http://bzuiam.webs.com

1. DIRECTIONS & PLANES
IN CUBIC UNIT CELL

2. Muhammad Umair Bukhari
Engr.umair.bukhari@gmail.com
www.bzuiam.webs.com
03136050151

3. Why we need Directions & Planes
• we need a way to identify directions and
planes of atoms
• Deformation under loading (slip) occurs
on certain crystalline planes and in
certain crystallographic directions.
• Before we can predict how materials fail,
we need to know what modes of failure
are more likely to occur.

4. Contd…
• Other properties of materials (electrical
conductivity, thermal conductivity, elastic
modulus) can vary in a crystal with
orientation.
• For example, magnetic properties of iron.
• And the electric conductivity of graphite.

5. Parallel layers of
Graphite

6. Plane
• A flat surface determine the position of 3
point in space.

7. Miller Indices
• Simplest notation for drawing Planes &
directions.

8. Miller Indices for planes
• As described in following procedure:
– Identify the points at which the plane intercepts the
x, y and z coordinates in terms of the number of the
lattice parameters.
– Take reciprocals of these intercepts.
– Clear fractions but do not reduce to lowest integers.
– Enclose the resulting numbers in brackets “()”.
– Negative numbers should be written with the bar over
the number.

9. -

12. Directions
• A line between two points and it is a vector .

13. Procedure:
• Define Origin
• Mention all axis on a cubic unit cell.
• Mention coordinates
• Find the intercept , divide the fraction by
biggest no
[221]=[111/2]
• Join points by head to tail rule
• The three indices are not separated by
commas. They are enclosed in square
Brackets: [uvw].

14. Important Notes
• Because the directions are vectors, a direction
and its negative are not identical; [100] is not
equal to [-100]. They represent the same line,
but opposite directions.
• A direction and its multiple are identical;
[100] is the same direction as [200].

16. [401]Direction

17. THANKS…..