Revealing 3D strain and carbide architectures in additively manufactured Ni superalloys

Abstract

Laser Additive Manufacturing (LAM)-induced directional solidification creates complex microstructures in nickel-based superalloys, featuring columnar grains with cellular sub-grains and carbides. Using Scanning 3D X-ray Diffraction (S3DXRD), we reveal orientation and intergranular strain relationships coupled to cellular sub-grain networks and primary cubic MC carbides. We analyzed 3D orientation and elastic strain fields across 82 γ grains and 37,000+ carbides in an ABD-900AM alloy produced via Directed Energy Deposition (DED). Cooling-induced solute segregation creates volumetric lattice parameter patterning in the γ phase, altering residual stress fields. Ti-, Ta-, and Nb-rich carbides form preferentially in these high-solute regions, exhibiting weak orientation relationships with parent γ grains. These results provide the first non-destructive 3D study linking rapid solidification segregation, deformation heterogeneity, and carbide architectures in additively manufactured Ni-superalloys. These insights provide crucial detail to rationalise LAM process parameter optimisation and the coupled spatially governed structural performance.

Researchers present a highly detailed, synchrotron resolved, 3D microstructural investigation of how tiny structures/defects form inside nickel superalloys during metal additive manufacturing, with the goal of helping engineers build tougher jet engines and turbine parts.

Introduction

Laser Additive Manufacturing (LAM) methods such as Laser Powder Bed Fusion (L-PBF) and Directed Energy Deposition (DED-LAM) enable the rapid production of near-net-shape components with complex geometries, offering substantial reductions in material waste and buy-to-fly ratios compared to conventional subtractive methods^1–4. These advantages make LAM attractive for high-value aerospace applications, particularly for Ni-based superalloy components requiring the most demanding high-temperature performance^5,6. Beyond reducing cost and waste, DED-LAM in particular enables the repair of critical components such as turbine blades⁷. DED-LAM provides faster build rates, larger melt passes than L-PBF and the flexibility for localised or site-specific builds, making it particularly suitable for large components and repair strategies.

Despite this promise, LAM of Ni-based superalloys remains challenging. Rapid, highly directional solidification that is inherent to the processes leads to anisotropic mechanical properties due to strong crystallographic texture^8–10, interdendritic cracking¹¹, and substantial residual strains^9,12–15. At smaller length scales, cellular sub-grain structures form; a feature that has been observed across several DED-LAM alloy systems, including stainless steels^16–19, Al-based alloys^20,21, CoCrMo alloys^22–24, and Ni-based superalloys^9,11,25,26. Honeycomb-like sub-grain networks emerge due to constitutional undercooling conditions when the preferred growth direction (〈100〉 in cubic systems) aligns with the maximum thermal gradient^16,22,27. The result is a highly inhomogeneous sub-grain microstructure—the cell boundaries, which solidify last, are solute-rich with high densities of dislocations and primary or secondary phase particles, while the cell cores are softer and solute lean^{12,16,26–29}. Cellular structures have attractive characteristics—they improve the strength of as-built components via hetero deformation-induced strengthening, which includes several underlying mechanisms: dislocation density modification^{16,28,30–32}, solute segregation^26,32,33, and precipitation strengthening^34–36. In DED-LAM-produced Ni alloys, the crystal structure and stoichiometry of inhomogeneous cell-boundary phases depend on the bulk composition. However, when elemental partitioning promotes the formation of phases such as Laves, δ and MC, mechanical properties, including impact hardness, fatigue life, and fracture toughness, are significantly compromised^37–42. The spatial distribution of precipitates is also an important factor; as an example, micron-sized MC carbides in DED-LAM IN718 have recently been shown to be a primary source of fracture⁴³. They have also been shown to modify the corrosion pathways due to the heterogeneous solute concentrations^44,45.

Given the importance of the cellular structure in LAM materials, recent studies have sought to obtain three-dimensional morphologies through two-dimensional imaging and Electron Back-Scatter Diffraction (EBSD) methods^17,46,47, as well as 3D modelling^48,49. However, investigations of precipitate phase distributions and crystallographic orientations—though mature and varied—have remained almost entirely two-dimensional, primarily due to the small size of precipitates relative to cellular length scales^28,36.

Recent advances using TriBeam serial sectioning that combines EBSD and Scanning Electron Microscopy (SEM) have enabled direct large-volume three-dimensional measurements of grain orientations and geometrically necessary dislocation (GND) densities in L-PBF-produced Ni-based superalloys^50–54. These studies also captured precipitate phase distributions through additional serial sectioning and imaging⁵⁰. Recent 20 nm resolution direct electron detection EBSD scans of LPBF-produced superalloys by Lamb et al.⁵⁴ have demonstrated how a high GND density exists along cell boundaries, which accommodate substantial misorientations between cells. Separately, non-destructive methods such as Dark Field X-ray Microscopy (DFXM) have provided valuable insights into cellular morphologies and elastic strain field components within individual grains of LAM-produced Ni-based superalloys⁹. Chen et al.⁹ also provided evidence for differences in measured elastic strain fields between the surface (measured with EBSD) and the bulk (measured with DFXM), highlighting the importance of non-destructive strain characterisation methods where the 3D polycrystalline aggregate imposes additional constraints on the strain state. The hierarchical nature of DED-LAM-induced microstructures, coupling sub-micron cell-decorating carbides⁴⁰ with highly-columnar grains spanning hundreds of microns⁵⁴, makes it fundamentally challenging to capture all microstructural phenomena with a single characterisation technique.

