Polarization contrast neutron imaging of magnetic crystallographic phases Materials Today Advances

Non-destructive characterization methods to observe phase transformations and thus, gain insights to transformation mechanisms in representative volumes are key for the development of advanced materials and manufacturing. Conventional methods are constrained to the surface and small sizes, thus, access to the bulk often implies tedious destructive approaches and hinders in-situ observations of phase evolution. In this work, we introduce a non-destructive technique that overcomes key limitations pre- vailing today for mapping the spatial distribution of magnetic phases in bulk materials. The use of polarized neutrons, being sensitive to sub-percent fractions of ferromagnetic phases and able to pene- trate centimeter sized samples, enables micrometer-scale spatial and second-scale time resolutions. We demonstrate ex-situ and in-situ quantitative mapping of magnetic phases, in particular the evolution of martensite induced by uniaxial- and biaxial deformation in metastable 304 steel. The quantitative results obtained during in-situ deformation testing prove polarization contrast neutron imaging to be partic- ularly effective in detecting small fractions of martensite. Especially during early stages of deformation where neutron diffraction, which in contrast does not provide full ﬁ eld spatial resolution, fails. The short exposure times and high sensitivity renders the method well suited for rapid 3D tomographic mapping and/or operando investigations of phase distributions. © 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


Introduction
Microstructural properties such as solid-state phase transformations and their distribution determine to a large extent the global mechanical properties of materials. It remains critically important to study e.g. the relationship of phase transformation kinetics and relate them with other microstructural properties such as dislocation density evolution, grain size or crystallographic texture to develop experimentally verified constitutive laws for computational tools. The development of such experimentally verified and robust computational tools will accelerate the development and utilization of advanced manufacturing and materials for addressing societal requirements of human welfare, safe and green transportation, sustainable infrastructure and clean energy.
The availability and advancement of characterization techniques remains essential to obtain a fundamental understanding of transformation mechanisms allowing the development of accurate phase transformation models [1].
Deformation or thermally induced martensitic phase transformations in ferrous alloys and steels give rise to important structural and functional properties, such as strength in transformation-induced plasticity (TRIP) steels [1] and shape memory or superelasticity effects in ferrous shape-memory alloys (SMAs) [2]. Their related properties are of particular importance for numerous engineering applications as structural materials in the automotive industry, biomedical industry, civil applications, as actuators etc. In these materials, the initial microstructure contains a fraction, or consists entirely of metastable austenitic face-centeredcubic (FCC) phase that transforms into martensite upon deformation, or during fatigue or cold working. Depending on the chemical composition of the material and the extent of deformation, two different martensitic phases are commonly created under load, the body-centered-cubic (BCC) a 0 -martensite and/or the hexagonal close-packed (HCP), ε-martensite [3]. Martensite with BCC crystal structure is particularly important as it hardens the material, while good ductility is maintained due to the presence of austenite. As such, an optimum trade-off between strength and ductility can be achieved [4].
Traditional techniques (e.g. optical microscopy, electron microscopy, electron backscatter diffraction, X-ray diffraction, magnetic and ultrasonic measurements) are constrained to the surface or to small-sized material samples (i.e. sub-millimeters) and are, thus, often not representative of the bulk. Access to the bulk implies destructive approaches hindering in-situ observations of phase evolution. Also recently developed advanced synchrotron X-ray techniques such as 3D-XRD [5] and X-ray diffraction contrast tomography [6] that provide unique insights through 3D microstructure maps, are typically limited to small sample volumes. Additional limitations, e.g. the degree of mosaicity, hinders studies of plastically deformed materials. Only neutrons [7e10] and high energy synchrotron X-ray diffraction [11] provide access to bulk microstructures. However, to gain crucial spatially resolved insights to meso-scale phenomena in the bulk of polycrystalline materials, novel neutron imaging methods have been developed continuously throughout past decades. In particular, wavelength resolved diffraction contrast neutron imaging [12,13] has been utilized extensively for 2-and 3-dimensional mapping of phase distributions [8,14e18] and observations of phase evolution [19e21]. Bragg edge imaging of crystalline phase distributions provides spatial resolutions down to a few tens of mm. However, to achieve high resolution and to identify small fractions and subtle changes of phase requires exposure times up to a few hours, depending on the instrumental method deployed [13,22]. However, being able to detect subtle changes and low fractions in-situ and with sufficient resolution is generally of particular relevance, like, for instance, in order to understand the degradation mechanisms in components made of ferrous SMAs, where accumulation of deformationinduced a 0 -martensite is non reversible and highly undesirable [23].
