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crystallography lv |
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Useful concept for crystallography & diffractionLattice 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 |
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Keep track of sets of planes by giving them names - Miller indices(hkl) Lattice planes |
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Miller indices (hkl) Choose cell, cell origin, cell axes:origin b a |
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Miller indices (hkl) Choose cell, cell origin, cell axes Draw set ofplanes of interest: origin b a |
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Miller indices (hkl) Choose cell, cell origin, cell axes Draw set ofplanes of interest Choose plane nearest origin: origin b a |
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Miller indices (hkl) Choose cell, cell origin, cell axes Draw set ofplanes 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 ofplanes 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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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesExercises |
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Lattice planesTwo things characterize a set of lattice planes: interplanar spacing (d) orientation (defined by normal) |
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Strange indicesFor hexagonal lattices - sometimes see 4-index notation for planes (hkil) where i = - h - k |
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Zones2 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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Zoneszone 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 latticeReal space lattice |
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Reciprocal latticeReal space lattice - basis vectors a a |
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Reciprocal latticeReal space lattice - choose set of planes (100) planes n100 |
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Reciprocal latticeReal space lattice - interplanar spacing d (100) planes d100 1/d100 n100 |
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Reciprocal latticeReal space lattice ––> the (100) reciprocal lattice pt (100) planes d100 n100 (100) |
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Reciprocal latticeThe (010) recip lattice pt n010 (100) planes d010 (010) (100) |
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Reciprocal latticeThe (020) reciprocal lattice point n020 (020) planes d020 (010) (020) (100) |
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Reciprocal latticeMore reciprocal lattice points (010) (020) (100) |
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Reciprocal latticeThe (110) reciprocal lattice point (100) planes n110 d110 (010) (020) (110) (100) |
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Reciprocal latticeStill more reciprocal lattice points (100) planes the reciprocal lattice (010) (020) (100) (230) |
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Reciprocal latticeReciprocal lattice notation |
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Reciprocal latticeReciprocal lattice for hexagonal real space lattice |
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Reciprocal latticeReciprocal lattice for hexagonal real space lattice |
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Reciprocal latticeReciprocal lattice for hexagonal real space lattice |
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Reciprocal latticeReciprocal lattice for hexagonal real space lattice |
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Reciprocal lattice |
«Crystallography lv» |