Miller indices
(rus. индексы Миллера)
—
indices describing the arrangement of atomic planes of a crystal lattice.
Description
Procedure for determining the Miller indices:
- find points of intersection of the crystal plane with the coordinate axes;
- translate the result into units of the lattice constants
, 
, 
;
- take back the reciprocal values of the of these numbers and bring them to the smallest integer multiples.
The result in brackets (
) represents the Miller indices of the crystal plane.
For example, if the plane intersects the axes at the points with the coordinates 1, 2 and 3 (Fig. a), then reciprocal values are 1, 1/2, and 1/3, and the smallest integers with the same ratio are 6, 3, and 2, i.e., the Miller indices for this plane are (632). If a plane is parallel to one axis, the point of intersection with this axis is considered equal to infinity, and the corresponding index equals to zero. If the plane intersects the axis in the negative region, the corresponding index will be negative. To indicate this the index is preceded by the minus sign: (
). As an example, Fig. b shows the Miller indices of some of the most important planes of a cubic crystal.
- find points of intersection of the crystal plane with the coordinate axes;
- translate the result into units of the lattice constants
, , ; - take back the reciprocal values of the of these numbers and bring them to the smallest integer multiples.
The result in brackets (
) represents the Miller indices of the crystal plane. For example, if the plane intersects the axes at the points with the coordinates 1, 2 and 3 (Fig. a), then reciprocal values are 1, 1/2, and 1/3, and the smallest integers with the same ratio are 6, 3, and 2, i.e., the Miller indices for this plane are (632). If a plane is parallel to one axis, the point of intersection with this axis is considered equal to infinity, and the corresponding index equals to zero. If the plane intersects the axis in the negative region, the corresponding index will be negative. To indicate this the index is preceded by the minus sign: (
). As an example, Fig. b shows the Miller indices of some of the most important planes of a cubic crystal. Illustrations
|
a — Shaded planes crosses axes  ,  ,  in points 1, 2, 3. Miller indices of this plane are (632). b — Miller indices of several critical planes of a cubic crystal. |
Authors
- Zotov Andrey V.
- Saranin Alexander A.
Sources
- Kittel Ch. Introduction to Solid State Physics. — Wiley, 1995. — 688 p.
- Oura K. et al. Surface Science: An Introduction // Springer, 2010 - 452 pp.