Here, we present the first Scanning 3D X-ray Diffraction (S3DXRD) study of an LAM-processed (DED-LAM) Ni-based superalloy: ABD-900AM, designed for high printability^11,55,56. The dataset captures grain-averaged orientations and 3D elastic strain tensor fields across hundreds of γ-phase (A1 crystal structure, using Strukturbericht designation) grains, together with the indexed positions and orientations of ~37,000 MC carbides. This comprehensive, volume-resolved dataset—essential for predictive modelling, alloy development, and resource-efficient manufacturing—enables direct examination of strain and orientation dependencies of both the γ matrix and carbides. S3DXRD adds to existing characterisation approaches by measuring elastic strain fields non-destructively with exceptional minor phase sensitivity, providing a more complete picture of microstructure-property relationships in LAM of Ni-based superalloys.

Results and discussion

Characterising the as-printed microstructure

S3DXRD was employed to capture three-dimensional localised crystallographic orientation, elastic strain fields, and phase information. A schematic of the experimental configuration is shown in Fig. 1b, with details of the acquisition process provided in the “Methods” section. Each S3DXRD layer was acquired via a sequence of sample rotations—the sample was rotated 360^∘ in ω with a step size δω = 0.125^∘ while diffraction images were collected. In total, 18 layers were collected to give a measured volume of 200 × 175 × 90 μm³ with a 5 μm Z (vertical) spacing between layers. The sample was oriented such that the height of the sample (build direction, see Supplementary Fig. 1) was approximately parallel to the laboratory Z axis.

Fig. 1. γ matrix and primary MC carbides revealed by SEM and S3DXRD.

a, d Backscatter electron micrographs of a sectioned sample with build direction parallel to the labelled Z-axis, at low (a) and high (d) magnifications. Annotated features include an example MC carbide circled in green in a and sub-grain cellular structures highlighted in white in d. b A monochromatic point-focused X-ray beam illuminates the sample mounted on the Nanoscope diffractometer (ID11, ESRF), showing stage names and the laboratory coordinate system. The sample is rotated in omega and translated transverse to the incident beam in Y. Diffraction patterns are collected downstream on the detector. c Reconstructed S3DXRD volume, γ phase, coloured by grain-averaged orientations (IPF-Z) showing the columnar as-printed microstructure. f A single γ grain comprising two dendrites (highlighted in yellow and pink) is isolated from c and shown in two perspectives. e The top Z-layer of γ grain from f, coloured by diffracted intensity with positions of MC overlaid in green (right).

To identify the phases, histograms of the observed diffracted intensity vs d^* (inverse d-spacing) across the full set of segmented diffraction peaks in all S3DXRD layers were generated, yielding a one-dimensional intensity profile; this is shown in Supplementary Fig. 6. Peak indexing confirmed the microstructure comprised γ (FCC, a_γ = 3.589 Å) and cubic MC (A1, a_MC = 4.39 Å) phases only. There is no evidence of the L1₂ structured γ′ precipitates, which would be present under thermodynamic equilibrium conditions¹¹. The Laves phase was also not observed. Thus, the as-built DED-LAM Ni-based superalloy sample studied here has a non-equilibrium microstructure with a highly supersaturated γ matrix.

The microstructure was spatially quantified by tomographic reconstruction of the S3DXRD measurements. The sample contained 82 γ grains and 37944 MC carbides, recorded across all Z layers with a mean of 60 γ grains per Z layer. A merged map of γ grains is shown in Fig. 1c, with grains coloured by their grain-averaged orientations via a Z-axis Inverse Pole Figure (IPF-Z). A highly columnar microstructure is observed, with the long axis inclined close to the Z axis (the build direction). The columnar feature of the grains was more evident when observing an isolated grain, as shown in Fig. 1f. Two 〈100〉 directions for the grain of interest are included, indicating a distinctive change in growth direction—this is likely attributed to a switch in the thermal gradient directions during the build process, while the laser pass direction reverses on the bi-directional thin wall build. In Fig. 1e, a single layer from this grain is shown, coloured by the diffraction intensity propagated by the tomographic reconstruction. Areas of low diffraction intensity (darker regions) within the γ grain are clearly visible—small spots of reduced intensity indicate the presence of an additional phase and/or porosity in the sample. By overlaying the centre-of-mass positions of the MC carbides associated with this grain in this Z-layer, they align well with many of the intensity gaps.

