Radiography and Totdmography With Polarized Neutrons

8102019 Radiography and Totdmography With Polarized Neutrons

httpslidepdfcomreaderfullradiography-and-totdmography-with-polarized-neutrons 111

Current Perspectives

Radiography and tomography with polarized neutrons

Wolfgang Treimer abn

a University of Applied Sciences Beuth Hochschule fuumlr Technik Berlin Department Mathematics Physics amp Chemistry Luxemburgerstr 10

D-13353 Berlin Germanyb Helmholtz Zentrum fuumlr Materialien und Energie Department G ndash GTOMO Hahn-Meitner-Platz 1

D-14109 Berlin Germany

a r t i c l e i n f o

Article history

Received 23 June 2013Received in revised form2 September 2013Available online 10 October 2013

Keywords

Radiography and tomographyImagingPolarized neutronsMeissner effectFlux trappingSuperconductivityMagnetic domains

a b s t r a c t

Neutron imaging became important when besides providing impressive radiographic and tomographic

images of various objects physical quanti1047297cation of chemical morphological or other parameters couldbe derived from 2D or 3D images The spatial resolution of approximately 50 mm (and less) yields realspace images of the bulk of specimens with more than some cm3 in volume Thus the physics orchemistry of structures in a sample can be compared with scattering functions obtained eg fromneutron scattering The advantages of using neutrons become more pronounced when the neutron spincomes into play The interaction of neutrons with magnetism is unique due to their low attenuation bymatter and because their spin is sensitive to magnetic 1047297elds Magnetic 1047297elds domains and quantumeffects such as the Meissner effect and 1047298ux trapping can only be visualized and quanti1047297ed in the bulkof matter by imaging with polarized neutrons This additional experimental tool is gaining more andmore importance There is a large number of new 1047297elds that can be investigated by neutron imagingnot only in physics but also in geology archeology cultural heritage soil culture applied materialresearch magnetism etc One of the top applications of polarized neutron imaging is the large 1047297eldof superconductivity where the Meissner effect and 1047298ux pinning can be visualized and quanti1047297ed Herewe will give a short summary of the results achieved by radiography and tomography with polarizedneutrons

amp

2013 Elsevier BV All rights reserved

1 Introduction

The applications of neutron radiography and tomography(shortly imaging) cover a large number and quite differentresearch disciplines that are all tasked with investigating thecomposition of samples under special conditions such astemperature pressure magnetic or electric 1047297elds etc andpossibly under additional boundary conditions which in1047298u-ence the measuring process The information one obtains fromthese experiments can always be distinguished into two largeclasses real space data (eg images) and reciprocal space data

(scattering pattern scattering curves) Both can be trans-formed into images or graphs whereas both presume a (lotof) theory that predicts and describes the information origin-ally collected Each light microscope provides real data infor-mation ie images from the surface of a sample On the otherhand radiography computer tomography (CT) or nuclearmagnetic resonance yield images from the bulk of a body Butone realizes the difference between images delivered by a

microscope and the ones recorded with a CT instrument bothmethods deliver real space images but the d ata acquisition andtreatment are quite different A similar situation occurs forneutron radiography and tomography where a number of different imaging techniques have already been realized Theapplicability of neutron imaging depends on the sample and onthe speci1047297c technique which must be used to obtain thewanted information

The different neutron imaging techniques are extensively describedin many publications (eg [1561617182324343539ndash4250ndash5254ndash56] however some basic principles will be given here with

emphasis on those that use polarized neutronsThis rather new tool of neutron scattering has lead to a number of different techniques which use absorption- phase- and spin-basedinteractions of the neutron with the samples Combinations of theseinteractions are often wanted and one can distinguish neutron radio-graphy (R) and tomography (CT) into the following topics

White beam and monochromatic neutron radiography (R) andtomography (CT)

Absorption RCT (white beam) Time resolved RCT (white beam) Energy selective RCT (monochromatic neutrons) Bragg-edge RCT (monochromatic neutrons)

Contents lists available at ScienceDirect

journal homepage wwwelseviercomlocatejmmm

Journal of Magnetism and Magnetic Materials

0304-8853$- see front matter amp 2013 Elsevier BV All rights reserved

httpdxdoiorg101016jjmmm201309032

n Corresponding author at University of Applied Sciences Beuth Hochschule fuumlrTechnik Berlin Department Mathematics Physics amp Chemistry Luxemburgerstr10 D-13353 Berlin Germany Tel thorn 49 304 5042 428 fax thorn 49 304 5042 220

E-mail address treimerhelmholtz-berlinde

Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198

8102019 Radiography and Totdmography With Polarized Neutrons

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Phase-based based neutron radiography (T) and tomography(CT) are

Diffraction enhanced RCT Phase contrast RCT Phase grating RCT Interferometer RCT Refraction contrast RCT

Ultra-small angle scattering RCTSpin based radiography and tomography with polarized neu-

trons combines absorption (attenuation) and phase based inter-actions ie with the option of polarized neutrons enormouslyenlarges the 1047297eld of applications Additionally new techniques areemerging that reach higher resolution and 1047298exibility such as theLarmor Labeling neutron imaging which uses the Larmor preces-sion of the neutron spin in magnetic 1047297elds (see eg Ref [9])

Investigations of matter by thermal and cold neutron beamsare very popular especially if magnetism comes into play Neu-trons have some very speci1047297c properties that make them superiorto other probes such as X- or gamma rays electrons protonsmolecular beams light and laser if one wants to investigate notonly surface but also the bulk of a sample The interaction of

(thermal and cold) neutrons with matter is described by thenuclear interaction potential given by the special isotope-differentiating scattering lengths and there is no dependency onthe atomic number The low attenuation of neutrons by mostelements with some exceptions allows for investigating largesamples (in comparison to electrons or X-rays) The spin interac-tion with the magnetism of a sample together with their lowvelocities (for time of 1047298ight measurements) make thermal andcold neutrons a unique probe for condensed matter research Theinteraction of neutrons with magnetically ordered matter includesthe interaction with the nuclei (coherent scattering length bc) andwith the electronic magnetic moments of incompletely 1047297lled3d- 4d- 4f- and 5f-shells (see eg [31]) The interaction withmagnetic 1047297elds H is described by the neutron spin (and the

resulting magnetic moment m) and the Larmor frequency ωL frac14γ L H with γ L the gyromagnetic ratio of the neutron One can determine

the number of spin rotations in a magnetic 1047297eld modulo 2π andthus calculate ldquobackrdquo the amount of H if the path length of theneutrons in H is known (see below)

