Operando X-ray scattering reveals ordering-mediated solidification in additive manufacturing

Abstract

Solidification in fusion-based metal additive manufacturing (AM) occurs under non-equilibrium conditions, often producing microstructures that deviate from classical theories, such as refined grains with high twin density arising from abnormal columnar-to-equiaxed transition (CET). While such feature has been linked to liquid atomic orderings, direct mechanistic evidence has been lacking. Here, we perform operando synchrotron X-ray total scattering measurement with rapid pair distribution function (PDF) analysis to probe atomic structures in AM melt pools. We resolve the evolution of short- and medium-range orderings and connect their selective consumption to distinct solidification pathways in Inconel 718 and other alloys. Our findings not only confirm the importance of icosahedral clusters in controlling solidification behavior, but also suggest a distinct nucleation and growth pathway responsible for abnormal CET. This insight offers opportunities for alloy design and microstructure control in metal AM.

Operando X-ray pair distribution function measurements reveal how atomic ordering in liquid metals governs solidification during laser additive manufacturing, providing direct atomic-scale insight into melt pool dynamics and microstructure control.

Introduction

Solidification is a fundamental process in metallurgy that governs the formation of micro-structure and consequently the mechanical and functional properties of metallic materials. Classical solidification theory has established well-defined relationships connecting nucleation and growth with factors such as thermal gradients (G), growth rates (R), and constitutional supercooling induced by solute redistribution. These principles have provided predictive frameworks for micro-structure selection in the conventional casting process. However, fusion-based metal additive manufacturing (AM) introduces extreme and non-equilibrium solidification conditions. Cooling rates reach 10³−10⁷K·s⁻¹, thermal gradients are on the order of 10⁴−10⁷K·m⁻¹, and strong melt flow further modifies the heat and mass transport¹. Under such conditions, AM metals often develop microstructures that deviate significantly from predictions based on current thermodynamic and kinetic models.

Achieving finer solidification microstructures has been a central objective in advancing AM technologies, particularly for high-deposition-rate processes such as directed energy deposition (DED) and wire-arc AM. Accordingly, a range of grain-refinement strategies has been explored, including tailoring the solidification sequence through compositional design², promoting heterogeneous nucleation via nucleant particles³, and disrupting coarse dendrites by applying external ultrasonic fields⁴. These approaches share a common working principle: leveraging extrinsic interventions to manipulate the competition between nucleation and growth within the classical solidification framework.

Among the various interesting solidification phenomena and the grain-refinement strategies reported in metal AM, the abnormal columnar-to-equiaxed transition (CET) has attracted particular attention recently. In contrast to the classical CET, which is governed by the G-R parameters, abnormal CET occurs locally within AM melt pools under conditions that are supposed to favour columnar growth^5–7. The microstructures produced are characterised by refined equiaxed grains and a high density of twin boundaries, suggesting a distinct solidification pathway that is not predicted by existing models. In several studies, fivefold twinned crystallographic relationships among neighbouring grains have been identified through postmortem characterization^5,7. These observations have led to the speculation that abnormal CET may originate from structural orderings in the liquid, particularly icosahedral short-range ordering (ISRO) or metastable quasicrystals, which may act as structural templates for nucleation and promote successive twinned grain formation.

The existence of ISRO in liquid metals was first proposed in the 1950s⁸. Since then, various topological orderings have been experimentally confirmed in molten metals using synchrotron X-ray and neutron scattering, most often through in-situ measurements with sample levitation^9–13. Computational studies have further highlighted their potential role under ultra-fast solidification conditions^14–18. Nevertheless, direct mechanistic evidence of ordering-mediated solidification under realistic AM conditions remains lacking. Most prior efforts have inferred mechanisms from postmortem characterization of solidified structures, leaving the atomic-scale structural dynamics within melt pools unresolved. This limitation has hindered progress in understanding abnormal CET and other non-equilibrium microstructures unique to AM.

In this study, we address this gap by establishing operando synchrotron X-ray total scattering measurement combined with rapid-acquisition pair distribution function (RA-PDF) analysis as a approach for probing melt pool structure under practical AM conditions. Using a customised wire-laser DED platform, we spatially and temporally resolve the evolution of liquid orderings in Inconel 718, 316L stainless steel, and pure Ni. To complement these measurements, we perform multi-physics simulations to capture melt flow and thermal gradients, and molecular dynamics (MD) simulations to resolve atomic structures of liquid metals. Together, this integrated experimental-computational framework enables systematic investigation of how short- and medium-range orderings, coupled with melt pool conditions, govern solidification pathways in fusion-based AM.

Results and Discussion

Processing map for wire-laser DED of Inconel 718

Prior to the operando characterization, we systematically explored the processing window required to trigger the abnormal CET during wire-laser DED of Inconel 718 by varying a wide range of key printing parameters. Based on the micro-structural features observed in single-line prints, we constructed a 3D processing map and identified four representative regimes (Fig. 1A). The Normal regime was characterised by coarse columnar grains (Fig. 1B), typical of DED samples. When the laser energy input was slightly insufficient, the wire feedstock only partially melted within the melt pool, resulting in unmelted wire segments and cracking (Fig. 1C), defining the Lack-of-Fusion regime. Interestingly, this condition also exhibited localised regions of refined equiaxed grains. By further fine-tuning the printing parameters, we identified a Transitional condition situated between the Lack-of-Fusion and Normal regimes, which exhibited localised grain refinement without the presence of unmelted wire or cracks (Fig. 1D). In fusion-based AM, linear energy density (LED) and volumetric energy density (VED), both functions of main printing parameters, are commonly employed to evaluate the overall printing performance. In the 3D processing map, we identified and marked constant values of LED and VED to delineate the three primary processing regimes defined above (Fig. 1A). Outside these regimes, when the energy input was either excessively low or excessively high, wire stubbing or dripping occurred, resulting in a distinct “Failed Deposition” regime.

