What Are Miller Indices?
Miller indices are a system of notation used in crystallography to describe the orientation of planes and directions in a crystal lattice. Represented as (h k l), these indices are based on the reciprocals of the fractional intercepts that a plane makes with the crystal axes.
Why Are Miller Indices Important?
- Describe Crystal Planes and Directions: Provide a standardized way to communicate crystallographic information.
- Analyze Physical and Chemical Properties: Crystal planes impact strength, optical behavior, and electrical conductivity.
- Guide Crystal Growth: Affect growth rates and surface properties for single-crystal fabrication.
- Enable Semiconductor Fabrication: Specific planes like (1 0 0) are used for silicon wafers in ICs.
- Aid X-ray Diffraction (XRD) Analysis: Identify planes responsible for diffraction peaks in XRD patterns.
- Surface Science and Catalysis: Determine catalytic activity and adsorption properties.
How to Determine Miller Indices
- Identify the intercepts of the plane with the x, y, and z axes.
- Take the reciprocals of the intercepts.
- Convert these reciprocals into integers by multiplying by a common factor.
- Write the indices in the form (h k l).