# Slip localization and grain boundary sliding analysis at sub-voxel resolution using phase contrast tomography

Pedro Damas Resende, Damien Texier, J. Genée, Malo Jullien, Henry

Proudhon, Julien Réthoré, Didier Bardel, Wolfgang Ludwig

► To cite this version:

Pedro Damas Resende, Damien Texier, J. Genée, Malo Jullien, Henry Proudhon, et al. Slip localization and grain boundary sliding analysis at sub-voxel resolution using phase contrast tomography. Tomography of Materials and Structures, 2025, 8, pp.100060. 10.1016/j.tmater.2025.100060. hal-04997733

HAL Id: hal-04997733

https://imt-mines-albi.hal.science/hal-04997733v1

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# Slip localization and grain boundary sliding analysis at sub-voxel resolution using phase contrast tomography

Pedro Damas Resende<sup>a,b,*</sup>, Damien Texier<sup>c,**</sup>, Julien Genée<sup>c</sup>, Malo Jullien<sup>c</sup>, Henry Proudhon<sup>d</sup>, Julien Réthoré<sup>e</sup>, Didier Bardel<sup>f</sup>, Wolfgang Ludwig<sup>a,b</sup>

## ARTICLE INFO

### Keywords:

Topography

Phase contrast tomography

Laser scanning confocal microscopy

Slip localization

Grain boundary sliding

Diffraction contrast tomography

## ABSTRACT

Microplasticity of a polycrystalline Ni-based superalloy was investigated using phase contrast tomography (PCT) and laser scanning confocal microscopy (LSCM). Incremental tensile testing was performed on three miniaturized specimens to investigate strain localization at low plastic deformation at room temperature and 650 °C. Microplasticity events, such as slip activity, deformation twinning, and grain boundary sliding, are free to emerge at the specimen surface and generate sub-micrometer topographic features. High resolution digital image correlation was conducted using LSCM to have a description of the in-plane and out-of-plane kinematics of the specimen surface. Despite slip amplitudes substantially smaller than the voxel size, PCT was capable to evidence the out-of-plane component of slip traces at the onset of plasticity. The technique was also used at 650 °C, a temperature at which grain boundary sliding occurs, but surface reactivity is severe enough not to allow for topographic measurements using LSCM. Therefore, PCT was found particularly adapted to evidence "surface" microplasticity events hidden by an extra surface oxidation layer.

## 1. Introduction

Plastic deformation of materials is an irreversible process that can involve the participation of different elementary deformation mechanisms. For metallic materials, single or multiple slip localization, deformation twinning, phase transformations, grain boundary sliding, cross-slip, dislocation climbing, etc., can be activated individually or simultaneously, depending on the material, the stress conditions, and the temperature range. This plastic deformation is directly related to the crystallographic grain microstructure of the material and shows local patterns, which are typically confined to the grain and sub-grain level [1-3]. At ambient temperature, single or multiple slip localization in the form of slip bands is a common deformation process for most metallic materials. It corresponds to the planar and discrete shearing of the grain apart from a gliding plane - or series of adjacent crystallographic planes

- along given crystallographic directions, the cumulated Burgers vector. The cumulated Burgers vector can be the sum of a single slip system direction or the combination of several slip system directions belonging to the same slip plane. Slip activity characterization - and generally the characterization of microplasticity events - is central to understanding, modeling, and predicting the mechanical response of polycrystalline aggregates. Furthermore, recent work has established a direct relationship between the strain localization capacity of a material, i.e., the density and intensity of localized slip bands, and the fatigue endurance of metallic materials [4]. Therefore, characterization of the slip - microplasticity - activity is of high importance.

Identifying the stress at which a slip band forms in addition to its activity (slip amplitude) aims to measure the critical resolved shear stress (CRSS) and gliding capacity of a slip system, respectively. Topographic characterizations of microplasticity at the sample surface are

<footnote><sup>a</sup> European Synchrotron Radiation Facility - ESRF, 71 Avenue des Martyrs, 38000 Grenoble, France</footnote>

<footnote><sup>b</sup> MATEIS INSA Lyon, CNRS UMR 5510, University of Lyon I, Villeurbanne, France</footnote>

<footnote><sup>c</sup> Institut Clement Ader (ICA) - UMR CNRS 5312, Université de Toulouse, CNRS, INSA, UPS, Mines Albi, ISAE-SUPAERO, Campus Jarlard, Albi Cedex 09, 81013, France</footnote>

<footnote><sup>d</sup> Mines Paris, PSL University, MAT - Centre des matériaux, CNRS UMR 7633, BP 87, 91003, Evry, France</footnote>

<footnote><sup>e</sup> Nantes Université, École Centrale Nantes, CNRS, GeM, UMR 6183, Nantes F-44000, France</footnote>

<footnote><sup>f</sup> Framatome, 2 rue Professeur Jean Bernard, Lyon 69007, France</footnote>

<footnote>* Corresponding author at: European Synchrotron Radiation Facility - ESRF, 71 Avenue des Martyrs, 38000 Grenoble, France.</footnote>

<footnote>** Corresponding author.</footnote>

<footnote>E-mail addresses: pedro.damas-resende@esrf.fr (P. Damas Resende), damien.texier@mines-albi.fr (D. Texier).</footnote>
much more widespread and convenient than in the volume, based on the diversity of available observation techniques. For decades, slip trace analysis at the surface of deformed tensile specimens aimed to evidence emergence of dislocations at a free surface using a variety of observation techniques [5,6]: optical microscopy [7–10,11], scanning electron microscopy [12,13,11,14–17], interferometry [18–20], confocal microscopy [21–23], electron channeling contrast imaging (ECCI) [24,25] and atomic force microscopy [15,24,26]. While basic (2D) observation techniques (in particular light microscopy) only provide information on the occurrence or not of slip bands, topographic techniques are capable to quantify height steps and therefore more sensitive to deformation mechanisms giving rise to out-of-plane deformation components. Pure in-plane shearing is thus not trivial to be characterized since almost invisible due to low topographic contrast. Therefore, adding features onto the sample surface to track sub-grain deformation is a solution to have access to the in-plane component of the deformation. Micro-grid techniques and microstructure observations are also very informative for quantifying the in-plane discrete shearing at slip bands or at grain boundaries. Quantitative strain localization analyses were then further developed using photomechanical techniques, such as high resolution digital image correlation (HR-DIC) [27]. This latter technique, by tracking features at the specimen surface before and after deformation, is capable to assess kinematics fields at the microstructure scale to capture and identify slip activity, deformation twinning or grain boundary sliding. Recent developments in HR-DIC under optical microscopy (OM) [28–30], scanning electron microscopy (SEM) [31–34–37–40–43] or laser scanning confocal microscopy (LSCM) [21, 22,44] aimed to first identify intragranular microplasticity mechanisms at room temperature. Slip localization coupled with electron back-scattered diffraction (EBSD) measurements can identify both slip traces and the active slip system using the projected cumulated Burgers vector at the kinematic discontinuity [42,45,46] or using the three-dimensional cumulated Burgers vector [21]. This latter technique is thus capable of describing both the in-plane and out-of-plane nature of microplasticity events. Assessment of the out-of-plane component of the kinematic field is of high importance for the characterization of grain boundary sliding events, which cannot be solely assessed based on discontinuities of the in-plane kinematic fields [47–49]. However, grain boundary sliding is more pronounced at high temperatures, generally in the temperature range where surface reactivity is of concern, leading to significant difficulties in speckle stability for HR-DIC [15,47,50]. Surface reactivity can lead to microplasticity smoothing due to the formation of the external oxide scale and ultimately prevent the characterization of microplasticity. Therefore, assessing microplasticity beneath the external oxide scale is of high interest for deformation analysis of materials in reactive atmospheres. As far as volume characterization of microplasticity is concerned, recent developments in synchrotron X-ray based diffraction microstructure imaging techniques make it possible to visualize slip bands in three dimensions in the bulk of polycrystalline aggregates [51,52]. Despite significant advances, these techniques require a grain by grain scanning procedure and rely on identification and establishment of appropriate diffraction conditions for each of the grains. Here we propose a complementary and experimentally simpler approach, exploiting the sensitivity of propagation based X-ray phase contrast tomography [53]. Small variations in the electron density of the material, as created by microplasticity events at the sample surface, give rise to interference effects (Fresnel diffraction) and intensity contrast in the reconstructed 3D images.

