Science method

Neutron Scattering - Science method

General group concerning neutron scattering techniques
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Dear RG community,
I have just started my research career in the field of neutron spectroscopy.
I would be grateful if you could suggest some important books to read to get a deeper understanding of the subject matter.
Research interests: Neutron scattering, Neutron diffraction, Neutron imaging.
Thank you.
Regards,
KP
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I recommend Andrew Boothroyds new book on Neutron Scattering :-)
For data evaluation you are welcome to join the McPhase community www.mcphase.de
with best regards MR
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How to draw the anisotropy in different direction like the below figure from elastic constant data. 
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This book is not published anymore. The full reference is : "Neutron Scattering from Hydrogen in Materials" ; Proceedings of the second Summer School on Neutron Scattering : Zuoz, Switzerland, 14-20 August 1994 ; A. Furrer (ed.) ; World Scientific Singapore ; 1994. I'm looking for a scanned copy of the whole book. Thanks for your help ! Regards. Nicolas.
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As mentioned above, the book "Neutron scattering from Hydrogen in materials" can be downloaded via the LibGen website. The book has been scanned by Evan MacA Gray in 2017.
In passing, I warmly recommend another book about Neutron scattering (and other Nuclear techniques) for Hydrogen in materials, which can also be found via LibGen : https://www.springer.com/gp/book/9783319227917
Editors : Fritzsche, Helmut, Huot, Jacques, Fruchart, Daniel.
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Dear all,
Please, any suggested publications to read about any real applications were performed using Bragg-edge neutron imaging BUT with "thermal" neutron beam (1.8 A° +/-), if existed, other than the most famous ones that use cold monochromatic beams for strain mapping or magnetism studies?
Thanks a lot in advance.
Mahmoud
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Spectral neutron tomography
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Two most important structural parameter of a molecule is size and shape. While there is many spectroscopic (like DLS, neutron scattering, fcs) and microscopic (SEM,tem, AFM, etc); for shape measurement as I know, we depend on microscopic techniques.
I want to know other than such imaging techniques are there any such techniques that can measure the shape of nanoparticle or protein?
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Yes, microscopy is essential but may not be quantitative and we often have a low contrast image for the materials that are described. Usually though we only have a 2D image of a 3 particle and 'sample preparation' (especially TEM) is a trap for the unwary. Cryo-TEM has had excellent success.
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In small angle neutron scattering SAS (actually small angle neutron scattering, SANS), I obtained a 1D pattern showing a peak which is located over 1 inverse angstrom. The actual peak position is approximately 1.2 inverse angstrom. What is the possible meaning of it??
The scattered specimen is martensitic steel including inclusions in dozen nanometers and precipitate particles in few nanometers. The peak exists always regardless of heat-treatment.
Can I get a small clue on it??
(Please see the attached figure.)
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At this scale, it is likely due to the atomic structure factor (ie correlation between the positions of first neighbors atoms).
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The thermal neutron scattering length depends on the relative spin orientation of neutron and nucleus. It is defined such that b>0 corresponds to a repulsive potential and b<0 to an attractive potential.
Looking at the example of neutron scattering on protons, the two scattering lengths are listed separately in textbooks and e.g. in http://www.ati.ac.at/~neutropt/scattering/RecommendedScatteringLengths.PDF
They all agree that a combined spin of the neutron-proton system of 1 has a positive scatternig length (repulsive) and a combined spin of 0 a negative scattering length (attractive).
My question is why does this not line up with the fact that the S=1 deuteron state is bound (i.e., attractive) and the singlet state is unbound (i.e., repulsive)?
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Hallo Sebastian,
how is it going at Garching? Here the the weather is pretty ugly today.
If I remember correctly the neutron scattering lectures at TUM some years ago, then a negative scattering length corresponds to a phase shift of 90deg of the neutron phase after the scattering process. This occurs for 1H, but not for most other elements and isotopes. If I am not fully mislead then 2H does not have a negative scattering length, neither for parallel or unparallel spin orientation. Tell me, if I am wrong. I think the reason is the difference of strong interaction between proton - protein and proton - deuteron.
Does this help? Those lectures are a while ago...