Figure 1a, d provides an overview of the sample microstructure from backscatter-electron images (BEI). While S3DXRD measurements were taken from a different region of the same sample, the images are representative of the as-built microstructural condition and confirm a complex grain morphology, exhibiting tortuous grain boundaries with a high density of carbides that are dispersed at both intragranular and intergranular locations. A small degree of porosity is also observable in the SEM images, which may explain the lack of complete carbide coverage of the darker regions in Fig. 1e, although it is challenging to verify that all carbides were correctly identified during the indexing stage, due to the relatively weak diffracted intensity and high degree of spatial clustering of carbide grains.

Lattice parameter mapping

Local unit cell refinement⁵⁷ was performed on the S3DXRD dataset. By averaging the local lattice lengths (a, b, c), the spatial variance in lattice parameter can be directly investigated, as shown in Fig. 2a–c, where a clear sub-grain cellular morphology is observed. Interestingly, the cell boundaries have ā ≈ 3.589 Å, indicating a lattice parameter very close to the size of the reference γ unit cell. Cell cores, in contrast, display consistently reduced lattice parameters, indicating a substantial depletion of the solute elements in these regions, induced by the rapid non-equilibrium solidification during the build process. These observations have been validated in the Energy Dispersive Spectroscopy (EDS) map (Fig. 2d), with images taken from the same area as Figs. 1a and 1d). The Ti distribution map is presented here—area maps of other elements are shown in Supplementary Fig. 7 with a line scan across a cell boundary in Supplementary Fig. 8. Chemical segregation between cell boundaries and cell cores is clearly observed, which is highly correlated with the observed lattice parameter variations.

Fig. 2. Local lattice parameter refinement reveals cellular sub-grain structures.

Lattice parameter maps viewed as a, a single Z layer (build direction out of page), with the grain boundaries (GB) in black, a grain of interest (GOI) indicated in magenta, and a magnified region bordered in green. In b, a magnified single grain is shown, and c the GOI viewed along the transverse to the vertical dashed line in a (build direction vertical). A change in solidification direction is captured in c, concomitant with a localised increase in mean lattice parameter. In d, solute segregation is clearly identified—an EDS map of the Ti concentration (wt.%) as an example element demonstrates that the solute concentration field matches the length scale of the lattice parameter modulation observed in the S3DXRD measurements.

A variation of grain and cell size and shape was observed within the sample cross-section, hypothesised to be due to changes in cooling rates and deposition directions during the building process. These variations correlate with regions of significant lattice parameter change. There may also be contributions from residual mechanical elastic strain. By taking a_γ as an unstrained reference unit cell, the full elastic strain tensor at each voxel can be computed. Maps of each strain tensor element for the layer shown in Fig. 2 are provided in Supplementary Fig. 9. The regions of significant lattice parameter change correlate with areas of substantial elastic strain, corroborating other 3D polycrystalline studies that showed larger strains are generally associated with smaller grains (e.g.,⁵⁸). Observations in this study are limited to just a few grains, so a generalised trend cannot be inferred. In our sample, where the lattice parameter field of a large central grain is plotted along the vertical build direction (Fig. 2c), a clear boundary layer is observed, which is associated with an increased overall lattice parameter—this could be explained by a deposition direction change during the bi-directional print that may have been captured within the measured volume. The grain growth directions align well with the 〈001〉 preferential growth directions^54,59 annotated in Fig. 2c, supporting this hypothesis.

MC spatial distribution

In Fig. 3a, carbide locations are denoted on the lattice parameter field. Note that the markers indicate the centre of mass positions of the MC carbides only; their volumes cannot be reliably determined from the experimental data, due to their variable compositions. The carbides preferentially decorate the cell and grain boundaries, corresponding to the regions of significant chemical segregation. This is supported by quantifying the observed change in lattice parameter as a function of distance from each MC carbide, as plotted in Supplementary Fig. 10, which yields an average cell size of ≈9.5 μm—significantly larger than typical cell sizes for other printing methods (sub-micron for LPBF^16,30)—but aligning well with prior DED-LAM studies on Ni superalloys^43,60 and with broader studies of eutectic solidifications⁶¹. Some preferential grain boundary decoration is also present, as explored quantitatively in Fig. 3c. By computing the likelihood that a random position in the sample volume would touch a grain boundary, the Random distribution was generated. When computing the observed spatial distribution of the MC carbides, a clear preference for grain boundary decoration is evident, at a significance of more than 5 standard deviations from the random distribution. 38032 carbides were used during this statistical test, which was performed across the full 18-layer dataset.

Fig. 3. Spatial and orientation distributions of MC carbides.

a Single Z layer with lattice parameter colouring for the γ phase, with the grain boundaries (GB) highlighted. The MC carbide positions are overlaid in magenta (when near a GB) and black (otherwise). Inset: detail view of grain-of-interest. Carbides clearly decorate sub-grain cellular boundaries in regions of increased mean lattice parameter. b Pole figures of misorientation density functions for the MC carbides with respect to their parent γ grains, coloured by multiples of random distribution (MRD). A weak orientation relationship is present. c Fraction of MC carbides (all layers) located within 1 μm of grain boundaries (MC) versus the expected distribution for random points (Random). The Z-score indicates the number of standard deviations between the random and observed distributions. Carbides are also shown to preferentially decorate grain boundaries.