The present study intends to demonstrate the capability of the combined use of phase and diffraction contrast tomography (PCT/DCT) to capture different strain localization events under experimental conditions that degrade and hide the speckle pattern used for HR-DIC from laser scanning microscopy techniques (LSCM). Ex-situ and in-situ tensile tests were conducted at room temperature and 650 °C, respectively, to activate different microplasticity mechanisms in the Alloy 718 samples, i.e., intragranular slip, slip in the vicinity of twin boundaries and grain

boundary sliding. The evolution of the elementary deformation mechanisms of Alloy 718 as a function of temperature has been intensively investigated in the literature over a wide range of temperatures. At room temperature, slip localization near and parallel to Σ3-twin boundaries and intragranular slip are the prominent strain localization events [21, 47,54–56]. In its precipitation-hardened form, Alloy 718 exhibits intense and very localized slip localization events in the form of slip bands. The intensity of the strain localization event depends on the fraction, size and morphology of the γ" precipitates [57]. Cryogenic temperatures are reported to favor deformation twinning in the form of intense strain localization events but also strain delocalization, leading to the formation of adjacent low intensity slip bands [58]. At 350 °C, slip localization near and parallel to twin boundaries and intragranular slip remain the principal deformation mechanisms [47]. However, testing Alloy 718 at 650 °C promotes strain localization in the vicinity of grain boundaries, leading to either grain boundary sliding (morphological sliding), grain boundary cavitation in the case of grain boundaries oriented normal to the loading direction, or grain boundary cracking due to intense intragranular slip [47]. The strain partitioning between intragranular slip and strain localization in the vicinity of the grain boundaries in Alloy 718 depends on the temperature [47], the grain size [48], and the strain rate [49]. Therefore, Alloy 718 is an interesting material candidate for the characterization of surface strain localization events at the microstructure scale over a wide range of temperatures. LSCM images (in-plane grayscale images and surface topography) were acquired before and after tensile testing to calculate displacement fields using HR-DIC, enabling the characterization of the three-dimensional nature of the microplasticity events. The strain localization events observed with PCT were compared with the in-plane and out-of-plane displacement jumps assessed using HR-DIC to demonstrate the sensitivity of PCT for detection of three-dimensional strain localization events on the sample surface. A first demonstration was conducted at room temperature for quantitative comparison between LSCM and PCT, considering in-plane and out-of-plane kinematics fields related to slip localization events. A second application was performed on a sample deformed at high temperature to compare height maps and PCT images to identify grain boundary sliding in addition to slip localization (HR-DIC was not possible here due to speckle pattern evolution). The last case concerns the use of PCT to detect strain localization events beneath a thick oxide layer, leading to inaccessible information on the out-of-plane measurement using LSCM. The method proposed hereafter emerges as a viable option to correlate crystallographic information and microplasticity events from in-situ experiments at a synchrotron beamline. The access to the third dimension allows discriminating grain boundary sliding and grain boundary cracking, which can be hard to differentiate using only LSCM measurements.

## 2. Material and experimental methods

### 2.1. Material

A polycrystalline Alloy 718 Ni-based superalloy was investigated in the present study. Its chemical composition is reported in Table 1. The material was provided as a rolled sheet by Huntington Alloys© in a solution-annealed condition. The sheet thickness was of 635 µm. Sample stripes were first machined from the rolled sheet using laser stencil techniques. They were then heat-treated to have grain sizes adapted to diffraction contrast tomography (DCT) experiments. The thermal treatment consisted of a 1050 °C dwell for 60 min under air, then water quenched, resulting in 100µm average grain size. The standard

<table><caption>**Table 1**
Nominal composition of the Alloy 718 Ni-based superalloy (in % (wt)).</caption><thead><tr><th>Element % (wt)</th><th>Ni</th><th>Cr</th><th>Fe</th><th>Nb+Ta</th><th>Mo</th><th>Ti</th><th>Al</th><th>C</th></tr></thead><tbody><tr><td>Alloy 718</td><td>Bal.</td><td>18.5</td><td>18.3</td><td>5.0</td><td>3.0</td><td>1.0</td><td>0.6</td><td>0.03</td></tr></tbody></table>
strengthening treatment was performed to obtain the conventional $γ''-γ'-γ$ metallurgical state: 720 °C for 8 h then 620 °C for 8 h. A cooling rate of 50 $°Ch^{-1}$ was used between 720 and 620 °C, followed by furnace cooling below 620 °C. Miniaturized dog-bone shape tensile specimens, compatible with the Nanox rig [59], were extracted from the sample stripes using electro-discharge machining (EDM). The samples had a total length 14 mm, a squared cross-section area close to 0.1 mm² (0.30 × 0.33 mm), and 2 mm gauge length. A schematic drawing of the sample geometry and its main dimensions is provided in the appendix A. The longitudinal direction of the tensile specimen was aligned along the rolling direction. The edge of the samples was then polished to remove the thermally affected layer and polished using a precision jig to ensure flatness and parallelism of the specimen [60]. One face of the specimen was polished down to P4000 SiC grit paper, and the opposite side was polished down to colloidal silica for electron backscattered diffraction (EBSD) analyses.

## 2.2. Description of the samples

Three samples, S1, S2, and S3, were tested in different experimental conditions. A summary of the used techniques and experimental conditions for each sample is provided in Table 2.

