Scholarly article on topic 'Energy-selective Neutron Imaging for Three-dimensional Non-destructive Probing of Crystalline Structures'

Energy-selective Neutron Imaging for Three-dimensional Non-destructive Probing of Crystalline Structures Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — S. Peetermans, M. Bopp, P. Vontobel, E.H. Lehmann

Abstract Common neutron imaging uses the full polychromatic neutron beam spectrum to reveal the material distribution in a non-destructive way. Performing it with a reduced energy band, i.e. energy-selective neutron imaging, allows access to local variation in sample crystallographic properties. Two sample categories can be discerned with different energy responses. Polycrystalline materials have an energy-dependent cross-section featuring Bragg edges. Energy-selective neutron imaging can be used to distinguish be- tween crystallographic phases, increase material sensitivity or penetration, improve quantification etc. An example of the latter is shown by the examination of copper discs prior to machining them into linear accelerator cavity structures. The cross-section of single crystals features distinct Bragg peaks. Based on their pattern, one can determine the orientation of the crystal, as in a Laue pattern, but with the tremendous advantage that the operation can be performed for each pixel, yielding crystal orientation maps at high spatial resolution. A wholly different method to investigate such samples is also introduced: neutron diffraction imaging. It is based on projections formed by neutrons diffracted from the crystal lattice out of the direct beam. The position of these projections on the detector gives information on the crystal orientation. The projection itself can be used to reconstruct the crystal shape. A three-dimensional mapping of local Bragg reflectivity or a grain orientation mapping can thus be obtained.

Academic research paper on topic "Energy-selective Neutron Imaging for Three-dimensional Non-destructive Probing of Crystalline Structures"

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Physics Procedia 69 (2015) 189 - 197

10 World Conference on Neutron Radiography 5-10 October 2014

Energy-selective neutron imaging for three-dimensional non-destructive probing of crystalline structures

S. Peetermansab *, M. Boppc, P. Vontobela, E. H. Lehmanna

aPaul Scherrer Institut, Neutron Imaging and Activation Group, CH-5232, Switzerland bEcole polytechnique fédérale de Lausanne, NXMM laboratory, IMX, CH-1015, Switzerland cPaul Scherrer Institut, Resonator Technology Group, CH-5232, Switzerland

Abstract

Common neutron imaging uses the full polychromatic neutron beam spectrum to reveal the material distribution in a non-destructive way. Performing it with a reduced energy band, i.e. energy-selective neutron imaging, allows access to local variation in sample crystallographic properties. Two sample categories can be discerned with different energy responses. Polycrystalline materials have an energy-dependent cross-section featuring Bragg edges. Energy-selective neutron imaging can be used to distinguish between crystallographic phases, increase material sensitivity or penetration, improve quantification etc. An example of the latter is shown by the examination of copper discs prior to machining them into linear accelerator cavity structures. The cross-section of single crystals features distinct Bragg peaks. Based on their pattern, one can determine the orientation of the crystal, as in a Laue pattern, but with the tremendous advantage that the operation can be performed for each pixel, yielding crystal orientation maps at high spatial resolution. A wholly different method to investigate such samples is also introduced: neutron diffraction imaging. It is based on projections formed by neutrons diffracted from the crystal lattice out of the direct beam. The position of these projections on the detector gives information on the crystal orientation. The projection itself can be used to reconstruct the crystal shape. A three-dimensional mapping of local Bragg reflectivity or a grain orientation mapping can thus be obtained.

© 2015The Authors.Publishedby Elsevier B.V. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Selection and peer-review under responsibility of Paul Scherrer Institut

Keywords:

neutron imaging, tomography, energy-selective, diffraction, crystal

1. Introduction

Neutron imaging relies on the attenuation of a neutron beam when traversing a sample of interest. It is commonly described by the Beer-Lambert law:

I = Io (1)

* Corresponding author. E-mail address: steven.peetermans@psi.ch

1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Selection and peer-review under responsibility of Paul Scherrer Institut

doi:10.1016/j.phpro.2015.07.027

with I0 the incident neutron beam intensity and I the transmitted one. It features an exponential decay of transmitted beam intensity depending on the sample thickness d and the macroscopic cross-section 2. The latter describes the interaction probability of neutrons with matter, variations of which allow to study spatial variation in material distribution (e.g. repairs in Renaissance bronzes van Langh et al. (2011) or water transport within fuel cells Oberholzer et al. (2012)). The neutron can either be captured or scattered (coherent or incoherent, elastic or inelastic) Marshall and Lovesey (1971). The probability of these to occur is however dependent on the energy (or wavelength A through the de Broglie relationship) of the incident neutron.

