Introduction / Structure of Metals and Alloys / Crystalline materials

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)

X-Ray Diffraction / Crystal Structure

It’s useful for studying Crystal structure

This method have the details about

• Grain size (or) Crystal size
• Orientation of the crystal
• Cold worked, Distorted and Internally stressed crystals
• Re-Crystallization
• Preferred orientation etc

Methods of Examining and Measuring the condition of Crystal Structure

1. The Laue back reflection method
2. The Rotating Crystal method
3. The DeBye- Scherrer (or) Powder method:

The Laue back Reflection method:
It’s applicable to single crystals (or) poly-Crystalline masses.
When a beam of Mono chromatic (i.e. of Single Wavelength) X-Ray is directed as a narrow pencil at a specimen of a metal diffraction takes place at certain of the crystallographic planes.



       

The Rotating Crystal method:
It’s a useful method for determining angles and positions of planes.
Crystallographic planes are brought in to reflecting positions by rotating a crystal (Specimen) about one of it’s axis while simultaneously radially it with a beam of mono chromatic x-Rays.
If crystal orientation planes are known, the angles and directions can be calculated.


The DeBye- Scherrer (or) Powder method:
The narrow pencil of monochromatic X-Rays is diffracted from the powder and recorded by the photographic film as a series of lines of varying armature.
By the Bragg Equation:

nλ=2d Sinθ

Where,

λ– Wave length of X-ray

d- Spacing of the atomic planes

θ – Angle of reflection