Fig. 1. 3D processing map for wire-laser directed energy deposition (DED) of Inconel 718 based on single-track printing.

A Variation in solidification micro-structure as a function of key processing parameters: laser power (P), scanning speed (V), and wire feeding rate (F). The yellow plane represents a constant volumetric energy density (VED) of 32.5 J·mm⁻³, while the purple line denotes the projection of a constant linear energy density (LED) of 46.7 J·mm⁻¹ onto the P-V plane. Representative solidification microstructures corresponding to the B Normal, C Lack-of-Fusion, and D Transitional regimes. Similar results were observed across three individual samples processed under identical conditions. Corresponding electron back-scattered diffraction (EBSD) inverse pole figure (IPF) maps are shown in B1, C1, and D1-D2, respectively. The white dashed curve in B1 marks the boundary between the substrate (below) and the melted region (above). The two insets in C1 show the {100} pole figures for the two featured regions, with the colour scale of measured texture strength ranging from 0 to 2.5. A full set of {100}, {110}, and {111} pole figures is provided in the Supplementary Materials (Fig. S17). D3 displays pole figures for the five grains marked in D2, revealing a fivefold rotational symmetry. In D2, twin boundaries and random high-angle grain boundaries are highlighted in white and black, respectively. A high-quality EBSD map corresponding to the abnormal columnar-to-equiaxed transition (CET) region is provided in the Supplementary Materials (Fig. S18).

We performed electron back-scattered diffraction (EBSD) using a scanning electron microscope (SEM) to compare the characteristic microstructures of samples processed in the three regimes. In the Transitional sample, the region of interest was located just above the track-substrate interface and consisted of equiaxed grains with an average size below 20 µm (Fig. 1D1). This contrasts sharply with the coarse columnar grains observed in the Normal sample (Fig. 1B1). The refined grain structure is consistent with the previously reported abnormal CET phenomenon⁵, as evidenced by the high fraction of twin boundaries (~12%) and the fivefold symmetry relationships occasionally observed among neighbouring grains (Figs. 1D2 and 1D3). The Lack of fusion sample contains equiaxed grains originating from both the abnormal CET and the unmelted wire segment (Fig. 1C1). These two fine-grain regions can be readily distinguished, as the unmelted wire segment typically exhibited printing cracks, distinct optical contrast, fewer twin boundaries, and a stronger crystallographic texture.

Operando pair distribution function measurement

To characterise the atomic structure of the melt pool and its dynamic evolution during the solidification process, we conducted an operando synchrotron high-energy X-ray diffraction experiment with a customised wire-laser DED system. The focused X-ray beam was fixed at a set distance from the printhead, while melt track deposition was achieved by translating the substrate¹⁹. This was essentially an Eulerian reference configuration, which enabled continuous X-ray probing of the melt pool at a specific location (Fig. 2A). Diffraction data from different regions of the melt pool were obtained by repeating the experiment on separate samples. Schematic and data shown in Fig. 2 represent a case in which the focused X-ray probed a fully liquid region of the melt pool.

Fig. 2. X-ray total scattering and pair distribution function (PDF) analysis of atomic-scale structure within the melt pool.

A Schematic illustration of the operando synchrotron X-ray expeTwith equal angular spacing. The positive printing direction corresponds to a configuration with two lasers positioned in front of the wire and one behind. With this configuration, a batch of X-ray scattering patterns, comprising n frames with an exposure time of ∆t per frame, can be collected from the same melt-pool location beginning at t₀, corresponding to the onset of the stable printing period. The inset pattern represents an individual frame collected with an exposure time of ∆t. B The summed diffraction pattern acquired during the stable printing period under the Transitional-Reverse (R) condition, corresponding to the dataset for X = 1.2 mm in Fig. 3I. C Total scattering structure function S(Q) derived from B. The inset shows a magnified view of the marked area, with two black arrows highlighting the second peak of S(Q) and the associated shoulder. D PDF profiles obtained via Fourier transformation of S(Q) in C and refined using small-box fitting. E Theoretical models of the atomic orderings in the melt pool, including icosahedral medium-range ordering (IMRO), icosahedral short-range ordering (ISRO), and FCC-like medium-range ordering (FCC-MRO). The interface exhibiting a near-twin boundary (TB) relationship is marked in red, while the relatively close-packed planes are highlighted in cyan colour.

During the steady-state printing period, a series of time-resolved diffraction patterns were collected and subsequently integrated over time (n × ∆t) (Fig. 2B). The structure function, S(Q), derived from the integrated total scattering pattern, exhibits a high signal-to-noise ratio (Fig. 2C). Notably, a small shoulder on the second peak of S(Q) (inset of Fig. 2C) indicates the presence of icosahedral orderings¹². In Fig. 2D, the reduced PDF profile, Gr_Exp, was obtained by Fourier transforming S(Q) and then analysed using small-box fitting. Based on existing knowledge of the liquid structures of FCC metals⁹, both icosahedral and FCC-like topological motifs were included in the fitting. The selection of these structural motifs was validated by testing a range of candidate models, as detailed in the Supplementary Materials (Sect. 4.3). The fitted profile, Gr_Calc, confirms the significant presence of both FCC-like and icosahedral orderings within the melt pool. Interestingly, the extended oscillations observed in Gr_Exp suggest the existence of medium-range orders (MRO) extending beyond 8 Å, much larger than the unit of ISRO.

