Neutron spin echo
Encyclopedia
Neutron spin echo spectroscopy is an inelastic neutron scattering
technique invented by Ferenc Mezei in the 1970's, and developed in collaboration with John Hayter.
In recognition of his work and in other areas, Mezei was awarded the first Walter Haelg Prize in 1999.
The spin echo
spectrometer possesses an extremely high energy resolution (roughly one part in 100,000). Additionally, it measures the density-density correlation (or intermediate scattering function) F(Q,t) as a function of momentum transfer Q and time. Other neutron scattering techniques measure the dynamic structure factor S(Q,ω), which can be converted to F(Q,t) by a Fourier transform
, which may be difficult in practice. For weak inelastic features S(Q,ω) is better suited, however, for (slow) relaxations the natural representation
is given by F(Q,t). Because of its extraordinary high effective energy resolution compared to other neutron scattering techniques, NSE is an ideal method to observe
overdamped internal dynamic modes (relaxations) and other diffusive processes in materials such as a polymer blend
s, alkane
chains, or microemulsion
s. The extraordinary power of NSE spectrometry was further demonstrated recently by the direct observation of coupled internal protein dynamics in the protein
s NHERF1 and Taq polymerase
, allowing the direct visualization of protein nanomachinery
in motion.
field of NMR
. In both cases the loss of polarization (magnetization) due to dephasing of the spins in time is restored by an effective time reversal operation,
that leads to a restituation of polarization (rephasing). In NMR the dephasing happens due to variation in the local fields at positions of the
nuclei, in NSE the dephasing is due to different neutron velocities in the incoming neutron beam.
The Larmor precession
of the neutron spin in a preparation zone with a magnetic field before the sample encodes
the individual velocities of neutrons in the beam into precession angles. Close to the sample the time reversal is effected by a so-called
flipper. A symmetric decoding zone follows such that at its end the precession angle accumulated in the preparation zone is exactly compensated
(provided the sample did not change the neutron velocity, i.e. elastic scattering), all spins rephase to form the "spin-echo". Ideally the full polarization is restored. This effect does not depend on the velocity/energy/wavelength of the incoming neutron.
If the scattering at the sample is not elastic but changes the neutron velocity, the rephasing will become incomplete and a loss of final
polarization results, which depends on the distribution of differences in the time, which the neutrons need to fly through the symmetric first (coding) and second (decoding)precession zones. The time differences occur due to a velocity change acquired by non-elastic scattering at the sample.
The distribution of these time differences is proportional (in the linearization approximation which is appropriate for quasi-elastic high resolution spectroscopy) to the spectral part of the scattering function S(Q,ω). The effect on the measured beam polarization is proportional
to the cos-Fourier transform of the spectral function, the intermediate scattering function F(Q,t). The time parameter depends on the neutron
wavelength and the factor connecting precession angle with (reciprocal) velocity, which can e.g. be controlled by setting a certain magnetic
field in the preparation and decoding zones. Scans of t may then be performed by varying the magnetic field. For some further explanations pertaining the NSE principle with animations see: pathfinder.neutron-eu.net.
It is important to note: all the spin manipulations are just a means to detect velocity changes of the neutron, which influence --for technical
reasons-- in terms of a Fourier transform of the spectral function in the measured intensity. The velocity changes of the neutrons convey
the physical information which is available by using NSE, i.e.
where
and 
.
B denotes the precession field strength, λ the
(average) neutron wavelength and Δv the neutron velocity change upon scattering at the sample.
The main reason for using NSE is that by the above means it can reach Fourier times of up to many 100ns, which corresponds to energy
resolutions in the neV range. The closest approach to this resolution by a spectroscopic neutron instrument type, namely the
backscattering spectrometer (BSS), is in the range of 0.5 to 1 μeV.
The spin-echo trick allows to use an intense beam of neutrons with a wavelength distribution of 10% or more and at the same time to be
sensitive to velocity changes in the range of less than 10-4.
Note: the above explanations assumes the generic NSE configuration --as first utilized by the IN11 instrument at the Institut Laue–Langevin (ILL)--. Other approaches
are possible like the resonance spin-echo, NRSE with concentrated a DC field and a RF field in the flippers at the end of
preparation and decoding zones which then are without magnetic field (zero field). In principle these approaches are equivalent concerning
the connection of the final intensity signal with the intermediate scattering function. Due to technical difficulties until now they have not
reached the same level of performance than the generic (IN11) NSE types.
research the structure of macromolecular objects is often investigated by small angle neutron scattering
, SANS.
The exchange of hydrogen
with deuterium
in some of the molecules creates scattering contrast between even equal chemical species. The SANS diffraction pattern—if interpreted in real space—corresponds to a snapshot picture of the molecular arrangement. Neutron spin echo instruments can analyze the inelastic broadening of the SANS intensity and thereby analyze the motion of the macromolecular objects.
