Introduction to Neutron Scatteringand ORNL Neutron Facilities

Student: Xiangshi Yin(Email: xyin3@utk.edu)

Instructor: Elbio DagottoCourse: Solid State II, 2010, Spring

Introduction to Neutron Scattering and ORNL

Neutron Facilities

Xiangshi YinDepartment of Physics and Astronomy, The University of Tennessee,

Knoxville, Tennessee 37996, USA

Dated:February 22, 2010

Abstract

Neutron scattering has been a very powerful probe in the research to the lattice and magneticstructures of various kinds of materials now. In this paper, I will first give a brief introduction of thehistory of neutron scattering. Then, in the second part, I will talk about the properties of neutronscattering, present its basic mechanism and unique properties. After that, I will give some examplesto illustrate the powerful function of neutron scattering in condensed matter physics research. Andfinally, I will talk a little about some general ways of getting neutrons and neutron facilities in OakRidge National Laboratory(ORNL).

1 Introduction

Neutron was first discovered by Chadwick [1] in1932 when he observed a penetrating form of radi-ation emanating from beryllium metal when acti-vated by alpha-particles from a radium source. Af-ter that, Elsasser [2] first suggested that the motionof the neutrons could be determined by wave me-chanics and thus would be diffracted by crystallinematerials. The experimental demonstration of thisidea was done by Halban and Preiswerk [3] and alsoby Mitchell and Powers [4]. In 1936, Bloch[5] firstpointed out that the scattering of neutron from thespin and orbital magnetic moment of atoms couldbe observable if the magnetic moment of neutronis at the same order as the measured value of pro-ton. That means neutron could be a probe to themagnetic structure of solid. The real foundationsof the neutron scattering technique were built inthe 1940s and 1950s when researchers from U. S.and Canada got significant flux of neutron from the

1st generation reactors. Wollan and Shulls work inORNL on the research into the ferimagnetic statesof Fe3O4 between 1948 and 1955 laid the basisfor the future neutron diffraction experiments. Bymeans of neutron scattering, they determined themagnetic structures of various alloys. And almostin the mean time, Bertram Brockhouse developedthe inelastic neutron scattering technique at ChalkRivers NRX reactor in the mid 1950s. He designedthe first triple-axis spectrometer to analyze thespectrum of neutrons after scattering. After hiswork, inelastic neutron scattering becomes a pow-erful tool to detect the elementary excitations insolid, such as phonons and spin waves. In 1994,both Shull and Brockhouse were awarded the No-bel Prize for their ”pioneering contributions to thedevelopment of neutron scattering techniques forthe study of condensed matter”.

1

2 ELEMENTARY PROPERTIES AND MECHANISM OF NEUTRON SCATTERING 2

Table 1: Basic properties of neutronProperty ValueMass 1.67492729(28)× 10−27kgCharge 0Spin 0Magnetic moment(in the unit of µN ) -1.9130427(5)

Figure 1: (a)Elastic scattering process (b)Inelastic scattering process[7]

2 Elementary properties and mechanism of neutron scattering

2.1 About neutron

2.1.1 Basic properties of neutron

When we start to look at neutron scattering tech-nique, intuitively, everyone will ask such question—why do we use neutrons? Actually, there are a lotof probes we could use, STM, AFM, SEM, TEM,XRD and we could also use photo emission tech-nique. Is neutron special to some extent? In orderto answer this question, let’s first have a quick lookat some basic properties of neutron.From table-1, it is obvious that neutrons haveunique properties that make them a powerful probeof various materials. They have no charge, and un-like electromagnetic radiation or electrons, theyonly interact with atoms in the materials via shortrange nuclear-nuclear interactions. The interac-tions between incoming neutrons and the detected

materials are so weak that generally neutrons canpenetrate the materials far better than charged par-ticles (like electrons) and X-rays(See Fig.2(Left)).So, it is a good probe to detect the bulk propertiesof materials. Neutrons also have spins and magneticmoments, so they can interact with the unpairedelectrons of magnetic atoms. This property makesthem ideally suitable to be used detecting the mag-netic structures as well as magnetic excitations,such as spin waves.

