What is the shape of the Wigner-Seitz unit cell of the cubic lattice?

What is the shape of the Wigner-Seitz unit cell of the cubic lattice?

The Wigner–Seitz cell of the body-centered cubic lattice is a truncated octahedron.

What is Wigner-Seitz method?

A method of approximating the band structure of a solid: Wigner-Seitz cells surrounding atoms in the solid are approximated by spheres, and band solutions of the Schrödinger equation for one electron are estimated by using the assumption that an electronic wave function is the product of a plane wave function and a …

What is Wigner-Seitz Cell write down the steps for the construction of Wigner-Seitz Cell?

To create a Wigner-Seitz cell simply complete the following steps.

1. Choose any lattice site as the origin.
2. Starting at the origin draw vectors to all neighbouring lattice points.
3. Construct a plane perpendicular to and passing through the midpoint of each vector.
4. The area enclosed by these planes is the Wigner-Seitz cell.

What is Wigner-Seitz primitive cell?

A Wigner–Seitz (WS) cell is a special primitive cell that contains one lattice point. The WS cell is defined for a general lattice as the smallest polyhedron bounded by planes that are the perpendicular bisectors joining one lattice point to the others. The WS cell has the smallest possible volume (3D) and area (2D).

How do you find the volume of a primitive cell?

The volume of a primitive cell is a 1 ⋅ ( a 2 × a 3 ) , and it has a density of one lattice point per unit cell.

What is space lattice in Mcq?

A three dimensional arrangement of imaginary lines which are connecting the atoms is called Space lattice. It divides the space into equal volumes with no space excluded. The atoms in a crystal are arranged in a three dimensional repeating pattern which is known as lattice structure.

What is the atomic radius of a bcc crystal structure Mcq?

What is the atomic radius of a BCC crystal structure? Explanation: Atomic radius is defined as half the distance between the centers of two neighboring atoms. The atomic radius of a simple cube and HCP is a/2 respectively, whereas it is a√2/4 and a√3/4 for FCC and BCC respectively.

What is the volume of a BCC unit cell?

When considering a one-atomic basis there are n=2 points per unit cell with a volume of Vsph=43πr3 V sph = 4 3 π r 3 each.

What is HKL plane?

Equivalently, (hkℓ) denotes a plane that intercepts the three points a1/h, a2/k, and a3/ℓ, or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane, in the basis of the lattice vectors.

What is the Wigner-Seitz cell algorithm?

One algorithm is the Wigner- Seitz cell Steps: (1) Draw lines to connect a given lattice point to all nearby lattice points (2) At the midpoint and normal to these lines, draw new lines (or planes in 3D) (3) The smallest volume enclosed in this way is the Wigner-Seitz primitive cell Wigner-Seitz cell Finding Wigner-Seitz cells

What is the volume of primitive unit cell?

4. Volume of primitive cell. PRIMITIVE UNIT CELL : A volume of space that, when tran slated through all the vectors in a Bravais lattice, just fills all of space without overlapping. There is an infinite number of choices for primitive unit cell. Two common choices are the parallelepiped and the Wigner-Seitz cell.

Why is the length of the edges of a cubic cell?

For the conventional unit cell a cubic one is chosen because it represents the symmetry of the underlying structure best. As before we denote the length of its edges by the letter a a .

How many nearest neighbours does each atom have in the BCC structure?

In the bcc structure each atom has c1 = 8 nearest neighbours (coordination number) at a distance of dc1 = 2r = √3 2 a ≈ 0.866a (3) (3) 2 r a 0.866 a and c2 = 6 next-nearest neighbours at a distance of dc2 = a ≈ 2.3r ≈ 1.15dc1. (4) (4) a 2.3 r 1.15 It is remarkable that there is a smaller number…