Lattice:Simple cubic

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SC or simple cubic is the simplest and most generic cubic lattice.

Canonical SC

Symmetry

  • Crystal Family: Cubic
  • Crystal System: Cubic
  • Bravais Lattice: P (pcc)
  • Crystal class: Hexoctahedral
  • Point Group: m3m
  • Space Group: Pm3m
  • Particles per unit cell:
  • Volume of unit cell:
  • Dimensionality:
  • Projected d-dimensional volume:
  • Solid angle:
  • Nearest-neighbor distance:
  • Assuming spherical particles of radius R:
    • Particle volume fraction:
    • Maximum volume fraction: when

Reciprocal-Space Peaks

peak    q value         h,k,l   m       f       intensity
1:      6.283185307180  1,0,0   6       1       6
2:      8.885765876317  1,1,0   12      1       12
3:      10.882796185405 1,1,1   8       1       8
4:      12.566370614359 2,0,0   6       1       6
5:      14.049629462081 2,1,0   24      1       24
6:      15.390597961942 2,1,1   24      1       24
7:      17.771531752633 2,2,0   12      1       12
8:      18.849555921539 3,0,0   30      1       30
9:      19.869176531592 3,1,0   24      1       24
10:     20.838968152189 3,1,1   24      1       24

LatticePeaks-SC.png

Alternating Simple Cubic

A simple cubic lattice where the particle identity (in every direction) alternates between two possibilities. Thus this lattice has 2 distinct particles, in a 1:1 ratio. The unit cell may be thought of as having 8 particles (4 of each type).

Sc alternating.png

Examples

Atomics