Constitutional supercooling⁴⁸ during solidification ultimately promotes primary carbide formation at the cell boundaries and controls their spatial distribution—the growing γ sub-grain cells reject solutes, enriching certain elements in the intercellular liquid. In this case, carbides are enriched in refractory elements Ti, Ta & Nb²⁸, evident from a prior study⁶² in the L-PBF condition. EDS analysis confirms Ti and Nb enrichment at cell boundaries (~+2.5 wt.%), with a concomitant depletion of Ni, Co and Cr. The reader is referred to Supplementary Figs. 7 and 8 for EDS maps and line scans of multiple elements. A similar result was observed for this alloy solidified at a faster rate²⁸ and in an AM-produced Haynes 230 Ni-base superalloy²⁶. This elemental segregation is key to rationalising the lattice parameter variation; Ti additions give rise to a significant increase (~0.004 Å/at.%) whilst Co, for example, seldom causes a change⁶³. Solutes that increase in lattice parameter will invoke a pseudo-hydrostatic strain; this describes the unit cell change with respect to a reference lattice parameter used for all γ grains. The solute redistribution can therefore be directly inferred from the lattice parameter maps (Fig. 2). The Ti and Nb enrichment at the cell boundaries (as shown in Supplementary Fig. 8) and their potency in changing the lattice parameter unambiguously indicate that the lattice parameter variation is induced by chemical segregation, rather than mechanical stress. This effect was also evident in a remelted region at a layer boundary, observed from a change in solidification direction within a γ grain (Fig. 2c), resulting in a local lattice parameter increase due to chemical segregation.

The identified carbide architecture has several technological implications. During elevated-temperature service or post-processing heat treatments, the primary MC carbides may decompose into other less stable types, via the reactions MC + γ → M₂₃C₆ or MC + γ → M₆C + γ′⁶⁴. The volume change associated with such carbide transformations can impose interfacial stresses and dislocations within the γ matrix, creating preferential sites for microcracking⁶⁵. Factors relevant to the current study that would exacerbate the propensity for cracking include local distortions that arise from a mismatch in thermal expansion coefficients and lattice parameters of the phases due to chemical segregation. Microcracking may occur when interfacing strengths are exceeded, either from process-induced residual stresses or when coinciding with externally applied service stresses. In this context, the implications of local deformation patterning are later considered.

MC-Ni orientation relationships

By fitting an orientation distribution function to the MC-γ misorientations for each carbide, pole figures were generated to infer the orientation relationship (OR) between each MC carbide and its parent γ grain, as shown in Fig. 3b. The misorientation pole figures indicate a cube-cube relationship, inferred from the four-fold symmetry for each of the (100) & (110) pole figures. However, the peak Multiples of Random Distribution (MRD) value of ≈3.5 reveals that this is not a particularly strong orientation relationship and that a large portion of the carbides deviates from the cube-cube OR. This is supported by the texture index t of the misorientation distribution function f(R), computed by the MTEX software⁶⁶ via t = ∫_SO(3)f(R)²dR (where SO(3) is the group of all 3D rotations), which was found to be t = 1.77, indicating a weak misorientation texture. This contradicts some prior Transmission Electron Microscopy (TEM) studies in Ni-based superalloys^67–71 that proposed strong and consistent ORs, although exceptions do occur where no OR was found⁷². While most of the cited studies investigated casting or powder pressing samples, where cooling rates are substantially slower than in DED-LAM,⁷¹ found an OR of [110]_MC∥[110]_γ in an L-PBF-produced sample of another Ni-based superalloy, CM247LC, post-heat-treatment. However, recent work on the evolution of MC carbides at elevated temperatures (750 ^∘C for 50–5000 h) reported a cube-cube, OR that did not change with increasing exposure time at elevated temperature, despite a change in interfacial plane⁶⁹. This may indicate that the effect of cooling rate and heat-treatment on the MC orientation is less significant, and that other factors, such as the MC chemical composition, could dominate the observed OR. Additionally, TEM characterisation inherently limits the number of carbides studied due to the small sample size—work by⁶⁷ found four observed orientation relationships in a study of 20 MC carbides, compared with over 38000 MC carbides explored in this work.

Deformation patterning

Stress shielding is an established description that explains the redistribution of stresses within Ni-based superalloy microstructures^73,74. In the case of the material studied here, stress shielding refers to the uneven sharing of load between different microstructural regions, caused by the high internal residual stresses and heterogeneous microstructure that DED-LAM introduces. In conventionally processed commercial alloys, the compositional and crystallographic differences between the γ and γ′ precipitates correspond with different elastic moduli for the respective phases, where E_γ < E_γ′. This effect is an important contribution to rafting during creep⁷⁵. Whilst there are no similar coherent precipitates such as γ′ in this alloy, the columnar microstructure with cellular-subgrain solidification pathway is analogous. To assess the residual mechanical stresses, scalar von-Mises stresses were calculated with single-slice maps presented (Fig. 4e).

