Multiscale characterization of the 3D network structure of metal carbides in a Ni superalloy by synchrotron X-ray microtomography and ptychography

Abstract Synchrotron X-ray microtomography and ptychography were used to characterize the 3D network structure, morphology and distribution of metal carbides in an as-cast IN713LC Ni superalloy. MC typed carbides were found to distribute mainly on the grain boundary between the matrix γ and γ' phase. The differences in solidification cooling rate had a minor influence on the volume fraction of the MC type carbides, but significantly affected the carbide size, distribution and network morphology. Depending on the local composition of the remaining liquid phase and geometric constraints, the carbides can form either spherical or strip or network morphologies. The research demonstrated clearly the advantage and technical potential of using the two complementary tomography techniques synergistically to characterize non-destructively complex multiple-phase structures in three dimensional space with a spatial resolution of ~30 nm.


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Synchrotron X-ray microtomography and ptychography were used to characterize the 3D network structure, morphology and distribution of metal carbides in an as-cast IN713LC Ni superalloy. MC typed carbides were found to distribute mainly on the grain boundary between the matrix γ and γ ' phase. The differences in solidification cooling rate had a minor influence on the volume fraction of the MC type carbides, but significantly affected the carbide size, distribution and network morphology. Depending on the local composition of the remaining liquid phase and geometric constraints, the carbides can form either spherical or strip or network morphologies. The research demonstrated clearly the advantage and technical potential of using the two complementary tomography techniques synergistically to characterize non-destructively complex multiple-phase structures in three dimensional space with a spatial resolution of ~30 nm. © 2020 Acta Materialia Inc. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ) Nickel based superalloys have been extensively used for making high-temperature structural components in aircraft and land turbine engines, rocket engines, nuclear power and chemical processing plants [1][2][3][4] . These superalloys are designed to have a unique microstructure where the ordered intermetallic γ '(Ni 3 Al) precipitates distribute coherently within a continuous γ (Ni) matrix. Such microstructural features provide substantial ordered and coherent interfaces to inhibit dislocation motion at higher temperature, delivering superior high-temperature strength and creep resistance [5][6][7] . For cast Ni superalloys, the γ -phase is the primary phase formed during solidification while the γ '-phase mainly nucleates and grows within the interdendritic region at the final stage of solidification.
Metal carbide is another important microstructure constituent in polycrystalline Ni-based superalloys due to its excellent high-temperature stability. The carbide is originally designed to improve high-temperature strength through strengthening the grain boundary and preventing grain boundary sliding [8][9] . However, carbide can also cause crack initiation and propagation during plastic deformation [10][11][12] . The morphology and spatial distribution of the carbides in cast Ni superalloys are mainly formed through the solidification process and therefore have an important influence on the solidified microstructures and the mechanical properties [13][14] . Although considerable researches have been carried out to investigate the nucleation, growth and morphology evolution of the carbides in Ni-based superalloys under different solidification conditions [15][16][17] , until now, the nucleation and growth dynamics of metal carbides, especially the true 3-dimensional (3D) network structure and morphology of metal carbides formed in different solidification conditions have not been fully understood.
Carbides in the as-cast Ni-based superalloys are usually MC ( M = Ti, Nb, Ta and V) type compounds with NaCl face-centredcubic structure. They form in the liquid melt due to strong segrega-  tion of C when its concentration is above 0.05% [18] . Depending on the solidification conditions, the carbides can form different spatial structure and morphologies. They could be octahedral or irregular blocky or script-typed morphologies in a 2D sectional view when they grew in slow-cooling, near-equilibrium solidification conditions [19][20][21] . In contrast, in a rapid cooling condition, such as in laser surface melting, the morphology of MC carbides can vary and form a peculiar structure, i.e. radially branched flower-like colonies [22][23] . These growth morphologies are proposed to be related to the typical faceted growth mechanism where the lateral growth from existing steps or ledges originating from the closed packed {111} planes, twins and screw dislocations on the growing crystal surfaces [15] . Until now, the carbide morphologies were mostly studied using 2D imaging methods, only giving limited information on their true 3D characteristics, and their spatial interconnections and correlations with other phases. Nonetheless, recent studies have shown that 3D phase differentiation and visualization of carbides in Ni-based superalloys are possible by focused ion beam (FIB) assisted Electron Back-Scattered Diffraction (3D-EBSD) [24] or atom probe tomography (APT) [25] . However, these techniques are normally for characterising local region of small volume in the diameter range of a few tens or a few hundreds of nanometres, not suitable for the measurement of volume fractions and the true 3D spatial distribution of the carbides.
In this paper, we were focusing on multiscale characterizing the metal carbides in an as-cast polycrystalline IN713LC Ni superalloy. Synchrotron X-ray microtomography and ptychography methods were used synergistically to study the 3D network structures, distribution and the correlations of the carbides with other solidified phases, providing quantitative and true 3D information for understanding the mechanism of phase formation and transformation during the solidification of this alloy.