Sample S1 was subjected to three ex-situ incremental loading steps at room temperature. LSCM, DCT, and PCT measurements were done between each deformation step. HR-DIC using LSCM micrographs was used to describe both in-plane and out-of-plane slip localization events. To facilitate joint PCT and DCT characterization, PCT observations were carried out using the same optical configuration of scintillator - visible light microscope-based X-ray detector system as used for DCT yielding 1.1 µm effective pixel size. These scans, hereafter referred to as low-resolution (LR-PCT) were collected for each incremental loading step. A high resolution PCT scan (HR-PCT), deploying a different configuration of the detector with 0.55 µm effective pixel size, was also conducted after the third loading step.

Sample S2 was deformed in-situ at 650 °C. A relatively fast linear load rate was used up to the onset of plasticity and back to the initial load, the resulting strain rate was $10^{-3} s^{-1}$. An attempt to reconstruct tomography data from the in-situ deformation failed as the distortions in the projections evolved considerably during the scan. Sample S2 was cooled to room temperature just after the load/unload cycle. The high temperature exposure was 20 min considering dwell before tensile testing, loading, and unloading phases, thus limiting oxidation. After that, both HR-PCT and LSCM measurements were performed.

Sample S3 was deformed in-situ at 650 °C in load control at a lower linear load rate up to the first evidence of plasticity/cracking. The strain rate of $5×10^{-6} s^{-1}$ was estimated from projection images using an optical flow algorithm at each deformation step yielding $R^2=0.94$. No further surface treatment was applied to the sample, apart from the thermally affected zone by spark cutting that was ground away with P4000 SiC grit paper. HR-PCT measurements were performed continuously during the loading. Each scan took 90 s, and the sample had a maximum elongation of order of 1 pixel throughout such a scan. The reconstruction quality was similar between a reference static scan and a continuous one, no blurring effects were found. The total time of high temperature exposure was 240 min, after which the occurrence of surface defects was noticeable in projection images. High temperature oxidation led to the formation of external oxide scale of a few microns thickness, compromising the ability of LSCM to detect strain localization

events beneath this oxide scale.

## 2.3. Electron backscattered diffraction

Electron backscattered diffraction (EBSD) characterizations were conducted to have the average orientation per grain to further correlate microplasticity to local microstructure and crystallographic features. EBSD characterizations were performed before speckle pattern application using a JEOL JSM 7100 F scanning electron microscope equipped with a CMOS Symmetry S2 EBSD detector (Oxford Instruments). EBSD maps of 1000 × 800 µm were acquired with a square grid of 0.6 µm and 0.4 µm for the S1 and S2 samples, respectively.

## 2.4. High-resolution digital image correlation using laser scanning confocal microscopy

LSCM was used to assess both the in-plane and out-of-plane nature of the microplasticity events for further comparison with PCT characterizations. A LEXT Olympus OLS5100 (now EVIDENT) equipped with a 405 nm wavelength laser was used. High-resolution laser reflectivity and topographic measurements were performed using an MPLA-PON100XLEXT lens and image size of 4096 × 4096 pixels with a field of view of 128 µm (X/Y pixel size of 32.5 nm). The height pitch of 120 nm allows a resolution of 12 nm due to the sensitivity of the height reconstruction algorithm developed by Olympus. Height difference calculations detailed in Ref. [21,23] were applied to further combine out-of-plane and in-plane discontinuity events and relate them to the microstructure.

For the HR-DIC technique, the speckle pattern was obtained by pre-oxidation for 15 min at 650 °C in air atmosphere, as for refs. [47–49]. The OpenCV optical flow algorithm was used to assess in-plane displacement fields from laser reflectivity micrographs [61,62]. Optical flow parameters are summarized in Table 3.

## 2.5. Synchrotron techniques

The synchrotron experiments were conducted at the ESRF Materials Science beamline (ID11 - ESRF). The measurements used a sCMOS imaging camera (Andor Marana 4.2B-11), whose sensor is 2048 × 2048 pixels, with 11µm pitch. The camera was mounted on a visible light microscope, coupled to a 12 µm thick transparent luminescent screen (LSO:Tb) [63] and interchangeable optical lenses. A $10×$ NA= 0.28 objective, yielding an effective pixel size of 1.1 µm was used for DCT and low resolution PCT (LR-PCT) measurements, whereas a $20×$ NA= 0.40 objective, yielding 0.55 µm effective pixel size, was used for high resolution PCT (HR-PCT) measurements. Both DCT and HR-PCT acquisitions

<table><caption>**Table 3**
HR-DIC parameters using the optical flow technique [61].</caption><thead><tr><th></th><th>Optical flow</th></tr></thead><tbody><tr><td>Subset Size</td><td>8 pixels</td></tr><tr><td>Step Size</td><td>3 pixels</td></tr><tr><td>Subset Shape Function</td><td>Rigid</td></tr><tr><td>Interpolant</td><td>Bilinear</td></tr><tr><td>Matching criterion</td><td>Zero-normalized sum of square differences (ZNSSD)</td></tr><tr><td>Number of pyramidal scales</td><td>5 (final step at 1)</td></tr><tr><td>Variational refinement</td><td>σ= 20, γ= 10, α= 5</td></tr><tr><td>Strain step</td><td>7 pixels</td></tr></tbody></table>

<table><caption>**Table 2**
Summary of techniques and conditions applied to each sample group.</caption><thead><tr><th>Group</th><th>EBSD</th><th>LSCM</th><th>DIC</th><th>HR-PCT</th><th>LR-PCT</th><th>Loading</th><th>Temperature</th></tr></thead><tbody><tr><td>S1</td><td>✓</td><td>✓</td><td>✓</td><td>At the end</td><td>At each step</td><td>Incremental</td><td>Room temp.</td></tr><tr><td>S2</td><td>✓</td><td>✓</td><td>✓</td><td>Beginning/end</td><td>-</td><td>10<sup>-3</sup>s<sup>-1</sup></td><td>650°C</td></tr><tr><td>S3</td><td>-</td><td>-</td><td>-</td><td>Continuous scans</td><td>-</td><td>10<sup>-6</sup>s<sup>-1</sup></td><td>650°C</td></tr></tbody></table>
were performed using full frames while LR-PCT had a centered region-of-interest size of 1024 × 1024 pixels.

### 2.5.1. *In-situ* and *ex-situ* tensile testing

Tensile tests were conducted at room temperature and 650 °C to screen different deformation mechanisms as well as high temperature oxidation on the detection capability of strain localization beneath an external oxide scale. A custom tensile test rig - Nanox [59] - was used to test the miniature tensile specimens either in an in-situ or ex-situ manner. The Nanox test rig has a piezoelectric actuator for fine displacement control. The load was continuously recorded using the instrumented axis (calibrated strain gauge) of the device. A manual pre-load of 2 N was applied before tensile testing to ensure a stable sample position during initial scan acquisition. This load corresponds to 20 MPa engineering stress, which is far below the yield stress of the Alloy 718 in the temperature domain and therefore incapable of triggering plasticity in 718 alloys. For the high-temperature testing, the pre-load was manually adjusted during heating to compensate for the thermal expansion of the assembly. A resistive furnace with windows for the incoming and transmitted X-ray beam was used for the in-situ test.