It should be noted that the atomic models of these motifs represent statistical averages of atomic positions rather than solid phases (Fig. 2E). The broadened PDF peaks are consistent with the liquid nature of the melt pool, and the fitted results necessarily incorporate tolerances in atomic positions and structural variants. Visualization of these motifs from MD simulations is provided in Supplementary Materials (Sect. 7.1), which also includes factors inherent to this operando characterization that may influence the corresponding PDF analysis (Sect. 4.2). Note that small-box fitting of PDF profiles relies on the preselection of structural motifs, which may increase uncertainty in operando measurements where unique peak fingerprints are less evident and liquid motifs are poorly defined. Big-box Reverse Monte Carlo (RMC) analysis with appropriate energy constraints would provide an ideal framework.

Atomic-scale structural evolution in melt pools

By repositioning the X-ray beam and repeating the above operando total scattering characterization, we spatially resolved the melt pool structure in order to understand the rapid laser melting and solidification behaviours. Operando X-ray imaging captured the melt pool morphology during steady-state printing under the three representative printing conditions: Normal (Fig. 3A), Lack-of-Fusion (Fig. 3B), and Transitional-R (Fig. 3C). The relative size and position of the focused X-ray beam are shown as purple rectangles, where the coordinate X denotes the distance from the triple laser focus. The structure evolution in the melt pool under each condition can thus be inferred from these diffraction patterns collected at various X values.

Fig. 3. Operando synchrotron X-ray characterization of melting and solidification behaviours under different printing conditions.

A–C X-ray imaging of melt pools during the stable printing period under Normal, Lack-of-Fusion, and Translational-R conditions, respectively. The purple rectangles indicate the probing locations in subsequent total scattering measurements, with spatial coordinates defined relative to the wire center (X = 0) and the substrate surface (Y = 0). D–F Focused beam diffraction patterns collected from various locations in the melt pools under processing conditions shown on their left. Each pattern (only a quadrant is displayed) was obtained with an exposure time of 3 ms. G–I Bar charts showing the evolution of volume fraction of each ordering structure, as obtained from the small-box fitting. Error bars were determined based on the ±10% deviation from the R_w value, the standard deviation between the small-box fitted profile and experimentally measured pair distribution function (PDF). The atomic displacement (i.e., the nearest inter-atomic distance on the outer shell) of each ordering structure is shown in the plots at the bottom. “FCC-Crystal” denotes the FCC solid phase without lattice distortion. The repeatability of our measurements was verified through five repeated experiments.

Under the Normal condition, the wire fully melted immediately upon entering the melt pool, as indicated by the absence of diffraction rings near the printhead (Fig. 3D). Coarse columnar grains formed during solidification, as evidenced by the appearance of discrete diffraction spots, rather than continuous rings/arcs, at X = 2.4 and X = 3.2 mm. Under the Lack-of-Fusion condition, in addition to diffuse scattering from the liquid metal, we observed sharp diffraction rings and strong diffraction spots in the melt pool region beneath the printhead, which persisted throughout the characterization range (Fig. 3E). Their intensities decreased as the X-ray beam was positioned farther from the printhead until X = 0.9 mm, after which they began to increase. Because these diffraction signals arise from the solid phase within the probed volume, this trend reflects the gradual melting of the feedstock wire in the melt pool, followed by the formation of fine equiaxed grains during solidification. In other words, under insufficient heat input, as in the Lack-of-Fusion regime, the wire was not fully melted by the lasers but softened substantially at elevated temperatures, allowing unmelted segments to be continuously fed through the melt pool and reach the mushy zone. The Transitional-R condition revealed a more unique scenario, where unmelted wire was initially present in the melt pool but completely melted by X = 1.2 mm, just ahead of the solidification front at X = 1.8 mm (Fig. 3F). During subsequent solidification, diffraction rings and arcs emerged, indicating the formation of fine equiaxed grains. It should be noted that Transitional-R denotes the reverse scanning direction, with one laser positioned in front of the wire and two behind. This configuration is more suitable for studying abnormal CET, as detailed in Supplementary Materials (Sect. 8).

With the high-quality diffraction data (i.e.. large q range and high signal-to-noise ratio), we performed RA-PDF analyses to quantify the volume fractions of different atomic clusters in the melt pools under three printing conditions, as well as their evaluation as functions of X (plots in the top row in Fig. 3G–I). The solid phase (labelled “FCC-Crystal”) was also considered in the analyses, which represents either unmelted wire or as-solidified grains. Additionally, we extracted the nearest inter-atomic displacement of different atomic structures at their outer shell (sketched in Fig. S19) and plotted the averaged values in the bottom row in Fig. 3G–I. We performed sensitivity analysis to establish the confidence of small-box fitting with pre-defined structural motifs, and the results are shown in Supplementary Materials (Sect. 4.3).

We observed a prevalence of MROs in melt pools under all three conditions prior to solidification, with icosahedral motifs particularly pronounced. Previous studies have proposed that the liquid metal structure could be influenced by melting conditions²⁰, temperature gradients²¹, and melt flow²². However, in our case, the melt pool conditions did not significantly affect the configuration of these MROs, as evident by their similar volume fractions and structural parameters in the melt pools before solidification. There are only small variations in the atomic displacement of MROs along X, indicating that the temperature gradient within the X-ray interaction volume has a negligible impact on the PDF measurement.

