Crystallography

1
Crystallography

• Dr. Valeriia Starovoitova

2

• Crystallography borders, naturally, on pure
• physics, chemistry, biology, mineralogy,
• technology and also on mathematics, but is
• distinguished by being concerned with the
• methods and results of investigating the
• arrangement of atoms in matter,
• particularly when that arrangement has
• regular features.
• Paul P. Ewald, Acta Crystallographica (1948), 1,
  2.

3
Crystal vs. Amorphous Meterial
4
(No Transcript)
5
Symmetry Operations

• Mirror planes
• Rotational symmetry, e.g., 90o, 180o
• Translational symmetry, e.g., chess board with
  identical chess pieces

6
Arrays

• 1-D line lattice
• 2-D plane lattice
• 3-D space lattice
• Lattice Set of points in space such that
• the surroundings of one point are identical
• with those of all others

7
Unit Cell

• Smallest possible structural unit that is
• repeated, 3-D
• Contains a full description of the structure
• as a whole
• Complete structure can be generated by
• the repeated stacking of adjacent unit cells,
  face
• to face, throughout three dimensional space
• Crystallographic analog of atom

8
Crystal Systems

• Seven unique unit cell shapes that can be
• stacked together to fill three-dimensional space

9
Bravais Lattices, 1845
10
Auguste Bravais

• 1811-1863, French physicist
• Naval officer
• hydrographic work near Algerian coast
• Recherché expedition (Laplandia)
• Taught math and astronomy in Lyon
• Chair of Physics Department in École
  Polytechnique

11
Cubic System
Phosphor
Aluminum
Tungsten
12
Coordinates
13
Directions
(x2, y2, z2) (x1, y1, z1) ? xyz
14
Planes

• Planes
• Miller Indices (xyz)
• - Determine intercepts
• - Take reciprocals
• - Clear fractions

15
Lattice Parameter and Atomic Radius
Lattice parameter (lattice constant) 10-10
m Atomic radius (size of atom) 10-9- 10-10 m
16
Coordination Number
Coordination number number of nearest neighbors
17
Packing Factor

• (Atomic) Packing Factor
• ( of atoms/cell)(Volume of each atom)
• Volume of unit cell

• 2 atoms per unit cell
• Vatom(4/3)pR3
• Vcell