MAT_101_Summer08Lecture_4

MAT_101_Summer08Lecture_4 - CRYSTALLOGRAPHY IV: PLANES c...

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CRYSTALLOGRAPHY IV: PLANES Plane (hkl) i. Find intercept with a, b, c ii. Intercept = 1/ h , 1/ k , 1/ l (Planes parallel to axis have an intercept at ) ii. Take reciprocal of intercepts iii. Clear any common integer iv. Plane (hkl) a b c 1/ h 1/ k 1/ l
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CRYSTALLOGRAPHY IV: PLANES (001) (110) (111)
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CRYSTALLOGRAPHY IV: PLANES Examples Plane A Intercepts x: ½ y: - ½ z: Plane: Clear common integer Plane: ( ) 0 2 2 ( ) 0 1 1 Instead of writing “-” sign in crystallographic notation We use a “bar” over the number ( ) 0 2 2 “Two two bar zero”
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CRYSTALLOGRAPHY IV: PLANES Specific plane: (hkl) Families of planes: {hkl} ( ) ( ) ( ) ( ) () ( ) 1 00 , 001 , 0 1 0 , 010 , 00 1 , 100 {} 100 :
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CRYSTALLOGRAPHY V: HEXAGONAL Hexagonal: | a | = a | b | = a | c | = c α = β = 90° γ = 120° Two crystallographic conventions: three-index and four-index [] [ ] () ' ) ( ' ' 2 3 ' ' 2 3 ' ' ' nw w v u t u v n v v u n u uvtw w v u = + = = = ( ) ( ) ) ( k h i hkil hkl + =
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CRYSTALLOGRAPHY: Close-Packed Planes FCC Metals: (111) HCP Metals: (0001) FCC Stacking …ABCABCABC… HCP Stacking …ABABABABAB…
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CRYSTALLOGRAPHY: Close-Packed Planes FCC Stacking (111) …ABCABCABC… HCP Stacking (0001) …ABABABABAB…
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POLYCRYSTALLINE MATERIALS: EXAMPLE Grain formation in solidification Squares: Represent unit cells Individual crystals or “grains” Grain boundaries
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CRYSTALS AS BUILDING BLOCKS • Some engineering applications require single crystals: • Crystal properties reveal features of atomic structure. --Ex: Certain crystal planes in quartz fracture more easily than others. --diamond single crystals for abrasives --turbine blades Fig. 8.30(c), Callister 6e. (Fig. 8.30(c) courtesy of Pratt and Whitney).
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MAT_101_Summer08Lecture_4 - CRYSTALLOGRAPHY IV: PLANES c...

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