Sahithyan's S1 — Properties of Materials

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 formed.

Density

\rho= \frac{\text{Mass/unit cell}}{\text{Volume/unit cell}} = \frac{M n}{v L}

Here:

$M$ - molar mass
$n$ - atoms per unit cell
$v$ - volume of the unit cell
$L$ - 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)

\text{APF} = \frac{\text{True volume}}{\text{Bulk volume}} = \frac{\text{Volume of atoms/unit cell}}{\text{Volume/unit cell}}

Geometrically maximum APF in real life (assuming spherical and identical atoms) is 74%. If a structure has 74% APF, the structure is called a close-packed structure. The APF can be increased to a maximum of 79% by adding impurities.

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.