Distance b/w two miller planes

[afrano]

I am having a hard time visualizing the distance b/w two Miller planes. I found this article that has a brief explanation:
http://www.mrl.ucsb.edu/~seshadri/2004_100A/100A_MillerBragg.pdf

which derives the common formula for the distance, which can be used for diffraction/crystallography purposes.

Can someone explain how the distance b/w two miller planes boils down to the distance from the origin to the nearest plane?

Thanks

 

[will.c]

Because all miller planes are equally spaced, and there is always one through the origin.

 

[charng]

Hello,

Thank you for sharing your question about the distance between two Miller planes. I can offer some insight into this topic.

Miller planes are a way to describe the crystal lattice structure of a material. They are imaginary planes that pass through a set of lattice points in a crystal. These planes help us understand the arrangement of atoms in a crystal and how they contribute to the material's properties.

The distance between two Miller planes is an important factor in crystallography because it determines the spacing of the atoms in the crystal. This distance is often measured in units of length, such as nanometers or angstroms.

The article you shared discusses the Miller-Bragg equation, which is a mathematical formula that relates the distance between two Miller planes to the angle of diffraction observed in X-ray crystallography. This equation is commonly used to determine the distance between planes in a crystal.

To answer your question about how the distance between two Miller planes boils down to the distance from the origin to the nearest plane, we need to understand the concept of a unit cell. A unit cell is the smallest repeating unit of a crystal lattice, and it contains all the information about the crystal's structure.

In a crystal lattice, the origin is defined as the point where the three axes of the unit cell intersect. The distance from the origin to the nearest Miller plane is equal to the distance between the origin and the nearest lattice point in the plane. This distance is known as the lattice parameter and can be calculated using the Miller-Bragg equation.

In summary, the distance between two Miller planes is a crucial aspect of crystallography and can be determined using the Miller-Bragg equation. This distance is related to the distance from the origin to the nearest lattice point in the plane, which is known as the lattice parameter. I hope this helps clarify your understanding of the concept.