2.1.2 Neutron temperatures

Neutrons are usually produced from a nuclear re-search reactor or a spallation source with energiesusually millions of electron volts (MeV) [6]. Then,it will be slowed down by the so-calledmoderator toget proper wavelength comparable to the atomic

2 ELEMENTARY PROPERTIES AND MECHANISM OF NEUTRON SCATTERING 3

Figure 2: (Left)Comparison of penetration depth of different probes[7]. (Right)A triple axis spectrom-eter built at the institute Laue Langevin in Grenoble, France

spacing in solid or liquid and proper energy com-parable to the dynamic processes in the materials.In the moderator, repeated collisions with atomicnuclei of small atomic weight (moderation) makethe neutrons to a near-equilibrium distribution at atemperature at little above that of the moderator.A small tube through the reactor shielding admitsa beam of the fast, intermediate and slow neutronsinto the experimental hall. Depending on differentmoderating process, we could get neutrons with awide range of energy as below: [8]Fast neutrons have energy greater than 1 eV, 0.1MeV or approximately 1 MeV, depending on thedefinition. Slow neutrons have an energy lessthan or equal 0.4 eV. Epithermal neutrons haveenergy from 0.025 to 1 eV. Hot neutrons haveenergy of about 0.2 eV. Thermal neutrons haveenergy of about 0.025 eV. Cold neutrons haveenergy from 5x10-5 eV to 0.025 eV. Very coldneutrons have energy from 3x10-7 eV to 5x10-5eV. Ultra cold neutrons have energy less than3x10-7 eV. Continuum region neutrons haveenergy from 0.01 MeV to 25 MeV. Resonanceregion neutrons have energy from 1 eV to 0.01MeV. Low energy region neutrons have energyless than 1 eV.The de Brogile wavelength λ could be expressed

like: λ = h

p

p = h̄k

E = p2√2mE

=⇒ λ =h√

2mE

So, if we consider the so-called thermal neutrons, ithas energy of 25meV, the corresponding de Brogliewavelength should be 1.8 . This value is compa-rable with the interatomic distances in condensedmatter, which makes the detecting of the specialstructure of materials possible. So thermal neu-tron scattering can yield structural information ofcondensed matter. Thermal and cold neutrons be-ing in the range from 0.1meV to 100meV matchvery well with energies of elementary excitations ofcondensed matter. This enables one to investigatethe dynamics of the elementary excitations of con-densed matter. For excitations with energies higherthan 100meV hot neutrons can also be used.Although there are so many advantages for usingneutron scattering as a powerful probe in condensedmatter research, there are also some disadvantagesin neutrons. The most significant one should bethe weak flux we could get. For now, even use themost powerful neutron source, we could only get aflux in the order of 104neutrons/mm2 ·s. However,in the X-ray instrument in the synchrotron source

2 ELEMENTARY PROPERTIES AND MECHANISM OF NEUTRON SCATTERING 4

at the same energy scale, people could get muchhigher flux to the order of 1018photons/mm2 · s.Weak flux means relative weak intensity in the fi-nal scattering spectra, which is a not so good orpeople need to wait for much longer time to get adecent result. In other words, neutron scattering isa signal-limited technique.Then, why people still use neutron scattering tech-nique? Well, the answer maybe that people don’thave other simpler and less expensive options toget such comprehensive information of materials asneutrons.

