How do you find the direction of the Miller indices?

Here is the 3-step process to find the miller indices for planes.

1. Find the point where the plane intersects each axis. If the plane never intersects an axis because it is parallel to that axis, the intersection point is ∞.
2. Take the inverse of each intersection point.
3. Put those 3 values in the proper (hkl) format.

Can you have negative Miller indices?

if any of the intercepts are at negative values on the axes then the negative sign will carry through into the Miller indices; in such cases the negative sign is actually denoted by overstriking the relevant number.

How do you represent negative Miller indices?

Miller-indices – A shorthand notation to describe certain crystallographic directions and planes in a material. Lattice directions are in direct space and are denoted by [ ] brackets. A negative number is represented by a bar over the number.

What are direction indices?

Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the direction indices.

How do you find the direction of a plane?

Vector Representation. A vector in a plane is represented by a directed line segment (an arrow). The endpoints of the segment are called the initial point and the terminal point of the vector. An arrow from the initial point to the terminal point indicates the direction of the vector.

What are crystallographic directions and crystallographic planes?

Crystal planes are defined as some imaginary planes inside a crystal in which large concentration of atoms are present. Inside the crystal, there exists certain directions along which large concentration of atoms exists. These directions are called crystal directions.

Which way is north on a coordinate plane?

Longitude values act like X values on a coordinate plane. From the origin, positive latitude values move up (north) and negative values move down (south) from the equator.

How the orientation of a plane is specified by Miller indices?

Miller Indices are a symbolic vector representation for the orientation of an atomic plane in a crystal lattice and are defined as the reciprocals of the fractional intercepts which the plane makes with the crystallographic axes.

Can the direction angle of a vector be negative?

A vector pointing any angle to the left of the origin will have a negative x-component. A vector pointing at any angle upward from the origin will have a positive y-component. A vector pointing at any angle downward from the origin will have a negative y-component.

What happens if the angle is negative?

a positive angle starts from an initial side and moves clockwise to its terminal side. A negative angle starts from an initial side and moves counterclockwise to its terminal side.