The chemical composition of the IN713LC Ni superalloy used in this study is shown in Table 1 . This alloy was melted and cast using a specially-designed mould to form wedge-shaped samples as shown in Fig. 1 a. This shaped sample resulted in different cooling rates at different locations of the sample. The cooling rates along the central symmetrical line of the wedge was calculated based on the temperature measurement. Plate samples with typical cooling rates of 0.27 K/s (in the thicker end) and 1.12 K/s (in the thinner end) were cut from the as-cast wedge samples for microstructure characterization.
The 2D microstructure observation of the carbides was carried out by using a Zeiss Evo60 Environmental scanning electron microscopy (SEM). The samples were ground and then polished. A chemical solution (100 ml C 2 H 5 OH, 100 ml HCl and 5 g CuCl 2 ) was used to deeply etch the sample surface to expose the carbides.
Synchrotron X-ray microtomography experiments were conducted at Beamline I13-2 of Diamond Light Source (DLS), UK [26][27][28] . For this experiment, the square bars cut from the wedge sample were further ground into circular needle shape (Insert in Fig. 1 a). The schematic experimental setup diagram and parameters used in this study can be found in the supplements and in Table 2 . Tomography reconstruction was performed using the computing cluster at I13 of DLS based on a filtered back projection algorithm [29] .
The ptychographic X-ray computed tomography (PXCT) experiment was carried out at the I13-1 Coherence Branchline of DLS, UK [26] . Ptychography is a scanning coherent small angle scattering technique with a lensless geometry, therefore aberration free and theoretically diffraction limited [30] . The diagram of experimental setup of PXCT can be found in the supplements and the details are described in Fig. 1 c of Ref [31] . The Excalibur detector was used to record the diffraction patterns in the far field [32] . The sample geometry for PXCT experiment is shown in the insert of Fig 1 a. The detailed experimental procedure can be found in the supplements. Ptychographic reconstruction on each scan projection was performed with PtyREX Code [33] while the 3D reconstruction was conducted with the Savu processing pipeline software [34] , using the ASTRA Recon GPU implementation of filteredback projection algorithm [35] . The segmentation, visualization and analyses for both synchrotron X-ray tomographic and 3D ptychographic datasets were conducted by using Avizo 9.4 software (FEI VSG, France). Fig. 1 b shows the obtained secondary electron SEM micrograph for the deep-etched sample with a cooling rate of 0.27 K/s. The primary dendrite is marked by the white dotted lines, showing a typical FCC structural growth morphology where the dendritic arms grew preferably along the low index crystal directions, e. g., 100 [36] . The carbides distributed either within the interval of secondary arms or in the interdendritic region. Several typical carbide morphologies in the Ni-based superalloy can be distinguished for both samples with 0.27 K/s and 1.12 K/s cooling rates. Fig 1 ce show the irregular blocky, strip and symmetric cross-petal-like morphologies of the carbides, respectively. All these carbide morphologies suggest that the carbide branches grew along {111} face of the cubic cores, as marked by yellow dotted rectangles in the figures. The octahedron with {111} face is the equilibrium MC carbide morphology due to the minimum carbide-liquid interface energy [20] . The cubic cores are the 2D projections of the octahedral MC carbides. The contrast variation surrounding the cubic cores suggests there might be chemical composition gradients and thus the formed carbides are composites, as reported in other studies for IN713LC Ni-base superalloy [37][38][39] . Fig. 1 f presents a typical complex script-like carbide network morphology, which also consists of octahedral cores and plate carbide branches. Fig. 2 a, b and the companying video #1 show the 3D network structure of the carbides in a relatively large volume for the two samples with different cooling rates. It is clear that the carbide network distributed along the edge of the secondary dendrite arms in 3D space and within the interdendritic region, consistent with the previous 2D observation. However, in contrast to the coarser secondary dendrite arm for the sample with a low cooling rate of 0.27 K/s ( Fig. 2 a), the interval of the secondary dendrite arms became smaller for the sample of a higher cooling rate of 1.12 K/s ( Fig. 2 b), which led to the smaller local volume for the carbide network. Moreover, it was found that the spherical (blocky type in 2D view) and irregular rod (strip type in 2D view) carbides were predominant in the sample with a high cooling rate in spite of sometime formation of some small carbide networks ( Fig. 2 d).
On the other hand, the spherical and rod carbides interconnected each other and formed compact and complex carbide networks in the sample with a low cooling rate of 0.27 K/s ( Fig. 2 c). Such feature is often observed as script-typed carbides in a 2D projection view. The complex carbide network is due to the further growth of the spherical and rod carbides and coalescence between each other [20] .