2.2 Rough picture of neutron scat-tering technique

2.2.1 Broad introduction[9]

As I said in the above section, there are basicallytwo main interactions we need to consider in theneutron scattering process, one is the short rangenuclear interaction, another is the magnetic inter-action between the spin in the materials and themagnetic moments carried by neutrons. So, neu-tron scattering result is kind of superposition ofboth the nuclear scattering and magnetic scatter-ing.If we consider the energy loss in the scatteringprocess, neutron scattering basically falls into twocategories: elastic scattering and inelastic scatter-ing.Elastic scattering(Figure.1a) is a scattering pro-cess after which the emitting neutrons have moreor less the same energy as the incident neutrons. Itcan be well applied to study the crystalline solids,gasses, liquids or amorphous materials and givecomplementary information containing both thelattice structure and the magnetic structure.Inelastic scattering(Figure.1b) is a scatteringprocess in which there is certain amount of en-ergy transfer between the incoming neutrons andmaterials. So, the outgoing neutrons usually havedifferent energy as the incoming ones. People usu-ally use it to probe some elementary excitations inthe materials, such as phonon excitations and spinwaves.

Based on different research purposes, there arenormally three categories of elastic scattering tech-nique people usually use: neutron diffraction, smallangle neutron scattering and neutron reflectory.Neutron diffraction is basically the simplest elasticscattering process, like the X-ray diffraction tech-nique, people could use it to investigate the latticestructure of condensed materials. And because ofthe deeper penetration, it is a good way to detectthe bulk structure. Small angle neutron scatteringis a good way to probe some larger scale structures.For example, in biophysics, people could use it toinvestigate some large molecules as DNA and pro-tein. Neutron reflectory is a technique which couldbe used in the research to the surface structure andproperties of materials. Although neutrons havedeeper penetration and seems to be not a surfacesensitive technique, it turns out that if the imping-ing angle between the incoming neutron wave vectorand the surface is smaller than certain critical an-gle, the reflectivity of neutrons become significant.This could be used in surface science.

2.2.2 Sample preparation

Intuitively, for a complete scattering process, weshould have a bullet and a target. The bullet here,obviously, is the neutron. As I mentioned above, wecould get neutrons carrying various energies fromneutron sources which could be used for differentresearch purposes. For the sample, it could be ei-ther single crystal sample or polycrystalline sample.For single crystal sample, people usually interest inthe properties of certain lattice plane. So, whatpeople usually do before scattering experiment isto rotate the sample to find the correct orientationthey want. For polycrystal sample, there is no suchproblem, because it is usually used to investigatethe overall structure and properties containing in-formations from lattice planes with various orienta-tions.

2.2.3 Scattering result

Normally, what people get from the neutron scat-tering experiment is the intensity of outgoing neu-trons as a function of the momentum transfer Q

2 ELEMENTARY PROPERTIES AND MECHANISM OF NEUTRON SCATTERING 5

and corresponding energy transfer E. There are alot of ways to measure the momentum transfer de-pending on different neutron sources and differentscattering process(elastic or inelastic).In nuclear reactor source, people usually usemonochromator to select single wavelength neu-trons in elastic neutron scattering technique andtriple-axis spectrometer in the inelastic scatter-ing technique. The monochromator is usually anassembly of single crystals(often mad of either py-rolytic graphite, silicon or copper) each correctlyoriented to diffract a mono-energetic beam of neu-trons towards the scattering sample. The triple-axisspectrometer is also an assemblies of single crystalswhich are used to set the incident neutron wavevec-tor and analyze the wavevector of the scatteredneutrons. It records the scattered neutron intensityat a single wave vector transfer and single energytransfer.In pulsed neutron sources, people usually use theso-called time-of-flight technique in which the de-tectors not only record the number of scatteringneutrons at certain angular position but also thetime when the neutrons arrive at the detector. Be-cause the time when the neutrons come out fromthe source is known, the velocity of neutrons couldbe calculated and hence the momentum. So, ba-sically the time-of-flight technique doesn’t chooseneutrons with certain wavelength, but only marknetrons with different energy.