Cheers,
Andreas
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I have a thin porous material whose saturation needs to be determined. The relative permeability for a multi-phase flow is to be determined through the porous material and in order to express relative permeability as a function of saturation, I need to determine the saturation. The sample is of the dimension of 10mmX5mm and thickness of approximately 500 microns. How can I effectively measure the water saturation. Also, I think the internal methods of saturation determination like X-Ray method, neutron scattering would be not very effective considering the small dimensions of the sample. Correct me if I'm wrong.
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If I understand correctly, it is an elongated tube that can serve as a waveguide. The electromagnetic waves can not penetrate the wall of the pipe, even at very high power. You have to couple the energy on one side of the wet diaphragm and measure the electromagnetic energy on the other side with a similar probe. Suitable coupling elements can be found here:
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How this Incoherent Scattering Component is high for 1H
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Neutron-nucleus interaction is spin dependent and characterized by a scattering length that has two values: one for the system in the J+1/2 state (called b^+) and another for the J-1/2 (called b^-). J, the spin of the target nucleus, also changes between the different isotopes.
Coherent scattering is caused by the average of those scattering lengths; the rest is incoherent. For nuclides with J=0 (even-even nuclei), there is only one possible neutron-nucleus state, only one value of the scattering length and all scattering is coherent. An example of that is O-16.
For some nuclides b^+ cancels with b^- and the average (or, for some elements, the scattering length of one isotope cancels the scattering length of another) and they have nearly zero coherent scattering (examples of that are H-1 or Vanadium).
For further reading I would recommend chap. 2 of "Thermal neutron scattering" by Squires.
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What is the magnetic propagation vector (k) of helimagnetic phase of Cr1/3NbS2?
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Cr1/3NbS2 exhibits a helimagnetic structure which originates from the Dzyaloshinskii–Moriya (DM) interaction that plays a key role in n formation of the helical magnetic order in the non-centrosymmetric Cr1/3NbS2 .
In this compound, a helimagnetic ground state with a period of about 480 A was reported (*).
(*)T. Miyadai, K. Kikuchi, H. Kondo, S. Sakka, M. Arai, and Y. Ishikawa,
J. Phys. Soc. Jpn.52 , 1394 (1983).
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Consider for a homogenous nuclear reactor which is a toroidial tube filled with something like plutonium or uranyl nitrate solution. The toroidal has an infinite neutron scattering medium around it such as a vast volume of water.
How do we calculate the geometric buckling of the system ?
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1. What is a toroidal tube? Do you mean the inside of a donut? Anyway, to basic principles...
Geometric buckling measures the curvature of the flux distribution which is determined by leakage out of the reactor. If the scattering reflector is infinite with zero absorption, then the neutrons have nowhere to go except back into the reactor, so the curvature is zero and so is the geometric buckling - k_eff=k_inf by definition. If the scattering medium has some absorption (real water, rather than an ideal "infinite scattering medium"), then you need to solve the diffusion equation in the appropriate geometry with some extrapolated endpoint appropriate to the properties of the reflector - make a guess to start with, based on the scattering/absorption ratio of the reflector. Use the analogy of a simple cylindrical reactor - if the flux goes to zero at the end, the diffusion equation tells you that the geometric buckling is Pi/L. Be aware that there are 11 co-ordinate systems for which exact solutions of the diffusion equation are known - check the mathematics literature - once you have clarified what is a toroidal tube. The computer code Maple has some of these already built in; Mathematica probably does too.
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whats the difference in hydrogen-neutron and deuteron-neutron interaction?
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Hi Debasish,
Neutron scattering cross-sections are proportional to the neutron scattering lengths (b). These scattering lengths can be positive or negative depending on whether the interaction between the scattering nucleus and the neutron is attractive or repulsive. Further, neutron scattering from several nuclei can be coherent or incoherent depending on whether the scattered waves from different scattering centers interfere or not.
In the former case of coherent scattering, the scattering length (bcoh) is the average scattering length (average over different nuclei) i. e. bcoh=<b> whereas in the case of incoherent scattering the scattering length (binc) is the mean squared deviation of scattering lengths, i.e. binc= <b2> - <b>2. In case of scattering from a single element, the difference in the scattering lengths arises from the different total spin states of the nucleus-neutron system. For example, for hydrogen with a nuclear spin of 1/2, the nucleus-neutron system can either be in triplet (S+=1) or a singlet (S-=0) state with the corresponding multiplicities of 3 and 1. In case of hydrogen the scattering lengths in these two spin states (let's say b+ and b-) have opposite signs (positive for triplet (b+), negative for singlet(b-)). Because of this, the average scattering length <b> (which is same as coherent scattering length bcoh) is negative and small. This is because the average of two numbers with opposite signs is smaller than the average of those numbers when they have the same signs. Thus bcoh=<b> for hydrogen is small and negative.