Despite the similar structures of the liquid metals under different printing conditions, we found that their solidification pathways differed substantially. Under the Lack-of-Fusion and Transitional-R conditions, where abnormal CET occurred, IMRO was preferentially consumed during solidification, leaving FCC-MRO as the dominant residual motifs in the liquid (Figs. 3H and 3I). In contrast, under the Normal condition, which produced coarse columnar grain growth, solidification selectively consumed FCC-MRO instead (Fig. 3G). The corresponding Gr profiles provided in the Supplementary Materials support this observation (Fig. S20). These findings imply that an additional driving force must exist and affect the evolution of atomic clusters during solidification, thereby giving rise to the distinct microstructures observed.

Multiphysics simulation of printing process

In order to identify the melt pool condition that triggers the abnormal CET, we performed multiphysics computational fluid dynamics (CFD) simulations for the Transitional-R condition (Fig. 4A–C). The feedstock wire fully melted after a short displacement from the printhead location. This formed a narrow, fully liquid region between the wire tip and the solidification front, denoted as the “concave” region (highlighted by dashed circles in Fig. 4A–C). This distinct melting behaviour arose from the coaxial triple-laser configuration around the wire, with two laser spots symmetrically distributed on either side of the rear melt pool surface. The resulting recoil pressure and thermocapillary force induced a strong downward flow that enhanced convective heat transfer (right panel of Fig. 4A), thereby accelerating wire-tip melting and facilitating formation of the fully liquid concave region.

Fig. 4. Local melt pool condition at abnormal columnar-to-equiaxed transition (CET) region.

A Multiphysics simulation of the wire-laser directed energy deposition (DED) process of Inconel 718 under the Transitional-R condition. (Left) Longitudinal and (Right) cross-sectional views of temperature distribution and melt flow in the melt pool. The red and blue curves outline the liquidus line (T_l) and solidus line (T_s), respectively. B 3D contour plot of the solid-liquid interface, defined by a solid fraction of 0.1, with the colour map indicating the vertical temperature gradient. The temperature gradients along other directions are provided in Fig. S21. C Melt flow velocity distribution in the melt pool. The simulated melt pool dynamics under the Normal condition are provided in Fig. S22 for comparison. Black arrows in A and C represent the local melt flow direction. White dashed circles indicate the unique concave region between the wire tip and the solidification front. D Measured pair distribution function profiles (G_r) at two locations in the melt pool (red and purple curves), along with the calculated G_r based on molecular dynamics (MD) simulation (black dots). E Correlograph analysis of the (200)_FCC diffraction from 200 consecutive frames of time-resolved X-ray diffraction patterns collected at the solidification front where abnormal CET occurred. F Scanning electron microscopy (SEM) data revealing twin boundaries and elemental segregation at the abnormal CET region. From left to right: secondary electron imaging, electron back-scattered diffraction (EBSD) band-contrast map, energy dispersive spectroscopy (EDS) Mo and Nb maps. In the EBSD band-contrast map, high-angle grain boundaries and twin boundaries are outlined in black and red, respectively. Yellow arrows point out several twin boundaries and their equivalent positions located on the elemental maps. Similar results were observed across three measurements.

Due to the coupled effect of wire melting and solidification, the concave region experienced a reduced temperature gradient along the printing direction, while the vertical gradient remained at the magnitude of 2 × 10⁵K·m⁻¹ (Fig. 4B), dominated by downward convective heat flow. Thus, although reduced, the overall temperature gradient alone was insufficient to trigger a regular CET under the established solidification criterion for Inconel 718²³. Furthermore, the concave region should not have much influence on the solidification rate, which was governed primarily by the scan speed and the geometry of the fusion boundary.

Melt flow is another critical factor known to affect solidification in both traditional metal processing and fusion-based AM^24,25. As shown in Fig. 4C, interaction between the downward melt flow from the track surface and the solid wire tip generated a complex flow vortex within the concave region, with flow velocities reaching ~200 mm·s⁻¹. We compared the PDF profiles measured from the concave region (Y = 300 µm) and an upper region of the melt pool (Y = 800 µm) (Fig. 4D). The upper region was estimated to be about 200 K hotter and exhibited a more streamlined melt flow pattern compared to the concave region. No discernible difference, however, was observed between the two measured PDF profiles.

The atomic structure of liquid metal at 2000 K was simulated using the MD method. Because the inter-atomic potential data file including all alloying elements in Inconel 718 is not available, our MD simulations were limited to the three principal elements (Ni-Fe-Cr). To mitigate this issue, we focused exclusively on the liquid structure. These secondary phases (e.g. carbides, Laves) are not present in liquid, and their volume fraction is also very small in solid at elevated temperatures. The calculated PDF, representing an equilibrium liquid state without melt flow, showed good agreement with the measurements. This observation further supports our earlier conclusion that the melt pool environment, including internal thermal gradients and melt flow, did not significantly affect atomic clusters in the fully liquid state, even within the concave region identified in the multiphysics simulation. However, the presence of the refined grain pocket in the Transitional sample at the concave region suggests that the reduced temperature gradient and complex melt flow in this region may have altered the subsequent evolution of atomic clusters during solidification, thereby triggering abnormal CET.

Mechanism of abnormal columnar-to-equiaxed transition

Our operando PDF measurement (Fig. 3G–I) revealed larger atomic displacements on the outer shell of IMRO compared to FCC-MRO and the FCC solid phase (FCC-Crystal). Direct epitaxial growth of icosahedral orderings into larger solid nanoparticles, as suggested by the ISRO-mediated nucleation mechanism⁵, would therefore impose substantial mismatch strain, even though the IMRO exceeds the critical nucleation size (~55 atoms for pure Ni at a given under-cooling condition¹⁸). Similarly, the domino-like directional attachment mechanism^26,27, which has also been hypothesised for ISRO-mediated solidification⁶, would be hindered due to the interfacial strain. However, considering only topological compatibility, the interface between FCC-MRO and FCC solid is highly coherent. This can potentially facilitate rapid columnar growth and the preferential consumption of FCC-MRO clusters during solidification, as observed under the Normal printing condition (Fig. 3G).

