# X-ray diffraction from Metals

Is X-ray crystallography is possible for metals? Or not due to absorption?

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## 2 Answers

X-ray diffraction is certainly possible for metals! Most X-ray diffraction experiments are carried out with hard X-rays (photon energies of about 4keV or higher); among the most frequently used photon energies in laboratories are 8.04keV (Cu K$\alpha$ fluorescense) and 18keV (Mo K$\alpha$), for example. There are mainly two reasons for choosing hard X-rays:

• Lower absorption, both in the sample material and also in air (removing the need to perform experiments in vacuum).
• Access to more diffraction orders. To see why this is so, look up Bragg's law and see how the angle of an diffraction peak changes with photon energy---shorter wavelength/higher energy means smaller angle.

The Center for X-ray Optics has some very useful online calculators for X-ray interaction with matter, which you can find here: http://henke.lbl.gov/optical_constants/ . In particular, the attenuation length of a solid calculator should be interesting for you. You will find that in the hard X-ray range, attenuation lengths vary from about 1$\mu$m to several hundred $\mu$m. This may not seem like much, but when thinking in terms of how many atomic layers this corresponds to ($10^4$ and upwards), you will hopefully be convinced that this is enough to have constructive interference from many layers and hence sharp diffraction peaks. However, the penetration depth is still sufficiently small to require that many experiments are performed in reflection geometry, meaning that the diffracted X-ray beam exits the sample material through the same face as the incoming beam entered. This makes it possible to keep the path length for the X-rays inside the sample sufficiently small to have an appreciable intensity of the diffracted beam (although one may need to apply correction factors to do quantitative analysis of the diffracted intensity).

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Yes, x-ray crystallography has been applied to minerals and metals for almost a century. Wikipedia notes Linus Pauling's work on $\text{Mg}_2\text{Sn}$ leading to his theory of complex ionic crystals in the 1920s. In general, crystallography is a powerful tool in material science research.

Why do you ask?

I should note that x-rays are typically broken into two categories, hard and soft, based on their energies (though I've heard some jokes about "tender" x-rays at 2-5 keV). These two categories use different optics and I believe that most diffraction experiments use soft x-rays.

Hope this is helpful.

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Thanks, My question is whether the absorption is important to note in X-ray diffraction or not? –  richard Mar 4 '13 at 5:40
Typically you scatter on thin materials and you have a strong incident source so it's not important in most cases. If you know the relevant electric properties of the metals you're interested in, then a rough calculation can be done for the amount of attenuation in the field over the depth of the material you're considering. This may be too naive, but you could probably try calculating this using the information in Chapter 9 of Griffiths' Electrodynamics text. I don't know how the thickness of a sheet used in scattering compares to the skin depths of metals... –  user2053414 Mar 4 '13 at 6:18
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