The incoherent scattering length is however the rms deviation, i.e. binc= <b2> - <b>2. Squared quantity always being positive means that <b2> is large and so subtracting a small quantity <b>2 (square of a small quantity (<b>) is an even smaller quantity) from that results in a large incoherent length. Therefore the incoherent neutron scattering cross-section of hydrogen is very large.
For deuterium (with nuclear spin of 1, S+=3/2, S-=1/2) on the other hand, as both b+ and b- are positive, their average <b> is relatively large. So the difference between <b2> and <b>2 is not very large. Consequently the incoherent neutron scattering cross-section of deuterium is not very large.
Hope you find this useful.
With best regards,
Siddharth
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I have read a lot of references about neutron scattering. But I am still confused by these phrases: coherent elastic scattering, incoherent elastic scattering, coherent inelastic scattering and incoherent inelastic neutron scattering? I learned that coherent elastic scattering is generally used for neutron diffraction measurement, and that coherent inelastic neutron scattering is used to measure phonon or magnon dispersion relations. But how about incoherent elastic scattering and incoherent inelastic scattering? What are their fundamental differences? What are their different applications in neutron scattering measurements?
How to understand diffuse scattering? What is the difference between elastic and inelastic diffuse scattering?
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Hi Ren,
In a typical neutron scattering experiment, scattered neutrons are measured as a function of change in their direction (related to momentum transfer, Q) and energy (Energy transfer, deltaE). While Q dependence tells you the structure of the scattering material, the deltaE dependence tells you about the dynamics in the material. Further, the scattered neutron waves from different scattering centers may or may not interfere. Based on this information, you have the following.
1. Elastic scattering - Does not discriminate scattered neutrons for the energy transfer, I. e. integrate the detected signal over all energy transfer. This means you lose 'dynamics' information and are left with structural information alone.
2. Inelastic scattering - Measures scattered neutrons as a function of both energy and momentum transfer. This means you have both 'dynamical' as well as 'structural' information. Further, if you study the variation of scattered intensity at a given energy transfer as a function of Q, you get dispersion relation which can give you information on the geometry of the dynamical process that occurs at that energy transfer.
3. Coherent scattering - When you have interference between scattered neutron waves from different scattering centers (different atoms), you get information on the relative positions of these atoms. Thus coherent scattering gives you information on the relative atomic positions - structure of the material. In terms of G(r,t), the coherent scattering gives you the probability of finding an atom (say A) at position r, at time t, given that the same atom (A), or any other atom was present at origin (r=0) at t=0.
4. Incoherent scattering - When you have no interference between the scattered neutron waves from different centers, you are basically following a single atom. Thus, you are losing the information on the relative positions of atoms or structure. What you are studying is the movement of the same atom in time. In terms of G(r,t), the incoherent scattering gives you the probability of finding atom A at position r, at time t, given that the same atom A (and not any other atom, contrast this with coherent scattering case above) was present at origin (r=0). Thus, while incoherent inelastic scattering can trace single atom dynamics, the coherent counterpart would give you information on the collective motion of atoms.
I hope you find this useful.
With best regards.
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This is highly related to the critical phenomena in strongly correlated electron systems. Through this challenging question, I would like to invite those active researchers who have long been involved in the field of statistical physics and theoretical condensed matter physics so that we can at least find some clue to proceed ahead.    
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We have, O. Cépas and myself (Phys. Rev. B 76, 020401(R) have studied the effects of disorder in manganites (microscopic approach) , more precisely  we have focused on correlated disorder... and have compared our calculations to Monte Carlo calculations in the case of uncorrelated disorder,... the spirit of our approach is somehow different from  what was done before, we proceed within a two step approach : (1) we calculate the effect of the disorder on the Mn-Mn couplings (disorder effects fully included) and then we treat the disordered Heisenberg model beyond mean field to calculate the magnetic properties TC, spin stiffness,...
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Neutron sources that produce fast neutrons uses a Spallation process but why not use a non-uniform magnetic field to act on the magnetic moment of the neutron to accelerate it, we know that the neutron will precess around the field say in the z-axis, then a gradient of the magnetic field in the plus z-direction will accelerate the neutron in the minus z-direct.