### 2.5.2. *Diffraction contrast tomography (DCT)*

The parallel X-ray beam was set to the Hf K-edge energy (65.3508 keV, $\lambda$ = 0.18972 Å) with a Laue-Laue type monochromator. For Diffraction Contrast Tomography (DCT), a set of slits was placed in the beam trajectory to give it a horizontal dimension of 0.6 mm and a vertical dimension of 0.12 mm, allowing full illumination of the cross-section of a vertical subvolume of the sample. The sample was placed on top of the 3DXRD end-station of the beamline at a 7.5 mm distance from the detector system. The effective pixel size of the imaging setup was 1.1 µm. A partially transparent beam-stop was placed in the direct beam part of the image to reduce the image background, whilst still allowing for reconstruction of the absorption contrast volume alongside the DCT volume. The images were acquired over a 360° rotation angle ($\omega$) range, with a step-size of 0.1° and 100 ms exposure time. The procedure to reconstruct the DCT volumes was similar to the one described in Ref. [64] with an added step to find missing grains using the forward model based, voxel-by-voxel indexing approach described in [65]. Adjacent voxels are assigned as grains with an orientation threshold of 3°.

### 2.5.3. *Phase contrast tomography (PCT)*

Phase contrast tomography (PCT) was acquired using the same detector system on the same endstation as DCT. The intermediate step scans of sample S1 were taken with an effective pixel size of 1.1 µm, whereas the final higher resolution scan was acquired with 0.55 µm effective pixel size. Samples S2 and S3 had all measurements performed with 0.55 µm effective pixel size. Projections were taken at every 0.1° over a rotation angle range of 360°, and 40 ms exposure time. The final higher-resolution scan had a similar setup but with an angular rotation step of 0.06°. The sample-to-detector distance was set to 100 mm. High resolution scans used a 20× magnification Mitutoyo lens (NA = 0.4), while the low resolution used a 10× lens (NA = 0.28). The horizontal field of view for all the scans is 1.126 mm.

Due to geometrical constraints inside the tube-shaped furnace, flat-field images were acquired before and after projection acquisition in both cases. The flat-field correction was performed using a principal component analysis approach, in which the collection of flats was decomposed in its principal components at a $3\sigma$ confidence level. A model was fitted to determine a weight value for each component that leads to the minimization of variance of the corrected projection. The procedure is performed in a per-projection fashion, allowing the correction of beam-profile variation during the measurement.

A projection alignment step was performed to account for small rigid-body movement errors that could degrade the quality of the reconstruction when using only a single center of rotation shift to all the

projections. Therefore, all the shifts are individually refined to a sub-pixel level. The alignment is based on the tomographic consistency principle. It is calculated by minimizing the norm of the residual between the measured projections and the forward projection of the reconstructed volume at a given iteration. The implementation details can be found in Ref. [66].

After flat-field correction and projection alignment, the volume was reconstructed using the filtered back-projection algorithm implemented in the ASTRA toolbox [67]. The surface of interest of the samples, i.e., the surface on which LSCM and/or HR-DIC was performed, was projected onto a 2D image to enhance the visualization of strain localization events. This microplasticity detection was achieved by decoupling contrasts generated by the overall sample shape, particularly the smooth curvature of the sample surface, from contrasts generated by plasticity events. The 3D volume was cropped to a subvolume of about 20 xz slices comprising the sample's surface surroundings. The subvolume was thresholded and filled to define the voxel index $y_{surf}$ where the free surface lay along $\vec{y}$ for every $(x,z)$ position. The subvolume was then filtered with a 3D Gaussian filter to obtain a smoothed version of its gray level distribution. This smoothed version was subtracted from the unfiltered volume in order to highlight the slip band contrasts and the voxel intensities corresponding to the surface location were extracted (i. e. projection of the 3D curved surface on a planar $(x,z)$ grid). However, the maximum slip band contrast is observed at a few pixel offset from the previously determined free surface position, therefore different $(x,y_{surf} + y_{offset}, z)$ maps were produced, from which the one with highest standard deviation was chosen as the final result. The main steps of the algorithm are presented in Fig. 1.

## 3. Results

### 3.1. *Slip localization at room temperature: comparison between all the imaging modalities*

Tensile tests were first conducted on the Alloy 718 at room temperature (sample S1) to validate the different techniques for microplastic events detection and evaluate their sensitivity. Fig. 2 shows an overall view of the different image modalities, i.e., localized contrast due to topographical variations using HR-PCT, a height map using LSCM, and in-plane longitudinal (U) and transversal (V) kinematic fields, of a small region of interest, illustrated by an EBSD (inverse pole figure representation with the macroscopic loading direction as a reference direction). This deformation state corresponds to the third loading step: a macroscopic stress of 1186 MPa and a plastic strain of 0.28 %.

As observed in Fig. 2(a), different grains are present in the region of interest. Discrete linear events, confined to grains, were observed in the HR-PCT modality (Fig. 2(b)). These discrete events are also found as discrete jumps in in-plane and out-of-plane kinematics fields (Figs. 2(f, j, n)). The analysis of the orientation map confirms that these events correspond to slip localization related to slip activity on {111}<011> systems (slip trace). Based on the 3D character of each slip system and crystal orientation, the discrete displacement jumps in the loading and transverse directions, and the out-of-plane direction are different from grain to grain and not directly correlated. Although the kinematic field along the loading direction shows most of the slip discontinuities using HR-DIC, some events are sometimes less resolved in the two other directions. Three line profiles were extracted for the different modalities (line width of 11 pixels for averaging profiles), and the graphical representations are depicted in Fig. 2. For the profile #1, the slip traces are hardly distinguished in the HR-PCT modality. The corresponding displacement jumps were small in all the directions, approximately of 10–20 nm. For the profile #2, slip traces are clearly observed in the HR-PCT modality and correspond to intense longitudinal (approx. 80–120 nm) and out-of-plane (approx. 35–75 nm) displacement jumps. Transverse displacement jumps are insignificant (approx. 5–10 nm). For
<figure><img src="image_2.png" /><figcaption>Fig. 1. Main steps used in projecting the sample's surface onto a 2D image to be compared to LSCM, EBSD, HR-DIC, and height difference maps.</figcaption></figure>

the profile #3, slip traces visible on the HR-PCT modality are also intense in the longitudinal (approx. 110 nm) and out-of-plane (approx. 80 nm) kinematic fields. Transverse displacement jumps are approximately tens of nanometers. Therefore, slip traces on HR-PCT maps seem to be related to both intense longitudinal and out-of-plane displacement jumps. Based on the Schmid relationship and the requirement of colinearity between the slip direction and the loading direction to activate a system, it is somehow difficult to activate systems with out-of-plane displacement jump much greater than in-plane ones.

