Interpretation:
Miller indices for the directions inthe hexagonal lattice using three- digit and four-digit systems.
Concept introduction:
Miller indices at the planes pass through the three points at edges of the crystal structure. In crystalline material, all the points, planes and directions are specified within the unit cell. The direction is defined as a line between two points.
Answer to Problem 3.57P
Miller indices of hexagonal lattice at given directions.
Explanation of Solution
Given:
The following hexagonal lattice:
Steps for calculating miller indices for given directions are:
- Find head point coordinate (direction of a head point from the origin (x,y,z) )
- Find-tail point coordinate (x,y,z)
- Head point coordinate − tail point coordinate
Miller indices for plane A:
Head points = 0,1,1
Tail point = 1/2, 1, 0
Head point − Tail point:
Four-digit system
Convert the three-digitsystem into a four-digit system.
Coordinates of four-digit system.
Miller indices for plane B:
Head points = 1,0,0
Tail point = 1, 1, 1
Head point − Tail point:
Four-digit system
Convert the three-digitsystem into a four-digit system.
Coordinates of the four-digit system.
Miller indices for plane C:
Three digit system:
Head points = 0,0,0
Tail point = 1, -1, 1
Head point − Tail point:
Four-digit system
Convert three systems into four-digit system.
Miller indices of hexagonal lattice at given directions.
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