Here, we introduce a different non-destructive approach that overcomes key limitations prevailing today for mapping the spatial distribution of crystalline phases in bulk materials by being sensitive to sub-percent phase fractions with micrometer-scale spatial and second-scale time resolution. We validate the linear dependence between the measured depolarization coefficient and the magnetic phase fraction using a set of samples consisting of different mixtures of ferromagnetic a-iron powder with paramagnetic austenitic 316L stainless steel powder. Subsequently, we demonstrate ex-situ and in-situ mapping of ferromagnetic phases, in particular the evolution of strain induced martensitic phase in metastable 304 steel induced under uniaxial-and biaxial deformation. The method capitalizes on the high sensitivity of the neutron's magnetic moment m n to magnetic fields and structures, as well as the high transmission capability of neutrons, rendering it a unique assessment tool for a wide range of conventional and advanced materials of high technological relevance. The spatial resolution based on pixel sizes of 50Â50 mm 2 is orders of magnitude better than in conventional neutron diffraction [13], while leveraging the integral flux of a broad wavelength range, i.e. a white beam, implies the method to outperform advanced wavelength resolved diffraction contrast imaging methods by orders of magnitude in efficiency, i.e. time resolution and sensitivity.

Method
A polarized incident white neutron beam is depolarized when interacting with the microstructure of magnetic domains in a ferromagnetic material [24,25]. Thus, analyzing the beam polarization after interacting with a sample enables detecting ferromagnetic phases in the material. While wavelength dispersive transmission measurements were used in the past and enable the characterization of average domain sizes [24,25], our spatially resolved technique with a highly intense white beam provides detailed images of the distribution of phases exhibiting ferromagnetism. The method, which has been similarly applied in the past to study the Curie temperature distribution in heterogeneous alloys [26,27], requires to equip a neutron imaging beamline that enables spatially resolved measurements through e.g. a pinhole geometry, with neutron polarization and polarization analyses capabilities [28,29]. The incident beam with a thermal or cold wavelength spectrum is polarized by a neutron spin filter (NSF), typically a polarizing supermirror device utilizing the different refractive index of the spin-up and spin-down components of an unpolarized beam in a strong magnetic field to reflect one and absorb the other component in a subsequent absorber layer coating on the backside of the mirror. However, polarized 3 He can serve as NSF as well. The high polarization of the neutrons transmitting the NSF is preserved in the beamline by a guide field aligned parallel to the transmitted polarization and ideally spanning the length up to the second NSF, the polarization analyzer. A sample to be measured is placed between the two NSFs as close as possible to the analyzer, without interfering with its magnetic stray field, in order to achieve the best possible resolution on the subsequent imaging detector. The deterioration of spatial resolution by the extended sample to detector distance implied by the need of the analyzer can be compensated by beam collimation, which has to be tailored to the experimental needs to not excessively sacrifice flux and, thus, efficiency. In order to measure the local beam polarization P (x, y), which is characterized by the ratio: an adiabatic fast passage p spin flipper [30] is installed upstream of the sample and allows to subsequently record both the spin-up intensity I [ (x, y) and the spin-down intensity I Y (x, y). Without a sample in the beam the measured polarization P 0 (x, y) is close to unity throughout an image. When the neutrons spin, however, they experience magnetic interactions with magnetic fields characteristic of a sample under investigation, they undergo Larmor precessions with the frequency u L ¼ gB according to the strength and orientation of the magnetic field B of e.g. magnetic domains and depending on the time spent in the field. g ¼ 4pm n /h is the gyromagnetic factor of the neutron with h being the Planck constant [31]. The time spent in the field, and thus precessing, depends on the extension of the field, like the domain size d and sample thickness t as well as on the neutron velocity n and therefore the wavelength l of the neutron (Eq. (4)). This leads to depolarization effects and, hence, a resulting polarization P (x, y) depending on local magnetic structures and phases. In analogy to the Beer Lambert law of attenuation: Iðx; yÞ ¼ I 0 ðx; yÞe Àmðx;yÞtðx;yÞ ; where where the depolarization coefficient h for a ferromagnetic material with randomly oriented domains is written as [24]:

Experimental section
Polarization contrast neutron imaging (PNI) measurements were carried out at the BOA beamline [32] of the Paul Scherrer Institut (Villigen, Switzerland). BOA is characterized by a cold neutron spectrum, with a peak wavelength of 2.8 Å and a mean wavelength of 3.8 Å, and is permanently equipped with a multichannel polarizing-bender unit [32] between the cold source and the beamline pinhole of 40Â40 mm 2 at the exit from the source monolith. The instrument was further equipped with an adiabatic p-spin flipper, a magnetic guide field and a 40Â40 mm 2 supermirror NSF used as spin analyzer (Fig. 1a)). The average instrumental white beam polarization P 0 of the setup was measured to have been around 86%. The neutron imaging detector comprised of a 200 mm thick scintillator screen (LiF/ZnS(Ag)) and an optical Andor iKon-M CCD camera (1024Â1024 pixels) with a Zeiss MAKRO-PLANAR 2/100 mm ZF.2 objective lens. The magnification of the lens was such to achieve an effective pixel size of 65 mm, implying a camera field of view of 67Â67 mm 2 . The effective field of view is, however, limited by the spin analyzer dimension.