Fig. 4. Solute segregation couples with residual stresses to produce highly complex stress patterning.

The hydrostatic stress field (a), produced by locally variable lattice parameter from solute segregation, combines with an intragranular stress field generated from rapid cooling (b), yielding a proposed von-Mises stress field (c) which is compared with observation (d), a grain-of-interest from a full 2D Z-layer (e) of the S3DXRD measurement volume, coloured by von-Mises stress computed from the measured elastic strain tensors.

Significant stress patterning is present in many grains, with hotspots exceeding 300MPa. Regions possessing higher stresses are generally located (i) near grain boundaries, or (ii) at the cell boundaries, correlating to locations where ā ≈ a_γ (Fig. 2). For (ii), it is noted that not all cell boundaries have a high von-Mises stress; however, such high stresses tend to correlate with the cell boundaries. A good example of this is the highlighted grain (Figs. 2b, and 4a–d), where the stress forms diagonal bands that track regions where ā ≈ a_γ. It is also unambiguous that the grains possessing the highest magnitude stresses correlate with those with the biggest range of lattice parameters. For example, the large central grain has low magnitude stresses & strains (σ_vM < 100 MPa & ε_zz = ±0.2 × 10⁻³), compared to those on the boundary exhibiting much higher magnitudes (σ_vM > 300 MPa & ε_zz = ±0.5 × 10⁻³).

Residual stresses operate at multiple hierarchical length scales⁷⁶, and in AM alloys, these comprise: Type I (macroscale) residual stresses arise from large thermal gradients during processing. Type II (intergranular) stresses originate from anisotropic crystallographic orientation and grain-to-grain mechanical constraints. Type III (intragranular) stresses develop within cells due to segregation-induced lattice mismatch. These stress types are well described for single-phase crystals embedded in a 3D polycrystal⁷⁷. Figure 4a–d proposes a combination of stress fields that rationalise the observed stress patterning:

• (i)As the stress tensors are sensitive to the choice of reference unstrained lattice parameter, the local lattice parameter variation will directly modify the hydrostatic component of the stress tensors.
• (ii)The lattice parameter change itself should therefore impose accommodating stresses at the interface between the cell boundary and cell core due to the mismatch in respective volumes.
• (iii)While not directly measured here, the chemical composition differences between the cell boundaries and core also produce elastic moduli differences (similar to E_γ / E_γ′); here $E_{\mathrm{cell}\mathrm{wall}}<E_{\mathrm{cell}\mathrm{core}}$. Higher Ti concentrations, known to reduce the elastic modulus in Ni alloys⁷⁸, explain the local reduction in cell boundary modulus.

These elements all contribute to the localised von Mises stress variation illustrated in Fig. 4a. Longer-scale Type I and II stress gradients (Fig. 4b) combine with these local variations to form the observed stress pattern (Fig. 4c, d).

It is well understood that these stresses, if sufficiently high, result in significant dislocation densities at cell boundaries^16,52,53, and that misorientations between cells result, as captured by DFXM⁹ and EBSD^52,79. Notable recent serial-sectioning EBSD work by Lamb et al.⁵⁴ captured sub-cell orientation fields at a 20nm spatial resolution, revealing a substantial degree of microstructural plasticity by mapping GND densities at cell boundaries in an L-PBF produced CoNi superalloy sample. While our S3DXRD measurements reliably capture local lattice parameter variations (the elastic component of the strain field), which reveal segregation-induced changes in local chemistry, accurate refinement of sub-grain orientation fields from tomographically determined grain-averaged orientations (the plastic component of strain) remains an open methodological challenge. This is an active area of research currently, and remains an ongoing challenge for the 3D diffraction community.

While elastic strains imposed by grain compatibility are synonymous with all polycrystalline materials, the tortuosity of the grain boundaries will increase the gradient and localisation of the associated stress fields^80,81. In the highly anisotropic microstructure created by DED-LAM, including the Ni-base superalloy studied here, the columnar grains generally have high-angle grain boundaries with boundary protrusions that exhibit localised triaxial stresses⁸². This is particularly relevant when considering carbide decoration at the cell and grain boundaries⁸³, which further discretises the stress distribution along these tortuous boundaries.