A coarse analogy would be a photo with a certain opening time instead of the SANS like snapshot. The opening time corresponds to the Fourier time which depends on the setting of the NSE spectrometer, it is proportional to the magnetic field (integral) and to the third power of the neutron wavelength. Values up to several hundreds of nanoseconds are available. Note that the spatial resolution of the scattering experiment is in the nanometer range, which means that a time range of e.g. 100 ns corresponds to effective molecular motion velocities of 1 nm/100 ns = 1 cm/s. This may be compared to the typical neutron velocity of 200..1000 m/s used in these type of experiments.
(TOF) or backscattering spectrometers rely on the huge incoherent neutron scattering
cross section of protons. The scattering signal is dominated by the corresponding contribution, which represents the (average) self-correlation
function (in time) of the protons.
For NSE spin incoherent scattering has the disadvantage that it flips the neutron spins during scattering with a probability of 2/3.
Thus converting 2/3 of the scattering intensity into "non-polarized" background and putting a factor of -1/3 in front of the cos-Fourier integral
contribution pertaining the incoherent intensity. This signal subtracts from the coherent echo signal. The result may be a complicated
combination which cannot be decomposed if only NSE is employed.
However, in pure cases, i.e. when there is an overwhelming intensity contribution due to protons, NSE can be used to measure their incoherent spectrum.
The intensity situation of NSE --for e.g. soft-matter samples-- is the same as in small angle scattering (SANS
). Which means that
molecular objects with coherent scattering contrast at low Q (momentum transfer) show a much larger intensity as the incoherent contribution
(which is the background level). But at larger Q usually somewhere around Q=0.3 A-1 the incoherent scattering becomes stronger
than the coherent part. At least for hydrogen containing systems contrast requires the presence of some protons and even pure deuterated
samples show spin-incoherent scattering from deuterons, however, 40 times weaker than the proton scattering.
Fully protonated samples allow successful measurements but at intensities of the order of the SANS background level.
This requires correspondingly long counting times.
Note: This interference with the spin manipulation of the NSE technique occurs only with spin-incoherent scattering. Isotopic incoherent
scattering yields a "normal" NSE signal.
Inelastic neutron scattering
Inelastic neutron scattering is an experimental technique commonly used in condensed matter research to study atomic and molecular motion as well as magnetic and crystal field excitations....
technique invented by Ferenc Mezei in the 1970's, and developed in collaboration with John Hayter.
In recognition of his work and in other areas, Mezei was awarded the first Walter Haelg Prize in 1999.
The spin echo
Spin echo
In magnetic resonance, a spin echo is the refocusing of precessing spin magnetisation by a pulse of resonant radiation. Modern nuclear magnetic resonance and magnetic resonance imaging rely heavily on this effect....
spectrometer possesses an extremely high energy resolution (roughly one part in 100,000). Additionally, it measures the density-density correlation (or intermediate scattering function) F(Q,t) as a function of momentum transfer Q and time. Other neutron scattering techniques measure the dynamic structure factor S(Q,ω), which can be converted to F(Q,t) by a Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
, which may be difficult in practice. For weak inelastic features S(Q,ω) is better suited, however, for (slow) relaxations the natural representation
is given by F(Q,t). Because of its extraordinary high effective energy resolution compared to other neutron scattering techniques, NSE is an ideal method to observe
overdamped internal dynamic modes (relaxations) and other diffusive processes in materials such as a polymer blend
Polymer blend
A polymer blend or polymer mixture is a member of a class of materials analogous to metal alloys, in which at least two polymers are blended together to create a new material with different physical properties. Section 3.2 Polymer Mixtures-History:...
s, alkane
Alkane
Alkanes are chemical compounds that consist only of hydrogen and carbon atoms and are bonded exclusively by single bonds without any cycles...
chains, or microemulsion
Microemulsion
Microemulsions are clear, thermodynamically stable, isotropic liquid mixtures of oil, water and surfactant, frequently in combination with a cosurfactant. The aqueous phase may contain salt and/or other ingredients, and the "oil" may actually be a complex mixture of different hydrocarbons and olefins...
s. The extraordinary power of NSE spectrometry was further demonstrated recently by the direct observation of coupled internal protein dynamics in the protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
s NHERF1 and Taq polymerase
Taq polymerase
thumb|228px|right|Structure of Taq DNA polymerase bound to a DNA octamerTaq polymerase is a thermostable DNA polymerase named after the thermophilic bacterium Thermus aquaticus from which it was originally isolated by Thomas D. Brock in 1965...
, allowing the direct visualization of protein nanomachinery
Molecular machine
A molecular machine, or nanomachine, is any discrete number of molecular components that produce quasi-mechanical movements in response to specific stimuli . The expression is often more generally applied to molecules that simply mimic functions that occur at the macroscopic level...
in motion.