Neutron imaging traditionally uses the full polychromatic incident beam spectrum s coming from the source to obtain high neutron intensity and short acquisition times. The detected transmission T for each pixel in the radiograph becomes:

f l0(A)e-2(A)ddA

T = ^- , (2)

Is l0(A)dA

I0 being the incident beam intensity, which in effect averages out the energy-dependent behaviour of the cross-section and all information it contains.

In order to obtain energy-resolving capability, one has to reduce the wavelength band using a monochromator (e.g. a mechanical neutron velocity selector Friedrich et al. (1989), a double crystal monochromator Schulz et al. (2009); Treimer et al. (2006) or a hybrid solution Peetermans et al. (2014b)) or the time-of-flight method Kockelmann et al. (2007). However, the higher the energy-resolution, the lower the intensity and the longer the exposure times, making it important to select the appropriate method for one's problem. An overview of typical values is presented in table 1.

Table 1: Typical values for neutron imaging with a polychromatic beam, using monochromators at the SINQ neutron source Bauer (1998) and time of flight (TOF) imaging at ISIS ISIS (2014). Though the time-averaged flux is lower, it allows to record all wavelength frames in parallel).

Monochromaticity АЛ/Л Field of view Exposure time Polychromatic - 15 X 15cm2 5s Mechanical Velocity Selector 15% 10 X 10 cm2 1 min Double Crystal Monochromator 2.5 % 10 X 10 cm2 5 min Time of Flight_< 0.5 %_2.5 X 2.5 cm2_2.5 h

This article will focus on coherent elastic scattering or diffraction in particular. The corresponding cross-section features very abrupt changes with neutron wavelength. It can be understood in the context of Bragg's law:

2dhki sin 0 = A , (3)

stating the condition for which a neutron beam of wavelength A can be diffracted from the crystal lattice planes of spacing dhkl on which it is incident under an angle 0. It is discussed how this interaction mechanisms manifests itself in case of polycrystalline material and for single crystals or few coarse crystallites (oligocrystals). The crystalline properties that can be deduced at high spatial resolution through energy-selective neutron imaging are given and illustrated by selected examples.

2. Polycrystalline material

2.1. Bragg edges

Polycrystalline material features a large number of randomly oriented crystallites. Ideally, all crystal orientations are represented w.r.t. the incident neutron beam. In terms of Bragg's law (eq. 3) this means that neutrons of all wavelengths can be diffracted out of the direct beam by the (hkl) crystal lattice planes, until A = 2dhkl. At longer wavelengths, these plains can not contribute to coherent elastic scattering anymore, and the cross-section decreases abruptly: the Bragg edge. The longest wavelength Bragg edge is also known as the Bragg cut-off, after which no

coherent elastic scattering at all is possible anymore. The wavelength-dependent microscopic cross-section pattern for a selected number of polycrystalline engineering materials is shown in figure 1, simulated using NXS Boin (2012).

Fig. 1: Total microscopic cross-section for selected polycrystalline materials.

2.2. Opportunities for neutron imaging

The Bragg edge pattern depends on the crystallographic phase. By comparing monochromatic radiographies at wavelengths slightly shorter and longer than a Bragg edge of a particular phase, one can enhance radiographic contrast for that phase compared to other phases with no Bragg edge at that position and a more slowly varying cross-section Salvemini et al. (2012); Woracek et al. (2014).

Radiography at a wavelength slightly longer than the last and highest Bragg edge features increased sample penetration depths as the cross-section is lowest here. For instance, lead has an average microscopic cross-section of 11.4 barn in a polychromatic thermal spectrum versus only 1.4 barn at 6 A, past the Bragg cut-off, increasing the penetration depth from 6 cm to 50 cm. Conversely, one can increase sensitivity of neutron imaging by radiography at wavelengths just short of the Bragg cut-off, where the cross-section is at its highest.

