**Crystalline Materials:**

- A crystalline material is one in which the atoms are situated in a repeating (or) periodic array over large atomic distances.

**Non Crystalline Materials:**

- Materials that do not crystallize are called non-crystalline (or) Amorphous materials

**Space Lattice:**

**Lattice** is the regular geometrical arrangement of points in crystal space.

- The atoms arrange themselves in distinct pattern in space is called a
**Space Lattice**.
- Atoms in crystalline materials are arranged in a regular 3 – Dimensional repeating pattern known as
**Lattice Structure**.
- They are divided by network of lines in to equal volumes, the points of intersection are known as
**Lattice Points**.

**Unit Cell:**

- It is the smallest portion of the lattice which repeated in all directions.
- 3D visualization of 14 Space Lattices are known as
**Bravai’s Space Lattice**.
- If a unit cell contains lattice points only at it’s corners, then it is called
**Primitive Unit Cell (or) Simple Unit Cell.**
- Three edge length x,y, & z and three interaxial angles α, β, & γ are termed as
**Lattice Parameters**.

**Crystal System:**

- It is a scheme by which crystal structures are classified according to unit cell geometry.

**Types of Crystal Systems:**

- Cubic
- Tetragonal
- Hexagonal
- Orthorhombic
- Rhombohedral
- Monoclinic
- Triclinic

**Crystal Systems**

**Simple Crystal Structure:**

**Body Centered Cubic Structure (BCC)**

- Unit cell contains 2 atoms
- Lattice Constant a= 4r / √3, where r is atomic radius
- Atomic packing factor APF = 0.68
- Metals are Vanadium, Molybdenum, Titanium, Tungsten

**Face Centered Cubic (FCC)**

- Unit cell contains 4 atoms
- Lattice Constant a= 4r / √2, where r is atomic radius
- Atomic packing factor APF = 0.72
- FCC structures can be plastic deformed at severe rates
- Metals are Copper, Aluminum, Phosphorous, Nickel, Cobalt etc

**Hexagonal Closed Packed Structure (HCP)**

- Unit cell contains 3 atoms
- Axial ratio c/a, where ‘c’ is Distance between base planes, ‘a’ is Width of Hexagon
- Axial Ratio varies from 1.58 for Beryllium to 1.88 for Cadmium (Therefore a=2.9787, c=5.617)
- Atomic packing factor APF = 0.74
- Metals are Zinc, Cadmium, Beryllium, Magnesium etc

**Crystallographic Planes and Directions**

The Layers of atoms in the planes along which atoms are arranged is known as “Atomic” (or) “Crystallographic planes”.

**Miller Indices:**

Miller Indices is a system of notation that denotes the orientation of the faces of a crystal and the planes and directions of atoms within that crystal.

**Miller Indices for Planes:**

**1. The (110) surface**

Intercepts : *a* , *a* , ∞

Fractional intercepts : 1 , 1 , ∞

Miller Indices : **(110)**

**2. The (111) surface**

Intercepts : *a* , *a* , *a*

Fractional intercepts : 1 , 1 , 1

Miller Indices : **(111)**

The (100), (110) and (111) surfaces considered above are the so-called low index surfaces of a cubic crystal system.

**3. The (210) surface**

Intercepts : ½ *a* , *a* , ∞

Fractional intercepts : ½ , 1 , ∞

Miller Indices : **(210)**