Crystal structure

Crystal structure

1. Structure formation

   • Lattice + Basis
   • Primitive vectors
   • Primitive cell
     • 1 - Draw lines to connect one lattice point to all nearby points
       • 2- Draw 'normal' lines at center of connecting lines
         • 3- Smallest area enclosed within the secondary lines = primitive cell
     • Volume of a primitive cell

2. Symmetry operations

   • Translation
   • Rotation
     • 2π, 2π/2, 2π/3, 2π/4, 2π/6
   • Reflections
   • Inversion
     • Rotation of π, reflection in plane normal to rotation axis

3. Examples

   • Sodium Chloride (NaCl)
     • FCC Lattice.
     • Six nearest neighbors.
   • Cesium Chloride (CsCl)
   • Diamond
     • FCC Lattice

4. Lattice types (CHOTTTM)

   • Triclinic
   • Monocylinic
   • orthorhombic
   • Tetragonal
   • Cubic
     • Characteristics
   • Trigonal
   • Hexagonal

5. https://www.youtube.com/watch?v=CsnNbuqxGTk

   • http://academic.brooklyn.cuny.edu/physics/tung/GC745S15/vg4-7.pdf
     • http://dao.mit.edu/8.231/BZandRL.pdf
       • http://www.physics.drexel.edu/~gyang/SOLID/lecture092310.pdf

6. Index system

   • 1- Plane through points s1a1, s2a2, s3a3
     • 2- Define the plane by the reciprocals 1/s1, 1/s2, 1/s3
       • 3- Reduce integers with same ratio h, k, l
         • 4- Plane is defined (h, k, l)
     • Plane intercepts a1, a2, a3 axes at 3a1, 2a2, 2a3. Reciprocals = 1/3, 1/2, 1/2. Smallest integers with this ratio = 2, 3, 3. Indices of the plane = (233)

7. reciprocal lattice

8. X-ray spectrum

   • reflection peaks
     • Face centered lattice, the hkl all odd or all even.
     • Body Centered Lattice - h+k+l = even
     • Systematic absences
       • Lattice centering - translational operations derived from lattice type
       • Screw axis - symmetry axis that imply rotation and an additional translation
       • Glide place - mirror places that imply reflection and additional translation

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