st. projection 2013er

7/25/2019 St. Projection 2013er

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X-Ray & TEM Lab

Stereographic Projection

Fig 2.25: {100} poles of a cubic crystal


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X-Ray & TEM Lab


Wulff Net


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X-Ray & TEM Lab


Fig 2.26: Angle between two planes


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Geographic map is equal area concept.

Crystallography is equiangular concept.

Plane of projection is placed normal to the

end of diameter of the sphere.

Other end of diameter is the source of projection- Imagine that a torch is placed there.

Plane of projection is normal to the diameter AB.

Projection is made from point B.

-If a plane has its pole at P,

-the stereographic projection of P is at P

-Obtained by drawing the line BP

-extend it until it meets the projection plane.

The stereographic projection of P is the shadow

cast by P on the projection plane with the light

source at B.

NESW is normal to AB and its shadow gives the

Great circle.

Fig 2.27: The Stereographic Projection


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Stereographic Projection of great & small circles

Fig 2.28: Stereographic Projection of great & small circles

Great circleANBS projects as the straight line NS.

Great circleAWBE projects as the straight line WE.

Inclined great circle NGSH projects as the circle arc

line NGS.

Small circles on the sphere also project

as circles projected center does not coincide

with their center on the projection.E.g., circleAJEK whose center P lies on

AEBW projects asAJEK.

Its center on the projection is at C,

located at equal distances from

A and E, but its projected centeris at P located at equal number of

degrees (45) fromA & E.


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X-Ray & TEM Lab


Fig 2.30: Angle between poles


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X-Ray & TEM Lab


Wulff NetFig 2.31: Angle between poles

rotation to put on same great circle


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X-Ray & TEM Lab


Fig 2.31: Rotation of poles P1 and P2 to put on same great circle


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X-Ray & TEM Lab


Fig 2.32: Trace of a pole (pole P2)


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X-Ray & TEM Lab


Fig 2.33: Measurement of angle between 2 poles

P1 and P2 by measurement of the angle of intersection of their traces


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X-Ray & TEM Lab


Fig 2.34: Rotation of poles about NS axis of projection


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Fig 2.35: Rotation of a pole about an inclined axis

Rotate A1

about

B1 by 40 in a

clockwise

direction.

Initial position

Rotate projection to bring B1 to the equator.

Bring B1 to the centre by rotating 48 about the N-S axis.

At the same time, A1 must also move to A2 along the

parallel latitude.The rotation axis is now perpendicular to the projection plane.

Required rotation of 40 brings A2 to A3 along a circular path

centered on B2.

The B1 to B2 operation needs to be reversed to bring B2 to its

original position.

B2 is brought to B3 and A3 to A4, by a reverse 48 rotationabout the N-S axis.

Final position


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Fig 2.35: Rotation of a pole about an inclined axis

Rotate A1

about

B1 by 40 in a

clockwise

direction.

Initial position

During its rotation about B1, A1 moves along the small circle.

Centre of this circle is at C on the projection & not at its

projected centre B1.

At the same time, A1 must also move to A2 along theparallel latitude.

To find C, we know that all points on the circle must lie at

equal angular distances from B1.

Measurement on a Wulff net shows that A1 and A4 are 76

from B1.

We locate any other point D which is 76 from B1.Knowing 3 points on the required circle allows us to locate

its centre by plane geometry.


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Table 2-3: Interplanar angles for cubic crystals.


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X-Ray & TEM Lab


Fig 2.25: {100} poles of a cubic crystal


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Standard Projection

Let us look at the standard (001) projection.

The {100} cube poles are obvious.

The {110} poles are located 45 from the

{100} poles & are 90 apart.

(011) Pole is on the great circle joining

(001) and (010) & at 45 from each.

Using hu+kv+lw = 0

We find (111) belongs to both

and101 011

Pole of (111) is located at the intersection of zone circle through

( ) ( ) ( )010 , 101 , 010 and ( ) ( ) ( )100 , 011 , 100

Angle between the (111) pole & (010) or (100) must be 54.7

u = k1l2 k

2l1

v = l1h

2 l

2h

1

w = h1

k2

h2

k1


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Standard Stereographic Projection

(001) and (011) standard projections


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Fig 2.34: Rotation of poles about NS axis of projection

st. projection 2013er

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