The investigation of samples with respect to their magneticproperties therefore bene1047297ts from polarized neutron beams Theknowledge of the initial and 1047297nal states of the neutrons ie thedetection of the polarization after the transmission of neutronsthrough a sample is a valuable information and determinescontrast of an image (Fig 1) In this 1047297eld last few years witnessedthe development of new polarizersanalyzers (eg the so-calledbenders based on supermirrors) which combine high transmis-sion with high polarization

2 Theoretical background

21 General remarks

Principally there are two different optical geometries forneutron imaging The 1047297rst method uses the pin hole techniqueie the neutron beam is collimated by an entrance aperture D anda long 1047298ight path L of approximately 5 m up to more than 10 m

The better the collimation ndash

here given as the LD ratio ndash

the betteris the spatial resolution at the 2D detector (see Fig 2) With such asetup one can use the whole white neutron spectrum (005ndash15nm) and thus an intense beam for strong-absorbing or time-resolved radiography or tomography This can be a disadvantagefor wavelength dependent radiographies and tomographies thatappear smeared and blurred at the 2D detector however veryoften the absorption contrast by some details in a sample is theimportant information which is to be visualized Using a highneutron 1047298ux (eg 107ndash108 neutronscm2) one must be aware of sample activation issues which may even ldquodestroyrdquo it

The pin hole technique is easily explained as shown in Fig 2The LD is the inverse beam divergence and determines the spatialdistance of two points at a given distance ld If the distance ld of two points in a sample to the detector is eg enlarged ie thedetector is placed at ldthorn x1 or ldthorn x2 then at a certain distance ldthe points in the image cannot be distinguished from each other asshown in Fig 3

The second ldquokindrdquo of neutron imaging uses a single crystal or adouble crystal monochromator the latter maintains the 1047298ight direc-tion of the neutron beam while selecting the wavelength [53] In thecase of a single or double monochromator crystal (often pyrolyticgraphite) a main wavelength and a certain wavelength band is Braggre1047298ected (thus selected) depending on the divergence of the incidentneutron beam and the mosaic spread of the monochromator The

selected wavelength band de1047297nes the momentum resolution ΔQ Q

(Q frac14 eth4π = λTHORN sin ethθ THORN) the LD ratio de1047297nes the spatial resolution andboth must be adapted and optimized to the imaging problem to besolved [5758]

In the case of a crystal monochromator the circumstances are alittle bit more complicated than for the pin hole techniquebecause the simple law of LD frac14ld does not hold any more [57]The crystal monochromator can be seen as consisting of manyldquopin holesrdquo (mosaic blocks) From each of these a beam is re1047298ectedwith the divergence of the incident beam Under certain boundaryconditions it is possible to optimize D and L with respect to thegiven mosaic spread and gain neutron intensity because L can bereduced and at the same time the spatial resolution can beimproved as shown by Fig 4 One sees that despite decreasingL P1 and P2 can be better resolved on the detector screen Thistechnique is very successfully applied to radiography and tomo-graphy especially with polarized neutrons [596162]

In the case of a double crystal monochromator two graphitecrystals are operated in the ldquoparallel arrangementrdquo [53] The 1047297rstcrystal selects a wavelength band out of the incident neutronbeam and the second one re1047298ects it back to the initial directionSo one can continuously change the wavelength between eg02 nm and 062 nm depending on the wavelength distribution of

Fig1 Layout of an instrument for imaging with polarized neutrons neutrons froma source are polarized and guided to the sample which eg depolarizes the beam

which is spin-analyzed and then 2D-detected

Fig 2 Pin hole geometry D frac14diameter of the aperture L frac14 distance of D from twopoints ldfrac14distance of the points from detector (screen) and d1 and d2 blurred

images of point 1 and point 2 respectively (see text)

W Treimer Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198 189

8102019 Radiography and Totdmography With Polarized Neutrons

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the incoming beam or geometric restrictions The distance of thesecond crystal to the sample determines as mentioned above thespatial resolution

The 2D image at the detector is smeared by several contribu-tions once there is the 1047297nite size of a detector pixel another onethe geometrical smearing due to the beam divergence andthe distance of the object from the detector (screen)1 furthermoreadditional smearing effects occur due to the 1047297nite thickness of thedetector (scintillator screen) This blurring and the resolution of animaging set-up are quanti1047297ed by the point spread function PSF

PSF eth x z THORN frac14 λ2=2π

frac121thorn λ2

feth x x0THORN2 thorneth z z 02geth3=2THORNeth1THORN

here λ is the slope of the tangent in x0 and z 0 and x0 and z 0 are thecoordinates of the center of the image point Often it is better (andeasier) to determine the edge spread function E ( x) which can be1047297tted to the measured data (background and amplitude must betuned to the data)

E eth xTHORN frac14 1

frac121 thorne λeth x x0 THORNeth2THORN

The determination of smearing effects involves the determinationof the spatial resolution of an imaging system which is usuallyperformed by measuring the modulation transfer function (MTF)

This can be done either by using absorption gratings with varyinglattice spacing and measure the contrast of the transmittedintensity as the function of the line pairs per unit length (eglpmm) or by measuring the edge spread function and 1047297t theimage of the edge to the function E ( x) The Fourier transform of thederivative of E ( x) FTE prime( x) yields the modulation transfer functionand thus at 10 FTE prime( x) the spatial resolution of the image [50ndash525455] In the case of polarized neutrons where an analysis of theneutron spin occurs two further sources of blurring must beconsidered one is the analyzer itself which causes blurringbecause its transmission can in1047298uence the geometry and anotheris due to small gradients of magnetic 1047297elds around the analyzer

which in1047298uence the Larmor precession of the analyzed spins andthus the detected image

