Space Lattice
An infinite set of equally-spaced points in a space.
Set of lines are used to connect these points to provide a useful guide to the eye. They are not part of the lattice.
Unit Cell
Smallest repeating parallelepiped inside the lattice. By stacking in all directions, the lattice can be generated.
Density
Here:
- volume of the unit cell - molar mass - atoms per unit cell - avagadro’s number
Crystalline systems
- All crystalline materials fall within one of the 7 possible shapes and 4 variants.
The shapes
Don’t have to memorize.
- Cubic
- Hexagonal
- Tetragonal
- Rhombohedral (Trigonal)
- Orthorrhombic
- Monoclinic
- Triclinic
The variants
- Simple: atoms at the corners only.
- Base-centered: atoms at the corners and center of 2 opposing sides only.
- Body-centered: atoms at the corners and center only.
- Face-centered: atoms at the corners and center of all faces only.
Bravais showed that only 14 of 28 (7 shapes x 4 variants) are possible in real life.
Only 4 of them are studied in s1.
- Simple cubic (sc)
- Body-centered cubic (bcc)
- Face-centered cubic (fcc)
- Hexagonal close packed or Close packed hexagonal (hcp/cph)
Coordination number
Coordination number of a lattice system is the number of particles that each particle contacts.
Atomic Packing Factor (APF)
Geometrically maximum APF in real life (assuming spherical atoms) is 74%. If a structure has 74% APF, the structure is called a close-packed structure.
Interstitial sites (aka holes, voids)
Empty space that exists between the packing of atoms in a crystal structure.
Octahedral interstices
Locations of void spaces available in an FCC. Located at the center of each edge and body-center of the unit cell.