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crystallography lv
crystallography lv
crystallography lv
crystallography lv
Lattice planes
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Reciprocal lattice
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Crystallography lv

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1crystallography lv. 25for planes (hkil) where i = - h - k.
2Useful concept for crystallography 26Zones. 2 intersecting lattice planes
& diffraction. Lattice planes. Think form a zone. plane (hkl) belongs to zone
of sets of planes in lattice - each plane [uvw] if hu + kv + lw = 0. if (h1 k1 l1)
in set parallel to all others in set. All and (h2 k2 l2 ) in same zone, then (h1+h2
planes in set equidistant from one k1+k2 l1+l2 ) also in same zone.
another. Infinite number of set of planes 27Zones. zone axis [uvw] is ui + vj +
in lattice. wk. Example: zone axis for (111) &
3Keep track of sets of planes by giving (100) - [011]. (011) in same zone? hu + kv
them names - Miller indices (hkl). Lattice + lw = 0 0·0 + 1·1 - 1·1 = 0. if (h1 k1
planes. l1) and (h2 k2 l2 ) in same zone, then
4Miller indices (hkl) Choose cell, cell (h1+h2 k1+k2 l1+l2 ) also in same zone.
origin, cell axes: origin. b. a. 28Reciprocal lattice. Real space
5Miller indices (hkl) Choose cell, cell lattice.
origin, cell axes Draw set of planes of 29Reciprocal lattice. Real space lattice
interest: origin. b. a. - basis vectors. a. a.
6Miller indices (hkl) Choose cell, cell 30Reciprocal lattice. Real space lattice
origin, cell axes Draw set of planes of - choose set of planes. (100) planes.
interest Choose plane nearest origin: n100.
origin. b. a. 31Reciprocal lattice. Real space lattice
7Miller indices (hkl) Choose cell, cell - interplanar spacing d. (100) planes.
origin, cell axes Draw set of planes of d100. 1/d100. n100.
interest Choose plane nearest origin Find 32Reciprocal lattice. Real space lattice
intercepts on cell axes: 1,1,? origin. b. ––> the (100) reciprocal lattice pt.
1. a. 1. (100) planes. d100. n100. (100).
8Miller indices (hkl) Choose cell, cell 33Reciprocal lattice. The (010) recip
origin, cell axes Draw set of planes of lattice pt. n010. (100) planes. d010.
interest Choose plane nearest origin Find (010). (100).
intercepts on cell axes 1,1,? Invert these 34Reciprocal lattice. The (020)
to get (hkl) (110). origin. b. 1. a. 1. reciprocal lattice point. n020. (020)
9Lattice planes. Exercises. planes. d020. (010). (020). (100).
10Lattice planes. Exercises. 35Reciprocal lattice. More reciprocal
11Lattice planes. Exercises. lattice points. (010). (020). (100).
12Lattice planes. Exercises. 36Reciprocal lattice. The (110)
13Lattice planes. Exercises. reciprocal lattice point. (100) planes.
14Lattice planes. Exercises. n110. d110. (010). (020). (110). (100).
15Lattice planes. Exercises. 37Reciprocal lattice. Still more
16Lattice planes. Exercises. reciprocal lattice points. (100) planes.
17Lattice planes. Exercises. the reciprocal lattice. (010). (020).
18Lattice planes. Exercises. (100). (230).
19Lattice planes. Exercises. 38Reciprocal lattice. Reciprocal lattice
20Lattice planes. Exercises. notation.
21Lattice planes. Exercises. 39Reciprocal lattice. Reciprocal lattice
22Lattice planes. Exercises. for hexagonal real space lattice.
23Lattice planes. Exercises. 40Reciprocal lattice. Reciprocal lattice
24Lattice planes. Two things for hexagonal real space lattice.
characterize a set of lattice planes: 41Reciprocal lattice. Reciprocal lattice
interplanar spacing (d) orientation for hexagonal real space lattice.
(defined by normal). 42Reciprocal lattice. Reciprocal lattice
25Strange indices. For hexagonal for hexagonal real space lattice.
lattices - sometimes see 4-index notation 43Reciprocal lattice.
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