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UoM E S1

Miller Indices

Miller Indices in Simple Cubic

Any vertex can be chosen as the origin.

Notation

  • Minus noted with a bar
  • Addition and subtraction is carried out like vectors
  • - Atom/Vertex
  • - Direction, no commas
  • - Family of directions
  • - Plane, no commas
  • - Family of planes
  • Always will be whole numbers. Fractions must be multiplied by LCM.

Direction

Equivalent directions are grouped into a family.

Direction families

<100>

  • No of planes:

<110>

  • No of planes:

<111>

  • No of planes:

Show the direction

To show the direction , for example:

Take the point . Divide by the highest number (, in this case) to bring the point inside the unit cell. The resulting point will be . The direction is given by vector from to the resulting point.

Close packed direction

All neighbour atoms in a direction touch each other. For example: of fcc.

Plane

Steps

  • If sitting on any axes, move the origin.
  • Find the intercepts. if parallel.
  • Find the reciprocals.

Plane families

100

  • Denotes as
  • No of planes:

110

  • Denotes as
  • No of planes:

111

  • Denotes as
  • No of planes:

The above are the common planes. There are other planes as well.

Show the plane

  • Divide by the smallest non-zero number.
  • Find the reciprocals. means parallel to the axis.

Close packed plane

All neighbour atoms in a crystal plane touch each other. For example: of fcc.

Planar Density / Aerial Density

Number of atoms in a unit area in a specific plane. Differs between different planes in a single crystal structure.