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Physica B 350 (2004) 113–119

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doi:10.1016

Atomic resolution neutron holography(principles and realization)

L!aszl !o Csera,*, B. Farag !ob, G. Krexnerc, I. Sharkovd, Gy. T .or .oka

aResearch Institute of Solid State Physics and Optics, Konkoly Thege str. 29-33, H-1121 Budapest, Hungaryb Institut Laue-Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble Cedex 9, France

c Institute of Experimental Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, AustriadSt. Petersburg State University, Institute of Physics, Chair of Optics and Spectroscopy, Ulyanovskaja Str.1, 198904

St. Petersburg, Russia

Abstract

Atomic resolution neutron holography constitutes a novel technique to obtain structural information. It is based on

the recording of the interference of neutron waves coherently scattered by atoms located on a crystal lattice with a

suitable reference wave. This process can be accomplished by two complementary schemes. In the frame of the first

approach, a point-like source of spherical neutron waves is required inside a single crystal. Such a source can be realized

owing to the extremely large value of the incoherent neutron scattering cross section of the proton. Hydrogen atoms

imbedded in a sample which is placed in a monochromatic beam of slow neutrons will emit spherical neutron waves as a

result of an incoherent scattering process. The interference between the undisturbed wave field and that part of the wave

which is scattered by neighboring atoms can be recorded, thereby producing a hologram. The second approach utilizes

a source of plane neutron waves outside the sample. The interference between the undisturbed and the scattered parts of

the neutron wave field is recorded by point-like detectors, i.e. strongly neutron-absorbing nuclei, which are placed inside

the crystal lattice that is to be imaged. The experimental feasibility of these two techniques is demonstrated.

r 2004 Elsevier B.V. All rights reserved.

PACS: 61.12.�q

Keywords: Neutron holography; Atomic resolution

1. Introduction

The concept of storing the appearance of athree-dimensional object in a two-dimensionalpicture and reconstructing it in such a way that

onding author. Tel.: +36-1-392-2222/1526;

-392-2501.

ddress: cser@sunserv.kfki.hu (L. Cser).

- see front matter r 2004 Elsevier B.V. All rights reserve

/j.physb.2004.04.007

one can perceive again the original object wasinvented by D!enes G!abor [1]. His original aim wasto develop a lensless microscope with atomicresolution by using the so-called holographicprinciple. The name holography is derived fromtwo Greek words: !Oloj (whole) and grdjein(write). A hologram is created when radiationemitted from a coherent source may take morethan one single path towards the detector. One

d.

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L. Cser et al. / Physica B 350 (2004) 113–119114

path is provided by the direct propagation ofradiation from the source to the detector (refer-ence beam), while additional paths arise when theemitted radiation scatters elastically from nearbyatoms (object beams) before the detector isreached. The pattern generated by the interferenceof the reference and the object waves can berecorded in a suitable way and is called ahologram. G!abor proposed the use of a pointsource of monochromatic electrons; however, dueto technical difficulties this could not be put intopractice for a long time. Only much later Sz .okesuggested [2] that photoelectrons could be used forrealizing electron holography and subsequentlyTegze and Faigel, in their theoretical work [3],analyzed the possibility of atomic-level holographyusing X- or g-rays.In the present review, we would like to

demonstrate that atomic resolution holographycan also be performed by using slow neutrons andthat both of the above-sketched approaches can beapplied.

2. Basic principles

Let us assume a point-like source of monochro-matic spherical waves of slow neutrons located atthe origin. The wave emitted by it will be scatteredby nuclei j; located at rj : Both the unscattered andthe scattered waves will be described by a wavevector k and detected at a distance R: The intensityof the neutrons is given by the expression

IðkÞ ¼ ðI0=R2Þ 1þ 2ReðX

ajÞ þX

ja2j jh i

; ð1Þ

where aj ¼ ð1=rjÞbj expð½iðrjk � rj � kÞÞ designatesthe wave amplitude scattered by a single nucleus,bj is the neutron scattering length (which fornuclear scattering of slow neutrons has no angulardependence), and rj is the position vector of thescatterer with respect to the source. The first termin the angle bracket represents the reference beamand the third one the object beam, while thesecond is composed of both the reference andobject amplitudes. It is this latter term whichcontains the holographic information.

As discussed earlier [3,4], the following condi-tions should be met in order to permit thesuccessful recording of a hologram:The sample has to be a single crystal in which

the source atoms are found at crystallographicallyequivalent positions.The monochromaticity of the radiation used

must obey the condition Dl=l5l=r; and l shouldbe smaller than the spatial resolution aimed at.The ratio l=a should fulfill the relation l=ao1

with a being the typical lattice parameter.The holographic term in expression (1) is on the

order of 10�3 as compared to the total number ofcounts registered by the detector from whichfollows that, to achieve satisfactory statistics, atleast (4–6) 106 counts have to be collected inresolution element of solid angle.In order to avoid distortions due to intensity

variations brought about by the geometry of thesample, this should preferably have the shape of asphere.Contributions arising from Bragg reflections

and inelastic scattering should be eliminated orminimized.Finally, in order to satisfy the above conditions

we need a point-like source or a point-like detectorof slow neutrons with a wavelength of lB1 (A.

