3D Solid State Crystal models
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3D Bravais Lattices
Bravais lattice is a lattice with translation symmetry which consists of
equivalent nodes. There are 14 different Bravais lattices in 3D. Only three
Bravais lattices with cubic symmetry
(with "planes" of mirror symmetry) are shown here.
Wigner-Zeitz cell consists of all points nearest to a node
and has point symmetry of the corresponding Bravais lattice.
Simple Cubic lattice
(5x5x5, 7x7x7 atoms cells).
You can choose ,  or  viewpoint direction. I've removed
perspective for all 7x7x7 lattices.
The Wigner-Zeitz cell for the Simple Cubic lattice is
cube (the cell coincides with the unit cell).
Body Centered Cubic (BCC) unit cell,
5x5x5 and 7x7x7 lattices.
α-Fe, Na, K, β-Ti have this structure.
The Wigner-Zeitz cell for the BCC lattice is
Face Centered Cubic (FCC) unit cell,
5x5x5 and 7x7x7 lattices.
Cu, Au, Ag, Al, Pt, Pd have this structure. Sorry, I don't know how to bind
nodes in FCC and BCC lattices because square grid breaks the nodes equivalence
(but the balls do not fall without grid :)
The Wigner-Zeitz cell for the FCC lattice is
Real crystal lattices
NaCl (KCl, MgO, BaO, CaO, SrO) unit cell.
You can see an atom name in your browser Status bar (thanks to
5x5x5 and 7x7x7 cells.
NaCl lattice consists of two FCC sublattices. The Na sublattice (white balls)
is displaced by [1/2,0,0] relative to the Cl sublattice (yellow
GaAs (ZnS, InAs, InP, AlAs, CdTe, HgTe)
unit cell (5x5x5, 7x7x7).
GaAs lattice consists of two FCC sublattices displaced by [1/4,1/4,1/4]
Si, Ge (or diamond) unit cell
(5x5x5, 7x7x7). Diamond
lattice is similar to the GaAs one but is made of atoms of one kind.
SrTiO3 (CaTiO3) unit
cell and 5x5x5 lattice.
is a high temperature superconductive crystal (Tc =
93oK). 7x5x5 lattice. Y are red,
Ba - blue, Cu - yellow and O are white balls.
Superconducting atomic Cu-O2 planes.
In crystal with cubic symmetry every [ijk] vector has perpendicular
atomic plane (ijk). E.g. parallel to the X axis 
vector is perpendicular to the (100) atomic plane.
You can easy break
NaCl crystall along (100), (010) and
(001) equivalent planes (blue color). But you cannot break NaCl
along (110) plane (red color) because you have to destroy more atomic
bonds (white lines). (111) atomic plane (green color) contains charged
atoms of one kind (Na+ or Cl -) and
you cannot break crystal along this direction due to electrostatic attraction.
You can break GaAs crystall along (110)
plane (red color). Atomic planes (100) and (111) are charged.
But you can breake Si along (111) plane (green color) because
it is uncharged.
Close packed lattices
Close packed Face Centered Cubic unit cell
(click an atom to start rotation). Close packed hexagonal
lattice (Mg, α-Co, α-Be)
consists of two types of close packed planes (A and B). FCC lattice
consists of three types of close packed planes. FCC and hexagonal lattices are
very similar except for FCC includes a close packed
plane of the third type (C plane - red balls). The C plane is
shifted relative to the first A plane in FCC lattice.
(100) Si surface reconstruction
The real crystal has broken (unoccupied) bonds on its surface which may lead
to the surface reconstruction. (100) Si surface
before reconstruction (rotated 4x4x2 and
6x6x2 lattices). White and blue balls show two FCC
sublattices of Si. 2x1 reconstruction of (100) Si surface
(RGBW colored and 6x6x2
Quantity of crystals is infinite! You can see much more examples here:
Structure Tutorials" has a ton of resources on crystal formations that might
be useful (thanks to Donna Kennan)
Science. Introduction to Concepts" by Simon Toh and
Teaching and Education in Crystallography.
Authors: Evgeny Demidov, Yury Drozdov IPM RAS
updated 28 Oct 2000