A set of samples consisted of different mixtures of ferromagnetic a-iron powder with paramagnetic austenitic 316L stainless steel powder. The 316L powder (FCC structure) has a particle size distribution of 15e45 mm (purchased from Carpenter Additive, USA), while the pure Fe powder (BCC structure) has a particle size range of 6e8 mm (purchased from Goodfellow, UK). The powder mixtures were contained in quartz cuvettes with sample thickness of 2 and 5 mm. Pure iron powder (with BCC crystal structure) was mixed at ratios of 0, 0.5, 1, 1.5 and 2 wt. % with 316L powder (with FCC crystal structure). The distribution of martensite resulting from the TRIP effect induced by uniaxial and biaxial deformation tests was investigated in a set of cruciform-shaped specimens of commercial hot-rolled AISI 304 (EN.1.4301) stainless steel purchased from SAUTER EDELSTAHL AG, Switzerland. Fig. 1b) shows a schematic of the cruciform sample geometry and indicates the directions of the load paths with respect to the hot-rolling direction of the steel plates during manufacturing. The field of view defined by the spin analyzer is indicated. The sample thickness gradually decreases from 8 mm at the gripping parts to an uniform 2 mm thick circular section with 24 mm diameter at the center of the sample, more information is provided in [33]. The deformation tests were carried out using the biaxial deformation rig of the neutron diffraction instrument POLDI at SINQ, Switzerland [34]. The samples investigated were an as received specimen (AR), two samples deformed under uniaxial tension (S1, S2) and one sample that had been subjected to non-proportional multiaxial loading (S3). S1 and S2 were loaded along the axis of the cruciform shape that was parallel to the hot-rolling direction, with up to 35 kN (S1) and 40 kN (S2), reaching a maximum equivalent strain of 12.7% and 21.4% respectively. S3 underwent loading with a force ratio of 49 kN:59 kN between the two orthogonal axes, reaching a maximum equivalent strain of 39%. The von Mises equivalent strain was calculated by definition of the analysis software of the implemented digital image correlation system (GOM Aramis®). Furthermore, an in-situ uniaxial tensile deformation experiment was performed using an additively manufactured dogbone sample of 304L stainless steel with 60 mm length and 6 mm gauge diameter. The sample was additively manufactured using a prealloyed, gas atomized 304L stainless steel powder, with a particle size distribution of 15e45 mm (purchased from Metalalpine GmbH, Austria). The adopted manufacturing technique was laser powder bed fusion (LPBF) using a Sisma MySint 100 printer with a laser spot size of 55 mm. The process parameters conveying a laser power of 175 W, a hatching distance of 83 mm, a scanning speed of 600 mm/s and a layer thickness of 30 mm were suited to achieve a proper material density. During the experiment the sample was loaded stepwise slightly above to the yield point, i.e. at 375 MPa (YP) and at 0.5%, 1%, 2%, 4%, 6% engineering strain before unloading back to 0 MPa. PNI measurements were performed with exposure times of 60 s per image. Open beam and sample images were recorded always for both spin-up and spin-down configuration. All images were corrected by dark-current background measurements without exposure and reduced first to map the background corrected transmission I/I 0 and polarization ratio P/P 0 and subsequently according to Eqs. (2) and (3) in order to achieve spatially resolved maps of m and h, respectively. In the case of the glass cuvettes used as sample containers, one of these has been measured in empty state, in order to correct also for its contribution to the signal, in particular the attenuation signal. Three samples in glass cuvettes could be exposed simultaneously, due to the spatially resolved character of the measurements.
