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3.14/3.40J/22.71J Recap Basic Crystallography and Miller Indices

3.14/3.40J/22.71J Recap Basic Crystallography and Miller Indices. Ting-Yun Huang 2012 Sep. 18 th. 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. BCC/FCC /HCP.

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3.14/3.40J/22.71J Recap Basic Crystallography and Miller Indices

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  1. 3.14/3.40J/22.71J RecapBasic Crystallography and Miller Indices Ting-Yun Huang 2012 Sep. 18th

  2. 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

  3. BCC/FCC /HCP BASIC STRUCTURES

  4. 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)

  5. 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

  6. 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)

  7. Notations/Hexagonal Systems/Stereographic Projection MILLER INDICES

  8. 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}

  9. 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.

  10. From 3D to 2D-Stereographic Projection

  11. 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]. _ (111) _ (220)

  12. From 3D to 2D-Stereographic Projection

  13. Thank you!

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