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crystallography lv
crystallography lv
Useful concept for crystallography & diffraction
Useful concept for crystallography & diffraction
Keep track of sets of planes by giving them names - Miller indices
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:
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
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
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
Strange indices
Zones
Zones
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
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

Презентация на тему: «Crystallography lv». Автор: . Файл: «Crystallography lv.ppt». Размер zip-архива: 367 КБ.

Crystallography lv

содержание презентации «Crystallography lv.ppt»
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1 crystallography lv

crystallography lv

2 Useful concept for crystallography & diffraction

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 Keep track of sets of planes by giving them names - Miller indices

Keep track of sets of planes by giving them names - Miller indices

(hkl)

Lattice planes

4 Miller indices (hkl) Choose cell, cell origin, cell axes:

Miller indices (hkl) Choose cell, cell origin, cell axes:

origin

b

a

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

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

planes of interest:

origin

b

a

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

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

planes of interest Choose plane nearest origin:

origin

b

a

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

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

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

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

9 Lattice planes

Lattice planes

Exercises

10 Lattice planes

Lattice planes

Exercises

11 Lattice planes

Lattice planes

Exercises

12 Lattice planes

Lattice planes

Exercises

13 Lattice planes

Lattice planes

Exercises

14 Lattice planes

Lattice planes

Exercises

15 Lattice planes

Lattice planes

Exercises

16 Lattice planes

Lattice planes

Exercises

17 Lattice planes

Lattice planes

Exercises

18 Lattice planes

Lattice planes

Exercises

19 Lattice planes

Lattice planes

Exercises

20 Lattice planes

Lattice planes

Exercises

21 Lattice planes

Lattice planes

Exercises

22 Lattice planes

Lattice planes

Exercises

23 Lattice planes

Lattice planes

Exercises

24 Lattice planes

Lattice planes

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

25 Strange indices

Strange indices

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

26 Zones

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.

27 Zones

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.

28 Reciprocal lattice

Reciprocal lattice

Real space lattice

29 Reciprocal lattice

Reciprocal lattice

Real space lattice - basis vectors

a

a

30 Reciprocal lattice

Reciprocal lattice

Real space lattice - choose set of planes

(100) planes

n100

31 Reciprocal lattice

Reciprocal lattice

Real space lattice - interplanar spacing d

(100) planes

d100

1/d100

n100

32 Reciprocal lattice

Reciprocal lattice

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

(100) planes

d100

n100

(100)

33 Reciprocal lattice

Reciprocal lattice

The (010) recip lattice pt

n010

(100) planes

d010

(010)

(100)

34 Reciprocal lattice

Reciprocal lattice

The (020) reciprocal lattice point

n020

(020) planes

d020

(010)

(020)

(100)

35 Reciprocal lattice

Reciprocal lattice

More reciprocal lattice points

(010)

(020)

(100)

36 Reciprocal lattice

Reciprocal lattice

The (110) reciprocal lattice point

(100) planes

n110

d110

(010)

(020)

(110)

(100)

37 Reciprocal lattice

Reciprocal lattice

Still more reciprocal lattice points

(100) planes

the reciprocal lattice

(010)

(020)

(100)

(230)

38 Reciprocal lattice

Reciprocal lattice

Reciprocal lattice notation

39 Reciprocal lattice

Reciprocal lattice

Reciprocal lattice for hexagonal real space lattice

40 Reciprocal lattice

Reciprocal lattice

Reciprocal lattice for hexagonal real space lattice

41 Reciprocal lattice

Reciprocal lattice

Reciprocal lattice for hexagonal real space lattice

42 Reciprocal lattice

Reciprocal lattice

Reciprocal lattice for hexagonal real space lattice

43 Reciprocal lattice

Reciprocal lattice

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