To additionally verify the presence of ferrite and martensite optically in the vicinity of the surface the samples were ground

FCC/BCC powder mixtures
The results of the reference measurements with the FCC/BCC powder mixtures are displayed in Fig. 2. Fig. 2a) shows the measured transmission and polarization ratio radiographs for the powder mixtures in the 2 mm cuvettes as well as an empty cuvette that was used for correcting the transmission and depolarization for the contribution of the glass material. The transmission and polarization ratio for each of the powders and different cuvette thicknesses, obtained by averaging for the whole sample area, are plotted against the nominal BCC weight fraction in Fig. 2b). The influence of the sample thickness in the two quantities is highlighted by the strong offset in the individual pair of curves. Nevertheless, the results confirm a linear dependence of the depolarization coefficient on the phase fraction of the ferromagnetic alpha iron. This is illustrated in Fig. 2c) where the linear attenuation and depolarization coefficients averaged over the sample areas are plotted against the nominal weight fraction of the magnetic BCC iron phase. This procedure yields linear attenuation coefficients that are the same within a maximum 6% error for all the samples measured. These results are as expected since the bulk density and the total attenuation cross sections of the powders should not change significantly for different concentrations of BCC powder. With respect to the linear depolarization coefficient, the results further underline the high sensitivity of the method to detect low phase fractions down to sub-percent resolution in the case of iron. This high sensitivity in addition reveals that the commercial austenitic powder contains ferromagnetic phases, which is apparent by the depolarization measured for the allegedly 100% FCC phase sample. Indeed, a simple check with a permanent magnet confirms that the powder is lightly magnetic, possibly due to the existence of hematite on the surface of the powder particles.
A first degree polynomial fit, h(BCC) ¼ m BCC þ h 0 , of the depolarization coefficient versus the nominal BCC weight fraction yields very similar values for the different sample thicknesses, with slope m equal to 1.21 cm À1 and 1.16 cm À1 for the 2 mm and 5 mm thickness respectively and the offset h 0 , due to the ferromagnetic phases in the austenitic powder, equal to 1.10 cm À1 and 1.14 cm À1 . Furthermore, the reference measurements reveal insufficient mixing of the powders as agglomerations of ferromagnetic iron phase in some regions of the sample become obvious in the depolarization images (Fig. 2a)). Fig. 3 shows the radiographic maps of the ferritic phase fraction for the four different cruciform samples. The ferritic phase fraction has been calculated by first obtaining the linear depolarization coefficient as for the powder mixtures. A thickness map has been obtained from the attenuation contrast map, to correct for varying thickness in the sample. For quantification, the resulting images are scaled according to a reference point of high martensite fraction probed by neutron diffraction [8]. In the AR sample (i.e. prior to deformation), a low ferritic phase fraction can be observed with streaks along one of the cruciform arms' directions. Deformation results in strain-induced martensitic phase transformation at the center of the cruciform sample S1 (a) with phase fraction up to 5%, as well as some martensite transformation at locations where stresses concentrate (b). Upon further uniaxial straining (sample S2), the fraction of the strain-induced martensite increases in the whole region (c) into a more uniform distribution of phase fraction. After biaxial loading with a 49 kN: 59 kN load ratio between the cruciform axes (S3), the strain-induced martensite fraction is observed to be higher than in the two uniaxially loaded samples (S1 and S2). The resulting martensite phase fraction map, shows heterogeneous martensite concentrations that are associated with the stress localization in cruciform samples, as previously reported using neutron diffraction and/or diffraction imaging [8,22]. The central region of sample S3 was measured by neutron diffraction by sampling an area of 3.8Â3.8 mm 2 , which is schematically shown in Fig. 2. a) Transmission and polarization ratio radiographs of the powder mixtures in the 2 mm thick cuvettes, as well as one empty cuvette. b) Average transmission (blue colors) and polarization ratio (red colors) for each of the five powder mixtures in the 2 mm thick (light colors and round marker) and the 5 mm thick (dark colors and cross marker) cuvettes. c) The linear attenuation and depolarization coefficients corresponding to the b) panel. Note that the same color and marker layout applies. In dashed black is shown a line fit using the depolarization coefficient profiles. Fig. 3. The phase fraction obtained by neutron diffraction, i.e. 6.8% in the center of the cruciform S3, was used as a reference for calibrating the depolarization coefficient, averaged in the exact same area of 3.8Â3.8 mm 2 in the center of S3. It should be noted that PNI does not distinguish between magnetic phases having different crystal structures unlike diffraction methods.