22 Theoretical background for imaging with polarized neutrons

The use of polarized neutrons for imaging can be traced back to1996 when at the Berlin research reactor (BER II reactor) of theHelmholtz Zentrum Berlin Wannsee (former Hahn Meitner Insti-

tute) the 1047297rst ldquo

tomographyrdquo of the stray 1047297eld of a small permanentmagnet could be reconstructed However it took several years

before this experiment was published [50ndash52] The basic layouthowever remained the same and is very similar to that used inmodern instruments for radiography and tomography with polar-ized neutrons such as ldquoPONTO IIrdquo at the BER II (Fig 5)

When comparing the existing instruments several differencesexist in the layout Some use a white beam and polarize neutronswith 3He 1047297lters reaching polarizations up to 90 for a largewavelength band Other instruments are situated at spallationsources such as PSI (Switzerland) SNS (USA) JPARC (Japan) ISIS(GB) or at the future European Spallation Source (ESS) in Lund(Sweden) Some others are designed for special uses [7193957]

Radiography and tomography with polarized neutrons utilizeboth the low attenuation by most of the elements and the stronginteraction with magnetic 1047297elds Imaging with polarized neutronsis therefore suitable for the investigation of magnetic 1047297eld dis-tributions in the bulk of materials as was shown in last years

When using polarized neutrons ndash not only for imaging ndash onemust consider the physics of interaction of neutrons with mag-netic 1047297elds and the microscopic magnetic moments In neutronphysics the technique of spin rotation and spin analysis is wellestablished First of all one has to determine the initial spin statewith respect to a given direction in space This is achieved by usingpolarizing devices ie and for the polarization of a neutron beamseveral options are available For neutron radiography and tomo-graphy so-called benders 3He-1047297lters [2012] or periscope-typepolarizer guides are used [34357] Benders use the differentangles of total re1047298ection for spin up ad spin down neutrons at a

magnetized surface [15] The geometry of such devices can be keptvery compact ( 30 mm length) which is bene1047297cial for spinanalyzers because the distance of the detector from the sampleshould be kept as small as possible much less than 100 mm(ignoring stray 1047297elds) 3He polarizers use different cross-sectionsfor spin up and down neutrons when they pass a spin polarized3He gas Neutron periscope work similarly to the double crystalmonochromators but they consist of two parallel polarizingneutron supermirrors that preserve both the beam collimationand the spatial resolution [3435] The use of one of these methodsdepends on the problem to be solved

The spin analysis is done either with a bender or with polarized3He gas Here several (competing) conditions must be optimizedThe distance from the sample to the detector shall be as short as

possible (cf Figs 2 and 3) on the other hand the change of thespin orientation caused by the sample must be analyzed ie thespin analyzer must be placed between sample and detector and itmust not in1047298uence the magnetism of the sample under investiga-tion ie stray 1047297elds (of the spin analyzer) must be kept as low aspossible External magnetic 1047297elds applied to the samples must notoverlap with the stray 1047297eld of the spin analyzer because they maychange the direction of magnetic 1047297eld at the analyzer and thus itsdirection along which the neutron spin is analyzed

The description of the neutron spin in a magnetic 1047297eld can betreated rather classically A neutron with a energy of some meV behaves like a classical particle thus the motion of the spin can bedescribed like a magnetic moment in a magnetic 1047297eld Startingwith circling motions of charges that produce a magnetic moment

one can imagine an electron for which motion creates a magnetic

Fig 3 For a given LD the distance ld of the detector screen from P1 and P2in1047298uences the resolution to distinguish the two points At ld P1 and P2 can beseparated as well as at ldthorn x1 at ldthorn x2 no separation is possible

Fig 4 Using a crystal monochromator the spatial resolution depends on L and onthe mosaic spread of the crystal Note that decreasing L improves the visibility of P1 and P2 in contrast to the classical pin hole technique

1 Note that points at or close to the surface of the object lay closer or further far

from the screen

W Treimer Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198190

8102019 Radiography and Totdmography With Polarized Neutrons

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8102019 Radiography and Totdmography With Polarized Neutrons

httpslidepdfcomreaderfullradiography-and-totdmography-with-polarized-neutrons 511

compared with calculated Radon transforms of the model Thepath integrals are projections of the Radon Transform R f [60ndash62]

R f

frac14 ^ f eth pα THORN frac14

Z 1

1

Z 1

1

f eth x z THORNδ eth p x cos ethα THORN z sin ethα THORNTHORNd x d z

eth9THORN

where p is the scanning variable over the 2D function f and α theangle under which the sample is scanned For investigations of 1047298ux trapping the samples were scanned under 01 and 901 with

respect to the neutron 1047298ight direction yielding for α frac140 and forα frac14901 the Radon transform for the sample orientations 01

(parallel to the neutron beam) and 901 (perpendicular to theneutron beam) However the neutrons are polarized in front of the sample and spin analyzed after the sample The spin-analyzedneutron intensity measured behind a sample orientated paralleland perpendicular to the neutron 1047298ight direction is given by

I eth x z THORN frac14 I 0T expeth

Z path

Σ ethsTHORNdsTHORN

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflzfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl I att eth x z THORN

12

1thorn cos ϕeth x z THORN

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflzfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl I spin eth x z THORN

I eth y z THORN frac14 I 0T expeth

Z path

Σ ethsTHORNdsTHORN |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflzfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl I att eth y z THORN

