  • Materials design
  • Alloy development
  • Crystal engineering
  • Semiconductor fabrication
  • Metallurgy

Essential APF Formulas

Basic APF Formula

APF = (n × Va) / Vc

where n = number of atoms, Va = atomic volume, Vc = cell volume

Atomic Volume

Va = (4/3)πr³

where r = atomic radius

Unit Cell Volume

Vc = a³ (cubic)

where a = cell edge length