## 3.2. Incremental mechanical loading and event detectability using LR-PCT

Three deformation steps were investigated to capture the evolution of the slip localization when increasing the macroscopic plastic deformation. Low-resolution PCT (LR-PCT) and LSCM measurements were done before deformation and after each incremental tensile step. The different image modalities as well as the grain orientation maps of this region of interest are depicted in Fig. 3.

Before deformation, height difference maps and LR-PCT reconstructed surface showed reliefs related to oxidized non-metallic inclusions (NMI) eruptions [68] (white arrows in Fig. 3(b) and (c)) and grain boundary engraving (black arrows in Fig. 3(b) and (c)) related to the slight pre-oxidation and surface preparation technique. It is worth mentioning that these features will remain after deformation and will interfere with the development of slip localization. Therefore, assessing this type of surface imperfections is necessary to separate pre-existent features from deformation-induced surface features.

At the onset of plasticity (974 MPa/0.07 % plastic strain), few events are observed on the in-plane strain map. Depending on the in-plane/out-of-plane character of the active slip system, slip bands are more or less visible on the height difference map and LR-PCT. The events observed on the LR-PCT modality correspond to the slip localization having the most intense out-of-plane jump. These intense events are located near and parallel to Σ3-twin boundaries, as pointed by green arrows in Fig. 3(d), (e) and (f). Slip localization events having nearly in-plane sliding character are neither visible on the height difference nor “Low resolution” PCT modalities (yellow arrow in Fig. 3(d), (e) and (f)). At higher deformation levels (1119 MPa/0.21 % plastic strain and 1186 MPa/0.28 % plastic strain), the number and amplitude of strain localization events increased and they are visible in all modalities. As for the lower deformation step, slip localization events are more visible on the in-plane

strain map modality and less on the LR-PCT modality. However, the main and most intense strain localization events appeared in all modalities, despite the difference in spatial resolution between modalities. In other words, the slip localization seems qualitatively well described by HR-DIC, LSCM height maps, and LR-PCT modalities.

Each strain localization event was manually segmented and then labeled to quantitatively capture the relationship between in-plane/out-of-plane displacement jump and the capability to observe or not slip localization events on the LR-PCT modality. Event detections for all the deformation steps are summarized and illustrated in Fig. 4. The “All/In-plane events” category corresponds to the events visible on the in-plane strain modality since all slip localization events were visible on the HR-DIC in-plane strain maps. As mentioned earlier, the amplitude of the out-of-plane component is related to the crystal orientation and some events are visible on the in-plane strain map but not on the height difference maps due to resolution limits. With increasing deformation, an increasing fraction of these events are detectable in the LR-PCT modality. At the onset of plasticity (974 MPa/0.07 % plastic strain), 34 slip localization events were detected using the measurement from the in-plane strain field along the loading direction. 62 % and 18 % of the events were visible on the height difference map and the LR-PCT map for this loading condition, respectively. Fig. 5(a) aimed at visualizing the relationship between the event visibility on the LR-PCT modality and the maximal in-plane/out-of-plane displacement jump measured for each slip localization event. The out-of-plane sliding amplitude is the main parameter to consider in the event’s visibility on the LR-PCT modality. Indeed, all the events having an out-of-plane sliding amplitude greater than 30 nm are visible on the LR-PCT modality. It is worth reminding that the voxel size of the LR-PCT reconstruction is 1.1 µm, i.e., one order of magnitude greater than this discrete displacement jump. Similar relationships are observed for higher deformation levels, but the intensity of the slip localization events changed the fraction of event detectability for the different modalities. At 1119 MPa/0.21 % plastic strain, 19 % of the events were detectable while intensification of the strain localization events led to 57 % of event detectability for the 1186 MPa/0.28 % plastic strain condition for the LR-PCT modality. Similarly, the fraction of detected out-of-plane sliding events is lower for the 1119 MPa/0.21 % plastic strain condition (81 %) compared to the 1186 MPa/0.28 % plastic strain condition (94 %), as shown in Fig. 4. As for the low deformation level, the out-of-plane character of the slip localization seems to be the dominant factor of the event detectability with LR-PCT modality with a threshold of approximately 35–40 nm. Some events are
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Representation of the different image modalities to identify slip localization on a small region of interest of sample S1 and three line profiles (averaged laterally over 11 pixels): (a) EBSD map with IPF along the loading direction (LD), (b, c, d, e) High resolution-PCT (HR-PCT), (f, g, h, i) In-plane displacement field along the loading direction obtained by HR-DIC, (j, k, l, m) In-plane displacement field along the transverse direction obtained by HR-DIC,(n, o, p, q) Height map obtained by LSCM measurements.</figcaption></figure>

observed on the LR-PCT modality at lower out-of-plane sliding amplitude but it is not a generality. Only one event, corresponding to an out-of-plane sliding of 50 nm and greater (evidenced by the red arrow in Fig. 5(c)) is not detected due to the presence of carbides, degrading the visibility of this slip localization event on the LR-PCT modality (Fig. 5(b) and (c)).

### 3.3. Comparison of event detectability using different PCT resolutions

The effect of the PCT resolution was investigated on the last deformation step of sample S1 (1186 MPa/0.28 % plastic strain). The comparison between the low resolution phase contrast tomography (LR-PCT) and the high resolution phase contrast tomography (HR-PCT) modalities are depicted in Fig. 6. The signal on the HR-PCT modality is sharper and neater than the one on the LR-PCT modality, leading to higher event detectability for the low amplitude discrete displacement
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Evolution of the slip localization as a function of the incremental loading for the three imaging modalities. The first row represents the sample at the initial state characterized by (a) EBSD, (b) height difference map from LSCM, and (c) LR-PCT. The rows 2–4 represent each of the mechanical loading steps applied to the sample at 0.07 %, 0.21 %, and 0.28 % of plastic strain, respectively. Figures (d, g, j) represent the in-plane strain field along the loading direction, (b, e, h, k) are height difference maps obtained from LSCM, and (c, f, i, l) are LR-PCT images. Black and white arrows point to grain boundary engravings and non-metallic inclusions, respectively. Green arrows point to the most intense out-of-plane events near and parallel to Σ3 twin boundaries at the onset of plasticity, visible in the height difference maps and LR-PCT. The yellow arrow points to an event with a strong in-plane character that is not visible in the height difference maps and LR-PCT images.</figcaption></figure>

events. For the last deformation stage, the event detectability increased from 57 % (LR-PCT) to 75 % (HR-PCT). One can expect that further improvement of the spatial resolution (i.e. the use of X-ray nano-tomography/projection microscopy) will improve the event detectability of PCT and reach values comparable to or better than LSCM.

The event detectabilities for LR-PCT and HR-PCT are plotted in Fig. 7. The increase in resolution significantly improved the detection of low-amplitude sliding events to a limit of 25–30 nm and allowed the identification of 195 events in HR-PCT against 148 events in LR-PCT for 260 events in total (HR-DIC) and 244 events detected on the height difference map (LCSM) modality. The increase in numerical aperture favors the detectability of slip localization events having an out-of-plane sliding amplitude of tens of nanometers. Some slip localization events with an out-of-plane sliding amplitude of 10 nm can be detected using the HR-PCT modality but not all of them due to event length, event proximity to a defect such as specimen edges, and non-metallic inclusions.