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Of course, one might think of a field gradient accellerating spin polarized neutrons. In practice you will have difficulties to (a) confine and steer a neutron beam this way and (b) generating significant energy differences with manageable fields (calculate e.g. the Zeeman energy splitting for a neutron in 100T, for example, think what field gradients could be manageable technically and make an order of magnitude estimate of the spatial scales involved...)
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I'm about to analysis some neutron scattering curves via Sasview. However, this is my first time to fitting neutron scattering data. I don't know which model to choose. Are there any principles for that? Thanks.
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Please do p(r) inversion in SASview (indirect Fourier transformation) and try to get p(r) function. The shape of p(r) should help with choice of model.
Of course, the best if you have information from other method like TEM, cryoTEM. After this you can check if model fit your data.
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I have a problem to understand how to calculate an MSD(t) (Mean Square Displacement), from a time trace, when the time intervalls between two consecutive points are not constant, and even change randomly, e.g. (data were recorded with the delta_t = 2 us):
t x
0.418424 -1.162677
0.418426 -1.187103
0.418432 -1.187103
0.418434 -1.206644
0.418436 -1.226185
0.418440 -1.235955
0.418442 -1.260381
0.418444 -1.245725
0.418446 -1.216414
0.418448 -1.187103
0.418452 -1.152907
0.418454 -1.123596
0.418456 -1.148021
0.418460 -1.167562
0.418462 -1.187103
0.418464 -1.172447
If somebody is able to write some steps (with my real values t and x) it would be great. How does the plot(MSD(t), t) look like?
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I am not familiar with your particular problem, however, in general, if you have a sampling f_i=f(t_i) you can always use interpolation available for example in programs such as Origin (or you can make your own, e.g., cubic spline interpolation) to create equidistant sampling times. 
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structure factor solid state debye waller factor 
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Shortly, the structure factor, S(q), is the Fourier transform of the ensemble average of the distances between pairs of scatterers, at a given time, i.e. evaluated "instantaneously". As an image, you can imagine taking a 3D snapshot of all the N atoms of the sample (although with different weights, depending on the technique). Then, from the snapshot, you compute all the distances between the N(N-1)/2 pairs. The resulting "histogram", G(r, t=0)=g(r) is the pair correlation function. Its spatial Fourier transform is the static structure factor S(q).
The dynamic structure factor, generalizes this definition to the fourth dimension, time, computing correlations at times tau and tau+t for all t (in practice t is limited by the instrument). G(r,t) is the resulting function (the van Hove function). The dynamic structure factor, S(q,w) is the space and time Fourier transforms of G(r,t).
In x-ray and neutron scattering, one measures S(q) through the integral over omega (w) of S(Q,w), what corresponds to the snapshot at t=0 defined above. However, because of the detailed balance, temperature must be taken into account, namely its magnitude as compared to the Debye temperature. See: L.V. Meisel and P.J. Cote, Phys. Rev. B 16, 2978 (1977), for more precise details.
In a solid, differences between S(q,w) and S(q) result mainly from: i) collective excitations (coherent scattering: phonons, spin waves, ...); ii) vibrations, taken into account by the Debye-Waller factor and inelastic components (also in incoherent scattering, in the case of neutrons).
The Debye-Waller factor is perfectly defined in solid state. Knowing the interatomic potentials and the lattice, it can be evaluated precisely, what is not the case for amorphous solids or liquids.
You can see the DW factor as a "delocalisation" of the scatterers due mainly to temperature, although at T=0 it remains the 0 point motion. Naturally, the usual form exp(-Q2.<u2>/3) is similar to the Guinier SAS approximation where the mean square displacement, <u2> is the equivalent of the radius of gyration of a particle. Within the harmonic approximation (low T), <u2> is proportional to T.
Because it represents a delocalisation, it depends only on q: a gradual decrease of the total scattered intensity with the scattering angle. Within quantum mechanics, it corresponds to the part of the radiation that is scattered inelastically.
Note: In studies of quasi-elastic neutron scattering, namely performed in back-scattering spectrometers, it is current the notation <u2> for all origins of decrease of the scattered intensity with q, even if they come from motions too slow to be "seen" by the instrumental resolution (without being "vibrations", strictly speaking).
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My vesicle samples were stable from 5 - 10 mM. What concentration should I prefer for the measurement of Small Angle Neutron Scattering? 