12

1 thorn cos ϕeth y z THORN

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflzfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl I spineth y z THORN

eth10THORN

3 Imaging with polarized neutrons of superconductors

The 1047297rst image of a magnetic 1047297eld of a small magnet wasrealized already in 1997 at the BER II and later published [50ndash52]Neutron radiography and tomography with polarized neutronsbecame more prominent when instruments and detector systemsfor neutron imaging were improved and more than 10 years latermuch better radiographies with polarized neutrons were pub-

lished Remarkable progress was achieved using phase contrastmainly pushed forward by the development of grating interfe-rometers [282943ndash45] and its application to imaging magneticdomains [25] The potential applications of imaging with polarizedneutrons are very large therefore the focus here is put on the very1047297rst use of this method in superconductivity It is well known thatsuperconductors exhibit zero electrical resistance and the Meiss-ner effect (magnetic 1047297eld expulsion) However it is less knownthat magnetic 1047297elds can be trapped or pinned in superconductorsAll these effects occur in the superconducting state of a materialie when it is cooled below its individual critical temperature T cwhen the electrical resistance disappears and magnetic 1047297eldsare expelled Innumerable investigations about the expelled andtrapped magnetic 1047297eld have been published since Landau [21]

tried to explain the magnetic pattern on the surface of a

superconducting sample and the magnetism inside it An inter-esting physics is the co-existence of two phases superconductingand normal conducting especially in superconductor type I sam-ples because in contrast to type II superconductors these shouldnot exhibit any 1047298ux trapping or 1047298ux pinning Thus investigations of the bulk of samples that are in the superconducting state unveilssize shape and structure of these trapped or pinned magnetic1047297elds and give answers on how this can happen

31 Imaging magnetic 1047297elds of superconducting samples

The main purpose of experiments with polarized neutrons wasto visualize expelled and trapped magnetic 1047297elds of samples in thesuperconducting state The samples were lead (superconductortype I) and niobium (superconductor type II) The suppressedMeissner effect and 1047298ux trapping are better known from super-conductor type II however as mentioned above they were alsoobserved in type I superconductors such as in lead To explain and

underline the precision of the experimental results the startingpoint was the image of the magnetic 1047297eld created by a Cu coilAn electric current in the coil creates an homogeneous magnetic1047297eld B as is known from fundamental electrodynamics Thestrength of B is given by the current I [Amperes] (varied from4 A up to 6 A) the length of the coil (90 mm) and the number of windings (205) With Eq (7) the number of the Larmor preces-sions can be calculated for each path through the coil which yieldsan image as shown in Fig 6

The spin analyzer behind the sample is transparent for parallelspins (spin up) and opaque for anti-parallel spins ie for a spin

rotation of π (spin down) The spin rotation angle ϕ (Eq (7)) isproportional to Bs and ldquosrdquo is the path length through the sampleas shown in Fig 6 Due to different ldquosrdquo (and given B) the spin

rotation angle ϕ changes which is analyzed with the spin analyzerin front of the detector

The images of Fig 6 hold for a magnetic 1047297eld which ishomogeneously distributed in the volume under investigation(coil) A similar behavior was expected in the case of the partiallysuppressed Meissner effect ie occurance of 1047298ux trapping in theintermediate phase a state where normal and superconductingvolumes occupy simultaneously different parts of a cylindricalsample

The samples used for the investigations of 1047298ux trapping insuperconductors were crystalline and polycrystalline lead bothhaving a high purity (999999 wt Pb) and the same dimensionsThe crystal samples were o1104 orientated the mosaic spreadwas 171 the diameter 12 mm and the length 30 mm The critical

magnetic 1047297eld Bc depends on the sample temperature according

Fig 6 (a) Polarized neutrons and a homogeneous magnetic 1047297eld create an image of non-equidistant fringe pattern and (b) theory and experimental result (neutron images)of the increasing B-1047297eld in the copper coil

W Treimer Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198192

8102019 Radiography and Totdmography With Polarized Neutrons

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to [8]

BcethT THORN frac14 Bc eth0 K THORN 1 T

T c

2

eth1N THORN eth11THORN

For Pb Bc (0)frac1480 mT N is the so-called demagnetization factorwhich depends on the geometry of the sample and is given by

N frac14 1 1

eth1thornetha=hTHORNqTHORN eth12THORN

where a (frac146 mm) and h (frac1415 mm) are the radius and the half length of the cylinder respectively and q is given by as

q frac14 43π

thorn 23π

tan frac12127 h=a ln eth1thorn a=hTHORN eth13THORN

Thus the demagnetization factor N of the Pb samples was equal to08837 The external 1047297eld Bext was 64 mT and at T frac1455 K it waswell below the critical Bcfrac1425 mT (see Fig 7)

Because the Pb samples had the same cylindrical shape as thecopper coil one would expect in the case of a partial Meissnereffect an homogeneous 1047298ux trappingpinning The Pb sampleshowever showed very different images For the measurementswith polarized neurons they were kept in a special Al holder in a

cryostat and cooled stepwise from room temperature down to 8 KThe magnetic 1047297eld (from Helmholtz coils) applied to the samplewas 64 mT orientated as shown in Fig 8 When the sample wasfurther cooled down to 55 K radiographs (without and withoutthe external magnetic 1047297eld) were recorded 1047297rst at T frac148 K and thenat T frac1455 K (with and without the external magnetic 1047297eld) Thecritical temperature T c of lead is 719 K

The axis of the lead sample was adjusted parallel to the neutron1047298ight direction and at the presence of the external magnetic 1047297eldimages were recorded at T frac148 K and 55 K At T frac1455 K a character-istic fringe pattern appears which is attributed to the expulsion of the magnetic 1047297eld (Fig 9) The asymmetry of the pattern can beexplained (and calculated) by a small disorientation of the samplewith respect to the neutron propagation direction When increasingthe temperature to T frac148 K (ie above T

c) the fringe pattern dis-

appears Fig 9 also shows that a fraction of the applied 1047297eld may betrapped in the sample ie 1047298ux trapping is possible At a second stepthe sample was again cooled down to T frac1455 K and in the presenceof the external magnetic 1047297eld was rotated by 901 perpendicular tothe neutron propagation direction In this con1047297guration the 1047297eldwas switched off and images were recorded as shown in Fig 10

If the rod axis is horizontally perpendicular to the incidentneutron beam direction the path length through the cylinderdepends only on the height ( z -value) of the beam and is at most 2r

if it passes through the middle of the cylinder (cf Fig 6) Thus theimage of the projection of the magnetic 1047297eld was assumed to besimilar to the image of the magnetic 1047297eld of the coil Fig 10 showsthe 2D-spin-analyzed images at T frac1455 K 68 K and 8 K One sees anearly perfect horizontal nearly equidistant fringe pattern atT frac1455 K which changes when the temperature is raised to 68 KAt T frac148 K ie above T cfrac14719 K the fringe pattern disappears