For quantitative statistical analysis of the 3D characteristics of the carbides, a high-level combination module with watershed, distance transform and numerical reconstruction algorithms in the Avizo software was firstly used to separate individual carbides in 3D space. The separated individual carbides were then grouped in three categories: spherical, rod and network carbides based on their 3D shape characteristics and further confirmed by visual in-  spection. Quantification analysis results for the different categories are given in Table 3. The total volume fraction of carbides in the sample of 0.27 K/s cooling rate is 1.04%, quite similar to the value (1.18%) in the sample of 1.12 K/s cooling rate. This result indicates that the variation of cooling rates in the present study had minor influence on the obtained carbide volume fraction. The average particle size for the spherical carbides was ∼13 μm 3 in both the samples with different cooling rates. Such results were consistent with previous reports which revealed that the cooling rate in a wide range from 0.10 to 50 K/s had little influence on either the solidification sequence or degree of micro-segregation [39][40] . This is mainly due to the facts that the formed carbides are MC-typed, for which the stronger C formation elements i. e. Ti and Nb can easily react with C. However, the average particle sizes for the rod carbides in the 0.27 K/s sample were 97 μm 3 , increased by 10% when compared to that (88 μm 3 ) obtained in the 1.12 K/s sample, confirming the further growth and coalescence of the carbides due to having sufficient diffusion time in the low cooling rate sample. In particular the average size of the network carbides changed from 288 to 328 μm 3 , increased by 14% when the cooling rate reduced from 1.12 to 0.27 K/s. Fig. 2 e and f shows the statistic distribution characteristics of the spherical and rod carbides. Due to the tiny amounts of the network carbides and the significant difference on volume be-tween the network carbides and the other two categorized carbides, the distribution of network carbides was not included in the figures. Fig. 2 e indicates that the reduction of cooling rate led to a slight increase in the average particle size (44 vs. 42 μm 3 ). Fig. 3 f presents the shape factor distribution for the spherical and rod carbides. The shape factor is defined as = S 3 36 πV 2 , where S is the measured total surface area for an individual carbide and V corresponds to its individual volume. This morphology parameter represents the shape characteristics of the individual carbides, and 1 represents a perfect sphere. The comparison of the shape fac- tor distribution for the samples with different cooling rates reveals that the individual carbides continuous growth transitions from the spherical morphology to rod morphology when reducing the cooling rate.
The skeletonization function in Avizo software was used to peel off parts of the typical 3D carbide networks down to a skeleton of 1 voxel in thickness. The 3D characteristics of the carbide branches can be visualized ( Fig. 3 a and b), illustrating the growth paths of the carbide branches during solidification [41] . The 3D characteristics of the carbide skeleton were then quantified by counting statistically the curve length between each node. The statistical curve length distributions are shown in Fig. 3 c. The statistic results followed Lognormal distribution for both cases in different cooling rates. The peak position in the 0.27 K/s sample slightly shifts into longer length when compared to that in the 1.12 K/s sample, indicating that the slow cooling rate produced more proportionally branches of a greater curve length. Fig. 4 shows the synchrotron X-ray ptychography image and tomographic morphologies for the 1.12 K/s sample. This imaging method provides a higher spatial resolution of 30 nm and also the correlation of different phases. Fig 4 a is a transmission projection perpendicular to the deep-etched surface, showing the interconnected carbide network in the region. The retrieved 2D projections at −83.5 °and 45 ° ( Fig. 4 b and c) revealed the stereo-morphologies of the interfaces for γ ' phases in the alloy. The reconstructed 3D tomography, however, presents the true 3D shapes of the irregular spherical and rod (plate in 2D view) carbides, as shown in Fig. 4 d and the accompanying video #2. All these carbides located at the grain boundaries between the matrix γ phase and γ ' phase ( Fig. 4 e, the γ phases are rendered as semi-transparent).  Fig. 4 f. Fig. 4 g and the accompanying video 2 also show the de- (g) shows the spherical carbide and its correlation with other phases; (h) is the strip carbide and its correlation with other phases. tailed correlations of the primary γ p , eutectic γ e , carbides and γ ' phase in 2D view. In Fig. 4 g, the γ ' phase demonstrated a relative homogenous constitution while the carbide presents a short blocky (spherical carbides in 3D) morphology embedded on the boundary of primary γ p , eutectic γ e and γ ' phases. The solidification path of this morphology was L → γ ; L → γ + MC + ( γ + γ '), as proposed by other researchers [39][40][41] . Fig. 4 g shows that parts of the core of the strip carbide seemed to be within the γ ' phase.
However, detailed observation of the carbides in most other slices indicated that the strip carbide cores were located at the boundary of γ phase. The different contrast within the γ ' phase suggested the γ ' phase was not homogeneous in composition, which might be due to the further segregation of Nb, Ti elements in this case. Taking into account the chemical composition of the IN713LC superalloy, Nb and Ti elements prefer to react first with C and also can segregate into γ ' phase during the solidification while Cr, Mo and Al can segregate into both γ phase and γ ' phase [37] . Therefore, the composition of γ ' phase on the vicinity of the MC carbide is likely a Nb-Ti rich phase, as indicated in Fig. 4 h. This result is similar to and consistent with that reported for IN713LC superalloy [39] . Hence, the solidification path in such case is proposed as L → γ ; L → γ + MC + ( γ + γ ') + (Nb-Ti rich phase).
In summary, synchrotron X-ray microtomography revealed and quantified the 3D characteristics of the spherical, strip and network structure of the metal carbides in an as-cast IN713LC Ni superalloy. Synchrotron X-ray ptychography revealed that the individual MC carbides were distributed on the grain boundary between the matrix γ and γ ' phases. The dominant growth directions of carbide branches were mainly determined by the local composition of the remaining liquid phase and geometric constraints.

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