Chapter3_lectures-Alamgir

Chapter3_lectures-Alamgir - Chapter 3 Crystal Structures...

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Many materials crystallize in a regular array with basic building blocks being at repeated regular intervals. The structure is determined by the bond character and energy minimization. Metals, ceramics, polymers can all form crystal structures. Properties are dependent upon the type of bond and the structure. Chapter 3 Crystal Structures
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Directions in a Crystal, Miller Indices- [hkl] 1. Get 2 points that lie in the direction. 2. Subtract coordinates of the tail from tip. 3. Clear fractions. 4. Write integers in square brackets. 5. Negative integers are indicated by putting a bar over the integer.
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Directions in a Crystal, Miller Indices- [hkl]
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Family of Directions in a Crystal 0,0,0 [ ] 100 [ ] 010 [ ] 001 100 010 001 [ ] [ ] [ ] 100 010 001 100 010 001 <100> cube edge
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Planes in a Crystal, Miller Indices- ( hkl) Cube Face 1. Identify coordinate intercepts of the plane. 2. Take the reciprocal of the intercepts. ( 1) (0 0 1) x y z 3. Write integers in parentheses, no commas. (100) (010)
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Planes in a Crystal, Miller Indices- ( hkl) Through the Cube 1. Identify coordinate intercepts of the plane. 2. Take the reciprocal of the intercepts. 1. Clear fractions by multiplying, but do not reduce to lowest integers. 4. Write integers in parentheses, no commas. ( 1/2) (0 0 2) x y z
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Planes in a Crystal, Miller Indices- ( hkl) 1. Identify coordinate intercepts of the plane. 2. Take the reciprocal of the intercepts. 1. Clear fractions by multiplying, but do not reduce to lowest integers. 4. Write integers in parentheses, no commas. 5. Negative integers are indicated by a bar over the integer. ( -1 ) (010 ) x y z (0,0,0)
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Planes in a Crystal, Miller Indices- ( hkl) x y z (110)
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Planes in a Crystal, Miller Indices- ( hkl) Plane A Plane B Plane C Plane D Plane F Plane E
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Family of Planes in a Crystal { } 100 (100) (010) (001) (100) (010) (001) (100) (010) (001) (010) (001) (100)
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Summary Positive and negative Miller Indices of
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