These expected high dislocation densities store significant energy and can initiate static recrystallisation. First-order estimates demonstrate the driving pressure of static recrystallisation is as high as 2.9 MPa in L-BPF-produced ABD-900AM⁸⁴. Given that the MC carbides are strong pinning sites for recrystallisation, their distribution at the given MC volume fraction inversely affects the pinning pressure. Recrystallisation is therefore less restricted due to the pinning effect compared to the L-PBF process, as carbides are larger and more sparsely distributed. In components fabricated via DED-LAM, microstructure-stress interactions must be carefully considered, especially when the as-built condition constrains structural performance. During fabrication, controlling thermal gradients and solidification behaviour is critical, as these factors directly influence cellular morphology/stress state and carbide distribution. Likewise, post-build heat treatments should be designed judiciously with the heat treatment temperatures selected for optimised microstructural features, including recrystallisation, texture, dislocation density and chemical homogeneity.

Integrating S3DXRD into the AM characterisation toolbox

A range of characterisation techniques has been employed in prior studies to better understand the influence of highly non-equilibrium processing conditions on the final microstructures of AM components. EBSD methods, including recent serial sectioning enhancements such as TriBeam^50,54, provide key insights into solidification-induced microstructural features via orientation and phase mapping, with high sensitivity to residual plastic strains at impressive spatial resolutions. DFXM offers non-destructive access to strain fields within individual embedded grains, improving the understanding of local intragranular processes^9,19. Recent developments in pink-beam DFXM⁸⁵ demonstrate that multimodal approaches⁸⁶ can produce dynamic, high-resolution movies of evolving microstructures, effectively bridging the gap between mesoscale statistics and nanoscale mechanisms in situ.

Comprehensive understanding of additively manufactured microstructures requires integration across multiple characterisation approaches, each contributing distinct capabilities to the analytical toolkit. EBSD and DFXM excel at mapping orientation fields with exceptional spatial resolution, providing indispensable insight into processing-induced residual dislocation networks. S3DXRD complements these approaches through its capacity for non-destructive elastic strain measurements across statistically significant grain populations, while maintaining sensitivity to minor phases that may be challenging to detect with surface-based or single-grain techniques. Recent work by Zhang et al.⁸⁷, Henningsson et al.⁵⁷ and Li et al.⁸⁸ has demonstrated how S3DXRD can characterise sub-grain strain fields in large numbers of grains, and Macieira et al.⁸⁹ have recently explored the suitability of S3DXRD to investigate multi-phase materials. Our work extends these capabilities by co-registering grain morphology, sub-grain cellular networks, chemical segregation, and the spatial distribution and orientation of more than 37,000 MC carbides within a single 3D dataset. The scanned region represents a statistically meaningful mesoscale volume, preserving build context and enabling unique insights into the coupling of residual mechanical strains and local chemical segregation. Full characterisation of AM components benefits from combining the spatial resolution of EBSD and DFXM with the strain and minor phase sensitivities of S3DXRD, where each technique occupies an essential role in the broader analytical framework. Beyond AM alloys, this acquisition and analysis framework provides a powerful tool to explore how localised chemical segregation drives 3D strain distributions and informs constitutive models in diverse multi-phase materials.

Methods

Sample preparation

The Blown Powder Additive Manufacturing Process Replicator (BAMPR)¹² was used to perform a thin-wall bidirectional print at a laser power of 150 W and speed of 1 mm s⁻¹. The system was housed within a Class I laser enclosure and comprises an inert-atmosphere chamber, a high-precision 3-axis stage (Aerotech, US), a coaxial DED nozzle, a 1070 nm continuous-wave Yb-doped fibre laser (0–200W; SPI Lasers Ltd, UK) and tuneable optics (Optogama, Lithuania). The laser has a focused spot size between 200–700 μm, giving a power density of 397–6366 W mm⁻², matching the range of industrial DED-AM systems. The laser is coaxial with the powder stream delivered normal to the substrate with an argon carrier gas from an industrial feeder (Oerlikon Metco TWIN-10-C). The feedstock used was an argon gas-atomised ABD-900AM Ni-based superalloy powder produced by Aubert & Duval with a mean size of 80 μm. The nominal composition of the alloy is Ni (bal.)-17Cr-19.9Co-3.1W-2.1Al-2.4Ti-2.1Mo-1.8Nb-1.4Ta-0.05C-0.005B⁸. The thin-wall was machined via EDM to a depth of ≈ 200 μm, followed by laser micromachining near the top of the thin wall to expose an isolated cuboidal region of ≈200 × 200 × 175 μm³, as described in Supplementary Fig. 1. Laser damage was subsequently removed by electropolishing in an aqueous solution of phosphoric acid (85 wt.%) for 60 s at a DC voltage of 3 V⁹.

Electron microscopy

To independently verify the microstructure observations made from the S3DXRD scans, electron microscopy was performed on a cross-section of the measured sample. A Zeiss Merlin field emission gun scanning electron microscope with a secondary electron detector was used to capture the microstructure under 15 kV and a beam current of 10 nA. Prior to EDS measurement, the sample was ion polished using a Gatan PIPS system at 8 kV and inclined at 8^∘. EDS mapping was conducted on a dual-beam scanning electron microscope Helios 5 Hydra from ThermoFisher Scientific Inc. The electron beam was set to 20 kV at a beam current of 3.2 nA.