In order to explain the observed images the trapped 1047297eld mustful1047297ll several boundary conditions The Radon transforms mustyield a fringe pattern as the one shown in Figs 9 and 10 Inaddition the trapped 1047297eld must be less than the applied Bext andthe sum of expelled and trapped 1047297elds must be less or equal theapplied magnetic 1047297eld (energy conservation) At the inside at thesurface of the sample B must become small because no fringepatterns were observed On the other hand outside of the samplethe expelled 1047297eld must follow an exponential law

The solution to this problem was a Gaussian shaped 1047297eldwhere only two parameters were 1047297tted to the experiment theFWHM of the function and the amount of the trapped 1047297eld

[6162] Fig 11 shows a series of calculated radiographs varying

Fig 7 Temperature dependence of the critical magnetic 1047297eld for the used Pb

sample geometry 01

At T frac1455 K the applied external magnetic 1047297

eld wasBextfrac1464 mT which is well below Bc frac1425 mT (blue curve) (For interpretation of the references to color in this 1047297gure legend the reader is referred to the webversion of this article)

Fig 8 External magnetic 1047297eld orientation with respect to the sample and neutron

1047298ight direction

Fig 9 Pb polycrystalline sample polarized neutron images of a partial Meissner effect rod axis 01 with respect to the neutron beam direction (a) T frac1455 K and (b) overlap

calculated image and experiments at T frac1474 K the fringes disappear (see text) (courtesy PRB)

W Treimer Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198 193

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the amount of trapped 1047297eld This series did not result in the best1047297t with respect to the FWHM which also had to be adapted

The Gaussian shaped 1047297eld is constant parallel to the rod axisbut squeezed around the rod axis the FWHM was estimated to be145(5) mm The expelled 1047297eld was also 1047297tted by a Gaussianfunction which has its maximum at the rod axis but is zero insidethe sample The 1047297t was compared with the experimental images asshown in Fig 11 a model of the calculated trapped 1047297eld is shown

in Fig 12

Besides the 1047297rst experiments with crystalline pure and mediumpure Pb samples one should mention recent experiments of compo-site samples ie samples which contain other elements and havedifferent critical temperatures The question was how do expelledand trapped magnetic 1047297elds behave if in the superconducting phaseof the main body of a sample (Pb) parts of lead were replaced bynon-superconducting parts (eg Al special steel air) For this reasona lead sample was modi1047297ed by inserting aluminum and iron screws

and creating a hole which remain normally conducting T frac14719 K

Fig 10 Pb polycrystalline sample rod axis 901 with respect to the neutron 1047298 ight direction (a) T frac1455 K (b) T frac1468 K and (c) T frac14 8 K No further images processing wasapplied to see these 1047297rst original images of a trapped magnetic 1047297eld which is not homogeneously distributed in the homogeneous sample (permitted reuse by courtsey of Phys Rev B)

Fig 11 (a) Variation of the trapped 1047297eld B FWHM is kept constant the 1047297eld was adapted to the geometry of the lead cylinder note the sensitivity of B on the fringe pattern

tuning further the FWHM of the Gaussian function the calculation agree perfectly with the pattern for both the suppressed Meissner effect ( Fig 9 and 1047298

ux trapping((Fig 10b) [61] permitted reuse by courtesy of Phys Rev B)

Fig12 3D model of the trapped magnetic 1047297eld The strength of B increases towards the rod axis and decreases to zero at the inner side of the sample surface [61] (permittedreuse by courtesy of Phys Rev B)

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where lead is superconducting The interesting result was that theldquosqueezingrdquo effect again could be observed but not in all parts of thelead sample Calculations (assuming non-symmetric 1047297eld sources)could partially prove this effect [6364] however further detailedmeasurements are necessary (Fig 13)

A similar behavior of anisotropic 1047298ux trapping but a completelysuppressed Meissner effect was observed in disc shaped niobiumsamples Niobium is a type II superconductor with T cfrac14925 K As apart of detailed investigations Nb samples were tested with polar-ized neutrons [2] Radiographies with polarized neutrons and spinanalyzed images should reveal the effect of surface polishing on thesuppressed Meissner effect as well as on the amount of 1047298ux trappingFigs 14 and 15 show the (surprising) results The procedure of themeasurement was the same as for the lead samples ie the sampleswere cooled by a cryostat down to T frac1411 K (ie above T cfrac14925 K) andthen images were recorded with and without an external magnetic1047297eld at the temperatures as shown in Figs 14 and 15

Fig 14 (and other images not presented here) shows that acomplete suppression of the Meissner effect could be imaged which

was con1047297rmed by other magnetic 1047297eld measurements It could also be

con1047297rmed that surface treatment has a great in1047298uence on themagnetic 1047297eld distribution as shown in Fig 15 Comparing the imagesfor T frac1455 K and T frac149 K in Fig 14 (untreated) with the same ones inFig 15 (treated) one realizes once the visualized position resolveddifference of 1047298ux trapping and then more homogeneous distribution

of the trapped 1047297eld seen as a decrease of the fringe pattern and fringecontrast in the radiographs of Fig 15

For this 1047297eld distribution ndash up to nowndash no unique description of the expelled and trapped magnetic 1047297eld could be found as for the leadsample One problem stems from the absorption ie one could notimage the bulk of the samples when their surfaces were parallel to theneutron 1047298ight direction (cf Fig14b 901 position) Additional problemsarise from the geometry and size of the samples This work will becontinued with other geometries and magnetic 1047297elds Internal stressand strain may also an impact that can be unveiled with imaging

32 Imaging magnetic domains

As a second 1047297eld of applications the investigations of

magnetic domains shall be given Magnetic domains are the

Fig 13 Observation of partial Meissner effect and 1047298ux pinning in a composed Pb sample (left sketch) [62] (permitted reuse by courtesy of Appl Phys Lett)

Fig 14 (a) Magnetic 1047298ux trapping in a Nb sample T cfrac14925 K The sample was not ldquotreatedrdquo (chemically polished) One recognizes a temperature dependence of 1047298uxtrapping (T frac1455 T frac149 K) that vanishes at T frac1411 K4T cfrac14925 K Only less than a quarter of the disc is shown (diameter 45 mm) (b) Nb sample with holder for the cryostat

