MATTER LogoIntroduction to Crystallography

Previous | Next

Indexing Directions and Planes > Directions in a 2-D Lattice

Description of Flash Animation.

Consider this 2-D lattice. The unit cell is defined by the lattice unit vectors: a and b. Move OD so it passes through the origin of the unit cell. Select any point that OD passes through - say P. Express the vector OP in terms of its number of unit vectors of a and b:     OP = 1a + 1/2b. A direction is expressed in the form [uv] where u and v are integers. The direction OD is thus given as [21]. In vector notation: OP =  1a + 1/2b. Direction of OD is [21].

This resource requires Flash Player 9 or above available to download from

It is necessary to express directions in crystals with ease. For example, to state the direction in a lattice along which an electron beam is passing or in which planes of atoms may slip during deformation.

Directions in lattices are determined relative to the crystal axes defined by the unit vectors of the lattice unit cell. A direction is expressed in terms of its ratio of unit vectors.

It is very important to be clear about which unit vectors of the lattice are being used.

Click to dismiss

Note the use of square brackets and no separating comma. The ratio is always reduced to its lowest terms.

Click to dismiss

A direction index, often called a Miller Index, in a 2-D lattice is expressed in the form [uv] where u and v are integers. If negative integers are required the notation is [u v], read as 'bar u bar v'.

© 1997-2007 University of Liverpool | More Information | Plugins Required