### 3.4. Slip and grain boundary sliding event detection at high temperature for short high temperature exposure

Sample S2 was deformed at 650 °C to activate grain boundary sliding in addition to slip localization, as reported in Refs [47–49] for the Alloy 718 Ni-based superalloy. Even though short, the exposure to high temperature promoted enough surface evolution to hinder the HR-DIC measurement due to slight surface reactivity and light interference with the semi-transparent oxide. Topographic measurements were still possible for height difference mapping using LSCM, as shown in Fig. 8. HR-PCT analyses were also conducted and similar plastic localized events were found in both image modalities. Intense events at grain boundaries on the height difference map appear as intense dark events on the HR-PCT modality with white surrounding artifacts. These events correspond to either grain boundary sliding (black arrows in Fig. 8) or grain boundary cracking (white arrows in Fig. 8), as identified in the volume reconstruction (Fig. 8(d)). Slip localization parallel to and in proximity of twin boundaries appears particularly intense at this temperature (green arrows in Fig. 8). Slip localization and grain boundary sliding can be detected in both modalities, even if slip intensity seems less intense in amplitude but more numerous per grain at high
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Bar chart of slip localization events frequency for each strain step depending on the HR-DIC in-plane strain ("All/In-plane events"), the height difference ("Out-of-plane events"), and the LR-PCT ("LR-PCT events") modality.</figcaption></figure>

temperature compared to room temperature deformation. Some slip arrest and cross-slip events are also observed in both modalities of this high temperature observation (dashed red circles in Fig. 8), while slip localization was transgranular and in single slip configuration in the room temperature observations of S1.

### 3.5. Slip and grain boundary sliding event detection at high temperature for long high temperature exposure

Uniaxial loading was performed at 650 °C with an imposed strain rate of approximately $5 \times 10^{-6} s^{-1}$ for 2 h. The total test time was enough to promote oxide growth and apparent roughness increased due to the surface reactivity at high temperature. Both HR-DIC and topographic measurements using LSCM fail due to the formation of the thick oxide layer. However, HR-PCT successfully kept track of the surface and bulk evolution of the sample as deformation increased. A 3D grain orientation map (DCT) (Fig. 9(i)) was acquired at room temperature, before the start of the high temperature tensile test.

Fig. 9 shows the evolution of the surface of sample S3 as the deformation progressed. Between the first two deformation steps depicted in Fig. 9(a) and (b), it is possible to observe the surface evolution in terms of apparent roughness due to accelerated growth of the passive oxide layer on the sample surface at high temperature. In Fig. 9(b), it is possible to identify the early stage of a localized plasticity event while the rest of the sample showed no significant change at this stage. At greater deformation levels, intense slip localization parallel to a $\bar{\perp}$3 twin boundary as well as grain boundary sliding were observed. Less intense intragranular slip is also observed as linear features, different from the contrast generated by the external oxide scale that has an arbitrary speckle pattern organization/contrast, leading to additional noise. Furthermore, some cracks close to the sample's surface can be detected and confirmed via inspection of sub-surface slices of the PCT volumes. While LSCM cannot clearly dissociate cracks from localized micro-plasticity events, the access to the third dimension offered by the HR-PCT modality enables this type of classification despite a lower spatial resolution. The early localization event evidenced in Fig. 9(b) and pointed by a red arrow tends to greatly intensify compared to other events, leading to a surface step in Fig. 9(c) that continues to evolve until the end of the test. This intense slip localization event arises from specific geometrical conditions: (i) slip localization near and parallel to the

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Event detectability using the LR-PCT modality depending on the in-plane versus out-of-plane sliding amplitude for each event for the different loading conditions: (a) 974 MPa/0.07 % plastic strain, (b) 1119 MPa/0.21 % plastic strain, and (c) 1186 MPa/0.28 % plastic strain condition. The red arrow points to an event with out-of-plane displacement higher than 50 nm that could not be identified in the LR-PCT due to interaction with other features.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Comparison of the PCT reconstructions at high and low resolutions to the other imaging techniques. (a) EBSD map, (b) in-plane strain field along the loading direction, (c) height difference, (d) low and (e) high resolution PCT surface images, respectively.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Comparison of the slip localization detectability as a function of the in-plane/out-of-plane sliding amplitude of the event for the (a) LR-PCT and (b) HR-PCT modalities. The red arrow in (a) points to an out-of-plane slide amplitude above 50 nm that was not detected due to the interaction with other features, as presented in Fig. 5.</figcaption></figure>

twin boundary and (ii) grain being exposed to two free surfaces, leading to the non-restrictive motion of grains apart from the slip band. Despite the intense contrast in the PCT modality, this slip localization event did not lead to crack formation. As a general observation, the projected images of the sample surface develop contrast which progressively highlights the grain microstructure of the material due to the most intense slip localization occurring either at grain boundaries (grain boundary sliding or cracking) or twin boundaries. Similar observations were found in Refs. [47,48] for the deformation of the Alloy 718 Ni-based superalloy at 650 °C under vacuum with fine-grain and medium-grain size microstructures. However, the same studies also confirmed the importance of intragranular slip localization, accounting for 60 % of the overall events. Albeit still visible in some of the grains, the observations on sample S3 do not show as pronounced and clearly distinguishable slip localization contrasts as previously observed for samples S1 and S2.

## 4. Discussion

The 3D results obtained by phase contrast tomography (PCT) were compared to results obtained from laser scanning confocal microscopy (LSCM), combining direct 2D imaging, topographic and HR-DIC measurements to identify in-plane and out-of-plane slip localization and grain boundary sliding in the Alloy 718, as reported in recent studies [47–49]. The events visible in HR-PCT correspond to discontinuities observed in HR-DIC and height difference map imaging modalities. However, there are differences in the ability to identify such strain localization events depending on the character of the slip and the resolution of the technique being used. When applicable (i.e., in the absence of oxide scale), the high resolution digital image correlation (HR-DIC) technique is the most sensitive technique to depict strain localization at the sub-grain level, followed by LSCM height maps for events having an out-of-plane displacement component. The combination of both in-plane and out-of-plane information to resolve strain localization at the microstructural scale (intragranular slip and grain boundary sliding) offers the advantages of the description of the 3D-kinematics field that HR-DIC and/or Heaviside-DIC (H-DIC) techniques using scanning electron microscopy (SEM) images cannot document, unless combined with LSCM or atomic force microscopy (AFM). The out-of-plane response is particularly important for multiple slip activity within the same slip band [21], surface reorientation [69], as well as morphologic sliding such as grain boundary sliding [47–49]. In our findings slip event identification at the onset of plasticity using LR-PCT

and the height map difference calculated from LSCM was impossible for the events with a main in-plane character. With the increase of macroscopic deformation, most events became visible in both techniques, showing the feasibility of using tomography above a certain threshold amplitude.