Fig 15 Images obtained from the same sample as in Fig 14 but the surface of the sample was this time chemical polished This treatment removes (mosaic) surfacestructures and apparently in1047298uences the trapped 1047298ux For T 4T c the patterns disappear

W Treimer Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198 195

8102019 Radiography and Totdmography With Polarized Neutrons

httpslidepdfcomreaderfullradiography-and-totdmography-with-polarized-neutrons 911

building blocks of macroscopic magnetism and they play afundamental role in the theory of micro-magnetism Thereforendash besides industrial and economical demands for low energyloss magnetic devices ndash the study of domains by means of neutrons has already a long tradition [3] With X-rays and bymeans of ldquoLang ndash topographyrdquo high resolution images of magnetic domain structures in thin samples (spatialresolution 10 mm) could be already realized [30] The 1047297rst

neutron topographies of magnetic domains were published bySchlenker and Baruchel [3637] Neutrons would be muchbetter suited but due to the much lower 1047298uxes which wereavailable at neutron sources and also due to the lack of suitableand optimized setups different techniques were used toexplore details of magnetic domains [34] The 1047297rst work with

neutrons used refraction of (unpolarized) neutrons by Blochwalls ie by the boundaries between two different orientatedmagnetizations Pioneering work was done by Schaumlrpf [3233]who applied dynamical diffraction to domain wall systems andgave the formulae for the scattered intensities These 1047297rstexperiments (performed at the low-1047298ux research reactor of the PTB Braunschweig) were continued with the high angularresolving double crystal setups at the BER II reactor (Berlin)

where the (zig-zag) structure and thickness of Bloch walls ino1104 Fendash4 at Si single crystals could be determineduniquely and with high accuracy [38] With the use of a doublecrystal diffractometer other details such as mosaic block dis-tributions and Bloch wall junctions [46ndash48] Bloch wall thick-ness [1314] and the shape of Bloch walls in the bulk of Nisamples could be determined ([142627]) and thus contributeto the understanding of the interplay of external magnetic1047297elds and forces on the domain structures in the samples

All studies of magnetic domains required either thin crystals (fortopography) or well orientated samples for spin-dependent refrac-tion of neutrons by the Bloch walls Very recently another attemptwas done using the special technique of a grating interferometryThis method was 1047297rst introduced to X-rays [2829] later on appliedto neutrons [101143ndash45] and used for three dimensional imagingof magnetic domains in a Fe 128-at Si single crystals [25]

The principle of a grating interferometer is based on theTalbot effect Three gratings GS GPh and GA (see Fig 16) arematched to each other at distances L1 and l1 and have periodi-cities pS pPh and pA A source grating GS provides a (partially)coherent wave front (with periodicity pS) illuminating the phasegrating GPh which is placed downstream at L1 ( 5 m) Theperiodicities pPh and pA of the gratings GPh (phase) and GA(absorption) are related to each other as pAfrac14 pPH2 Using the(Talbot) condition pSl1frac14 pAL1 GA is at the 1047297rst fractional Talbotdistance l1 The 1047297rst fractional Talbot distance l1 is given by

eth pA2=2 λTHORN Thus the wavelength λ determines the periodicities of

pPh and pA and of course L1 The phase grating modulates the

beam causing a phase shift of λ2 between neighboring beams inthe 1047297rst fractional Talbot distance The absorption (analyzing)grating GA scans the pattern which is modulated by the sampleThe imaging signals are absorption refraction and ultra-smallangle scattering measured as a damping a phase shift andsmearing of the oscillating curve when GA or GS is movedperpendicular to the beam

Therefore a tomography consisting of many radiographies of asample obtained using phase grating interferometry involves a quitecomplicated scanning and reconstruction The idea can be explainedby experiments with a special double crystal diffractometer whereabsorption refraction and small angle scattering could be determinedsimultaneously and so 2D and 3D reconstruction of samples from

Fig 16 Design of a grating interferometer ([25] permitted reuse by courtesy of Nat Commun)

Fig 17 Measured transmitted intensity with the grating interferometer ([25]permitted reuse by courtesy of Nat Commun)

Fig 18 TalbotndashLau neutron radiographies of magnetic domains (a) Sketch of the FeSi sample (b) ndash(f) Radiographic projection images at different external magnetic 1047297elds

(c)ndash(f) Equal 1047297eld strength in (c) and (h) (white bar frac143 mm) ([25] permitted reuse by courtesy of Nat Commun)

W Treimer Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198196

8102019 Radiography and Totdmography With Polarized Neutrons

httpslidepdfcomreaderfullradiography-and-totdmography-with-polarized-neutrons 1011

projections could be achieved [494041] In this case the scanningprocedure is more complicated because for each projection the phaseshad to be scanned over one period (Fig 17)

The achieved results are shown in Figs 18 and 19 Differentslices could be extracted and magnetic domains identi1047297ed

With these measurements it could be demonstrated that ran-domly orientated magnetic domains could be detected even in the

bulk of massive samples It must be mentioned that the limitedspatial resolution allowed for imaging of rather large domainssmaller ones could not be detected but in comparison withstandard classical methods phase grating interferometry is a goodstep forward in this 1047297eld This technique is very young and there-fore ndash as happened in other disciplines ndash many new experimentswill bring new results and deeper understanding of matter

4 Summary

Imaging with polarized neutrons is widely used [23] and the 1047297eldof applications is increasing because of the large potential of thismethod Up to now imaging with polarized neutrons is still some-

thing exotic it requires knowledge about radiography and

tomography about neutron scattering in general and about polarizedneutron scattering in detail Furthermore it requires good polariza-tion and spin-analyzing components (P 495) to achieve a goodspin-upndashspin-down ratio (spin contrast) a well collimated beam toavoid smearing effects due to different depolarization effects nomagnetic stray 1047297elds from other devices (sample magnet etc) Thebeam collimator polarizer and spin-analyzer also reduce the inten-

sity of the neutron beam So for certain experiments sometimes theuse of 3He polarizer is a big advantage because it allows for using thefull neutron spectrum For a detailed analysis of the bulk magnetismof a sample monochromatic neutrons yield ldquosimplerrdquo results becausethey allow a de1047297ned analysis of the transmitted neutron spin Up tonow there are a lot of new ideas what can be realized with polarizedneutron imaging and in the future there will certainly be a polarizedneutron imaging instrument at the European Spallation Source (ESS)in Lund Sweden where most of the fascinating new ideas will berealized and lead to exciting new physics and results

