How to find reciprocal lattice vectors

In summary, a reciprocal lattice is a concept used in solid-state physics to describe the periodicity of a crystal in reciprocal space. It is necessary for understanding diffraction patterns and plays a crucial role in crystallography for determining atomic arrangement and properties. Reciprocal lattice vectors can be determined by taking the inverse of direct lattice vectors and can have negative values.
  • #1
girlinphysics
25
0
So I know that the basis vectors of an FCC in a symmetric form are:
[tex] a = \frac{a}{2}(\hat{x} + \hat{y}) [/tex]
[tex] b = \frac{a}{2}(\hat{y} + \hat{z}) [/tex]
[tex] c = \frac{a}{2}(\hat{x} + \hat{z}) [/tex]

And that the reciprocal lattice vectors are the basis vectors of the BCC cells.
I'm having a hard time doing the cross products correctly, so if anyone could walk me through an example of the math that would be very helpful.
 
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  • #2
Oh yes it was! I've edited it now, thanks.
 
  • #3
please read book by Kittle, introduction to solid state physics.
 

1. What is a reciprocal lattice?

A reciprocal lattice is a mathematical concept used in solid-state physics to describe the periodicity of a crystal lattice in the reciprocal space. It is a representation of the Fourier transform of the direct lattice and is essential for understanding the diffraction patterns of crystals.

2. Why do we need to find reciprocal lattice vectors?

Reciprocal lattice vectors are used to describe the periodicity of a crystal in reciprocal space, which is necessary for understanding the diffraction patterns produced by the crystal. They also play a crucial role in calculations related to crystal structures and properties.

3. How do we determine the reciprocal lattice vectors?

The reciprocal lattice vectors can be determined by taking the inverse of the direct lattice vectors, multiplied by a scaling factor of 2π. This can be done using various methods, such as the Laue method, the Ewald construction, or the direct space method.

4. Can reciprocal lattice vectors be negative?

Yes, reciprocal lattice vectors can have negative values. This is because they represent the magnitude and direction of the periodicity in reciprocal space, which can be in any direction relative to the direct lattice vectors.

5. What is the significance of the reciprocal lattice in crystallography?

The reciprocal lattice is essential in crystallography as it helps in understanding the diffraction patterns produced by crystals, which are used to determine their atomic arrangement and crystal structure. It also plays a crucial role in the study of crystal properties such as electrical and thermal conductivity, as well as in the design and development of new materials.

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