How it works
Basically NSE is a time-of-flight technique. Concerning the neutron spins it has a strong analogy to the so-called Hahn echo, well known in thefield of NMR
NMR
NMR may refer to:Applications of Nuclear Magnetic Resonance:* Nuclear magnetic resonance* NMR spectroscopy* Solid-state nuclear magnetic resonance* Protein nuclear magnetic resonance spectroscopy* Proton NMR* Carbon-13 NMR...
. In both cases the loss of polarization (magnetization) due to dephasing of the spins in time is restored by an effective time reversal operation,
that leads to a restituation of polarization (rephasing). In NMR the dephasing happens due to variation in the local fields at positions of the
nuclei, in NSE the dephasing is due to different neutron velocities in the incoming neutron beam.
The Larmor precession
Larmor precession
In physics, Larmor precession is the precession of the magnetic moments of electrons, atomic nuclei, and atoms about an external magnetic field...
of the neutron spin in a preparation zone with a magnetic field before the sample encodes
the individual velocities of neutrons in the beam into precession angles. Close to the sample the time reversal is effected by a so-called
flipper. A symmetric decoding zone follows such that at its end the precession angle accumulated in the preparation zone is exactly compensated
(provided the sample did not change the neutron velocity, i.e. elastic scattering), all spins rephase to form the "spin-echo". Ideally the full polarization is restored. This effect does not depend on the velocity/energy/wavelength of the incoming neutron.
If the scattering at the sample is not elastic but changes the neutron velocity, the rephasing will become incomplete and a loss of final
polarization results, which depends on the distribution of differences in the time, which the neutrons need to fly through the symmetric first (coding) and second (decoding)precession zones. The time differences occur due to a velocity change acquired by non-elastic scattering at the sample.
The distribution of these time differences is proportional (in the linearization approximation which is appropriate for quasi-elastic high resolution spectroscopy) to the spectral part of the scattering function S(Q,ω). The effect on the measured beam polarization is proportional
to the cos-Fourier transform of the spectral function, the intermediate scattering function F(Q,t). The time parameter depends on the neutron
wavelength and the factor connecting precession angle with (reciprocal) velocity, which can e.g. be controlled by setting a certain magnetic
field in the preparation and decoding zones. Scans of t may then be performed by varying the magnetic field. For some further explanations pertaining the NSE principle with animations see: pathfinder.neutron-eu.net.
It is important to note: all the spin manipulations are just a means to detect velocity changes of the neutron, which influence --for technical
reasons-- in terms of a Fourier transform of the spectral function in the measured intensity. The velocity changes of the neutrons convey
the physical information which is available by using NSE, i.e.
where and .B denotes the precession field strength, λ the
(average) neutron wavelength and Δv the neutron velocity change upon scattering at the sample.
The main reason for using NSE is that by the above means it can reach Fourier times of up to many 100ns, which corresponds to energy
resolutions in the neV range. The closest approach to this resolution by a spectroscopic neutron instrument type, namely the
backscattering spectrometer (BSS), is in the range of 0.5 to 1 μeV.
The spin-echo trick allows to use an intense beam of neutrons with a wavelength distribution of 10% or more and at the same time to be
sensitive to velocity changes in the range of less than 10-4.
Note: the above explanations assumes the generic NSE configuration --as first utilized by the IN11 instrument at the Institut Laue–Langevin (ILL)--. Other approaches
are possible like the resonance spin-echo, NRSE with concentrated a DC field and a RF field in the flippers at the end of
preparation and decoding zones which then are without magnetic field (zero field). In principle these approaches are equivalent concerning
the connection of the final intensity signal with the intermediate scattering function. Due to technical difficulties until now they have not
reached the same level of performance than the generic (IN11) NSE types.
What it can measure
In soft matterSoft matter
Soft matter is a subfield of condensed matter comprising a variety of physical states that are easily deformed by thermal stresses or thermal fluctuations. They include liquids, colloids, polymers, foams, gels, granular materials, and a number of biological materials...
research the structure of macromolecular objects is often investigated by small angle neutron scattering
Small angle neutron scattering
Small angle neutron scattering is a laboratory technique, similar to the often complementary techniques of small angle X-ray scattering and light scattering, used for investigations of structure of various substances, with spatial sensitivity of about 1 - 1000 nm...
, SANS.
The exchange of hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
with deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...
in some of the molecules creates scattering contrast between even equal chemical species. The SANS diffraction pattern—if interpreted in real space—corresponds to a snapshot picture of the molecular arrangement. Neutron spin echo instruments can analyze the inelastic broadening of the SANS intensity and thereby analyze the motion of the macromolecular objects.