Recent advances on multiply twinned nanomaterials have provided important insights into the thermodynamically stable atomic configurations - those containing a single twin boundary are calculated to possess lower potential energy than their icosahedral counterparts²⁸. Inspired by this, we propose an alternative mechanism of ordering-mediated solidification to explain the abnormal CET as follows. IMRO clusters decompose into more stable twinned nuclei near the mushy zone, which then undergo epitaxial growth to form refined equiaxed grains with a high density of twin boundaries. A more detailed discussion and illustration of this mechanism, together with insights from MD simulations, are provided in the Supplementary Materials (Sect. 9). Similar twinned nuclei have been proposed for the directional solidification of multi-crystalline Si²⁹, solidification of hard sphere models³⁰, and multiply twinned Au nanoparticles³¹.

Two additional pieces of evidence support the presence of twinned nuclei in the present abnormal CET phenomenon. First, we applied correlograph analysis, which is a method that calculates angular autocorrelations within 2D X-ray or electron diffraction patterns, to identify the rotational symmetry of nanocrystals in the melt pool³². We analysed hundreds of diffraction patterns continuously collected in our operando X-ray experiment and obtained summed all individual correlographs together to achieve the autocorrelation function. At the solidification front where abnormal CET occurred, the (200)_FCC diffraction statistically exhibited an angular correlation of 118°, closely matching the 110° interplanar angle characteristic of FCC twinning (Fig. 4E). This observation suggests a preferred twinning relationship among grains at the solidification front. The 8° discrepancy primarily arises from misorientation between the twinned grains, as detailed in the Supplementary Materials (Sect. 5.2), where the corresponding correlograph analysis for the Normal printing condition is also provided for comparison. Note that the correlation peaks close to 90° and 180° correspond to the perpendicular (200) planes in the cubic structure and to the crystal misorientation gradient perpendicular to the incident high-energy X-ray, respectively. The peak at ~160° does not correspond to triple or high-order twinning, but may instead arise from specific tilt boundaries in the material³³. A detailed description of this approach is provided in the Supplementary Materials (Sect. 5.1). Second, we characterised the same abnormal CET region using EBSD and energy dispersive spectroscopy (EDS) mapping (Fig. 4F). In contrast to random high-angle grain boundaries, twin boundaries exhibited only minimal segregation of Mo and Nb, two solute elements with partition coefficients <1 in Inconel 718³⁴. Collectively, these findings suggest that twin boundaries were developed at an early stage of the ordering-mediated nucleation and growth.

The role of icosahedral orderings in abnormal CET can be rationalised by considering its coupled effects on viscosity, melt flow, and nucleation energy barrier. Icosahedral clusters increase the viscosity of the liquid³⁵, thereby reducing atomic mobility and allowing these clusters to persist long enough to serve as structural templates. In the melt pool, the local convection can trap such clusters within the concave zone, where the thermal gradient is reduced. Although the introduction of a twin boundary raises the nucleation barrier by ~15% (calculated in Supplementary Materials, Sect. 9.2), the combined influence of elevated viscosity and convective transport facilitates the stabilisation and eventual transformation of MRO clusters into twinned nuclei. This interplay provides a mechanistic link between local melt pool conditions, ordering-mediated solidification, and the emergence of abnormal CET. Recent microgravity experiments enabling precise control of melt flow have made its influence on solidification particularly evident³⁶. Although structural ordering in liquids is hypothesised to be involved in this process, it has often been treated cautiously because melt flow is presumed to be too macroscopic and too slow relative to these motifs and their structural dynamics²². Our observation of sluggish variation in liquid structure within the melt pool and distinct evolution during solidification (Fig. 3G–I) supports and helps reconcile this long-standing controversy.

Consistent with previous studies, we observed fivefold symmetric grain clusters in the abnormal CET region, which cannot be fully accounted for by our proposed mechanism. Meanwhile, it should be noted that the fivefold twin sets, though exist, are rare in the abnormal CET region. Instead, twinning pairs consisting of only two grains are dominant (Fig. S18). A simplified analysis considering only the increase in twin-boundary energy revealed that a five-grain twinned nucleus could increase the nucleation energy barrier by ~40% (compared with ~15% for two-grain twinned nuclei) relative to the classical nucleation event (Supplementary Materials, Sect. 9.4). Therefore, we argue that under melt pool conditions that favour abnormal CET, the formation of fivefold twin sets is possible, but expected to occur with a much lower probability than the proposed two-grain twinned nucleus. In addition, large-scale MD simulations have demonstrated successive twin formation on pre-existing grains¹⁴. Such a local heterogeneity model suggests that nuclei, particularly motifs like ISRO, may form heterogeneously within the liquid due to fluctuations in local atomic order. This indicates that the formation of fivefold twin sets is possible.

Abnormal columnar-to-equiaxed transition beyond single-track Inconel 718

In addition to Inconel 718, we also performed operando PDF measurements on 316L stainless steel and pure Ni (Fig. 5A, B), two systems where ISRO-mediated solidification has also been reported during AM processes^6,37. Although 316L and Inconel 718 share similar principal alloying elements, they differ in elemental fractions and minor additions. Interestingly, their melt pools exhibited highly similar atomic structures, with good agreement between experimental results and corresponding MD simulations. By contrast, the S(Q) profile of the Ni melt pool differed from those of the two alloys, as indicated by variations in the position and shape of the second S(Q) peak. Its PDF analysis revealed a slightly lower fraction of icosahedral orderings. Moreover, the simulated PDF profile of pure Ni exhibited an earlier termination of oscillations than the measured results of all three metals. Experimentally, we successfully printed a single-track 316L bead that developed refined equiaxed grains within a localised region (Fig. 5C–E). The micro-structure showed micron-scale grain size, weak crystallographic texture, and an elevated fraction of twin boundaries (~11%).

