# How would a diffraction pattern change if the atoms were triangular instead of spheres?

On a related note, what's a good book/source that would answer questions that go very in depth with these kinds of "what if" questions because I am also asked the same if the atoms were long cylinders instead of spheres.

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Assuming the "shape" you are referring to is the shape of the electron probability distribution around the atom, changing the shape of the atoms would be reflected in the atomic form factor $f(\mathbf{Q})$ in X-ray diffraction, where $\mathbf{Q} = \mathbf{k}_\text{out} - \mathbf{k}_\text{in}$ is the momentum transfer. This results in a change in intensity of the diffraction peaks, but the positions of the diffraction peaks are unchanged compared to the spherical case.

For electron diffraction, the changes are qualitatively the same as for the X-ray case, but exactly how much the intensity would change in each diffraction peak would be more difficult to analyze. For neutron diffraction, only the nucleus interacts with the wave, so there would be no change at all.

As for your book request, you are probably in need of a good book on diffraction in general. The first references that come to mind are "X-ray diffraction" by Warren and "Elements of modern X-ray physics" by Als-Nielsen & McMorrow.

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First of all atoms are not spheres except for the s state . Higher angular momenta have various shapes . s is l=0, p l=1, d l=2

The shapes of the first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz. The colors show the wave function phase. These are graphs of ψ(x, y, z) functions which depend on the coordinates of one electron.

and here are the d orbitals

The five d orbitals in ψ(x, y, z)2 form, with a combination diagram showing how they fit together to fill space around an atomic nucleus.

Atoms when in a solid will have even more distorted shapes so it does not have much meaning to talk about triangles and cylinders

this is an example in a crystal .

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