Materials Of Sci. & Materials Of Sci. & TechnologyTechnology

Crysatallographic Planes & Crysatallographic Planes & DirectionsDirections

By – Boricha Paras H (130280105004)

3.9 Crystallographic Directions in Cubic 3.9 Crystallographic Directions in Cubic SystemSystem

► Determination of the directional indices in cubic Determination of the directional indices in cubic system:system:

Four Step Procedure (Text Book Method)Four Step Procedure (Text Book Method)1.1. Draw a vector representing the direction within the unit Draw a vector representing the direction within the unit

cell such that it passes through the origin of the cell such that it passes through the origin of the xyzxyz coordinate axes.coordinate axes.

2.2. Determine the projections of the vector on Determine the projections of the vector on xyzxyz axes. axes.3.3. Multiply or divide by Multiply or divide by common factorcommon factor to obtain the three to obtain the three

smallest integer values.smallest integer values.4.4. Enclose the three integers in Enclose the three integers in square bracketssquare brackets [ ]. [ ].

e.g.e.g. [ [ uvwuvw ] ]

uu , , vv , and , and ww are the integers are the integers

Crystallographic DirectionsCrystallographic Directions1. Vector repositioned (if necessary) to pass       through origin.2. Read off projections in terms of      unit cell dimensions a, b, and c3. Adjust to smallest integer values4. Enclose in square brackets, no commas

[uvw]

ex: 1, 0, ½ =>   2, 0, 1 =>  [ 201 ]

-1, 1, 1

families of directions <uvw>

z

x

Algorithm

where overbar represents a negative index

[ 111 ]=>

y

Crystallographic Directions in Cubic SystemCrystallographic Directions in Cubic System

[120]

[110]

[111]

Crystallographic Directions in Cubic SystemCrystallographic Directions in Cubic System

Head and Tail Procedure for determining Head and Tail Procedure for determining Miller Indices for Crystallographic DirectionsMiller Indices for Crystallographic Directions

1.1. Find the coordinate points of head and tail Find the coordinate points of head and tail points.points.

2.2. Subtract the coordinate points of the tail Subtract the coordinate points of the tail from the coordinate points of the head.from the coordinate points of the head.

3.3. Remove fractions.Remove fractions.4.4. Enclose in [ ]Enclose in [ ]

Indecies of Crystallographic Directions in Cubic SystemIndecies of Crystallographic Directions in Cubic System

Direction A

Head point – tail point

(1, 1, 1/3) – (0,0,2/3)

1, 1, -1/3

Multiply by 3 to get smallest integers

3, 3, -1

A = [33Ī]

_ _ B = [403]

C = [???] D = [???]

Direction BHead point – tail point(0, 1, 1/2) – (2/3,1,1)-2/3, 0, -1/2Multiply by 6 to get smallest integers

Indices of Crystallographic Directions in Cubic Indices of Crystallographic Directions in Cubic SystemSystem

A = [???]

_ _ C = [0I2]

B= [???] _

D = [I2I]

Direction C

Head Point – Tail Point

(1, 0, 0) – (1, ½, 1)

0, -1/2, -1

Multiply by 2 to get the smallest integers

Direction DHead Point – Tail Point(1, 0, 1/2) – (1/2, 1, 0)1/2, -1, 1/2Multiply by 2 to get the smallest integers

Crystallographic Directions in Cubic SystemCrystallographic Directions in Cubic System

[210]

Crystallographic Directions in Cubic SystemCrystallographic Directions in Cubic System

THANKS

…THA

NKS…