Neutron and x-ray inelastic scattering

prehisto

Hi guys!
Im i have to write a paper on neutron an x-ray inelastic scattering.

So far I have red a bit of information on this subject.
As far as i can tell the main use x-ray an neutron inelastic scattering is determining the phonon energy,wave vector,intensity and so on. The thing is that phonon energy usually is in range of meV. So logically the difference between energy of incident and scattered particle would be more easily determined in case of particle with similar energy like thermal neutrons. But x-ray photons has energy 100eV to 100keV. Here is where im getting confused.
In literature there is a lot of examples on x-ray scattering and mathematical descriptions.
Why x-ray photons are used at all,if they have such huge energy therefore the diference between incdient and scattered photon is harder to determine?
Is this true that neutrons where used first because of their energy and x-ray use started only when apparatus became more sensitive ?

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M Quack

Hi guys!
Im i have to write a paper on neutron an x-ray inelastic scattering.

So far I have red a bit of information on this subject.
As far as i can tell the main use x-ray an neutron inelastic scattering is determining the phonon energy,wave vector,intensity and so on. The thing is that phonon energy usually is in range of meV. So logically the difference between energy of incident and scattered particle would be more easily determined in case of particle with similar energy like thermal neutrons. But x-ray photons has energy 100eV to 100keV. Here is where im getting confused.
In literature there is a lot of examples on x-ray scattering and mathematical descriptions.
Why x-ray photons are used at all,if they have such huge energy therefore the diference between incdient and scattered photon is harder to determine?
This is indeed a problem. In only works because at a synchrotron source you have so many more photons than neutrons at a neutron source that you can afford to throw away almost all of them. Amazingly, the final count rates for x-rays and neutrons are almost the same.

There are two main reasons for using x-rays instead of neutrons:

1) You can focus x-rays into a much much smaller spot than neutrons. Because of that you can study much smaller samples, like
samples in a diamond-anvil high pressure cell, or samples that simply cannot be grown large enough.

2) For neutrons, there is a "forbidden" zone of energy transfer at low momentum transfer, because of the mass of the neutron. For x-rays this zone is much much smaller. With neutrons, this problem is usually circumvented by going to a higher Brilloiun zone. This does not work if there is no Brillouin zone, e.g. in liquids or amorphous materials.

Is this true that neutrons where used first because of their energy and x-ray use started only when apparatus became more sensitive ?
Yes. The real starting point for inelastic x-rays was the availability of enormous flux from undulator sources at synchrotrons.

http://www.esrf.eu/UsersAndScience/Experiments/DynExtrCond/ID28/IntroIXS

M Quack

One might add that photons couple mostly to the charge of the electrons, whereas neutrons couple to the nucleus and spin of the electrons.

Therefore photons can also detect some other electronic excitations, many of which are at higher energy. E.g. plasmons.

http://journals.jps.jp/doi/abs/10.7566/JPSJ.82.021015

karu

Hi prehisto,

Here's a few more points and details:

-Actually the use of IXS is split roughly 50/50 between studies of vibrational and electronic excitations.
-IXS divides to resonant and non-resonant (RIXS and just plain IXS). In the first case the incident photon energy is scanned across a core electron absorption resonance and the outgoing photons at lower energies are observed. This enhances the inelastic cross section, but at the same time makes interpretation more challenging as the process involves absorption and re-emission instead of just a good old collision type of process. Resonant studies are done at both hard and soft x-ray energies i.e. 100eV-tens of keV. Non resonant studies almost exclusively use incoming photons with energies above 5 keV. Take a look at the NIST photon-electron interaction cross section database if you're wondering why. Or just ask me.
-The electronic part includes electron-hole pairs of various types, i.e. excitons, interband excitations. Excitations of core electrons into valence states
are also observable and in that case the scattering cross section basically gives one an x-ray absorption spectrum recorded with IXS!
One can also just kick electrons into continuum states at very high energy and momentum transfers. The scattering process then probes the ground state electron momentum density. This regime is called Compton scattering in the x-ray business. Also as M Quack pointed out, you see plasmons in IXS and in some cases the plasmon dominates the energy loss spectrum.
-In the RIXS case one can also observe magnetic excitations as with neutrons. But then what one can actually observe depends on wether or not there is spin-orbit coupling in the core excited state.
-INS studies are more focussed on phonons and magnetic excitations (i.e. single spin flips, spin waves). And indeed detecting low energy phonons or magnetic excitations is easier with INS due to the lower probe particle energy and also because the instrument resolution functions have more favorable shape (Gaussian vs Lorentzian in a first approximation).
-There was a recent INS paper that demonstrated that it can also be used to observe higher energy electronic excitations in the few eV range. The study also quite nicely highlights how big the needed sample size difference is. This INS study was done using 500g of NiO which is something like 50 cubic centimeters of sample. With x-rays you can do the same with a sample volume of (10 microns)^3.
-For some elements the incoherent neutron scattering factors are dominating and studies are very difficult (if not even impossible, but I'm not sure as I'm not an expert on neutrons). These elements include at least vanadium and iridium.

edit. Maybe I should also point out that many textbooks, especially the "classical ones" have very outdated information on INS and IXS and the wikipedia pages don't have too much info either. You'll be better off with recent books or review articles.

In the case that this wasn't too much already, I can give you some references and I'll be happy to answer esp. IXS related questions.

prehisto

Hi karu,
I have to agree with you that unfortunately many textbooks and vast majority of papers have outdated information and therefore its hard to understand the whole picture.

There was a recent INS paper that demonstrated that it can also be used to observe higher energy electronic excitations in the few eV range. The study also quite nicely highlights how big the needed sample size difference is. This INS study was done using 500g of NiO which is something like 50 cubic centimeters of sample. With x-rays you can do the same with a sample volume of (10 microns)^3.
Could you please point out the paper which describes the sample size difference?

RIXS possible processes seems not classical for me. As far i can understand there is direct and indirect RIXS. Its easy to understand the direct RIXS, electron from core level is excited to valence band then electron from lower energy state decays and anhilates with core-hole resulting in photon emission. Thus process results in hole-electron pair excitation with energy equal to difference between incident and emiting photon energy.
My understanding of indirect RIXS : electron is excited from core-level, then there is ultra-fast Columbus interaction between core-hole and the rest of system. But then there is the confusing par for me. After the Columbus interaction there is electron transition in another level. As seen in the image(link below). I dont have understanding why does it occur,maybe this Columbus interaction gives energy to this electron?
http://postimg.org/image/geco6hzt3/

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