MILLER INDICES

Last Update 27/ 03/ 2001

in English/ in Esperanto/ in French/ in Portuguese

The application mil2 shows a cube in perspective and seven buttons with the Miller indices in sequence from top to bottom (1 0 0),  (2 0 0) until (1 1 1). Those indices define seven selected crystallographic planes in order to clarify on reciprocal relations, parallelism and perpendicularity. The sequence of planes (1 0 0), (2 0 0) e (5 0 0) represents on the figure the reciprocal relationship between the Miller indices and its distance from the origin, respectively. These are parallel planes indicated by the proportionality of the h, k and l indices of any two of them. It is noticeable the plane (1 0 0) as this face symbol is just the face of the cube.

Plane (5 8 2) has no special features.

The last of the sequence, that with Miller indices (1 1 1) is of outstanding importance, it is used to define the octahedron face when it is oriented with its three four fold axis parallel with directions x, y and z.

The other two planes are perpendicular.

Bibliography

1. Brown, F.C., Física de los Sólidos, Editorial Reverté, S.A., Barcelona, 1970.

2. Keer, H.V., Principles of the Solid State, John Wiley & Sons, New York, 1993.

3. Kittel, C., Introduction to Solid State Physics, John Wiley & Sons, New York, 1996.

4. Stout, G.H. and Jensen, L.H., X-ray Structure Determination, Macmillan, London, 1972.

5. Woolfson, M.M., X-ray Crystallography, Cambridge at the University Press, London, 1970.

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Table of subjects.
Presentation
Chemistry Analytical Chromatography
Elemental organic analysis
Volumetric analysis, simulation
Crystallography 3 fold screw axis
4 fold inversion axis on tetrahedron
5 fold rotation axis absent in crystallography
Binary axis and reflection plane in stereographic projection
Bravais lattices
Conic sections under symmetry operators
Converting from spherical coordinates to stereographic projection
Crystal lattice and unit cell
Determination of unit cell
Elements of symmetry in action - animation
Elements of symmetry in action - cube game
Elements of symmetry in action - dodecahedron game
Elements of symmetry in action - icosahedron game
Elements of symmetry in action - octahedron game
Elements of symmetry in action - tetrahedron game
Ewald sphere and crystal measurements
Extinctions
Five classes in the cubic system
Five classes in the rhombohedral system
From tetrahedron to prism
Gnomonic projection
Improper symmetry axis
Miller indices
Miller indices - animation
Miller indices - cube game
Miller indices - octahedron game
Miller indices - rhombic dodecahedron game
Miller indices - tetrahedron game
Mirror plane
Mirror planes and Miller indices game - tetrahedron
Orientations of the cube
p2mm
Plane symmetry groups
Question on point group
Rotation axis in octahedron and Werner compounds
Rotation axis on tetrahedron and organic molecules
Rotation of objects about an arbitrary axis
Rotation of the parallel and stereographic projections of the cube
Rotation of the stereographic and parallel projection of the cube III
Seven faces in stereographic projection
Seven classes in the hexagonal system
Seven classes in the tetragonal system
Six elements of symmetry in seven orientations
Spherical projection of the octahedron
Stereographic projection
Stereographic projection of six polyhedra in different orientations
Straight line equations and symmetry elements
Symmetry, 2 fold axis
Symmetry, 2, 3 and 6 fold axis in benzene
Symmetry, 3 fold axis in the cube
Symmetry, 4 fold axis in the cube
Symmetry, 4 fold axis in the unit cell of gold
Symmetry elements and Miller indices game
Symmetry elements and Miller indices game - octahedron
Symmetry in art and in crystallography
Three classes in the monoclinic system
Three classes in the orthorhombic system
Twin crystals
Two classes in the triclinic system
Unit cell in hexagonal net
General Butane conformations
Density
Electrochemical cell
Ethane conformations
Oxidation and reduction
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold