Finding Distances to Brillouin Zone Borders from Origo

In summary, the conversation discusses difficulties understanding the Brillouin zone in a bcc lattice and the distances from the origin to the zone boundaries. It is noted that the distances in 3D should be half the magnitude of the G-vector, with the smallest G-vector being used. There is a question about finding the distances from the origin to the first BZ zone boundaries, with the basis vector in the reciprocal space being 2pi/2. It is mentioned that the favorite distance would be (\pi/\sqrt2)a. There is also a mention of four directions in the middle of the figure 4.16 Ashcroft & Mermin, with the ability to calculate for the remaining eight directions. The conversation concludes with the speaker
  • #1
rubertoda
33
0
Hi, i have problems understanding the Brilluoin zone to the bcc lattice

First, i wonder what the distances are, from the origo to the brillouin zone plane borders.
I firts thought it would be half the distance of the basis vectors (mine are 2pi/a, where a is my lattice constant, BUT its only true for 2-D calculations for square lattices.

I know that the distances in 3D should be |G-vector|/2, and i take the smallest possible G.


But i still don't know

ANyone who knows how to find the distances from origo to the first BZ zone boundaries, knowig that the basis vector in the reciprocal space is 2pi/2?are they all the same??
 
Physics news on Phys.org
  • #2
I think if the direct lattice constant is a, then the reciprocal lattice constant would be[itex]2\pi/a[/itex] hence your favorite distance is [itex](\pi/\sqrt2)a[/itex].
 
  • #3
Thanks a lot. and this goes eveforryone of the 12 directions in the BZ?
 
  • #4
No, it was for the four direction located in the middle of the figure 4.16 Ashcroft & Mermin. you can easily calculate it for remained 8 directions (see the figure).
 
  • #5
ok thanks. I am jut interested in the 110-direvtion, from origo to N,in the Ʃ-direction
 

1. How is the distance to Brillouin zone borders from Origo determined?

The distance to Brillouin zone borders from Origo is determined using the reciprocal lattice vector. This vector is perpendicular to the plane of the crystal lattice and can be calculated using the lattice parameters of the crystal. The distance to the Brillouin zone border is then calculated by taking the dot product of the reciprocal lattice vector and the vector pointing from Origo to the specific Brillouin zone border.

2. Why is it important to know the distances to Brillouin zone borders from Origo?

The Brillouin zone is a key concept in condensed matter physics and plays a crucial role in understanding the electronic and vibrational properties of crystals. Knowing the distances to Brillouin zone borders from Origo allows us to calculate important parameters such as the density of states and band gap, which are essential for understanding the behavior of electrons in a crystal.

3. Can the distance to Brillouin zone borders from Origo be measured experimentally?

Yes, the distance to Brillouin zone borders from Origo can be measured experimentally using techniques such as X-ray diffraction or neutron scattering. These methods allow for the determination of the lattice parameters and reciprocal lattice vectors, which can then be used to calculate the distances to Brillouin zone borders.

4. How does the distance to Brillouin zone borders from Origo affect the electronic properties of a crystal?

The distance to Brillouin zone borders from Origo is directly related to the band structure of a crystal. As the distance changes, the electronic properties of the crystal, such as the band gap and energy levels, will also change. This can have a significant impact on the conductivity, optical, and magnetic properties of the crystal.

5. Are there any limitations to calculating the distance to Brillouin zone borders from Origo?

One limitation is that the calculation assumes a perfect crystal lattice, which may not be the case in real materials. In addition, the calculation does not take into account the effects of defects or impurities in the crystal, which can also affect the electronic properties. Therefore, experimental measurements may be more accurate in these scenarios.

Similar threads

I Electron scattering in the Brillouin zone boundary
    • Atomic and Condensed Matter
Replies
4
Views
2K
A Why is the Brillouin zone a torus?
    • Atomic and Condensed Matter
Replies
18
Views
7K
K vector in first brillouin zone
    • Atomic and Condensed Matter
Replies
4
Views
8K
I Questions Regarding Primitive Unit Cell
    • Atomic and Condensed Matter
Replies
4
Views
2K
Brillouin Zones: Primitive Reciprocal Lattice Vectors
    • Atomic and Condensed Matter
Replies
1
Views
2K
A Basic questions on crystal lattice: k-vectors and Brillouin
    • Atomic and Condensed Matter
Replies
2
Views
2K
Dispersion relation for the free electron model
    • Atomic and Condensed Matter
Replies
1
Views
7K
How can the band-gap structure be determined using the E-k graph?
    • Atomic and Condensed Matter
Replies
1
Views
5K
First Brillouin Zone: Unravelling Why [-pi/a,pi/a)
    • Atomic and Condensed Matter
Replies
2
Views
7K
Brillouin Zones, Phonons, Energy Propagation through a Crystal
    • Atomic and Condensed Matter
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top