How can (220) in bcc diffract?

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In summary, the question concerns the diffraction pattern of bcc structure, specifically the (220) plane. However, after further research, it was determined that the (220) plane is not actually diffracting, but rather the (110) plane is giving a second order and higher order diffraction peaks. The confusion stemmed from sources that listed the (220) plane as a diffracting plane.
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Sveto
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Dear xrd experts,

I need help in explaining the diffraction pattern of bcc structure. Specifically, (220) is listed among the planes that give constructive interference since (h2 + k2 + l2) = 8; (h+k+l) = even number. But I am blind to see a single atom on a (220) planes in bcc structure: attached is a picture illustrating (220) planes. I am missing something here. In advance, greatly thankful for helping me.

Sveto
 

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Dear all,

I came across the same type of question concerned with 200 reflection of simple cubic structure at https://www.physicsforums.com/showthread.php?t=465354. Since 220 is a second order diffraction of (110) plane it means there is no need for a (220) plane; like a harmonic in waves. So, all is clear!

The confusion came from the sources that use language like:
"Diffracting planes in BCC crystals: 110,200,211,220,222" See "Materials science for engineering students" By Traugott E. Fischer, p. 544.. There are more textbooks like this one.

Thus, it is not 220 plane that is diffracting , but 110 plane that gives a 2-nd order (and higher orders) diffraction peaks.
 

1. How does the atomic structure of a bcc crystal affect diffraction of (220) planes?

The bcc (body-centered cubic) crystal structure has a unique arrangement of atoms, with one atom at the center of the cube and eight atoms at each corner. This arrangement creates a diffraction pattern with strong reflections at specific angles, including the (220) plane. This is due to the close packing of atoms in the bcc structure, which allows for constructive interference of X-rays or electrons at certain planes.

2. What is the significance of the Miller indices (220) in bcc diffraction?

The Miller indices represent the orientation of a crystal plane in relation to the crystal lattice. For bcc crystals, the (220) plane is perpendicular to the body diagonal of the unit cell and has the highest diffraction intensity, making it an important plane for crystallographic analysis.

3. How can we determine the spacing between (220) planes in a bcc crystal?

The spacing between (220) planes in a bcc crystal can be calculated using the Bragg equation: nλ = 2dsinθ, where n is the order of diffraction, λ is the wavelength of the incident radiation, d is the spacing between planes, and θ is the angle of diffraction. By measuring the angle of diffraction and knowing the wavelength of the radiation, we can solve for d.

4. Can (220) planes in a bcc crystal diffract X-rays and electrons equally?

Yes, both X-rays and electrons can be diffracted by (220) planes in a bcc crystal. However, the diffraction patterns may look different due to the differences in the wavelength and scattering properties of X-rays and electrons. X-rays have longer wavelengths and are scattered by the entire atom, while electrons have shorter wavelengths and are scattered by the individual electrons within the atom.

5. How does the size of the bcc unit cell affect the diffraction of (220) planes?

The size of the bcc unit cell does not directly affect the diffraction of (220) planes, as long as the relative positions of the atoms remain the same. However, a larger unit cell may result in a larger diffraction angle, which can make it easier to distinguish between different lattice planes in the diffraction pattern.

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