References

[1] S Anderson RL McGreevy HZ Bilheux (Eds) Neutron Imaging and Applica-

tions Springer Verlag New York 2009

Fig19 Reconstruction from a TalbotndashLau neutron tomography of a FeSi wedge (a) and (b) Sketches of the FeSi wedge ((a) front view and (b) side view) (c) Horizontal slicesat different wedge thicknesses as indicated in (b) (d)ndash(g) Cross-sections through the TalbotndashLau neutron tomogram along different planes (dotted by (d)ndash(g) in (a) and (b))that show the high complexity of the 3D shape of magnetic domains (h) Horizontal slice (as in (c)) (i) Enlargement of the area marked in red in (h) ( [25] permitted reuse bycourtesy of Nat Commun) (For interpretation of the references to color in this 1047297gure legend the reader is referred to the web version of this article)

W Treimer Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198 197

8102019 Radiography and Totdmography With Polarized Neutrons

httpslidepdfcomreaderfullradiography-and-totdmography-with-polarized-neutrons 1111

[2] S Aull O Ebrahimi N Karakas J Knobloch O Kugeler W Treimer J PhysConf Ser 340 (2012) 012001

[3] G Badurek M Hochhold H Leeb R Buchelt F Korinek A proposal tovisualize magnetic domains within bulk materials Physica B 241ndash243 (1998)1207ndash1209

[4] G Badurek Buchelt H Leeb R Szeywerth Neutron interferometric recon-struction of magnetic domains Physica B 241ndash243 (2003) 1207ndash1209

[5] J Banhart (Ed) Advanced Tomographic Methods in Material Research andEngineering Oxford Univ Press New York 2008

[6] J Banhart A Borbeacutely K Dzieciol F Garcia-Moreno I Manke N KardjilovAR Kaysser-Pyzalla M Strobl W Treimer Int J Mater Res 101 (2010) 9

[7] P Boumlni W Muumlnzer A Ostermann Phys B Condens Matter 404 (17) (2009)2620ndash2623

[8] EH Brandt Physica C 332 (1ndash4) (2000) 99ndash107[9] DNIWP ESS Dutch Neutron Instrumentation Work Packages for the Design

Update Phase of the ESS Design of Instruments for Polarized Neutrons UsingLarmor Labeling Techniques September 2011

[10] C Gruumlnzweig et al Neutron decoherence imaging for visualizing bulkmagnetic domain structures Phys Rev Lett 101 (2008) 025504

[11] C Gruumlnzweig C David O Bunk M Dierolf G Frei G Kuumlhne R SchaumlferS Pofahl HMR Roslashnnow F Pfeiffer Bulk magnetic domain structuresvisualized by neutron dark 1047297eld imaging Appl Phys Lett (2008)112505-1

[12] W Heil J Dreyer D Hofmann H Humblot F Tasset 3He neutron spin 1047297 lterPhysica B 267ndash268 (1999) 328ndash335

[13] A Houmlfer Entwicklung eines Vielfach-Doppelkristalldiffraktometers fuer Neu-tronenkleinwinkelstreuung und Untersuchungen der Domaumlnenstrukturverschieden orientierter Nickeleinkristallen (Dissertation) TU Berlin 1997

[14] A Houmlfer W Treimer Bloch wall thickness of a distorted o1004 1091-Blochwall in a nickel single crystal Physica B 241ndash243 (1998) 1231ndash1233

[15] T Krist SJ Kennedy TJ Hick F Mezei Physica B 241ndash

243 (1998) 82ndash

85[16] N Kardjilov P Boni a Hilger M Strobl W Treimer Nucl Instrum Methods A542 (1ndash3) (2005) 248ndash252

[17] N Kardjilov I Manke M Strobl A Hilger W Treimer M Meissner T Krist J Banhart Nat Phys 4 (2008) 399ndash403

[18] N Kardjilov E Lehmann E Steichele P Vontobel Nucl Instrum Methods A(2004) 527

[19] Y Kiyanagi T Kamiyama H Sato T Shinohara T Kai K Aizawa M Arai et alNucl Instrum Methods A 651 (1) (2011) 16ndash20 httpdxdoiorg101016jnima201102075

[20] J Kulda A Wildes A Martin-Martin W Miiller W Heil Tasset HF HumblotPhysica B 241ndash243 (1998) 136ndash138

[21] L Landau Nature 141 (1938) 688[22] A Lange MP Hentschel AKupsch Computed tomography reconstructions by

DIRECTT-2D model calculations compared to 1047297ltered backprojection MPMater Test 50 (2008) 272ndash277

[23] EH Lehmann PRAMANA ndash J Phys 71 (4) (2008) 653ndash661[24] I Manke N Kardjilov A Hilger M Strobl M Dawson J Banhart Nucl

Instrum Methods A 605 (1ndash2) (2009)

[25] I Manke N Kardjilov R Schaumlfer A Hilger M Strobl M DawsonC Gruumlnzweig et al Nat Commun 1 (2010) 125

[26] J Peters W Treimer On Bloch walls in a nickel single crystal Phys Rev B 64(2001) 214415

[27] J Peters W Treimer On the in1047298uence of external forces on the Bloch wallthickness in a nickel single crystal J Magn Magn Mater 241 (2 ndash3) (2002)240ndash248

[28] F Pfeiffer T Weitkamp O Bunk C David Phase retrieval and differentialphase-contrast imaging with low-brilliance X-ray sources Nat Phys 2 (2006)258ndash261

[29] F Pfeiffer C Gruumlnzweig O Bunk G Frei E Lehmann C David Phys Rev Lett96 (21) (2006) 1ndash4

