MCE 230_ F10_lec_8 - z y x O O x z y   1 Hexagonal...

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MCE 230 Materials Science Fall 2010 Lecture - 8
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Crystalline Structure
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Crystallographic Planes Miller indices (h k l) Procedure: 1. If a plane passes through the origin, either another parallel plane must be constructed, or select a new origin. 2. Determine the points at which the plane intersects each axis 3. If the plane is parallel to an axis the intersection with that axis is considered infinite ( ) 4. Take the reciprocals of the intercepts 5. Multiply or divide by a common factor to get a set of smallest integers 6. Represent the integer indices, enclosed by parentheses and not separated by commas ( h k l )
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z y x x y z Intercepts 1 Reciprocal 1 0 0 (1 0 0)
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z y x x y z Intercepts 1 Reciprocal 0 0 1 (0 0 1)
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z y x x y z Intercepts 1 1 1 Reciprocal 1 1 1 (1 1 1)
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z y x x y z Intercepts 1 1 Reciprocal 1 1 0 (1 1 0)
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z y x If the plane is passing through origin: construct a parallel plane that is not passing through the origin. All parallel planes are equivalent. x y z Intercepts 1 Reciprocal 1 0 0 (1 0 0)
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x' y' z' Intercepts -1 Reciprocal -1 0 0 OR: Select a new origin
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Unformatted text preview: z y x O O' x' z' y'   1 Hexagonal Crystals  Miller-Bravais indices are used to represent a plane in hexagonal crystal (hkil) h= 1/ intersection with a1 k= 1/ intersection with a2 l= 1/ intersection with z i = - (h + k) which represent intersection with a3 Hexagonal Crystals  Ex: Intersection 1 -1 1 a1 a2 z Reciprocal 1-1 1 h k l i = -(h + k) = -(1-1) = 0 Miller-Bravais indices (1 1 0 1) • Family of planes: are planes that are crystollographically equivalent ( having the same atomic packing) and • Family of planes is represented by {hkl} • Example: for cubic systems Equivalent Planes • For cubic systems; planes having the same indices irrespective of the order or signs are equivalent ( this does not apply for other crystal systems ) . • A direction having the same indices of a plane is normal to it • Example: [101] is normal to (101) Equivalent Planes...
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