In 1850, August Bravais established the theory of space lattices, which presents that the internal structure of a crystal is a regular, cyclical and indefinite distribution of some atoms in space. This atom network is called a crystal lattice. There are indefinite families of parallel planes in a crystal lattice. Miller Indices (usually expressed by *hkl*) are a symbolic vector representation for the orientation of theses crystal planes.

To determine the Miller Indices (*hkl*) of a plane, one must take the following steps:

- Choose an atom as the origin of the coordinate system and three crystallographic directions
- Determine the intercepts of the plane along each of the three crystallographic directions
- Take the reciprocals of the intercepts to obtain the values for
*hkl* - If this results in fractions, then multiply each value by the denominator of the smallest fraction

In our VRML applications, the Miller Indices *hkl* are directly specified by the user via selectors for each of the three values. The corresponding intercepts are calculated and their values as well as the resulting plane are displayed.

110 plane (enlarge) |
020 plane (enlarge) |

Load the VRML Model for a Cubic Lattice (32K) |

The Silicon diamond lattice consists of two interleaving face-centered cubic (fcc) cells displaced by 1/4 of the lattice constant. The density of atoms in different Miller Indices planes determines properties related to etching or oxidization.

111 plane and atoms on the plane (enlarge) |
110 plane and atoms on the plane (enlarge) |

Load the VRML Model for a Silicon Lattice Cell (52K) |

- Miller Indices by Alan J. Jircitano, Pennsylvania State University
- Miller Index Notation by Roger Nix, Queen Mary University of London
- Crystallography - Miller Indices by David Jessey, California State Polytechnic University - Pomona
- Miller Indices by Paul Schroeder, University of Georgia
- Surface Explorer by Klaus Hermann and Fritz Rammer, Fritz-Haber-Institute, Germany
- Miller Indices on Silicon wafers by ASTEP (Advanced Software for Teaching), includes VRML models
- Miniaturization Science - Bulk Micromachining (pdf file) by Marc Madou, University of California, Irvine
- Introduction to Semiconductor Materials and Crystal Structures (pdf file) by Meikei Ieong

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