Без темы <<  Creative Alumni Outreach Strategies CS136, Advanced Architecture  >>
 crystallography lv Useful concept for crystallography & diffraction Keep track of sets of planes by giving them names - Miller indices Miller indices (hkl) Choose cell, cell origin, cell axes: Miller indices (hkl) Choose cell, cell origin, cell axes Draw set of Miller indices (hkl) Choose cell, cell origin, cell axes Draw set of Miller indices (hkl) Choose cell, cell origin, cell axes Draw set of Miller indices (hkl) Choose cell, cell origin, cell axes Draw set of Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Lattice planes Strange indices Zones Zones Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice Reciprocal lattice

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## Crystallography lv

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### Useful concept for crystallography & diffraction

Lattice planes

Think of sets of planes in lattice - each plane in set parallel to all others in set. All planes in set equidistant from one another

Infinite number of set of planes in lattice

3

(hkl)

Lattice planes

4

origin

b

a

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### Miller indices (hkl) Choose cell, cell origin, cell axes Draw set of

planes of interest:

origin

b

a

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### Miller indices (hkl) Choose cell, cell origin, cell axes Draw set of

planes of interest Choose plane nearest origin:

origin

b

a

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### Miller indices (hkl) Choose cell, cell origin, cell axes Draw set of

planes of interest Choose plane nearest origin Find intercepts on cell axes: 1,1,?

origin

b

1

a

1

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### Miller indices (hkl) Choose cell, cell origin, cell axes Draw set of

planes of interest Choose plane nearest origin Find intercepts on cell axes 1,1,? Invert these to get (hkl) (110)

origin

b

1

a

1

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Exercises

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Exercises

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Exercises

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Exercises

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Exercises

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Exercises

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Exercises

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Exercises

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Exercises

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Exercises

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### Lattice planes

Two things characterize a set of lattice planes: interplanar spacing (d) orientation (defined by normal)

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### Strange indices

For hexagonal lattices - sometimes see 4-index notation for planes (hkil) where i = - h - k

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### Zones

2 intersecting lattice planes form a zone

plane (hkl) belongs to zone [uvw] if hu + kv + lw = 0

if (h1 k1 l1) and (h2 k2 l2 ) in same zone, then (h1+h2 k1+k2 l1+l2 ) also in same zone.

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### Zones

zone axis [uvw] is ui + vj + wk

Example: zone axis for (111) & (100) - [011]

(011) in same zone? hu + kv + lw = 0 0·0 + 1·1 - 1·1 = 0

if (h1 k1 l1) and (h2 k2 l2 ) in same zone, then (h1+h2 k1+k2 l1+l2 ) also in same zone.

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### Reciprocal lattice

Real space lattice

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### Reciprocal lattice

Real space lattice - basis vectors

a

a

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### Reciprocal lattice

Real space lattice - choose set of planes

(100) planes

n100

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### Reciprocal lattice

Real space lattice - interplanar spacing d

(100) planes

d100

1/d100

n100

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### Reciprocal lattice

Real space lattice ––> the (100) reciprocal lattice pt

(100) planes

d100

n100

(100)

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### Reciprocal lattice

The (010) recip lattice pt

n010

(100) planes

d010

(010)

(100)

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### Reciprocal lattice

The (020) reciprocal lattice point

n020

(020) planes

d020

(010)

(020)

(100)

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### Reciprocal lattice

More reciprocal lattice points

(010)

(020)

(100)

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### Reciprocal lattice

The (110) reciprocal lattice point

(100) planes

n110

d110

(010)

(020)

(110)

(100)

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### Reciprocal lattice

Still more reciprocal lattice points

(100) planes

the reciprocal lattice

(010)

(020)

(100)

(230)

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### Reciprocal lattice

Reciprocal lattice notation

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### Reciprocal lattice

Reciprocal lattice for hexagonal real space lattice

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### Reciprocal lattice

Reciprocal lattice for hexagonal real space lattice

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### Reciprocal lattice

Reciprocal lattice for hexagonal real space lattice

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### Reciprocal lattice

Reciprocal lattice for hexagonal real space lattice

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### Reciprocal lattice

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