Cruciform sample load tests
As aforementioned, in the low phase fraction regime, visible for the AR cruciform sample, the presence of strongly directional ferritic bands is observed, which are aligned parallel to the rolling direction. These are assumed to be caused by the presence of dferrite, due to their relatively low ferritic phase fraction and their strikingly strong directional shape. d-Ferrite is known to form in hot-rolled austenitic steel plates, and studies report that an austenitic matrix can contain up to 9% of d-ferrite [35].
The structural direction of the d-ferrite corresponds to the direction of the hot-rolling, and this was validated by repeating the PNI measurement after rotating the sample 90 around the beam direction axis. A corresponding rotation of the d-ferrite was observed confirming this was not an effect produced by background image artifacts. Fig. 4 shows an optical microscope measurement of a part of the cruciform sample after grinding the outer surface of the sheet, followed by polishing and etching. In the panel a), and especially in the highlighted area the presence of a band of d-ferrite, aligned with the hot-rolling direction, in the microstructure is confirmed. As such, the superimposition of all the d-ferrites can be revealed using PNI. It can be observed from the attenuation radiographs that the tensile load leads to an elongation and thus thinning of the sample from an initial diameter of 6 mm down to a final diameter of 5.8 mm for the 6% engineering strain load. However, the attenuation contrast does not exhibit significant contrast changes for the different stress load steps. In contrast, the depolarization contrast shows a gradual increase of strain-induced martensite, as the stress load increases, which becomes highly visible at the 2% engineering strain. At 6% engineering strain, the depolarization ratio reaches its maximum. The evolution of the strain-induced martensite was also measured with neutron diffraction at POLDI with a twin specimen, up to engineering strain of 20%, as shown in Fig. 5c). Utilizing the calibration of the previous sample S3 it can be seen that the initial stages of deformation match well between the two methods, and PNI is able to capture very well the transformation behavior up to strains of 6% engineering strain. At such low fractions neutron diffraction struggles to obtain reliable values, whereas PNI is especially sensitive in capturing the initial stages of the transformation.

Conclusion
Polarization contrast neutron imaging has been applied to study the presence of magnetic phases in iron-based materials and in metastable austenitic samples that partially transform to martensite upon deformation. The method introduces a multimodal approach for the analysis of the material microstructural properties through the complementary and simultaneous measurement of the attenuation of the neutron beam and the depolarization caused by the existence of magnetic phases. Experimentally, the method is based on highly efficient measurements in radiographic mode and it is seen to be exceptionally Fig. 3. Spatial mapping of the ferritic phase fraction (%) of the central part of the cruciform samples as it goes from as received (AR) condition, through two uniaxial loads (S1 and S2) and finally, a 49 kN: 59 kN biaxial loading (S3). The load directions are identical to those in Fig. 1b). Note the different phase fraction amplitude range in the color bars. The marked red box shows the 3.8Â3.8 mm 2 region used for the calibration, corresponding to the neutron diffraction gauge volume. sensitive in observing low ferritic/martensitic phase fractions, which are often obscured when using conventional diffraction techniques, as for instance the presence of d-ferrite needles in hot rolled steels. Unlike diffraction-based methods, depolarization imaging is not affected by grain size (e.g. poor grain statistics) or crystallographic texture in the material. In particular, the method offers good spatial resolution and allows to capture phase distributions of full scale bulk samples. The quantitative results during an in situ deformation test of a metastable austenitic steel agree well when related to conventional measurements, while PNI is particularly effective in detecting small fractions of martensite, during early stages of deformation. Finally, the method requires exposure times of only a few tens of seconds to a few minutes, making it promising in particular for time-resolved studies, e.g. to follow the evolution of the crystalline phase transformations in response to external loads, but also for tomographic measurements with many angular projections and correspondingly high spatial resolution.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.