Albeit being less accessible for routine measurements, the combination of DCT and PCT measurements using synchrotron light offers interesting possibilities for the study of strain localization during in-situ experiments, carried out at high temperatures. By correlating grain orientations at the sample surface (DCT) and intensity contrasts observed in the PCT images, it is possible to identify active slip planes and grain boundary characters related to strain localization. Each strain localization event has a specific gray-level signature, depending on the surface topography created by the deformation process. For a given amplitude of shear displacement, emergence angles of slip bands at the specimen surface close to 90° (i.e., dominant out-of-plane component) will give maximum density contrast and visibility in the PCT modality. As shown in the height profiles, LSCM can distinguish between 'positive' and 'negative' steps (i.e., positive and negative emergence angles - see Fig. B.1). Note that PCT can also discriminate between 'positive' steps, giving rise to black-white fringe contrast and 'negative' steps, giving rise to the reverse contrast behavior in the reconstructed images. The observed contrast allows to qualitatively rank different localization events according to their out-of-plane amplitudes. However, unlike LCSM, PCT measurements do not provide quantitative values for these out-of-plane displacements since the amplitude is typically below the voxel size of conventional PCT measurements. On the other hand, the 3D information provided by these tomographic techniques allows for (i) simultaneous study of all sample surfaces, (ii) better discrimination of cracks via inspection of related image contrasts in the sub-surface microstructure and (iii) studying the impact of the sub-surface grain microstructure on the strain localization events at the sample surface, i. e., triple junctions of grains in the volume, as reported by Charpagne et al. [55] or grain boundary inclination in the volume [47]. The source of contrast in PCT is briefly discussed in the appendix C.

When considering all types of strain localization events under experimental conditions similar to the ones used for sample S3 (in Ref. [47]), more than 60 % were attributed to intragranular slip at 650 °C. The strain rate of the present study was, however, one order of magnitude lower. At lower strain rates, strain partitioning between intragranular slip and grain boundary sliding favors grain boundary sliding, thus limiting intragranular slip, as recently reported in Ref. [49]. Furthermore, the microstructure size and interaction with a free surface
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Representation of the different image modalities to identify slip localization and grain boundary sliding for deformation of sample S2 at high temperature and short exposure time. (a) EBSD map with IPF about the loading direction (LD), (b) height map obtained by LSCM measurements, (c) high resolution-PCT (HR-PCT) modality for surface reconstruction, and (d) high resolution-PCT (HR-PCT) modality for slice reconstruction beneath the surface of interest. Green arrows point to strain localization close and parallel to twin boundaries. Black arrows point to grain boundary sliding events, and white arrows point to grain boundary cracking.</figcaption></figure>

can also affect strain partitioning [48]. Therefore, limited observation of intragranular slip for such oxidizing conditions remains an open question due to strain rate, microstructure, and/or free-surface effects or technique resolution. The first detected localization event in sample S3, shown in Fig. 9(b) occurred at 0.8 % strain and around 400 MPa. The strain value in this case accumulates elastic and plastic deformation because the sample was under tension when the projection images were acquired. Nevertheless, it accounts for, at least, double the plastic strain at the last step of deformation in sample S1, where sharp and well-defined slip localization events could already be seen at this stage.

There are a number of possible explanations for the observed disparity, which could partly be caused by differences in the active deformation mechanism(s). In parallel, this observation could also be linked to a progressive loss of the technique's ability to retrieve weak slip localization events from images acquired after deformation and elongated exposure to the high temperature oxidative atmosphere. The

reduced visibility of slip localization events for sample S3 may be due to a combination of factors like: (1) the lack of surface polishing, (2) the development of pronounced surface relief due to plastic deformation, which progressively highlights the grain microstructure of the material and (3) progressive oxidation of the surface steps created by slip localization, leading to a reduction of the amplitude in (electron) density contrast at the sample surface. The first two mechanisms create spurious image contrasts which can reduce the visibility of the slip bands and highlight the importance of good surface preparation. The existence and contribution of the latter mechanism could be evaluated from additional experiments carried out under vacuum.

Between the LR-PCT and HR-PCT, the sensitivity for identifying out-of-plane events has been improved by increasing the spatial resolution of the detector system (smaller effective pixel size). The present study achieved this by increasing the numerical aperture of the visible light objective deployed in the detector system. For all the detected events,
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** (a-h) Temporal evolution of sample S3 surface retrieved from the HR-PCT acquired during in-situ high-temperature tensile tests. Test times for each step are (a) 0, (b) 22, (c) 31, (d) 52, (e) 73, (f) 95, (g) 108, and (h) 130 min. (i) DCT reconstruction at the surface of sample S3, colors represent the average orientation of each grain according to an IPF map about z. The red arrow in (b) points to the location of the first strain localization event related to a twin boundary pointed in (i).</figcaption></figure>

either in LR or HR-PCT, the magnitude of the out-of-plane displacement associated with the slip localization is at least one order of magnitude smaller than the voxel size and far below the theoretical resolution limit of the imaging system. We anticipate that significant further sensitivity enhancement can be expected by deploying X-ray projection microscopy, a propagation based phase contrast tomography variant using X-ray optical magnification [70,71]. The smaller effective voxel size (down to 50 nm) should allow for the identification of shorter (parallel to the trace) and less intense (out-of-plane) localization events and might even enable quantification of the out-of-plane displacement, which starts to be spatially resolved at this resolution.

For a small sub-set of engineering materials, exhibiting a suitable dispersion of precipitates or two-phase microstructure giving rise to image contrast in the tomographic reconstruction, the use of digital volume correlation techniques [72–74] might allow to capture the evolution of the 3D displacement field in the bulk of the material. Combined with crystallographic analysis (DCT), this could bring the study of strain localization to the next level, enabling quantitative analysis of shear amplitudes and directions in the bulk of polycrystalline

samples.

As stated earlier, more advanced 3D X-ray diffraction microstructure imaging techniques such as topotomography [51,75,76], scanning-3DXRD[77], differential aperture X-ray microscopy (DAXM) [78, 79] and X-ray dark-field microscopy [52] show potential to detect and characterize strain localization events based on small variations in lattice orientation and elastic strain fields observed in vicinity of the associated dislocation structures.

## Conclusions

The present study focused on the comparison of different imaging modalities to detect and quantify slip localization and grain boundary sliding events using high resolution digital image correlation (HR-DIC), laser scanning confocal microscopy (LSCM) for topographic measurements, and high/low resolution phase contrast tomography (HR-PCT). The main take-home message to consider are:
* In-plane HR-DIC was the most resolved technique to assess slip localization using optical techniques. Topographic measurements using the LSCM modality were highly resolved but some events could not be detected with this technique due to the dominant in-plane sliding component of their active slip system. HR-PCT was sufficiently resolved to identify out-of-plane slip localization and grain boundary sliding events but with a lesser resolution;

* The spatial resolution of the PCT detector system (numerical aperture of the visible light microscope) has a strong influence on the event detectability: higher resolution clearly enhances the capability to detect microplasticity events with amplitudes far below the (spatial) resolution limit of the detector system;

* The PCT modalities deployed in this study do not spatially resolve the actual surface height relief. They capture intensity contrasts (Fresnel diffraction) created by local variations of the material's electron density. The surface roughness caused by microplasticity events gives rise to local variations of the electron density, which induce phase shifts in the transmitted X-ray beam. The phase shifts give rise to refraction effects and free-space propagation turns these into intensity modulations (Fresnel diffraction - edge enhancement regime) observed in the radiographs and tomographic reconstructions.