2.3 Neutron scattering mechanism

2.3.1 Coherent and incoherent scattering

It turns out that[10]if we consider the interactionbetween neutron and materials to be the so-calledpseudo potential as

V (~r) =2πh̄2

m

∑i

bj ıδ(~r − ~ri)

and if we apply Born approximation, we could getthe intensity of outcoming neutrons as

I( ~Q,E) =1

h

k′

k

∑i,j

bibj

∫ ∞−∞〈e−i ~Q· ~ri(0)ei

~Q· ~rj(t)〉e−iEt/h̄dt

Here, k and k’ are wave vectors before and afterscattering, bi and bj are the scattering length ofdifferent nucleus labeled by i and j. And the an-gluar bracket here means thermodynamic averagevalue. Actually, the scattering length depends onspecific spin states involved, and if we average theabove equation over the nuclear spin states, thesumation part in the equation above becomes∑

i,j

〈bibj〉Aij =∑i,j

〈b〉2Aij +∑i

(〈b2〉 − 〈b〉2)Aii

[11] The first term corresponding to the so-calledcoherent scattering, and the second part corre-sponding to the so-called incoherent scattering.Or, in the other words, the real scattering inten-sity we get is basically the superposition of thecoherent scattering and incoherent scattering. Thecoherent scattering is actually the interference re-sult of scattered neutrons from different neucleis,while the incoherent scattering is normally simplesummation of neutron signals from different nucleiwhich means the phase of scattered neutrons arenot correlated.Of course, consider the energy loss, we have elasticcoherent and inelastic coherent scattering, and alsowe have elastic incoherent and inelastic incoherentscattering. They normally carry different informa-tion of materials. Elastic coherent scattering tellsus the equilibrium atomic distribution or the latticestructure of material, and inelastic coherent scatter-ing carrys information of excitations of collectivemotions of atoms. Elastic incoherent scatteringis normally the same in all directions, so it usu-ally contributes as a background, while inelasticincoherent scattering usually contains informationabout the atomic diffusion in the material.

2.3.2 Neutron diffraction

Neutron diffraction is the simplest elastic neutronscattering. In this process, the Bragg’s Law alsoworks.

2dSinθ = nλ

Q = 4πSinθλ

d = 2πQ

3 NEUTRON SOURCES AND NEUTRON SCATTERING FACILITIES IN ORNL 6

Figure 3: (a)Powder X-ray diffraction pattern of Hg0.7Cr0.3Sr2CuO4.6 (b)Observed and profile-fitteddiffraction patterns for Hg0.7Cr0.3Sr2CuO4.6, the difference pattern is shown at the bottom (c)Aschematic of the refined structure[12]

Like the X-ray diffraction technique, what weusually get is a spectra of intensity of scatteredneutrons as a function of the scattering angle 2θas Fig.3(a). If we apply the Bragg’s law, we couldget a set of d values corresponding to various lat-tice planes with different orientations. Normally, itis not so easy to reproduce the real lattice structurefrom the diffraction sepctra, because it doesn’t giveus any information about the atomic distributionin the materials. So, people usually resort to sometheoretical models,shift the atoms around until thepredicted scattering spectra fits the real experimen-tal result. Actually, Fig.3 is a really good examplefor this procedure, it is about a cuprate supercon-ductor Hg0.7Cr0.3Sr2CuO4.6

2.3.3 Inelastic scattering

In reality, not all neutron scattering processes areenergy conserved(neutron energy). In some cases,

neutrons can experience some energy loss or evengain some energy. They can absorb or emit certainamount of quantized energy values which corre-spond to the phonon or spin wave energy. So, bymeasuring the energy change between outcomingand incident neutrons, we could get some idea ofsome elementary excitation process in condensedmatters. And, the most frequently used methodis the so-called ”constant-Q method” developed byBrockhouse, in which people fixe the Q value andmeasure the corresponding energy loss and gainof neutrons. Fig.4(Left) is an example of phononexcitation peaks in the iron based superconductorCaFe2As2, and Fig.4(Right) is an example of thespin wave excitation peaks in the LCMO systemwith different dopings. In Fig.4(Right) you can seeone peak splits into two peaks with positive andnegative energy, which corresponds to the processof creat and annihilate a spin wave.

3 Neutron sources and neutron scattering facilities in ORNL

3.1 Neutron sources

There are two general ways to get neutrons, one isthe research reactors and another is the spallationsources.