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Depends on the instrument you plan to use, the contrast you will use, and what you are interested in. Your best bet is to ask the instrument scientist at the facility you will be using.
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Neutron scattering
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In a sectrometer you record all scattered neutrons, both coherent and incoherent.
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I am trying to analyze the SANS data using the Guinier-Porod model.
There are five parameters in the model: Guinier Scale, Dimension Variable, Rg, Porod Exponent and Background.
The Dimension Variable, Rg and Porod Exponent are strongly dependent on the Guinier Scale and background when I was fitting my data.
However, I read the papers using this model and cannot find the details about how to determine the Guinier scale and background.
Is the Guinier scale related to the volume fraction?
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Xiao,
 If the intensity declines to a constant "flat background" at high Q you may be able to get your background established that way without having to include it in the model fit.
Jeff
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In a neutron diffraction experiment, how will the S(Q) look for strong absorbing atoms? Will it only affect low-Q range, high-Q range, or it will just shift the whole baseline downward at a constant value for the whole range?
and probably how do we correct it?
Thank you!
For example of a system with Li-6 isotopes in it.
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For Li there are two istopes 6Li and 7Li for which the nuclear spins are I = 1 and 3/2 respectively. Their absorption cross sections are 70.5 and 940 barns. So 7Li will be very strongly ansprbing whereas 6Li will be managable. Fortunately what Li you buy is already depleted of 7Li and you get almost pure 6Li. This is convenient for neutron diffraction but even then the absorption is rather high. So if you study neutron diffraction from compounds with 6Li you have to use annular cylindrical sample holders and also do absorption correction.
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What technique could one use to create a 3 dimensional image/composition analysis of a material that is made of two isotopes of the same element? For instance, if I make a disc of magnesium, and then coat it with a thin layer of a magnesium isoptope, what technique/instrument could I use to tell me the dimensions/volume/area/thickness of the isotope layer, and could also render an image that differentiates the two? The only thing I have found is neutron scattering (XRD for isotopes), but I want a volumetric analysis.
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Hi Michael,
Atom probe tomography will distinguish between two isotopes of the same element and also provide a 3D reconstruction.  I routinely conduct atom probe tomography and one of outputs is atom counts as a function of  mass/charge ratio.  So, one can identify all the naturally occurring isotopes and also obtain data in the form you require.  Please feel free to write back if you have more questions.
Monica
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As you may know, neutrons are electrically neutral and can only be deflected by a magnetic field. The magnetic field interacts with the spin of neutrons i.e. the magnetic moment of neutrons and their trajectory is influenced in the presence of the magnetic field due to the magnetic force.
I know that the CST or COMSOL package can be used for tracking of charged particles such as electrons or protons in electromagnetic field.
However I need to design a certain type of magnetic field by putting several magnet together and then pass the neutrons through the magnetic field and study the trajectory of neutrons.
Do you have any idea if COMSOL or CST are capable of neutron tracking? or if they are not, could you please introduce any other package that you know?
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For electrons the comsol software support tracking but neutrons are are neutral and the magnetic field interact with neutron spin. A purely quantum mechanical phenomenon which i am afraid is not supported by comsol applications
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In a cold neutron scattering experiment, the time-scale of the neutron-(phonon/magnon) interaction is often assumed to be in the range 1-10 ps. For a magnetic order this means that the order will appear static to the neutron probe if its dynamics is much slower than 10 ps or if it has an energy lower than about 0.5 meV. How can this time-scale be calculated?
The resolution of a neutron scattering diffractometer can be calculated via its energy resolution. An excitation of energy much smaller that the width in energy of the Bragg peak cannot be resolved. Typically an excitation of less than 1-0.1 meV cannot be resolved.
However it appears difficult to relate a resolution that is inherently dependent of the instrument to a physical quantity the timescale of the neutron-(magnon or phonon) interaction that is universal.
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We can very easily resolve energy of the order of 1 micro-eV (nano seconds) by back scattering spectrometer. We can even have better energy resolution with a spin-echo spectrometer.
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Please provide references related to the topic.
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Neutron Scattering in general is a very good probe for polymer. As neutrons are neutral, the penetration is high, therefore with very low (thermal) energy neutrons, which does not damage the polymer, one can probe the bulk properties of polymer. SANS is one of the many techniques that uses neutron as probe. This is suitable to study the shape and size of dispersed colloidal (or nano) particles in a matrix (liquid or solid). I mainly work with surface and have experience of working with Neutron Reflectivity for polymer samples. You may see the following ref.