A coarse analogy would be a photo with a certain opening time instead of the SANS like snapshot. The opening time corresponds to the Fourier time which depends on the setting of the NSE spectrometer, it is proportional to the magnetic field (integral) and to the third power of the neutron wavelength. Values up to several hundreds of nanoseconds are available. Note that the spatial resolution of the scattering experiment is in the nanometer range, which means that a time range of e.g. 100 ns corresponds to effective molecular motion velocities of 1 nm/100 ns = 1 cm/s. This may be compared to the typical neutron velocity of 200..1000 m/s used in these type of experiments.
NSE and spin-incoherent scattering (from protons)
Many inelastic studies that use normal time-of-flightTime-of-flight
Time of flight describes a variety of methods that measure the time that it takes for an object, particle or acoustic, electromagnetic or other wave to travel a distance through a medium...
(TOF) or backscattering spectrometers rely on the huge incoherent neutron scattering
cross section of protons. The scattering signal is dominated by the corresponding contribution, which represents the (average) self-correlation
function (in time) of the protons.
For NSE spin incoherent scattering has the disadvantage that it flips the neutron spins during scattering with a probability of 2/3.
Thus converting 2/3 of the scattering intensity into "non-polarized" background and putting a factor of -1/3 in front of the cos-Fourier integral
contribution pertaining the incoherent intensity. This signal subtracts from the coherent echo signal. The result may be a complicated
combination which cannot be decomposed if only NSE is employed.
However, in pure cases, i.e. when there is an overwhelming intensity contribution due to protons, NSE can be used to measure their incoherent spectrum.
The intensity situation of NSE --for e.g. soft-matter samples-- is the same as in small angle scattering (SANS
Small-angle neutron scattering
Small angle neutron scattering is a laboratory technique, similar to the often complementary techniques of small angle X-ray scattering and light scattering, used for investigations of structure of various substances, with spatial sensitivity of about 1 - 1000 nm...
). Which means that
molecular objects with coherent scattering contrast at low Q (momentum transfer) show a much larger intensity as the incoherent contribution
(which is the background level). But at larger Q usually somewhere around Q=0.3 A-1 the incoherent scattering becomes stronger
than the coherent part. At least for hydrogen containing systems contrast requires the presence of some protons and even pure deuterated
samples show spin-incoherent scattering from deuterons, however, 40 times weaker than the proton scattering.
Fully protonated samples allow successful measurements but at intensities of the order of the SANS background level.
This requires correspondingly long counting times.
Note: This interference with the spin manipulation of the NSE technique occurs only with spin-incoherent scattering. Isotopic incoherent
scattering yields a "normal" NSE signal.
Existing spectrometers
- IN11 (Institut Laue-LangevinInstitut Laue-LangevinThe Institut Laue–Langevin, or ILL, is an internationally-financed scientific facility, situated in Grenoble, France. It is one of the world centres for research using neutrons...
,ILL, Grenoble, France) - IN15 (Institut Laue-LangevinInstitut Laue-LangevinThe Institut Laue–Langevin, or ILL, is an internationally-financed scientific facility, situated in Grenoble, France. It is one of the world centres for research using neutrons...
,ILL, Grenoble, France) - J-NSE (Juelich Centre for Neutron Science JCNS, Juelich, Germany, hosted by FRMII, Munich (Garching), Germany)
- NG5-NSE (NIST CNRF, Gaithersburg, USA)
- NSE@SNS (JCNS SNS, Oak Ridge)
- RESEDA (FRM II Munich FRMII, Munich, Germany
- V5/SPAN (Hahn-Meitner Institut, Berlin, Germany)
- C2-2 (ISSP, Tokai, Japan)
See also
- Biological small-angle scattering
- Larmor precessionLarmor precessionIn physics, Larmor precession is the precession of the magnetic moments of electrons, atomic nuclei, and atoms about an external magnetic field...
- Neutron resonance spin echo
- NMRNMRNMR may refer to:Applications of Nuclear Magnetic Resonance:* Nuclear magnetic resonance* NMR spectroscopy* Solid-state nuclear magnetic resonance* Protein nuclear magnetic resonance spectroscopy* Proton NMR* Carbon-13 NMR...
- Protein domainProtein domainA protein domain is a part of protein sequence and structure that can evolve, function, and exist independently of the rest of the protein chain. Each domain forms a compact three-dimensional structure and often can be independently stable and folded. Many proteins consist of several structural...
- Soft matterSoft matterSoft matter is a subfield of condensed matter comprising a variety of physical states that are easily deformed by thermal stresses or thermal fluctuations. They include liquids, colloids, polymers, foams, gels, granular materials, and a number of biological materials...
- Spin echoSpin echoIn magnetic resonance, a spin echo is the refocusing of precessing spin magnetisation by a pulse of resonant radiation. Modern nuclear magnetic resonance and magnetic resonance imaging rely heavily on this effect....