Fig. 5. Abnormal columnar-to-equiaxed transition (CET) in other materials and bulk Inconel 718 sample.

A S_Q and B reduced pair distribution function profiles (G_r) of the melt pools of Inconel 718 (dark red circles), 316L (blue circles), and pure Ni (pink circles). The inset in A shows a magnified view of the area marked by the black box. The equilibrium liquid structures of these three materials were simulated using molecular dynamics (MD) simulation, as presented by the green curves in B. Only the principal elements were considered in the simulations. C–E Observation of abnormal CET in a single-track 316L sample printed using wire-laser directed energy deposition (DED) with a tailored set of parameters. F–G Abnormal CET regions, highlighted by red dashed boxes, observed in a bulk Inconel 718 sample. BD stands for building direction and TD for transverse direction. Similar results in C–G were observed and confirmed across two samples processed under identical or closely matched conditions.

Regarding alloying elements, prior studies have attributed abnormal CET in Inconel 718 to the stabilising effect of Nb, an order-forming element thought to enhance ISRO in the liquid^6,38. Unmelted carbides have also been proposed to induce localised Nb enrichment in melt pools³⁹. However, our earlier work confirmed that incomplete melting of carbides alone is insufficient to trigger abnormal CET⁴⁰. In this study, we observed a modest increase in Nb concentration within the abnormal CET region compared to adjacent columnar grains (Supplementary Materials, Fig. S23). While Nb additions could refine microstructures in DED-processed Inconel 718^41,42, such effects typically require large Nb additions and are often accompanied by significant formation of brittle Laves phase, which we did not detect in our samples. Moreover, the subgrain- and grain-scale solute segregation shown in Fig. 4F is also a common feature in regions dominated by coarse columnar grains (Fig. S16) and thus is unlikely to drive significant grain refinement. To confirm this, we conducted MD simulations on Ni-Nb systems with varying Nb concentrations at 2000 K. The calculated PDFs exhibit only negligible differences across the compositions considered (Supplementary Materials, Fig. S15). Therefore, the magnitude of the measured compositional variation in our samples appears insufficient to alter solidification behaviour, as discussed in detail in the Supplementary Materials (Sect. 10.3). We thus believe that the modest increase in Nb concentration observed in regions with different grain structures is a consequence of solidification occurring through different modes, rather than a cause of abnormal CET. Nevertheless, we acknowledge that more sophisticated theoretical studies would be valuable for assessing the influence of Nb on liquid structure dynamics.

A recent study further reported that the appearance of twinned dendrites in 316L is sensitive to the Cr/Ni ratio³⁸, attributing twin boundary formation and grain refinement (yet not equiaxed grains) to ISRO-mediated nucleation promoted by reduced Cr. However, our PDF measurement (Fig. 5B) and partial PDFs from MD (Supplementary Materials, Sect. 7.2) indicate only a limited influence of alloying elements on the prevalence of IMROs in the melt pools of these Ni- and Fe-based alloys away from the solidification front. Although both principal and minor elements may still affect the kinetics and stability of local orderings, we believe their effects must work in synergy with melt pool conditions to account for the localised presence of equiaxed grain zone within the melt track.

Single-track samples were studied in our operando synchrotron X-ray experiments. Although the substrate did not affect the melt pool composition (Methods Section), single-track printing may exhibit melt pool behaviour that differs from bulk printing. To rule out possible substrate effects on the micro-structure of single-track samples, we fabricated a bulk Inconel 718 specimen in which the abnormal CET micro-structure was repeated across successive deposition tracks (Fig. 5F–G). Notably, the abnormal CET regions in the bulk sample are slightly smaller than those in the single-track sample, which can be explained by the differences in geometry and thermal conditions of the melt pools (Supplementary Materials, Sect. 10.5) arising from machine/parameter variation and track-to-track interactions. Similar observations were also reported in previous work on bulk Inconel 718 produced with a comparable wire-laser DED technique⁵. Together, the 316L and bulk Inconel 718 samples underscore the critical role of melt pool conditions in enabling abnormal CET and highlight the potential of ordering-mediated solidification as a strategy for micro-structure control in practical AM processes. The discussion of other potential factors influencing CET in AM is expanded and summarised in Sect. 10 of the Supplementary Materials.

In summary, we employed operando synchrotron PDF measurement and MD simulation to uncover the dynamic atomic arrangements within active melt pools during fusion-based metal AM. This method allowed us to resolve the coexistence and evolution of icosahedral and FCC-like orderings in liquid metals and to reveal their role in governing solidification pathways. Unlike prior assumptions that emphasised direct nucleation from ISRO or metastable quasicrystals, often inferred solely from postmortem characterization, our operando characterization indicated that MRO clusters preferentially disassemble in melt-pool regions characterised by moderated thermal gradients and localised vortex melt flow, where they likely form twinned nuclei for subsequent solidification, as supported by our correlograph analysis and other complementary evidence. This selective reconfiguration, rather than straightforward templating or attachment, provided a mechanistic explanation for abnormal CET, where refined equiaxed grains and a high density of twin boundaries emerge under conditions that would normally favour columnar growth.