Macromolecules 2007, 40, 1073-1080
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Topological spin structure or skyrmion is really a hot topic since discovered from neutron scattering in MnSi from 2009. While magnetic bubble domain is found much earlier in many materials with an out of plane anisotropy. In principle the magnetic bubble domain (with the size around several micrometer) may also show the same topological effect as the skyrmion(with the size around 100nm) if the spin structure changes in all x, y, and Z direction in the domain wall(which is not thin compred to the bubbles). Is that true?
Besides, according to:"Phys. Rev. Lett. 105, 197202", dipolar dipolar interaction can induce giant skyrmions which is similar to the bubbles. I want to ask: "Is the magnetic bubble domain a topological spin structure? "
For the typical out of plane anisotropy materials, during the spin rotation from one side to the other, it will form some nucleation points in the beginning and some pinning points which really need high field to rotate(a tail structure in the hysteresis). Are the nucleation and pinning points topological spin structures?
Low Temperature MFM or faraday microscopy will help to see the domain structure, is anyone know where I can perform such measurements?
Thank you very much for the help!
 
 
 
   
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Dear Kai Chen,
I will reply to your questions one by one.
As modern skyrmions is stabilized by DMI, the magnetic bubble domain is stabilized by dipolar-dipolar interaction, right? Yes.
Topological hall effect is found in skyrmions, in principle it will also be observed in the materials with magnetic bubble domains, am I right? In principle, yes. The topological Hall effect follows from the spherical topology that is a common property of bubbles and chiral Skyrmions. The chirality does not influence the effect. The strength of the contribution of each skyrmionic spin structure (bubble or chiral Skyrmion) to the topological Hall effect is proportional to the Skyrmion number. Skyrmions in materials with DMI are (mostly) defect free, i.e., they all share the same Skyrmion number and the effect increases linearly with the number of Skyrmions. Bubbles, on the contrary, may have defects and the Skyrmion number might take any integral value. That is, the accumulated effect might cancel out in these systems. In addition, to my knowledge, bubble lattices of macroscopic extent have thus far been observed in insulating materials only, which is why the topological Hall effect in such systems has not been measured up to now.
As the DMI effect will cause an asymmetric form in the energy, is there any asymmetric form in the magnetic bubble domain materials from DDI interaction? If there is, it could be a new way to induce exchange bias since DMI can induce exchange bias from the theoriests. No, the dipolar interaction is perfectly symmetric. Bubbles of both chiralities co-exist with equal probability, which is not the case for chiral Skyrmions. I am surprised, though, why such asymmetry in case of chiral Skyrmions should cause an exchange bias. To my knowledge, there is no asymmetry for the z-component of the spins in any case.
Best regards,
Felix Büttner
 
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Traditionally neutron scattering is used to investigate magnetic properties of the condensed matter. This is because of strong interaction of neutron spin with the unpaired electron spin. X-rays being electromagnetic waves interact also with unpaired electrons. The interaction strength however is much smaller compared to that of neutrons. This should not be a great drawback because of the very high photon flux of the modern synchrotron sources and this flux is getting higher and higher. So far two magnetism sensitive X-ray methods have become quite useful, viz. X-ray magnetic scattering and X-ray magnetic circular dichroism (XMCD). But other X-ray spectroscopic techniques could also be sensitive to magnetism. Can anyone illuminate me about the modern developments in these fields?
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The two main disadvantages of x-rays vs. neutrons for studies of magnetism are a very unfavourable ratio of magnetic to charge signal, and the heat load of the x-ray beam - for temperatures below ~10K.
The first can be overcome by doing difference measurements where you can flip the sign of the magnetic signal by changing polarization or magnetization. Conceptually this is similar to a flipping ratio in polarized neutron scattering. In most cases these techniques work only for ferromagnets or the ferromagnetic component of more complex structures.  One exception to this rule is magnetic linear dichroism, XMLD as Kai mentioned. XMLD actually measures a quadrupole moment which is time-even, but induced by the primary magnetic order.
There are many of these difference techniques: several flavous of dichroism, but also scattering based, e.g. magnetic Compton scattering, resonant interference scattering, non-resonant interference scattering. Most of these are fairly old.