S3DXRD acquisition

To extract highly localised crystallographic orientation and phase information in a three-dimensional volume, Scanning Three-Dimensional X-Ray Diffraction (S3DXRD)⁹⁰ on the Nanoscope station⁹¹ of the ID11 beamline at the European Synchrotron Radiation Facility (ESRF) was employed, as shown in Fig. 1b. A 65 keV monochromatic X-ray beam was focused to a beam size of 250 nm with two one-dimensional silicon compound refractive lens stacks (392 lenses horizontal, 264 vertical)⁹² with an aperture of 50 μm and a focal distance of approximately 150 mm. A DECTRIS Eiger2X CdTe 4M detector was placed at a sample-detector distance of 140 mm, and the detector geometry and beam wavelength were calibrated with an undeformed pure silicon single crystal calibrant of known lattice parameter.

The beam size was measured using a Goodfellow 5 μm tungsten wire plated in gold with an approximate thickness of 35 nm. The wire was raster-scanned through the beam path, and the gold X-ray fluorescence signal was captured with a multi-channel SiriusSD X-ray fluorescence detector. The beam size was measured via the FWHM of the gold signal as a function of sample position within the beam. Detector spatial distortions were corrected by collecting multiple powder patterns at different detector translations with a static beamstop and fitting each detector submodule as an independent flat panel⁹³.

A S3DXRD layer was acquired via a sequence of sample rotations – the sample was rotated 360^∘ in ω with a step size δω = 0.125^∘ while diffraction images were collected at an exposure time of 0.005 s per frame. Between each 360^∘ rotation, the diffractometer was translated along Y via the Δy motor with a step size equal to the beam size. 541 rotations were collected for each S3DXRD layer, defining a slice of reconstruction space in the XY plane. 18 layers were collected overall, giving a total measured volume of 200 × 175 × 90 μm³ with a 5 μm Z (vertical) spacing between layers. The sample was oriented such that the build direction was approximately parallel to the laboratory Z-axis.

Data analysis

A short summary of the primary data analysis steps is provided—the reader is referred to the Supplementary Information for a detailed description of each analysis step accompanying the Jupyter notebooks employed. First, diffraction peaks in the raw images (Fig. 1a) were segmented via a single-value threshold to separate signal from background. A total of ~ 2.4 billion peaks were identified across all layers, which were stored along with their Δy and ω motor positions. These peaks were then merged across ω and Δy to generate a reduced peaks dataset where each Bragg peak only appeared once per grain, significantly reducing the total number of peaks used for indexing.

Grain orientation identification used the standard indexing algorithm employed in the open-source ImageD11 3DXRD data analysis package⁹⁴. In this approach, peaks were first assigned to diffraction rings based on their lengths, which identified the {hkl} of each peak. Peaks were then paired, and the observed angle between their scattering vectors was computed. This was compared to the expected scattering angles between peaks, which were calculated from the unit cell symmetry. Peak pairs with angles close to expected values form two basis vectors in the crystal, and a cross-product between them gives the third, thereby determining the direct lattice basis vectors in the sample reference frame, represented by the matrix product ${\left(\mathrm{U.B}\right)}^{-1}$. These candidate ${\left(\mathrm{U.B}\right)}^{-1}$ matrices were then scored by computing $\overrightarrow{H_i}={\left(\mathrm{U.B}\right)}^{-1}\overrightarrow{G_i}$ where $\overrightarrow{H_i}$ is the expected reciprocal lattice vector of a scattering vector $\overrightarrow{G_i}$. The metric for assigning a peak to a candidate grain was computed by determining the Euclidean distance between $\overrightarrow{H_i}$ and its nearest integer value—peaks were considered to be indexed by a grain if this distance was less than a supplied threshold. Grains with more than a minimum number of expected peaks (computed by the multiplicity of the peaks supplied to the indexer) were accepted as meaningful grains in the sample.

Reconstruction of the γ phase grain shapes followed the general tomographic approach employed in⁹⁵ with several modifications to improve reconstruction quality. For each identified grain, merged peaks were assigned based on the previously described Euclidean distance criterion. Following this, the list of unmerged peaks (thereby extended over ω and Δy based on the Bragg condition width and grain shape) for each grain was determined. A sinogram image for each grain over (ω, Δy) was formed, and intensity was accumulated in this image from the observed diffraction peak intensities of the assigned unmerged peaks. Peak intensities were normalised by their structure, Lorentz and polarisation factors prior to sinogram accumulation. Once a sinogram was produced per grain, filtered back-projection was employed to yield a real-space map of scattering intensity of each grain, which encoded the grain shapes. These real-space maps were thresholded and combined across the entire measured layer, thereby producing a map of grain labels which could be used to determine an initial grain-averaged orientation field.