These findings extended current solidification theory by correlating short- and medium-range liquid orderings with non-equilibrium microstructures, and by demonstrating how melt pool dynamics regulate the stability and consumption of atomic clusters. The combined experimental and computational framework developed here provided strong evidence for ordering-mediated solidification and connected atomic-scale processes with micro-structural outcomes in a way that classical G-R theory cannot capture.

Beyond Inconel 718 and 316L stainless steel presented here, our study demonstrated a valid strategy for micro-structure engineering in AM. By stabilising or consuming liquid orderings through tailored processing conditions, it becomes possible to promote refined grains, engineer grain boundaries, and improve property isotropy in structural alloys. Such an approach, combined with continued advances in alloy development, holds promise for producing high-performance components for aerospace, energy, and biomedical applications. More broadly, operando PDF provides a general framework to integrate liquid-state topology with non-equilibrium kinetics in metal AM. Future efforts that couple this approach with external fields or advanced simulations may further extend control over ordering-mediated solidification, reshaping both our understanding of solidification science and the practise of materials manufacturing.

Methods

Wire-laser directed energy deposition process

Wire-laser DED was performed using two commercial systems: μPrinter (Additec, USA) and M450 (Meltio, Spain). The μPrinter featured a triple-laser configuration and was modified for operando synchrotron experiments. All bulk samples studied in this work were fabricated using the M450 printer, which was equipped with six laser sources and offered better productivity for manufacturing large-scale samples. The printheads in these DED systems have similar configurations: the laser beams were focused centrosymmetrically on a wire feedstock delivered through the center of the stationary printhead. The deposition process was realized by scanning the built platform. The key printing parameters used in this study are listed in Table S1 in the Supplementary Materials.

Ex-situ micro-structure characterization

Samples for postmortem characterization were sectioned using wire electrical discharge machining (EDM). The sample surfaces were mechanically ground using sandpapers of progressively finer grits, followed by sequential polishing with diamond suspensions and a final polish using a colloidal silica suspension. SEM was conducted using a Helios UC G4 dual-beam SEM equipped with an Oxford EBSD detector. Post data analysis was performed using the software Aztec Crystal. Metallographic analysis was performed using a Hirox digital light microscope. Prior to imaging, samples were electrolytically etched in a 10% oxalic acid solution at 3 V.

Operando synchrotron X-ray experiment

Operando synchrotron experiments were conducted at the 1-ID-E beamline of the Advanced Photon Source (APS), Argonne National Laboratory. A superconducting undulator generated high-energy flux, and a monochromator was used to select X-rays with an energy of 100.0 keV. Full-field imaging was carried out using a Pointgrey GS3-U3-23S6M-C CMOS camera, a 5× objective lens, and a 25 µm-thick LuAG:Ce scintillator, achieving a pixel resolution of 1.172 μm and a frame rate of 80 Hz. For diffraction characterization, the X-ray beam was focused using a series of compound refractive lenses and then collimated using slits into a 50 µm (width) × 30 µm (height) rectangular shape. A PILATUS3X CdTe 2 M detector was mounted downstream to continuously capture 2D diffraction patterns at a frame rate of 250 Hz with an exposure time of 3 ms for each frame. Photographs and a detailed description of our operando characterization setup at the beamline are shown in Fig. S1 and provided in Sect. 2 of the Supplementary Materials, respectively.

In this study, the single-track deposition of Inconel 718 and 316L SS was performed on substrates of the same material (e.g., 316L on 316L), and the substrate surfaces were carefully polished to remove the surface oxide layer and thoroughly cleaned before the experiment. The single-track deposition of pure Ni was carried out on a 316L SS substrate due to a better deposition quality than using a pure Ni substrate. Under the studied printing condition, the dilution zone is minimal, with negligible melt-pool penetration into the substrate and significantly low Fe diffused from the substrate to the Ni bead, as confirmed by the SEM-EDS measurement.

Total-scattering structure function and pair distribution function analysis

The time-resolved X-ray diffraction patterns collected at each specific location underwent the following steps for total scattering and pair distribution function analyses. Details of each operation are described in the Supplementary Materials (Sect. 3).

1. For each individual measurement with the X-ray probing at a specific location, diffraction patterns corresponding to the stable printing period (i.e., excluding the initial and final stages of the laser deposition) were picked out from the entire sequence (200 ~ 300 frames out of 2000 frames). These patterns were summed and integrated into a one-dimensional (1D) profile across the entire azimuth range using the software GSAS II⁴³.

2. Each 1D scattering profile was processed using PDFGetX2 software for background correction and PDF profile extraction⁴⁴.

3. Following background correction, the 1D scattering intensity profile I(Q) was converted to the total-scattering structure function S(Q) and reduced G(r). These conversions from I(Q) to S(Q) and G(r) were carried out using PDFgetX2 software based on the following mathematics:

$$S\left(Q\right)=\frac{I\left(Q\right)}{{⟨b⟩}^2}$$ 1

$$G\left(r\right)=\frac{2}{\pi }{\int }_0^{\infty }Q\left[S\left(Q\right)-1\right]\sin \left(Qr\right)dQ$$ 2

where $⟨b⟩$ indicates the compositional average of the atomic scattering amplitude. The range of wavevector Q used for the PDF extraction was from 0.82 to 14.82 Å⁻¹.

Small-box fitting of PDF profiles

Each extracted PDF profile, G(r), was imported into the software PDFgui for small-box fitting⁴⁵. The atomic models presented in Fig. 2e were utilized for fitting. Parameters, including the isotropic Gaussian atomic displacement parameter (ADP), scale factor, linear atomic correlation factor δ₁, and lattice parameters, were refined for each phase and atomic clusters within an r range of 1–80 Å. The fraction and atomic displacement of each structure illustrated in Fig. 3 were calculated based on the refined scale factors and lattice parameters, respectively.

