# 3D Solid State Crystal models

You need a VRML viewer plugin to see 3D models below (see also the page at www.ibiblio.org).

# 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 [100], [110] or [111] 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 truncated octahedron 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 rhombic dodecahedron.

# Real crystal lattices

 NaCl (KCl, MgO, BaO, CaO, SrO) unit cell. You can see an atom name in your browser Status bar (thanks to Sandy Ressler). 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 balls). 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. YBa2Cu3O7 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.

# Crystallographic planes

In crystal with cubic symmetry every [ijk] vector has perpendicular atomic plane (ijk). E.g. parallel to the X axis [100] 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 lattices).

Quantity of crystals is infinite! You can see much more examples here:
"Crystal Structure Tutorials" has a ton of resources on crystal formations that might be useful (thanks to Donna Kennan)
"Materials Science. Introduction to Concepts" by Simon Toh and
Teaching and Education in Crystallography.

E-notes     Authors: Evgeny Demidov, Yury Drozdov IPM RAS
updated 28 Oct 2000