Spacing between three dimentional lattice planes

In summary: Can you explain it in a way that is easier to understand?In summary, the spacing between three dimensional lattice planes means the distance between planes in the lattice. The reciprocal lattice is a lattice you can create to describe any normal lattice. It's the Fourier transform of the real lattice.
  • #1
abhaymv
9
0
What, exactly,does spacing between three dimensional lattice planes mean?Does it refer to the formula

d=2*pi/(translation vector)?

*I am an engineering undergraduate and this word is in my syllabus in topic crystallography.I was wondering what it meant?


Also, can someone tell me in simple words what reciprocal lattice means?When I go to wikipedia they go complicated including vectors:confused:.But I don't think it is needed in my study.
 
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  • #2
You probably already know some of this but I'll just lay it out so it's clear what we're talking about.

A crystal can be described as a basis of atoms, repeated on each point of an infinite mathematical lattice. The simplest 3-D lattice would be a cubic array (repeated through all of space), and the simplest basis would be a single atom. In crystallography we generally want to use this framework not to describe points in a crystal, but directions or planes.

So we can use this formalism to describe a plane hkl in a crystal, but it's not a single plane, it's an entire set of parallel planes with a specific orientation with respect to the crystal. And each plane in this set will be separated from the next by a perpendicular distance which is characteristic of that set of planes. That's the spacing you are asking about.The reciprocal lattice is a second lattice you can construct for any normal ("real space") lattice you can think of. While the real lattice is associated with the actual position of atoms, the reciprocal lattice is more abstract. Each point in that lattice represents one of the sets of planes I was talking about above, and the distance from the origin to the point is the interplanar spacing that you asked about. If you're familiar with Fourier transforms, then I can tell you that it's the Fourier transform of the real lattice. Its most common application is in explaining x-ray diffraction from crystals.

If the reciprocal lattice seems abstract, don't worry. It takes a while to really grasp.
 
  • #3
Thank you for the explanation. :)
I think I understand, but the reciprocal lattice is, as you said, a little hard to understand(and visualize).
 

1. What is the significance of the spacing between three dimensional lattice planes?

The spacing between three dimensional lattice planes, also known as the interplanar spacing, is an important characteristic of a crystal lattice. It determines the distance between adjacent planes of atoms in the lattice and plays a crucial role in the physical and chemical properties of the material.

2. How is the spacing between three dimensional lattice planes measured?

The spacing between three dimensional lattice planes is typically measured using X-ray diffraction techniques. This involves directing a beam of X-rays onto the crystal and measuring the angles at which the X-rays are diffracted. The spacing can then be calculated using Bragg's law.

3. What factors affect the spacing between three dimensional lattice planes?

The spacing between three dimensional lattice planes is primarily determined by the type of crystal lattice and the arrangement of atoms within the lattice. It can also be affected by external factors such as temperature, pressure, and the presence of impurities in the lattice.

4. How does the spacing between three dimensional lattice planes impact the properties of a material?

The spacing between three dimensional lattice planes can affect various physical and chemical properties of a material. For example, a smaller spacing can lead to a higher density and increased strength, while a larger spacing can result in lower density and increased reactivity. It also plays a role in determining the material's optical, electrical, and magnetic properties.

5. Can the spacing between three dimensional lattice planes be changed?

Yes, the spacing between three dimensional lattice planes can be altered by manipulating the arrangement of atoms in the lattice. This can be done through processes such as annealing, alloying, and doping. External factors such as temperature and pressure can also affect the spacing. However, the spacing is ultimately determined by the crystal structure and cannot be changed significantly without altering the lattice itself.

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