Preferred orientation or texture can lead to large deviation of the Bragg edge pattern Boin (2012); Kockelmann et al. (2007). Orientations that are overrepresented compared to the random distribution will lead to increased scattering (higher cross section) for the corresponding Bragg wavelength at the expense of under-represented orientations. Mapping of texture variations across a sample of interest is thus possible Lehmann et al. (2014).

The Bragg edge position itself is determined by the lattice spacing, which becomes smaller or larger under compression or tension. The local shift in observed Bragg edge position is a measure for mapping strain across a sample Santisteban et al. (2002); Abbey et al. (2012).

Energy-selective neutron imaging past the Bragg cut-off, means coherent elastic scattering is suppressed and one becomes insensitive to the sample's crystallographic properties. This strategy, which allows for better quantification, is illustrated in the next subsection.

2.3. Application in copper disc integrity Problem setting

The linear accelerator for the SwissFEL free electron laser is composed of a series of copper cavities, soldered together and put under a high RF field to accelerate an electron beam. These cavities are custom built, by precise ma-

chining out of 99.99 % pure copper discs (113 mm diameter, 23 mm thickness) that were forged to preclude occurrence of porosities from casting.

However, pitting was observed on the surface of the final product (figure 2a). It would have a detrimental effect on the accelerator performance, as a smooth cavity surface is required to prevent electrical discharges.

To address the question if these are due to the machining or the result of porosities already present in the pristine copper discs, several such discs were inspected using neutron imaging (figure 2b). The large sample thickness impeded the use of X-rays as transmission would be too low (around 1 % only at 100 keV): copper has an attenuation coefficient yu=1.97 cm-1 whereas the total macroscopic cross-section 2=1.07 cm-1.

Fig. 2: Copper cavity segments showing surface pitting after machining (a) and neutron radiography set-up of a pristine forged copper disc (b).

Initial examination at NEUTRA

Initial examination took place using a polychromatic thermal neutron spectrum at the NEUTRA imaging beamline at Paul Scherrer Institut (PSI). Experimental parameters are listed in table 2. Radiographies were made with the sample in contact with the scintillator's aluminium backing substrate to obtain the highest spatial resolution for observing potential small porosities.

Large spatial variations in transmission are observed over the sample (figure 3a). Clear cupping artifacts due to scattering contributions are visible: the observed transmission tapers off at increasing disc radius. The effect is aggravated by the close contact between sample and detector.

In order to calculate the thickness based on the Beer-Lambert law (equation 1), a constant macroscopic cross-section of 2=0.9 cm-1 is assumed, found by averaging the theoretical copper cross-section over the NEUTRA spectrum. A thickness of 15 mm is found in the center of the disc, a gross underestimation of the reality. Moreover, thickness variations of over a millimetre are found superposed to the cupping profile, unrealistically large to be attributed to production flaws.

Therefore, spatial variation in macroscopic cross-section instead of thickness is suspected to exist, as crystallo-graphic properties (e.g. texture and grain size) and density might vary due to the manufacturing process.

Energy-selective neutron imaging at BOA

The hypothesis is verified by energy-selective imaging at wavelengths longer than the Bragg cut-off for copper (i.c. the (111) Bragg edge at 4.17 A ). At such long wavelengths, coherent elastic scattering is no longer possible and the cross-section (and a fortiori the neutron digital radiograph) becomes insensitive to the sample's crystallography. The experiment was conducted at the BOA beamline at PSI, using the double crystal monochromator in combination with a Beryllium filter. Further experimental parameters are listed in table 2.

Indeed, the transmission image at 4.5 A now appears homogeneous. Cupping artifacts are no longer present. The spatial variation in transmission observed for polychromatic thermal neutron radiography, can thus be attributed to spatial variation in the sample's crystallography instead of thickness or density variations. The nature of the variations in crystallographic properties are however beyond the scope of this investigation. Taking the theoretical macroscopic cross section of 2 = 0.88 cm-1 at 4.5 A , a thickness of 22.3±0.5 mm is found. No porosities were detected.

S. Peetermans et al. / Physics Procedia 69 (2015) 189 - 197 Table 2: Experimental parameters for polychromatic thermal neutron imaging at NEUTRA (a) and energy-selective neutron imaging at BOA (b).

