- Books Name
- Kaysons Academy Chemistry Book

- Publication
- Kaysons Publication

- Course
- JEE

- Subject
- Chemistry

**CRYSTAL LATTICES **

- Lattice: Regular 3-D arrangements of equivalent LATTICE POINTS in space.
- UNIT CELLS

- Smallest repeating internal unit that has the symmetry characteristic of the solid.

- Actual unit cell
- Unit cell as drawn
- Whole crystal

**CRYSTAL LATTICE GEOMETRY **

- Based on shape of unit cell ignoring actual atomic locations
- Unit cell = 3-dimensional unit that repeats in space
- Unit cell geometry completely specified by
*a, b, c*(distance in x, y & z axis)&*a, b, g*(angles between a,b & c (lattice parameters or lattice constants) - Seven possible combinations of a, b, c & a, b, g, resulting in seven basic crystal systems

**14 Bravais Lattices: seven basic lattices and fourteen overall**

**14 Bravais Lattices from seven basic lattices **

**Cubic Unit Cells **

There are 7 basic crystal systems, but we are only concerned with CUBIC.

**DIFFERENT CUBIC UNIT CELLS **

**ATOM SHARING AT CUBE FACES AND CORNERS**

Atom shared in corner

à 1/8 inside each unit cell

Atom shared in face

à ½ inside each unit cell

Atoms shared on edges

à ¼ inside each unit cell

Atoms inside the unit cell

à 1 inside each unit cell

**NUMBER OF ATOMS PER UNIT CELL**

**PACKING FRACTION **

a = edge length of unit cell

R = radius of atoms( assuming they are hard spheres)

Z= no of atoms in one unit cell

**PACKING FRACTION: SC**

**PACKING RACTION: BCC**

**PACKING FRACTION: FCC**

**Voids**:- gaps between atoms in a crystal are called voids.

- There are two types of voids
- Tetrahedral voids and octahedral voids

**HOW TO LOCATE VOIDS**

- No. of tetrahedral voids = 2 x effective atoms/unit cell

- No. of octahedral voids = 1 x effective atoms/unit cell

**COMPARISON OF CRYSTAL STRUCTURES**