2.1. The point-like inside-source concept

This method requires a point-like inner sourceof monochromatic spherical neutron waves. Thiscan be most effectively realized by a nucleuspossessing an extremely high incoherent scatteringcross section [4] since incoherent scattering redis-tributes the incident neutron waves isotropicallyinto a solid angle of 4p: The most favorablesituation is found in the case of incoherentneutron–proton scattering, the cross section ofwhich is close to B80 barns thereby exceeding thecross sections of many other nuclei by about twoorders of magnitude. The principle of the techni-que is illustrated in Fig. 1.Multiple elastic incoherent scattering from

protons need not be considered since subsequentto incoherent scattering, the neutron always formsa spherical wave completely independent of anyearlier scattering processes.

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Fig. 1. A monochromatic incident neutron beam illuminates the sample. Neutrons incoherently scattered by hydrogen nuclei form

spherical waves. The detector which is placed at a larger distance can be reached by these waves either directly or after having

undergone a coherent scattering process by neighboring nuclei. By moving the detector along the surface of a sphere around the sample,

the interference pattern of these waves can be recorded.

L. Cser et al. / Physica B 350 (2004) 113–119 115

In the case of an internal source, specialattention should be paid to disturbing Braggreflections due to the diffraction (i.e. elasticcoherent scattering) of the incident neutron beam.There are several ways to remove them.

* One possibility consists of using spatial filteringwhich requires highly accurate angular localiza-tion and a precise cutting out of the areascontaining Bragg reflections.

* An alternative way to suppress Bragg peaks isthe use of a polarized neutron beam. Coherentlyscattered neutrons forming Bragg peaks willalways be polarized along the same direction asthe incident beam. Conversely, one can becertain that all neutrons having changed theirspin state in relation to the incident beam havebeen scattered incoherently so that Braggscattering cannot be found in this case. Byinserting a polarization analyzer in front of thedetector, one can easily distinguish neutronshaving preserved their spin state from thosehaving changed their polarization in the courseof the scattering process.

* Finally, Bragg diffraction can be avoidedaltogether by simply choosing a geometrical

arrangement where the detector is held at aconstant scattering angle which does not fulfillthe Bragg condition. Since the measured holo-graphic intensity depends only on the relativeorientation of the sample and the detector, it ispossible to replace any movements of thedetector in an appropriate way by equivalentrotations of the sample and to leave the detectorfixed. This permits one to choose the scatteringangle, which is defined by the direction of theincoming beam and the detector position, at aconstant value well off the angles where Braggscattering is observed.

Inelastic scattering can be taken into considera-tion in terms of the Debye–Waller factor, i.e. theholographic modulation is decreased when theincident neutrons excite or absorb phonons.Inelastic scattering gives rise only to a smoothbackground and can be accounted for by propermathematical treatment of the recorded hologram.

2.2. The point-like inside detection concept

Neutron holography can also be accomplishedby an alternative method using the principle of

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L. Cser et al. / Physica B 350 (2004) 113–119116

optical reciprocity [5,6]. In this technique thepositions of the source and the detector areinterchanged. The plane wave from a far-fieldsource reaching a particular nucleus in the sampledirectly can be considered as the reference beam,while the wave amplitudes due to coherentscattering from neighboring nuclei serve as theobject beam.The ‘detector nucleus’ should possess a high

cross section for neutron capture and the absorp-tion process should trigger a prompt nuclearreaction, generating either a g-ray cascade orother nuclear products (e.g. a- or b-radiation).The measured quantity is the total nuclear reactionyield. Some typical highly neutron-absorbingisotopes were listed in Ref. [4].It is evident that isotopes producing a-particles,

conversion electrons or protons, due to their verysmall path lengths in condensed matter, can beused only for surface investigations. For thestudy of bulk matter one has to utilize samples

Fig. 2. A monochromatic plane neutron wave emitted by a distant sou

serves as the reference beam. The scattered part of the wave forms the o

neutron density modulation is converted by the detector nucleus (mor

the prompt g-rays. The intensity IðkÞ of these g-rays is registered by

containing isotopes emitting g-rays followingneutron absorption. Such specimens can be pre-pared, e.g. in the form of alloys or suitablecompounds.The experimental setup in this case will be

extremely simple (see Fig. 2). The samples aremounted on a goniometer and placed into a well-collimated and duly monochromatized neutronbeam. The g-rays following neutron capture willbe detected by a g-detector. In the only inside-detector experiment performed thus far [7], scin-tillation detectors (NaI and BGO) were used tomeasure the g-ray intensity which offered theadvantage of combining high efficiency andruggedness. However, their energy resolution isonly moderate and does not always allow todistinguish reliably between variations in the countrate due to holographic intensity modulations ofthe g-rays emitted by detector nuclei and variousspurious effects of different origin which can arisein an environment formed by a nuclear reactor.

rce propagates towards the target nucleus and at the same time

bject beam and interferes with the reference wave. The resulting

e precisely: many detector nuclei) into intensity modulations of

the detector.

