DIRECTIONS & PLANES IN CUBIC UNIT CELL

Muhammad Umair Bukhari

Engr.umair.bukhari@gmail.com

www.bzuiam.webs.com

03136050151

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.

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.

Parallel layers of

Graphite

Plane

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

Miller Indices

• Simplest notation for drawing Planes & directions.

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.

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Directions

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

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].

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].

[401]Direction

THANKS…..