NEUTRA BOA

Wavelength 1.5-3.5 A 4.5A

Scintillator 50um 6LiF ZnS 200um 6LiF ZnS

Field of view 129.6x153.6 mm2 138x138 mm2

Pixel size 60 um 135 um

Exposure time 60 s 195 s

Fig. 3: Radiographies of copper discs for SwissFEL linear accelerator cavities to be machined out of: measured using a polychromatic thermal spectrum at NEUTRA (a), a monochromatic one at 4.5 A at BOA (b) and the transmission profile (c).

Conclusion

Polychromatic thermal neutron imaging is subject to artifacts as scattering contributions and sensitive to spatial variation in crystallography across the sample that impede quantitative determination of copper disc thickness and porosity presence. Energy-selective imaging in the absorption range yields correct thickness results and does not pick up any porosities above the noise level.

3. Single crystals and Oligocrystals: Bragg dips

In case of a single crystal sample or an ensemble of a few large (i.e. of dimensions above the spatial resolution of the imaging set-up) crystallites or oligocrystals, the wavelength-dependent cross-section pattern no longer exhibits Bragg edges. The number of crystal lattice plane orientations 6 within the neutron beam is now limited. Bragg's law can only be fulfilled at specific wavelengths (eq. 3), at which the wavelength-dependent transmission pattern will feature distinct dips.

Figure 4 shows the experimental values of the wavelength-dependent total microscopic cross-section for a body centered cubic (BCC) iron single crystal. It was recorded using an MCP detector Tremsin et al. (2009) at the ROTAX beamline ISIS (2014) at the ISIS pulsed spallation source, located at the Rutherford Appleton Laboratory in the UK.

The Bragg dip pattern can be indexed and serves as a finger print for crystal orientation, the dips' wavelength full widths at half maximum (FWHM) as a measure for the mosaicity. As it is recorded for each pixel behind the sample, crystal orientation and mosaicity mapping at high spatial resolution becomes possible. Details will be described elsewhere Peetermans et al. (2015).

Fig. 4: Recorded wavelength-dependent total microscopic cross-section of a body centered cubic iron single crystal showing distinct dips instead of Bragg edges.

However, such wavelength scans at high spatial and temporal resolution are very time consuming. What information can already be obtained from a single radiograph of reduced wavelength bandwidth?

Again we turn to Bragg's law (eq. 3). Suppose we have two neighbouring crystallites. By definition, they are misoriented w.r.t. each other. As such, they will diffract at different wavelengths. By restricting the beam spectrum to a narrow wavelength band, one will observe a region of reduced intensity in the digital radiograph, corresponding to projections of the crystallite oriented as such as to diffract at a wavelength within that band. Information on crystallite morphology can thus readily be obtained (e.g. Peetermans et al. (2013)), without the need for time-consuming energy-scans at high energy resolution. Choosing a wavelength band above the Bragg cut-off, no diffraction by the crystallites is possible anymore and one only observes a change in the elemental distribution within the sample.

Energy-selective neutron imaging of single crystals or coarse-grained material can thus provide maps at high-spatial resolution of such crystallographic sample properties as crystal orientation, mosaicity and crystallite shape. Such analyses have great potential in characterizing neutron monochromator crystals or choosing the gauge volume in crystal samples for fundamental condensed matter physics research on scattering instruments.

4. Diffraction imaging

High energy-resolution is required to resolve all Bragg peaks of cross-section, the FWHM of the Bragg peaks of the iron crystal examined in the previous section (fig. 4) e.g. being on the order of 0.02 A. Neutron imaging at such high energy-resolutions is only present at time of flight facilities.

Working with an incident wavelength bandwidth larger than the crystal's Bragg peak FWHM leads to a loss of image contrast (typically around 0.1 A FWHM for a double crystal monochromator). As the recorded transmission radiograph is defined by the ratio of the wavelength-integrated beam intensity with and without the crystal (eq. 2), small variations in the crystal's local Bragg reflectivity or orientation will hardly be picked up.