Magnetic scattering can be observed at resonances (absorption edges), or non-resonant. The resonance gives larger signals and a very characteristic polarization dependence that can be exploited to determine details of the magnetic structure.
For antiferromagnets the magnetic peaks are away from the dominant charge peaks. For good single crystals the signal/noise ratio allows direct measurement of magnetic scattering. For powders the bad signal/noise ratio makes the experiment nearly impossible.
The last 10 years or so a lot of work was done on higher order multipoles that are induced by a fundamental magnetic order, e.g. the famous "orbital order".
New developments are going on in inelastic x-ray scattering (RIXS) that is sensitive to electronic structure and thus magnetism.
The use of imaging techniques is growing, as Kai pointed out. This includes coherent imaging and reconstruction techniques.
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In Monte Carlo simulation dedicated to criticality study of TRIGA reactor, thermal neutrons scattering of graphite is very important. Such data are calculated by THERMR module of NJOY99 data processing code. ENDF-B7.1 TSL data are treated and the obtained results show that coherent elastic scattering is represented as cumulative probability instead of cross section. However inelastic scattering is reproduced correctly and agree very well with values given by NEA JANIS code.
The results are attached to this message.
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May I call your attention to the Neutron Instrument Simulation Package (NISP)? The module Graphite.f includes 277 explicit Bragg edges. The elastic cross section at a given wavelength is a sum over all accessible Bragg spacing - in that sense, it IS a cumulative probability. Here is the abstract of the module:
C********** G R A P H I T E **********
C
REAL*8 FUNCTION GRAPHITE(LAMBDA, TIN, ABSORB, TWOSINTH, ISEED)
C
C Neutron attenuation length (mm) of polycrystalline Graphite at
C temperature TIN (optional, default 300K), as a function of neutron
C wavelength LAMBDA in Angstroms. May also return the fraction of
C the cross section which is nuclear absorption (ABSORB). May also be
C used to scatter from a random selected plane spacing and return
C TWOSINTH. A special case is TWOSINTH=2, indicating isotropy in the
C C.M. system.
C
C From J. M. Carpenter et al., SIGAL, January 16, 1986 (IPNS Note 32)
C Thermal treatment from Freund, Nucl.Inst.Meth. 213 (1983) 495.
C 25 Jan 1995: converted from Al to Be [PAS & Bob VonDreele]
C 30 Sep 2003: added optional parameter TIN to calling sequence;
C updated parameters; added temperature dependence [PAS]
C 09 Mar 2006: added optional ABSORB ratio to calling sequence [PAS]
C 18 May 2009: added optional TWOSINTH and ISEED, to select a random
C d-spacing; changed variables to REAL*8; restructured
C increased NMAX from 28 to 200; series expansion for
C single-phonon contribution [PAS]
C 24 May 2009: change normalization to match SIGfree at hi-E [PAS]
C 24 Jun 2009: make test of same LAMBDA single-precision [PAS]
C 31 May 2010: converted from Be to Graphite, NMAX=200 [PAS]
C 03 Jun 2010: correct expansion of SIGsph, RHO (4 atoms/cell) [PAS]
C 07 Jun 2010: NMAX=277, changed normalization of SIGcoh [PAS]
The full code is available as part of the NISP library MCLIB, which can be downloaded from
If you think I can be of any help, my email is PASeeger@losalamos.com.
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To solve the Schrödinger equation using the Impulse Approximation by Fermi Pseudopotential
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Dear Alexandra,
Thank you for your interest and for the sent paper.
But I need more...
I am interested in a new exp/th way of neutron – electron scattering length, bne. First this question was analyzed by E. Fermi in 1947. The main idea of the issue is that the neutron has an internal structure and according with the old Yukawa theory on nuclear forces the neutron is a system of proton + negative pion (the pions cloud). This fact gives reason to measure the electric dipolar moment of neutron and the n-e scattering length.
It is obviously that the electric dipolar moment of neutron has a very small value and deviation of neutron beams in intense electric fields have not given a certain final results and the conclusion was that neutron polarization and scattering length can be evidenced in the vicinity of nuclei. First experiment was proposed in an experimental setup which until nowadays is still respected with some modifications and improvements.
The neutron – electron scattering length is of order of -10-3 fm and therefore it is very difficult to measure effects caused by such small value. Taking into account that the interaction between neutron and electron has a small asymmetry in the center of mass system it is possible to evidence the presence of electric dipolar moment of neutron in the interaction of slow neutrons with noble gases (noble gases – to avoid magnetic interaction between neutrons and electrons).
