Lattice:Packing fraction

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The packing fraction (or particle volume fraction) for a lattice is given by:

Where N is the number of particles per unit cell (which has volume ). For a sphere, the volume is so:

For a cubic unit cell of edge-length a:

Examples

For a SC lattice, the packing fraction is 0.524:

  • Nearest-neighbor distance:
  • Assuming spherical particles of radius R:
    • Particle volume fraction:
    • Maximum volume fraction: when

For a FCC lattice, the packing fraction is 0.740:

  • Nearest-neighbor distance:
  • Assuming spherical particles of radius R:
    • Particle volume fraction:
    • Maximum volume fraction: when

For a BCC lattice, the packing fraction is 0.680:

  • Nearest-neighbor distance:
  • Assuming spherical particles of radius R:
    • Particle volume fraction:
    • Maximum volume fraction: when

For a diamond lattice, the packing fraction is 0.340:

  • Nearest-neighbor distance:
  • Assuming spherical particles of radius R:
    • Particle volume fraction:
    • Maximum volume fraction: when