Primitive lattice vectors, reciprocal lattice, wigner seitz cell

In summary, primitive lattice vectors are the shortest vectors used to describe the arrangement of atoms or particles in a crystal lattice. A reciprocal lattice is a mathematical construct that represents the Fourier transform of a crystal lattice and is used to analyze diffraction patterns. The Wigner-Seitz cell is a geometric shape that represents the volume of space occupied by a single lattice point in a crystal lattice. The significance of primitive lattice vectors in crystallography lies in their ability to provide a fundamental basis for describing the structure of a crystal. The reciprocal lattice and Wigner-Seitz cell are closely related and together provide a comprehensive understanding of the symmetry and structure of a crystal.
  • #1
solas99
69
1
How can i develop a sketch of the lattice and reciprocal lattice from vector form

a=i+4j
b=3i

i know how to draw the wigner site cell, but I am having problems developing a sketch from vectors.
what is the method for working it out..please help
 
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  • #2
I have one question.
Why for construct reciprocal lattice we must exchange non-bravies lattice to a bravies lattice?
 

1. What are primitive lattice vectors?

Primitive lattice vectors are the shortest vectors that can be used to describe the arrangement of atoms or particles in a crystal lattice. They form the basis of a unit cell, and all other lattice vectors can be expressed as linear combinations of these primitive vectors.

2. What is a reciprocal lattice?

A reciprocal lattice is a mathematical construct that represents the Fourier transform of a crystal lattice. It is used to describe the diffraction or scattering patterns produced by a crystal, and provides a convenient way to analyze the properties of a crystal structure.

3. How is the Wigner-Seitz cell related to a crystal lattice?

The Wigner-Seitz cell is a geometric shape that represents the volume of space occupied by a single lattice point in a crystal lattice. It is constructed by drawing perpendicular bisectors between neighboring lattice points, and the resulting shape defines the fundamental unit of a crystal lattice.

4. What is the significance of the primitive lattice vectors in crystallography?

The primitive lattice vectors are important in crystallography because they provide a fundamental basis for describing the structure of a crystal. They allow for the determination of crystal symmetry, unit cell parameters, and the arrangement of atoms or particles within the crystal lattice.

5. How do the reciprocal lattice and Wigner-Seitz cell relate to each other?

The reciprocal lattice and Wigner-Seitz cell are closely related, as they both describe the properties of a crystal lattice. The reciprocal lattice is used to analyze the diffraction patterns produced by a crystal, while the Wigner-Seitz cell represents the fundamental unit of the crystal lattice. Together, they provide a comprehensive understanding of the symmetry and structure of a crystal.

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