Packing Efficiency Calculator

Calculate Crystal Packing Parameters and Void Spaces

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Atomic Packing Factor Calculator

Calculate packing efficiency for different crystal structures.

Packing Factor: -

Void Space Calculator

Calculate tetrahedral and octahedral void sizes and locations.

Void Spaces: -

Understanding Crystal Packing

Crystal Structures

Common packing arrangements:

  • Simple Cubic (SC): APF = 52.4%
  • Body-Centered Cubic (BCC): APF = 68.0%
  • Face-Centered Cubic (FCC): APF = 74.0%
  • Hexagonal Close-Packed (HCP): APF = 74.0%

Void Spaces

Types of interstitial sites:

  • Tetrahedral Holes: 4 nearest neighbors
  • Octahedral Holes: 6 nearest neighbors
  • Trigonal Holes: 3 nearest neighbors
  • Radius Ratios: Determine stability

Applications

Packing efficiency affects:

  • Material density
  • Mechanical properties
  • Ionic conductivity
  • Intercalation chemistry
  • Crystal growth
  • Phase transitions

Advanced Concepts

Additional considerations:

  • Coordination Number: Nearest neighbors
  • Radius Ratio Rules: Structure prediction
  • Defect Formation: Vacancy creation
  • Non-spherical Packing: Molecular crystals

Essential Packing Formulas

Packing Factor

APF = (Volume of atoms)/(Unit cell volume)

Void Radius

r(void) = R(0.225 to 0.414) for tetrahedral

Radius Ratio

ρ = r(cation)/r(anion)