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L. Cser et al. / Physica B 350 (2004) 113–119 117

Germanium detectors with their excellent energyresolution, on the other hand, would permit one toclearly identify those g-rays originating from thedetector nuclei thereby removing any possibleambiguities. Unfortunately, the first tests haveshown that owing to the excessively high back-ground level in the vicinity of a neutron scatteringexperiment in a nuclear reactor, this appearsnot to be feasible with a single-detector setup.Nevertheless, the use of multi-detector Comptonsuppression arrangements deserves closer consid-eration and could prove a successful alternative toscintillation detectors in the future.Since the inside-detector concept is not influ-

enced by the presence of Bragg peaks and theexpected value of the signal-to-noise ratio is highenough, it is considered rather promising andsimple in its realization.

2.3. Comparison of the two concepts

A principal difference between the two methods(i.e. inside-source and inside-detector) arises fromthe fact that the incoherently scattering nuclei usedin the inside-source approach can be used assources of spherical neutron waves an arbitrarynumber of times while the neutron-absorbingisotopes used in the inside-detector technique willno longer be available for a further detectionprocess once the first neutron absorption processhas occurred.Further, one more subtle point should be

emphasized: In the inside-source approach theinterference pattern is recorded directly. By way ofcontrast, in the inside-detector technique this is nolonger the case. The modulations of the neutronwave field created by the interference becomeeffective by changing, correspondingly, the neu-tron absorption probability at the sites of thedetector nuclei. This, in turn, entails modulationsof the number of prompt g-rays generated. Theseg-rays are, on the average, emitted isotropically inall directions and, therefore, the position of the g-detectors can, leaving out practical considerations,in principle be chosen in an arbitrary way. Theobservation of the respective variations of the g-ray intensity requires that a large number ofneutron absorption processes continuously take

place involving an equally large number ofdetector nuclei which, however, as already pointedout can be used only once (though this number israther large, on the order of up to 107 s�1, it is ofcourse still very small in comparison with thenumber of nuclei present in samples typically usedin a neutron scattering experiment). On the otherhand, the inside-source method permits, at least ina gedankenexperiment, to reuse the same nucleusand its atomic environment as often as is requiredin order to obtain a sufficiently accurate hologram.Finally, the interference pattern observed in an

inside-source experiment depends only on therelative orientation of the sample and the detectorwhile in an inside-detector experiment it willdepend only on the relative orientation of thesample with respect to the direction of the incidentbeam.

3. Experimental recording of neutron holograms

with atomic resolution

3.1. Inside-source concept

Searching for candidate systems demonstratingthe feasibility of this approach, one is naturally ledto consider hydrogen-containing samples satisfy-ing the conditions listed above. In Ref. [4], wediscussed rare-earth metal hydrides such as Y(H),Lu(H) and Sc(H).A Canadian group made a choice for a single

crystal of natural simpsonite [8], a rare oxidemineral containing aluminum and tantalum withthe chemical composition Al4Ta3O13(OH).The experiment was performed on the N5

instrument located at the National ResearchUniversal reactor (Chalk River, Canada). Usinga neutron wavelength of l ¼ 1:3 (A and an angularresolution of about 2�, the holographic data werecollected during a 10-day measurement. The Braggpeaks were carefully excluded. After carrying outall necessary corrections the reconstruction of theatomic positions around the H nuclei was achievedby applying an appropriate mathematical trans-form to the recorded hologram. In the cited study,the positions of seven oxygen atoms were identi-fied and validated by comparison with the results

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Fig. 3. The spots representing the positions of the 12 Pb atoms

forming the first neighbors of the Cd nucleus define the surface

of a sphere and their positions can be given in spherical

coordinates (R; w;j): For all spots R ¼ 3:49 (A ¼ a=ffiffiffi2

p; a being

the lattice parameter. The (w; j) values, given in degrees, are: (1)(78, 24); (2) (165, 45); (3) (108, 72); (4) (53, 84); (5) (123, 135);

(6) (69, 156); (7) (107, 202); (8) (18, 225); (9) (77, 252); (10) (132,

264); (11) (62, 317); and (12) (114, 335). The x-axis is the

direction of the incident beam, the z-axis is the same as in the

coordinate system of the D9 diffractometer.

