Posted tagged ‘Bravai’


August 23, 2011

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.

01-lattice-crystal structure


  • 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:

01-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

0I-bcc-structure-body center cubic02-bcc-structure-body center cubic

03-bcc-structure-body center cubic


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

02-fcc-structure-face center cubic-unit cell

0I-fcc-structure-face center cubic-unit cellHexagonal 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

0I-hcp-structure-Hexagonal close packed-unit cell

0I-hcp-structure-hexagonal close packed

0I-hcp ball-structure-Hexagonal close packed-unit cell



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

02-miller indices-crystalographic planes


Intercepts :   a , a , ∞

Fractional intercepts :   1 , 1 , ∞

Miller Indices :   (110)


2. The (111) surface

03-miller indices-crystalographic planes


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

04-miller indices-crystalographic planes


Intercepts :   ½ a , a , ∞

Fractional intercepts :   ½ , 1 , ∞

Miller Indices :   (210)