CHE217 LECTURE 1-4

QUIZ 1

MILLER INDICES

standard notation used for expressing locations, directions, and planes within crystal lattice systems.

square brackets [uvw]

used for directions featured in the unit cell

parenthesis (hkl)

used for planes featured in the unit cell

x, y, z

used for points featured in the unit cell

POINT COORDINATES

expressed as fractional multiples of the unit cell edge lengths along the x, y, and z axes.

CRYSTALLOGRAPHIC DIRECTIONS

defined as a vector between two points. it is enclosed in square brackets [uvw]

INDEX OF DIRECTIONS [uvw]

4-STEP PROCESS FOR DETERMINING DIRECTIONS

1,. Determine 2 points

2. Subtract origin from lead point

3. Clear fractions and reduce

4. Express as [uvw]

note: place a bar over negative integers

CRYSTALLOGRAPHIC PLANES

specified using Miller indices enclosed in parentheses (hkl)

INDEX OF PLANES (hkl)

4-STEP PROCESS FOR DETERMINING PLANES

1. Determine 3 points (intercepts)

2. Reciprocate

3. Clear fractions (DO NOT REDUCE TO LOWEST TERMS)

4. Express as (hkl)

note: bar on top of negative integers

HEXAGONAL MILLER INDICES

use a four-axis coordinate system: three coplanar axes (a₁, a₂, a₃) at 120° angles to each other, and a vertical c axis perpendicular to them.

HEXAGONAL SYSTEM FORMULA