L. Cser et al. / Physica B 350 (2004) 113–119118

of X-ray structure investigations [9]. Relativelylarge deviations of about 70.3 (A from theexpected positions were observed. In the opinionof the authors [8] this is due to several reasons,most notably neglect of the conjugate image,insufficient statistics and the strongly asymmetricshape of the sample. Nevertheless, the coincidenceof the atomic positions obtained by the twomeasurements is satisfactory.

3.2. The insight detector concept

In order to provide experimental evidence of thefeasibility of this concept, a spherically shapedsingle crystal of Pb0.9974 Cd0.0026 with a mosaicwidth of about 1.5� was used as the sample [7]. Theabsorption cross section of Cd is more than fourorders of magnitude larger than for Pb so that theCd atoms act as highly efficient detectors. Thecrystal structure of the alloy is face-centered cubicas it is in pure lead and the lattice parameter of thealloy is a ¼ 4:935 (A. Since the Cd concentration isvery low, usually all lattice sites surrounding anyone Cd atom are expected to be occupied by Pbatoms. The lead nuclei play the role of the objectwhile the cadmium nuclei serve as point-likedetectors inside the sample. The experiment wascarried out at the D9 four-circle diffractometer atthe Institute Laue-Langevin (Grenoble). Thesample was mounted on a cradle and rotatedabout the angles w and j through ranges of 45�

and 354�, respectively. The angular step-widths of3� resulted in a mesh of 16 119=1904 pixels. Theneutron wavelength used was l ¼ 0:84 (A. Theprompt g-rays emitted by the Cd nuclei weredetected using scintillation detectors (300 300 NaIand 200 200 BGO). In order to decrease theinfluence of slow variations of the incident beamintensity, the measuring time for one pixel waslimited to 30 s. Short-time variations were checkedby a monitor counter. The data collection timeneeded to cover the entire mesh of 1904 pixelsamounted to about 18 h. During the course of theexperiment, 14 such cycles were completed result-ing in typically 2.5 107 counts in one pixel for theBGO detector and 1.5 107 counts for the NaI(Tl) detector. The data were corrected for theslowly varying background level by fitting a

smoothly varying function after filtering outFourier components of very low frequency. Thereconstruction of the holographic picture wasachieved by performing a convolution of conver-ging spherical waves with the data matrix of thescanned (w;j) surface. Fig. 3 displays the restoredhologram of the 12 equidistant nearest neighboratoms around a Cd detector nucleus. The latticeparameter a ¼ 4:93 (A obtained from the holo-graphic data is in very good accordance with thevalues determined in the usual way by X-ray andneutron diffraction measurements. The orientationof the sample was reconstructed from the holo-gram using a model calculation providing thepositions of the expected spots for some arbitraryorientation. Coincidence of the measured andcalculated positions was achieved by suitablyrotating the z- and y-axis giving the declinationangle from the z-axis of the diffractometer y ¼�5973� and the initial value of the rotationaround the j-axis j0 ¼ 2173�:

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L. Cser et al. / Physica B 350 (2004) 113–119 119

After completing the holography experiment,the orientation of the sample was determined inthe usual way using Bragg reflections. The result-ing angles were y ¼ �60:3� and j0 ¼ 20:3� ingood accordance with the holographic data there-by demonstrating the power of the technique.

4. Conclusions and future prospects

In view of the two independent experimentsdescribed above, the feasibility of both concepts ofatomic resolution holography as proposed in Ref.[4] can be considered proven. Holographic experi-ments provide much structural information. Forexample, the neutron hologram recorded in ourinside-detector experiment provides unambiguousevidence that the Cd atoms occupy Pb sites in thealloy. The atomic distances between the Cddetector nucleus and the neighboring Pb nucleiwere determined with a precision of a fewhundredths of an (Angstrøm. The crystal latticecan be restored from the hologram withoutmaking use of any a priori knowledge about theorientation of the sample. Owing to the small sizeof the scattering centers (i.e. the size of atomicnuclei), interatomic distances can be measuredwith extremely high accuracy. This accuracy ispresently limited by the collimations and thewavelength spread of the neutron beam used.The above results hold some promise for future

practical applications. On the one hand, there area large number of substances containing substan-tial amounts of hydrogen such as metal–hydrogensystems, numerous organic substances and many

minerals of geological importance. On the otherhand, the recording of holograms based onmagnetic scattering may open up a new perspec-tive on the investigation of magnetic materials.Further experiments studying carefully selectedsamples will help to explore both future technicalimprovements and novel applications.

Acknowledgements

The authors are indebted to several colleagues—M. Kocsis, L. Rosta, G. Vasp!al, and M. Prem andthe RTD ENPI program (HPRI-CT-1999-5001)for various kinds of support.

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