* Events detected using the PCT modality are strongly dependent on the out-of-plane character of the microplastic events. In-plane events are nearly invisible for the PCT reconstruction as they do not contribute to variations of the material (electron) density at the sample surface;

* Tests at high temperature demonstrate the interest of the HR-PCT modality to detect both slip localization, grain boundary sliding events, and grain boundary cracking. Surface reactivity leads to the formation of oxide scale and limits the use of HR-DIC and LSCM topographic measurements for microplasticity event detection in these conditions;

* HR-PCT enables simultaneous characterization of all sample surfaces and access to the third dimension allows to distinguish strain localization events from cracks via inspection of the reconstructed material volume in the sub-surface area.

## License

This research was funded, in part, by The European Research

Council, project HT-S₄DefOx - Grant number 948007. A [CC-BY public copyright license] has been applied by the authors to the present document and will be applied to all subsequent versions up to the Author Accepted Manuscript arising from this submission, in accordance with the grant's open access conditions.

## CRediT authorship contribution statement

**Julien Genée:** Visualization, Methodology, Investigation. **Damien Texier:** Writing – original draft, Visualization, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Pedro Damas Resende:** Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Wolfgang Ludwig:** Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Didier Bardel:** Writing – review & editing, Supervision. **Julien Réthoré:** Writing – review & editing, Supervision. **Henry Proudhon:** Writing – review & editing, Methodology, Investigation, Data curation, Conceptualization. **Malo Jullien:** Methodology, Investigation, Formal analysis, Data curation.

## 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.

## Acknowledgements

This work was supported by the European Research Council [project HT-S₄DefOx - Grant number 948007]. P. Resende has received funding from Marie Skłodowska-Curie Actions under grant agreement No 847439 (InnovaXN). The authors acknowledge the European Synchrotron Radiation Facility for acceptance of the MA-6061 session [DOI: doi.esrf.fr/10.15151/ESRF-ES-1531407153], and MA5413 [DOI: doi.esrf.fr/10.15151/ESRF-ES-953230844]. D. Texier is very grateful to EVIDENT (before OLYMPUS) for providing the LEXT Olympus OLS5100 LSCM microscope for the MA6061 ESRF session.

## Appendix A. Sample geometry

<figure><img src="image_13.png" /><figcaption>Fig. A.1. Sample geometry for the Nanox device used in this work.</figcaption></figure>
## B. Contrast behaviour for positive and negative emergence angles

<figure><img src="image_14.png" /><figcaption>Fig. B.1. Surface topography created by slip bands in the case of tension (top) and compression (bottom) loading and associated contrasts observed in PCT (middle). The emergence angle in tension loading is between +90 (upward step) and -90 (downward step) degrees - compression loading will lead to angles bigger than 90 degree but similar image contrast in PCT.</figcaption></figure>

## C. Slip localization events in PCT - Source of contrast

From the out-of-plane measurements we observed that the height jumps associated with the slip localization events are below the spatial resolution of the detector system by an order of magnitude. Therefore these displacements can not be *spatially* resolved - they might still be visible in a reconstructed volume in terms of 'intensity contrast'.

As discussed by Margaritondo and Hwu [80], the contrast observed in tomography projections results from a combination of different mechanisms. Absorption contrast might be enhanced by refraction effects producing a pair of dark-bright fringes depending on the path of rays close to the surfaces. The width of these fringes ($w_f$) increases with propagation distance ($d_p$) and the deflection of angle ($\mu$) caused by the object's surface as $w_f \sim d_p\mu$. However, this contribution tends to fade with increasing distance. Another source of enhancement that plays a major role is edge enhancement by Fresnel diffraction, which oppositely to the prior, always increases with the propagation distance and produces more than a single pair of dark-bright fringes next to discontinuities in the phase shift of the transmitted wavefront. Our observations, depicted in Fig. C.2, suggest that the source of the modulations in the detected wavefront is of the latter type (i.e. increasing with propagation distance) and hence due to the local difference in the electron density created by slip bands and associated surface steps at the sample surface. These local modulations lead to contrasts (fringes with a period of up to several pixels) related to features one order of magnitude smaller than the spatial resolution of the detector system. After tomographic reconstruction, these image contrasts translate to intensity variations of voxels situated in the neighborhood of discontinuities in the material's electron density, such as internal voids or irregularities and relief at the sample surface. Fig. C.1 shows the sample's surface in one projection where the surface of interest is slanted and a pair of parallel slip events are seen (pointed by the blue arrow). Fig. C.2 depicts the same projections as in Fig. C.1 filtered with a high-pass Butterworth filter. At 50 mm propagation distance, we can observe the contrast provided by the sides of the sample, producing typical fringes related to the overall sample shape. These fringes increase laterally as the propagation distance increases. One can also observe that at the same time, the slip localization events become more visible at the sample's projection. In Fig. C.2(d) it is possible to notice a complex contrast from the combination of the sample's shape and the slip bands.
<figure><img src="image_15.png" /><figcaption>Fig. C.1. Projections taken from sample S1 at (a) 50 mm, (b) 75 mm, (c) 100 mm, and (d) 200 mm propagation distances showing slip localization events at the surface of interest. The blue arrow points to the parallel slip localization events.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. C.2. Butterworth high-pass filtered projections taken from sample S1 at (a) 50 mm, (b) 75 mm, (c) 100 mm, and (d) 200 mm propagation distances showing slip localization events at the surface of interest. The blue arrow points to the parallel slip localization events.</figcaption></figure>

In Fig. C.3 we present the surface of the sample extracted from PCT reconstructions as we show in our results, a high-pass Butterworth filter was applied to the image to highlight slip bands. We see that all the propagation distances produce contrast from the slip bands, as all the acquisitions performed are above the minimum distance to have detected phase contrast at the combination of wavelength and effective detector system pixel size. Similarly to what was observed in the projection images (Fig. C.2) the increase in propagation distance increases the width of the reconstructed contrast. However, the increase of propagation distance is not always interesting in promoting event visibility as slip events that occur close to each other might merge in a single broad event.
<figure><img src="image_17.png" /><figcaption>Fig. C.3. Images extracted from high-resolution PCT reconstructions around a pair of slip bands. The acquisitions were performed at (a) 50 mm, (b) 75 mm, (c) 100 mm, and (d) 200 mm propagation distances. The image was filtered with a high-pass Butterworth filter.</figcaption></figure>

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