Using this orientation field as a starting point, the per-voxel orientation and strain fields were then refined using a reconstruction algorithm⁵⁷ recently implemented inside ImageD11⁹⁴. For each voxel, diffraction peaks were selected that were recorded while the beam was illuminating it—those for which the beam centre lay within one beam width of the voxel—and repeated observations of the same reflection were merged into single intensity-weighted peaks. The crystal orientation was refined by weighted least squares, so that the measured scattering vectors mapped as closely as possible onto integer Miller indices, with each peak weighted by how centrally the beam had passed through the voxel. Each merged peak was then reduced to a single strain value along its scattering direction by comparing the measured scattering vector with the one predicted from the refined orientation and an undeformed reference lattice. The six independent components of the elastic strain tensor were recovered from these directional strains by a second weighted least-squares fit, combining the beam-proximity weight with the measurement noise propagated through to each strain value. Values more than 3.5 standard deviations from the mean were rejected as outliers, and the whole procedure was carried out independently for every voxel and every candidate orientation.

As each Z layer was independently reconstructed, an additional post-processing step was employed to detect multiple observations of the same γ-phase grain at different Z heights. Between each pair of adjacent Z layers, all grain pairs were checked for similar orientations using the Orix Python library^96,97 to compute misorientation angles. Grains were considered similar if they had a misorientation of < 1^∘ and if their reconstructed binary masks overlapped by more than 10 pixels. Once similar grains were identified between each adjacent z layer, a graph theory-based approach using the NetworkX Python library⁹⁸ was employed to group all unique γ-grain observations across all layers.

The MC carbides, of A1 crystal structure, were indexed and mapped with a different approach. Diffraction peaks from the γ phase were removed, then peaks from the MC carbides were isolated via their expected d^* values and intensity-filtered to remove extremely weak signals. Peaks were paired using a Friedel-pair based approach by identifying peaks with opposite-sign scattering vectors via a k-dimensional tree clustering algorithm⁹⁹. As each peak on a given (Δy, ω) frame represents a ray traced through the sample by the beam, the origin of diffraction of any single diffraction peak cannot be uniquely identified. However, with a Friedel pair comprising two peaks from the same origin point with unique (Δy, ω) values, the origin point can be uniquely determined, generating an origin of diffraction for each pair. After pairing, a two-dimensional histogram of diffraction-origin positions was produced for all identified pairs. In this histogram, increased signal regions correspond to the centre-of-mass positions of the carbide grains. Each centre-of-mass position was then independently indexed (following the previously described indexing method) using only peaks within a specified distance tolerance. MC carbides were associated with their parent γ grain if their fitted position (from the Friedel pair triangulation) overlapped with the map of γ grain IDs determined from the tomographic reconstruction approach. The MTEX MATLAB library^66,100 was used to compute misorientations between the γ phase and MC carbides to determine pole figures.

Statistics & reproducibility

Given the grain size of the γ phase, the size of the sample was chosen to accommodate a statistically significant number of grains and carbides in the measured volume. The investigators were not blinded to allocation during experiments and outcome assessment. The experiments were not randomised. All analyses performed are end-to-end reproducible following the included Jupyter Notebooks^101,102 which are described in more detail in the Supplementary Information.

Author contributions

J.A.D.B.: Software, Formal analysis, Data Curation, Writing – original draft, review and editing, Visualisation. Y.C.: Conceptualisation, Resources, Investigation, Methodology, Data Curation, Formal analysis, Writing – review and editing. D.M.C.: Conceptualisation, Formal analysis, Investigation, Methodology, Writing – original draft, review and editing, Visualisation, Supervision. Y.T.T.: Investigation, Visualisation, Writing – review and editing. J.P.W.: Conceptualisation, Software, Methodology, Formal analysis, Data Curation, Investigation, Writing – review and editing. C.Y.: Formal analysis, Writing – original draft, review and editing. J.R.: Investigation, Data Curation, Writing – review and editing.

Peer review

Peer review information

Nature Communications thanks Ashley Bucsek and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

C.Y. discloses support from the ERC Starting Grant “D-REX" nr 10116911. Y.T.T. discloses support from the Engineering and Physical Sciences Research Council (EPSRC) for his New Investigator Award under grant number UKRI2998. Y.C discloses travel funding provided by the International Synchrotron Access Program (ISAP) managed by the Australian Synchrotron, part of ANSTO, and funded by the Australian Government.

Data availability

The S3DXRD data generated in this study have been deposited in the ESRF Data Portal database under accession codes 409840930, 447646593 and 473825696, and under the listed https://doi.org/10.15151/ESRF-ES-409840930¹⁰³, https://doi.org/10.15151/ESRF-ES-447646593¹⁰⁴ and https://doi.org/10.15151/ESRF-ES-473825696¹⁰⁵. The processed per-layer S3DXRD data and associated Jupyter notebooks are available on the ESRF Data Portal database under accession code 2345154341 and under the listed https://doi.org/10.15151/ESRF-DC-2345154341¹⁰².

Code availability

The S3DXRD data reduction pipeline, reduced merged S3DXRD data, and figure generation scripts are available on Zenodo under the listed https://doi.org/10.5281/zenodo.20322134¹⁰¹.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77198-5.