When talking about slip systems, the it is important to speak the language. There is a common way for defining crystallographic lines and planes within the unit cell.

### Lines/Directions

Lines or directions are defined by two points. The first point is the origin on the unit cell. Then the other end of the vector is projected onto the three axes measured by the unit cell dimensions. The three indices are then reduced to the smallest possible integer values. Finally the values are given in brackets [uwv] Overbars are used to represent negative numbers so instead of [-100] we would write [100]. Unfortunately in wordpress in overline is a little bit annoying to use so I will sometimes use the less compact form with the negative in front.

Hexagonal crystals (like sapphire) use a four-axis (Miller-Bravis) coordinate system. The first three axes are all on the x-y plane with 120 degree separation between them. The fourth axis is the z-axis.

### Planes

Although planes are typically defined by the direction normal. Crystallographers define them by their Miller indices (hkl). Let a plane intersect not pass through the origin. Then let the plane pass through the x, y and z axes at the points a, b, c. If the plane passes doesn’t pass through an axis, assign the value of ∞. Then the reciprocal of these numbers (when moved to a lowest common integer) are the Miller indices. For example (001) is the xy plane

### Slip

Slip is the usual method of plastic deformation in metals by blocks fof the crystal sliding past one another along definite crystallographic planes. There exists a slip plane, and a slip direction. The plane is the plane which gets moved and the slip line is the direction. Generally slip occurs in the plane of greatest atomic density and the direction is the closest packed direction with the plane. This is because slip keeps a single crystal as a single crystal.

### Dislocations

A dislocation is a type of defect in the crystal structure. Specifically it is a line defect. It is what is responsible for slip. Typically, it is an extra half plane of atoms in the crystal lattice. This half plane can then move easily move perpendicularly through the crystal.

(In Future Include and describe some figures).

Sources:

Callister, William D. *Materials Science and Engineering*.