Diffraction contrast radiography

However, one can think of the crystal as a monochromator in itself. Depending on its orientation in a white or pink neutron beam, it will diffract neutrons of specific wavelengths A under an angle 26 out of the direct beam as stipulated by Bragg's law. With the whole crystal volume illuminated, these diffracted neutrons will form a projection of that volume on any position-sensitive detector they fall on. The principle is illustrated in figure 5a. As a practical

demonstration, a pyrolytic graphite crystal of 1.3° mosaicity, measuring 50x10x1 mm3, was put 45 mm in front of an imaging detector (a 1024x1024 pixel2 CCD camera in combination with a 200 um thick 6LiF ZnS scintillator screen). The crystal was rotated to 22.5°. Apart from the traditional 'shadow' projection of the crystal through attenuation of the incident neutron beam (a transmission T<1), one can clearly observe another projection of the crystal, formed by additional diffracted neutrons on top of the incident direct neutron beam (T>1). Note that the polycrystalline screw mounting recognizable in the transmission projection does not contribute to the diffraction projection. Instead, the holes in the crystal for the screws to fit are observed.

Working now outside the direct beam area, one only detects the diffracted neutrons1, by default obtaining the highest possible intensity contrast for the coherent elastic scattering process.

The position of the diffraction projections on the detector is determined by the orientation of the crystal. A higher orientation sensitivity can be obtained than for the case of energy-selective transmission imaging. Consider e.g. a BCC iron crystal, with (110) plane oriented to diffract neutrons towards a detector at 90°. A misorientation of 0.1° will lead (taking the derivative of Bragg's law) to a change of the diffracted wavelength by 0.005 A - a number hard to pick up even with time of flight. On the other hand, the position of the diffracted neutron projection on that detector, placed 50 mm away, will change by 175 um, well above the typical spatial resolution of neutron imaging detector systems.

(a) (b)

Fig. 5: Principle of diffraction contrast imaging (a) and the acquired neutron detector image of a pyrolytic graphite crystal showing a reduced transmission behind the sample (right), whereas the diffracted neutrons increase the transmission level, forming a projection as well (left).

Diffraction contrast tomography

Rotating the crystal in a white beam, the Bragg angle and the related position of the diffraction projection will change. After a full turn, sufficient diffraction projections under various angles through the sample are recorded to allow for tomographic reconstruction. To this end, these projections are first segmented out of the recorded detector image. They are subsequently renormalized as they represent different wavelengths diffracted out of the incident beam spectrum, the effective scintillator thickness depends on the neutron incidence angle and the different structure factors for different diffracting crystal lattice plane families. Finally, the diffraction projections are assumed to originate from a virtual source along the diffraction projection direction behind the sample, so they can be reconstructed using existing transmission based-algebraic reconstruction algorithms. Whereas the reconstruction of the transmission projections yields a three-dimensional distribution of the macroscopic cross-section, the diffraction contrast tomography allows to investigate changes in the local Bragg reflectivity Peetermans and Lehmann (2013).

1 apart from a background formed by scattering from the surroundings and incoherent sample scattering

Oligocrystals require the additional step of grouping diffraction projections to their grain of origin prior to reconstruction. The result is a three-dimensional grain map, with grain orientation determined from the diffraction projection positions and shape based on the projection itself. The example of a diffraction contrast tomography of a polycrystalline aluminium cylindrical sample is shown in figure 6 as an illustration Peetermans et al. (2014a).

Fig. 6: Grain map of an aluminium cylindrical sample as reconstructed based on the neutron diffraction projections. The grains are color coded based on their Rodrigues vector, representing crystal orientation by a rotation from the sample reference system around the vector over an angle determined by the vector length. The result of the transmission tomography is shown as a semi-transparent overlay.

Diffraction imaging can be performed simultaneous to traditional transmission imaging, yielding a Bragg reflectivity or grain orientation map in addition to the material distribution. No high energy-resolution is required, making it a valid alternative to energy-selective neutron imaging with a monochromator at continuous sources. The method lends itself to well tomographic expansion as one does not deal with the long exposure times associated with full energy-scans.

5. Summary

The method of energy-selective neutron imaging was introduced and shown to yield information on the underlying crystallographic structure of samples of interest. Two categories of samples have been discussed: polycrystalline material featuring Bragg edges and single crystals featuring distinct Bragg dips in their wavelength-dependent transmission spectrum. An alternative neutron imaging method was presented. Neutron diffraction contrast imaging allows to study the sample's crystalline features by imaging the diffracted neutrons.

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