3.1.1 Research reactors

Research reactors are nuclear reactors that serveprimarily as a neutron source. The intrinsicmechanism is the neutron-fission chain reactions(Fig.5(left)) where a neutron plus a fissionable atomcauses fission resulting in a larger number of neu-trons than was consumed in the initial reaction.

3 NEUTRON SOURCES AND NEUTRON SCATTERING FACILITIES IN ORNL 7

Figure 4: (Left) Energy scans taken atQ = (2.5, 1.5, 0) of iron based superconductor CaFe2As2 at roomtemperature and at a temperature far below the structural phase transformation. The calculated phononstructure factors for nonmagnetic and spin-polarized are shown in the upper and lower panel, respectively.For better visibility the calculated profiles(dashed lines) in the lower and upper panels are shifted downby 200 counts. The insert in the upper panel shows the q dependence of the phonon linewidths of thebrach around 18 meV(filled red circles) and around 24 meV(open blue circles). The lines were obtainedby linear regression. The insert in the lower panel shows the displacement pattern of the zone boundarymode at E = 18meV . Only the Fe atoms are shown. All other atoms are at rest for this mode[13].(Right)Constant-q scans at[1+q,0,0] for LCMO20 at q = 0.14rlu (a). LCMO25 at q = 0.08rlu (b). and LCMO30at q = 0.08rlu (c). The solid lines are resolution-limited Gaussian fits to the data. The weak nonmagneticcontribution to the scattering ath̄ω = 0 has been subtracted from identical measurements at 10K[14]

This process will continue if the number of neu-trons produced in a single reaction is capable ofproducing another fission process.The so-called fissionable material here typically isthe highly enriched uranium, typically 20% U-235.The elementary reactions involved are:

n+23592 U →236

92 U

23692 U →144

56 Ba+8936 U + 3n+ 177MeV

As I mentioned before, the neutrons coming fromthe reactor usually have high energy in the order ofMeV. In order to slow them down, the reactors areusually surrounded by a neutron moderator such asregular water, heavy water, graphite, or zirconiumhydride, and fitted with mechanisms such as con-trol rods that control the rate of the reaction.

3.1.2 Spallation sources

Spallation is a process in which fragments of mate-rials (spall) are ejected from a body due to impactor stress. Here, in the nuclear physics which we areinterested in, the spallation is basically a process inwhich a heavy metal target (like mercury and tanta-lum) is hit by an incoming high energy species (likeproton) and expel a large amount of neutrons(20to 30 per impact). This concept of nuclear spalla-tion was first coined by Nobelist Glenn T. Seaborgin this doctoral thesis on the inelastic scattering ofneutrons in 1937[15]. Fig.5(Right) is a picture il-lustrating the basic process of nuclear spallation.For the target, people tried the depleted uranium(DU, primarily composed of the isotope U-238)before because of its intense neutron production.However, its life time is too short. So generally,tantalum has been used.s

3 NEUTRON SOURCES AND NEUTRON SCATTERING FACILITIES IN ORNL 8

Figure 5: (Left)”Chain reaction process” (Right) Spallation process[16]

Figure 6: The relation between incident photon energy and the neutron yield[17]

Fig. 6 is a plot of the neutron yield as a functionof the incoming proton energy. We can find that theproton energies in the range of 1 to 3 GeV proveoptimal for neutron production via spallation reac-tions in heavy-metal targets, and production rate isdirectly related to the power deposited on the tar-get.As I mentioned before, the neutrons emergingfromthe spallation source usually carry energy inthe order of MeV which is not suitable for the nor-mal neutron scattering measurement. So, we alsoneed a slow down process and corresponding mod-erator for this process. The velocity distributionis ultimately determined by the temperature of themoderator. Similarly, water at room temperatureand liquid methane or liquid hydrogen at cryogenictemperature is most often used in it.