Both the FCC solid and FCC-like atomic clusters were fitted using crystal models with the $Fm\overline{3}m$ space group. In comparison, the FCC-like atomic cluster, due to its amorphous nature, exhibited a notably higher ADP value and a size parameter, spdiameter. Consequently, the increased ADP and size effects manifested as significant peak broadening and diminished oscillation amplitude with increasing r in the G(r) profiles. The detailed fitting procedure is provided in Sect. 4.1 of the Supplementary Materials.

Correlograph analysis of time-resolved diffraction

The correlograph analysis was performed for individual diffraction patterns. This method was previously developed and successfully applied to identify the local symmetries in disordered materials based on X-ray or electron diffraction patterns^46,47. In our analysis, (200)_FCC diffraction was integrated over the entire azimuth range in a step size of 1° in $\mathrm{\Delta }\mathrm{\Phi }$. Each diffraction pattern yielded a diffraction intensity profile as a function of the azimuth angle, $I\left(\mathrm{\Phi }\right)$. Subsequently, the normalized angular correlation function was applied to the profile:

$$C\left(\mathrm{\Delta }\mathrm{\Phi }\right)=\frac{{⟨I\left(\mathrm{\Phi }\right)I\left(\mathrm{\Phi }+\mathrm{\Delta }\mathrm{\Phi }\right)⟩}_{\mathrm{\Phi }}-{⟨I\left(\mathrm{\Phi }\right)⟩}_{\mathrm{\Phi }}^2}{{⟨I\left(\mathrm{\Phi }\right)⟩}_{\mathrm{\Phi }}^2}$$ 3

where $\mathrm{\Delta }\mathrm{\Phi }$ is the variable of angular offset, and the 〈〉 operation was applied to a uniform averaging over all azimuth angles from 0 to 360°. This analysis was carried out sequentially over 200 frames and subsequently summarised. Higher C values at specific angles indicate stronger angular correlations in the diffraction pattern and corresponding rotational symmetry of the crystal structure of solidified grains.

Molecular dynamics simulation

A heating simulation was performed using the MD package LAMMPS⁴⁸. A large crystalline model containing 864,000 atoms was constructed from an initial FCC lattice. Three compositions were examined: pure Ni, Ni₅₉Fe₁₉Cr₂₂ to approximate IN718 alloy, and Ni_11.4Fe₆₉Cr_19.6 to approximate 316L stainless steel. Trace elements were excluded due to the lack of suitable inter-atomic potentials for covering all minor alloying species. Inter-atomic potentials among Fe, Cr, and Ni were described using the embedded-atom method (EAM)⁴⁹, with the applied Fe-Cr-Ni potential developed by Bonny et. al⁵⁰. Simulations employed a Nose-Hoover isothermal-isobaric (NPT) algorithm, with pressure fixed at 1 bar and the target temperature of 2000 K. The NPT melting process was applied for 400,000 timesteps of 1 fs each, with data collected every 100 timesteps. Simulated data were analysed in OVITO⁵¹, using coordination analysis to compute the pair distribution function g(r). The final simulation frame was used to calculate the 1D g(r) profile, which was then converted to the reduced PDF G(r) via $G\left(r\right)=4\pi {\rho }_0\left[g\left(r\right)-1\right]$, where ρ₀ is the atomic density of the material. The resulting G(r) profiles were compared with experimental measurements.

Multiphysics computational fluid dynamics simulation

The multiphysics simulation integrating dynamic laser absorption and CFD was conducted to evaluate the thermal conditions and melt flow within the melt pool during wire-laser DED of Inconel 718. The commercial software Flow-3D (Flow Science Inc., USA) with the AM module was utilized to reconstruct the printing process. The model solved governing equations for multiple fields, including velocity, pressure, volume-of-fluid advection, and conservation of energy, momentum, and mass. Detailed governing equations are described in our previous work⁴⁰. Critical physical phenomena considered in the simulation included phase transformations, gravity, Marangoni convection and surface tension, thermal conduction, laser-matter interactions, laminar turbulence, and viscosity effects. The geometric configurations of the laser beams, as well as the dimensions of the wire feedstock and substrate, were identical to those employed experimentally. A universal mesh size of 0.15 mm was applied across the entire simulation volume, complemented by a finer mesh of 0.075 mm within the melt pool region. The simulation encompassed the printing of an 18 mm line track, using a time step of 0.005 s. These parameters were determined to effectively balance computational accuracy and efficiency. Further details on the model configuration are provided in Section 6 of the Supplementary Materials.

Author contributions

L.G.: Writing—review & editing, Writing—original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. K.M.: Writing—review & editing, Software, Methodology, Investigation, Formal analysis. Z.R.: Writing—review & editing, Investigation, Formal analysis. Z.Y.: Writing—review & editing, Visualization, Formal analysis. X.L.: Writing—review & editing, Investigation, Software, Formal analysis. C.C.: Writing—review & editing, Validation, Methodology, Formal analysis. T.S.: Writing—review & editing, Writing—original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Peer review

Peer review information

Nature Communications thanks Atieh Moridi, who co-reviewed with Kaushalendra Singh; and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

T.S., X.L., and K.M. discloses support for the research of this work from National Science Foundation [DMR-2427686]. Z.R. discloses support for his partial effort for this work from the 18-ID (FXI) beamline of the National Synchrotron Light Source II (NSLS-II), a U.S. Department of Energy Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory [DE-SC0012704].

Data availability

All data are available in the main text or supplementary materials. Source data are provided with this paper. All the raw data relevant to the study are available from the corresponding authors upon request. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-73647-3.