In the present the experiments have evidenced scattering length with values higher and lower than -1.4 fm. According to Yu. A. Alexandrov (Oxford, 1992) the value lower than -1.4 fm contradicts the Yukawa theory and consequently the questions related to this issue are of actual interest. The carried out measurements are based on Fermi experimental setup and also need for a lot of corrections which affect the evaluations. From here the question that arises: it is possible a new experimental setup for n-e scattering length and neutron polarizability measurements?
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I would like to measure the residual stress in a steel sample using time-of-flight (TOF) neutron diffraction. The collimators have an angular range of say 30 degrees when viewed from a plan view. Does this also mean that there is a similar vertical angular range for the collimator which makes the diffracted neutron beam a cone-like shape from the scanned gauge volume?
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This question would be best directed to an instrument scientist at the specific beam line you are thinking of using, otherwise the answer won't be of much use. If you want to know about the NRSF or VULCAN instruments at Oak Ridge you can contact me directly.
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Why is charge ordering not possible in large-bandwidth manganites, e.g. the case of La1-xSrxMnO3. Is it due to its highly symmetric (i.e. untitled cubic/tetragonal) crystal structure, or is it something else?
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Large bandwidth occurs when atomic orbitals are strongly over-lapping. In this case valence electrons are more delocalized, whereas charge-ordering is a fully localized electron phenomenon.
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Hexagonal manganites RMnO3 (R = Y, Dy, Ho, Er, Tm, Lu etc.) are multiferroic materials with ferroelectric transition at about 1000 K whereas the magnetic transition is at about 100 K. Unlike the orthorhombic manganites, here the cause of ferroelectricity is geometric and is not due to the magnetic ordering through inverse D-M effect. These hexagonal manganites show strong magnetostriction of the lattice parameters (external magnetostriction) near the magnetic phase transition and this can be easily measured by NPD or by XRPD. We have measured the external magnetostriction by NPD on D20 at ILL. But our attempt to measure small displacements in atomic coordinates and bond distances below T_N (internal magnetostriction) did not give any conclusive results from these NPD data. The inherent problem is probably the strong correlations between magnetic and structural parameters for the magnetic structure with propagation vector k = 0. For these structures, the magnetic reflections are on top of nuclear reflections and give rise to strong correlations. We tried to solve the problem by measuring neutron diffraction intensities up to a very high Q with a diffractometer (POWGEN) on a spallation source (SNS) and refine the magnetic structure with the low-Q data and the nuclear structure with high-Q data, but even this strategy did not succeed. Has anyone any better suggestions or explanations?
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The answer is very simple. Here we are concerned with the atomic positions of relatively heavy rare-earth element like Ho (atomic number Z = 67) , transition element Mn (Z = 25) and the lighter O (Z = 8). Now you know the X-ray atomic scattering factor f is proportional to the total number of electrons or the atomic number Z. Again X-ray diffraction intensity is proportional to the square of the atomic scattering factor or Z^2. Z^2 for Ho, Mn, and O are 4489, 625 and 64 and therefore f^2 of these Ho, Mn, and O are in the ratio 70:10:1. So O will scatter X-rays 70 times less than Ho and 10 times less than Mn. So the X-ray scattering from HoMnO3 will dominated by Ho and Mn atoms and O will scatter very little. So you see O positions will not be determined very well by X-ray diffraction. Now neutron scattering lengths (which plays the same role as atomic scattering factor for neutrons) of Ho, Mn and O are 8.08, -3.73, and 5.80 and therefore neutron diffraction intensities for these atoms will in the ratio 65:14:34 or 4.6:1:2.4. So for neutron diffraction O will scatter very well. That is why for rare earth manganites neutron diffraction is better suited for determining the atomic positions, especially the O positions.
Now Brajesh do some home work. Go to the library and read the books:
Neutron Diffraction, G.E.Bacon, Oxford (1975)
Magnetic Neutron Scattering, ed. Tapan Chatterji, Elsevier (2006).
If you do not understand something then just ask me.
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The "incoherent approximation" is used In many papers relating to thermal neutron scattering, but can you give one that gives detailed information why they use this approximation. Do you know the origin?
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ok,I will contact with the publisher. thank you!