Ting-Yun Huang, 2012/09/18Page 1
3.14/3.40J/22.71J Recap
Basic Crystallography and Miller Indices
Ting-Yun Huang
2012 Sep. 18th
Outline• Basic Structures
– Cubic: FCC/BCC
– HCP
• Miller Indices
– From 3D to 4D: Miller indices for hexagonal crystals
– From 3D to 2D: Stereographic Projection
– Zone axis
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BASIC STRUCTURESBCC/FCC /HCP
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Basic Structures: BCC
• Coordination number = 8
• Number of atoms in unit cell = 2
• α-Fe(room temperature) , δ-Fe(high T), β-Ti(high T), Zr (high T)
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Basic Structures: FCC• Coordination number =
12
• Number of atoms in unit cell = 4
• Closest packing
– ABCABC packing
• γ-Fe, Cu, Ag, Au, Al, Ni, Pb, Pt
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Basic Structures: HCP
•Coordination number = 12
•Number of atoms in unit cell = 2(*)
•Closest packing
– ABAB packing
•Mg, Zn, α-Ti, Be, Cd, Zr (low T)
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MILLER INDICESNotations/Hexagonal Systems/Stereographic Projection
Presentation Author, 2003Page 7
Miller Indices-Notations• Directions
– Specific Direction: [u1 u2 u3]
– Family of Directions: <u1 u2 u3>
• Planes
– Reciprocal of the intercepts
– Specific Plane: (u1 u2 u3)
– Family of Planes: {u1 u2 u3}
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From 3D to 4D-
Miller indices for HCP structures• Constraints:
– [u1u2u3v]→u1a1+u2a2+u3a3+vc
– u1+u2+u3 = 0
• Redundant coordinate system which is not orthogonal
• But we can still perform inner product.
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From 3D to 2D-Stereographic Projection
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Zone axis
In this TEM diffraction, the structure
is FCC and the zone axis is [112].
The (11-1) and (2-20) plane have the
same zone axis [112].
Presentation Author, 2003Page 11
_(111) _
(220)
From 3D to 2D-Stereographic Projection
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Thank you!
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