Structure Of Body Centered Weigner Seitz Cell-Solid State Physics-Presentation, Slides of Solid State Physics

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Structure Of Body Centered

Weigner Seitz Cell

Intro. To Solid State Physics

It is the largest branch of condensed matter

physics and the study of rigid matter, or solids,

through methods such as quantum mechanics,

crystallography, electromagnetism and

metallurgy.

Unit Cell:

 The smallest building block of a crystal, consisting of

atoms,ions,or molecules,whose geometric arrangement defines

a crystal's characteristic symmetry and whose repetition in

space produces a crystal lattice.

 Here we discuss the types of unit cell:

There are several different types of unit cell which we mention

below:

Types of Unit Cell (Ctd):

Radius:

 we have one atom completely inside the cube plus eight atoms (at each corner) where only one eighth is inside the cube.  1 + (1/8 * 8) = 2 atoms per unit cell  We can also calculate the size of the unit cell based of the radius of the atoms in the cell.  In the body-centered cubic the atoms along the diagonal (crossing the center of the cube) are touching.Therefore if each atom has a radius of 'r' then the diagonal of the cubic is 4r.

Calculation Of Radius:

 Usually, the length of the cell edge is represented by a. The direction from a corner of a cube to the farthest corner is called body diagonal ( bd ). The face diagonal ( fd ) is a line drawn from one vertex to the opposite corner of the same face. If the edge is a , then we have:

fd^2 = a^2 + a^2 = 2 a^2

bd^2 = fd^2 + a^2

= a^2 + a^2 + a^2 bd^2 = 3 a^2

Packing Fraction of BCC:

Volume of unit cell: Vc: e^

Atomic Volume:Av:

=2(4/3)pir^

Now

e =4r/sqrt(3)

PF=100*Av/Vc

=100pisqrt(3)/

Different views Of BCC:

Bcc Structure In GERMANY docsity.com

Construction Of Wigner Seitz Cell

 To create a Wigner-Seitz cell simply we have to do the

following steps.

 Choose any lattice site as the origin.

 Starting at the origin draw vectors to all neighbouring lattice

points.

 Construct a plane perpendicular to and passing through the

midpoint of each vector.

 The area enclosed by these planes is the Wigner-Seitz cell.

Characteristics of Wigner Seitz Cell

 Wigner-Seitz cells associated with all lattice points are identical in size, shape and orientation as follows with the translational symmetry of the lattice.

 When stacked the Wigner-Seitz cells fill all space.

 The Wigner-Seitz cell is a polyhedron.

 The Wigner-Seitz cell has the full point symmetry of its lattice point.

 The co-ordination number of Bcc is “8”.

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