[30] M Polcarova AR Lang X-ray topographic studies of magnetic domainscon1047297gurations and movements Appl Phys Lett 1 (1) (1962) 13 ndash15

[31] W Prandl Topics in current physics in H Dachs (Ed) Neutron Diffraction1987 p 112L Passel RI Schermer Phys Rev 150 (1) (1966) 147ndash151

[32] O Schaumlrpf Theory of magnetic neutron small angle scattering using thedynamical diffraction theory instead of the Born approximation I and II J Appl Cryst allogr 11 (662ndash630) (1978) 631ndash636

[33] O Schaumlrpf R Seifert H Strothmann W Treimer G Goeltz Determination of the Bloch wall thickness in Fendash4 at Si single crystals by Neutron small anglescattering Colloid Polym Sci 259 (1981) 666

[34] M Schulz A Neubauer S Masalovich M Muumlhlbauer E Calzada B SchillingerC P1047298eiderer P Boeni J Phys Conf Ser 211 (2010) 012025

[35] M Schulz A Neubauer M Muumlhlbauer E Calzada B Schillinger C P1047298eidererP Boumlni J Phys Conf Ser 200 (2010) 112009

[36] M Schlenker J Baruchel Neutron techniques for the observation of ferro andantiferromagnetic domains J Appl Phys 49 (1978) 3

[37] M Schlenker J Baruchel Observation of magnetic domains by neutrondiffraction IEEE Trans Magn MAG 17 (6) (1981) 1996ndash2001

[38] R Seifert W Treimer O Schaumlrpf H Strothmann Multiple neutron refractionby a single or several different Bloch walls Acta Crystallogr A 37 (1981) 291

[39] T Shinohara et al Nucl Instrum Methods A 651 (1) (2011) 121ndash125[40] M Strobl W Treimer A Hilger First realisation of a three-dimensional

refraction contrast computerized neutron tomography Nucl Instrum Meth-ods A 222 (3ndash4) (2004) 653ndash658

[41] M Strobl W Treimer A Hilger Small angle scattering signals for (neutron)computerized tomography Appl Phys Lett 85 (3) (2004) 488

[42] M Strobl W Treimer P Walter S Keil I Manke Magnetic 1047297eld induceddifferential neutron phase contrast imaging Appl Phys Lett 91 (25) (2007)254104

[43] M Strobl W Treimer N Kardjilov A Hilger S Zabler On neutron phasecontrast imaging Nucl Instrum Methods A 266 (1) (2008) 181ndash186

[44] M Strobl W Treimer N Kardjilov a Hilger S Zabler On neutron phasecontrast imaging Nucl Instrum Methods A 266 (1) (2008) 181ndash186 httpdxdoiorg101016jnimb200710016

[45] M Strobl C Gruumlnzweig A Hilger I Manke N Kardjilov C David F PfeifferNeutron dark-1047297eld tomography Phys Rev Lett 101 (12) (2008) 1ndash4

[46] W Treimer Neutron topography of imperfect FeSi and Ni crystalsZ Kristallogr 167 (1984) 166

[47] W Treimer R Seifert Study of the Bloch wall junctions in nickel singlecrystals by neutron scattering Physica B 136 (1986) 455ndash457

[48] W Treimer A Houmlfer H Strothmann Use of a multi-double-crystal diffract-ometer to investigate nickel domains J Appl Crystallogr 30 (1997) 849ndash853

[49] W Treimer M Strobl a Hilger C Seifert U Feye-Treimer Refraction asimaging signal for computerized neutron tomography Appl Phys Lett 83 (2)(2003) 398

[50] W Treimer M Strobl A Hilger HJ Peschke IEEE 52 (1) (2005)386ndash388[51] W Treimer in B Kramer (Ed) Advances in Solid State Physics vol 45

Springer Verlag Berlin Heidelberg 2005 pp 407ndash420[52] W Treimer A Hilger N Kardjilov M Strobl Nucl Instrum Methods A

542 (1ndash3) (2005) 367ndash375[53] W Treimer M Strobl N Kardjilov A Hilger I Manke Appl Phys Lett (2006)

203504-1[54] W Treimer Imaging in W Reimers AR Pyzalla A Schreyer H Clemens

(Eds) Neutrons and Synchrotron in Engineering Materials Science Wiley-VCH Verlag Weinheim Germany 2008 pp 257ndash286 (Chapter 15)

[55] W Treimer in J Banhart (Ed) Advanced Tomographic Methods in MaterialResearch and Engineering Oxford University Press New York 2008

[56] W Treimer in IA Anderson RL McGreevy HZ Bilheux (Eds) NeutronImaging and Applications Springer Verlag 2009 pp 81ndash108 (Chapter 6)

[57] W Treimer SO Seidel O Ebrahimi Neutron tomography using a crystalmonochromator Nucl Instrum Methods A 621 (1ndash3) (2010) 502ndash505

[58] W Treimer U Feye-Treimer On coherence in neutron imaging Nucl InstrumMethods A 651 (1) (2011) 117ndash120

[59] W Treimer O Ebrahimi N Karakas SO Seidel Nucl Instrum Methods A 651(1) (2011) 53ndash56

[60] W Treimer U Feye-Treimer Calculation of scattering patterns from phaseshifting objects using the Radon Transform J Appl Crystallogr 44 (6) (2011)1157ndash1163

[61] W Treimer O Ebrahimi N Karakas R Prozorov Polarized neutron imagingand 3D calculation of magnetic 1047298ux trapping in bulk of superconductors PhysRev B 85 (18) (2012) 1ndash9

[62] W Treimer O Ebrahimi N Karakas Appl Phys Lett 101 (2012) 162603-1ndash162603-4

[63] W Treimer O Ebrahimi N Karakas Imaging quantum mechanical effects insuperconductors with polarized neutrons Phys Procedia 42 (2013) 31ndash38

[64] W Treimer O Ebrahimi N Karakas Imaging of quantum mechanical effectsin superconductors by means of polarized neutron radiography Phys Proce-dia 43 (2013) 243ndash253

W Treimer Journal of Magnetism and Magnetic Materials 350 (2014) 188ndash198198