3.2 Neutron scattering facilities inORNL

3.2.1 HFIR (High Flux Isotope Reactor)

The ORNL High Flux Isotope Reactor (HFIR) isthe highest flux reactor-based source of neutronsfor condensed matter research in the United States.HFIR is a beryllium-reflected, light-water-cooledand -moderated, flux-trap type reactor that useshighly enriched uranium-235 as the fuel. The pre-liminary conceptual design of the reactor was basedon the ”flux trap” principle, in which the reactorcore consists of an annular region of fuel surround-ing an unfueled moderating region or ”island.” Thisdesignation allows fast neutrons emerging from thereactor source to be moderated in the island andthus produces a region of very high thermal-neutron

3 NEUTRON SOURCES AND NEUTRON SCATTERING FACILITIES IN ORNL 9

Figure 7: (a)Top view of HFIR and HFIR beam tubes and experiment locations (b)Top view of SNS andschematic picture of SNS components[18]

flux at the center of the island. This highflux neutrons may be tapped by extending empty”beam” tubes into the reflector, thus allowing neu-trons to be beamed into experiments outside thereactor shielding. Finally, a variety of holes in thereflector may be provided in which to irradiate ma-terials for experiments or isotope production.

3.2.2 SNS(Spallation Neutron Source)

SNS is an accelerator-based neutron source in OakRidge, Tennessee, USA. It provides the most intensepulsed neutron beams in the world for scientific re-search and industrial development.The basic process for generating neutrons in SNSis like this:Negatively charged hydrogen ions are produced by

an ion source. Each ion consists of a proton orbitedby two electrons. The ions are injected into a linearaccelerator, which accelerates them to very highenergies. The ions are passed through a foil, whichstrips off each ion’s two electrons, converting it toa proton. The protons pass into a ring where theyaccumulate in bunches. Each bunch of protons isreleased from the ring as a pulse. The high-energyproton pulses strike a heavy-metal target, which isa container of liquid mercury. Corresponding pulsesof neutrons freed by the spallation process will beslowed down in a moderator and guided throughbeam lines to areas containing special instrumentssuch as neutron detectors. Once there, neutrons ofdifferent energies can be used in a wide variety ofexperiments.

REFERENCES 10

References

[1] J. Chadwick, Nature (London) 129 312 (1932)

[2] W. M. Elsasser, C. R. Acad. Sci. Paris 202 1029 (1936)

[3] H. Halban and P. Preiswerk, C. R. Acad. Sci. Paris 203 73 (1936)

[4] D. P. Mitchell and P. N. Powers, Phys. Rev. 50 486 (1936)

[5] F. Bloch, Phys. Rev. 50 259 (1936)

[6] B. N. Brockhouse, Nobel Lecture, December 8, 1994

[7] R.Pynn, Neutron Scattering: A Primer(Los Alamos Science, 1989)

[8] http://en.wikipedia.org/wiki/Neutron_temperature

[9] http://en.wikipedia.org/wiki/Neutron_diffraction

[10] L. Van Hove, Phys. Rev. 95, 249 (1954)

[11] T. Chatterji, Neutron Scattering from Magnetic Materials(World Scientific, 2005)

[12] J. B. Mandal, B. Bandyopadhyay, B. Ghosh, H. Rajagopal, A. Sequeira and J. V. Yakhmi, Journalof Superconductivity. Vol 9, No.2(1996)

[13] R. Mittal, L. Pintschovius, D. Lamago, R. Heid, K-P. Bohnen, D. Reznik, S. L. Chaplot, Y. Su, N.Kumar, S. K. Dhar, A. Thamizhavel and Th. Brueckel, Phys. Rev. Lett.102, 217001(2009)

[14] P. Dai, J. A. Fernandez-Baca, E. W. Plummer, Y. Tomioka and Y. Tokura, Phys. Rev. B64, 224429(2001)

[15] http://www.khwarzimic.org/takveen/seaborg.pdf

[16] http://irfu.cea.fr/en/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=2215

[17] J. R. Alonso The spallation neutron source project, Proceeding of the 1999 particle acceleratorconference, New York, 1999

[18] http://neutrons.ornl.gov