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High-Temperature Alloys: Research Summary Vol. 60, No.7 pp. 26-30

The Three-Dimensional Reconstruction of the Dendritic
Structure at the Solid-Liquid Interface of a
Ni-Based Single Crystal

J. Madison, J.E. Spowart, D.J. Rowenhorst, and T.M. Pollock

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Figure 1
The recession rates for serial sectioning of René N4 with RoboMET.3D™ system.


Figure 2
The 3-D reconstruction of the mushy zone in the commercial nickel-based superalloy René N4.


Figure 3
Top views of reconstruction showing four-fold dendritic symmetry and secondary and tertiary arms.


Figure 4
An optical micrograph showing a typical region of primary dendrite cores for PDAS measurement.


Figure 5
An optical micrograph showing a typical region of a single primary dendrite core for SDAS measurement.


Figure 6
A planar section of reconstruction for PDAS measurement.


Figure 7
A planar section of reconstruction for SDAS measurement.


Figure 8
A comparison of 2-D and 3-D measures for PDAS.

Figure 9
A comparison of 2-D and 3-D measures for SDAS.


Figure 10a
(a) The volume fraction solid as a function of height
Figure 10b
(b) the 3-D reconstruction of René N4 at the mid-melt solid-liquid interface where primary growth direction and height coincide and are demarcated by the green arrow.


Figure 11
Reconstructed liquid in the 3-D reconstruction of René N4 at the mid-melt solid-liquid interface.








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© 2008 The Minerals, Metals & Materials Society

Directional solidification of nickel-based single crystals requires control of the heat transfer, fluid flow, and phase transformations at the solid–liquid interface during withdrawal in the Bridgman process. While the morphological details of the dendritic structure at the solid–liquid interface influence defect formation processes, there is an incomplete understanding of this structure as a function of alloy composition and processing conditions. A three-dimensional serial sectioning and image reconstruction approach for characterization of the solidification front has been developed and structural characteristics of the dendritic structure are quantified.


Nickel-based superalloys are commonly used in their single-crystal form in the production of turbine blades for industrial gas turbines and aircraft engines. Reliable mechanical performance of these single crystals in the turbine environment requires that no high angle boundaries, including “stray” misoriented grains or freckles, be present as casting defects in the component. Not only are these components costly to fabricate, the service cost associated with repairing or replacing these components is expensive as well.

As such, the prevention of casting defects is of particular interest. Traditionally, predictors for the formation of freckles have called upon estimates for the presence of convective flow,1,2 which has been identified as the precursory event for the formation of freckles and some types of misoriented grains.3–7

While values for the viscosity, thermal diffusivity, and other physical properties governing flow in nickel alloys can, with effort, be measured experimentally or computationally assessed,8,9 the dendritic geometry through which molten material is flowing has only been evaluated in relatively small two-dimensional (2-D) domains.10–12 To evaluate fluid flow processes on a larger scale in three dimensions, a serial sectioning and imaging protocol that captures the dendritic structure at the solidification front and reconstructs the resulting microstructure for further analysis has been developed.


Within an ALD Vacuum Technologies, Inc. furnace, a 5.4 kg ingot of the commercial superalloy René N4 was directionally solidified in conventional Bridgman mode at the University of Michigan. The nominal composition of the ingot was 4.2Al-0.05C-7.5Co- 9.8Cr-0.15Hf-1.5Mo-0.5Nb-4.8Ta- 3.5Ti-6.0W-Ni (wt.%)13 with solidus and liquidus temperatures confirmed by differential thermal analysis of 1,300°C and 1,345°C, respectively.14 A withdrawal rate of 2.5 mm/min. and thermal gradient of 40°C/cm was used. During withdrawal, the investment mold was fractured to capture the dendritic front mid-melt by quickly evacuating all remaining molten liquid from the mold. A rectangular base plate with a cross-sectional area normal to the growth direction of 11.5 cm × 3 cm was cast. Using a slow-speed milling saw, samples approximately 1 cm3 in size were extracted from the solidification front. Samples were then vacuum impregnated using Buehler’s EpoHeat™ thermosetting epoxy.

The samples were hand polished parallel to the primary growth direction down to a 1.0 μm diamond finish for metallographic documentation of the structure. A representative sample was then selected, polished, and imaged using the prototype RoboMET.3D™ serial sectioning system at Wright-Patterson Air Force Base.15 Successive polishing was performed using Allied 1.0 μm diamond lapping film while imaging was performed using a Zeiss Axiovert inverted microscope at 10x. Material removal rates were obtained by measuring thickness changes in the sample with a Mitutoyo Absolute™ table-mounted, pneumatic actuator digital micrometer over image intervals of seven to ten slices. Average removal rates observed were 2.2 μm/slice. Material removal rates are shown in Figure 1. Images were taken congruent to the polishing plane and parallel to the primary growth direction. Each slice consisted of an eight-image montage with each image possessing a standard resolution of 0.52 μm/pixel. In raw form, each slice was 15–20 MB in size. A total of 727 slices were used in this reconstruction for ~12.6 GB of data. Additional details of the RoboMET.3D system have been previously discussed.16,17

Table I. Interdendritic Voids: Range, Magnitudes, and Overall Contribution
Volume Threshold (mm2)
Voxel Threshold
No. of Independent Bodies
Void Fraction (%)
Contribution to Total
Voided Regions (%)
*Single voxel volume is 38.07 μm3

Following serial sectioning, image segmentation was performed using ITT Visual Information Solutions’ Interactive Data Language (IDL)® along with Adobe Photoshop® to render each slice a cleaned, binary image properly aligned for stacking. The segmentation process consists of seven operations: image shifting, coarse cropping, fine cropping, cleaning, conversion to binary, size setting, and size reduction. Interactive Data Language was used primarily for all image refining while Photoshop was utilized for cleaning and binary conversion. Although batch processing was employed for certain procedures, very little automated segmentation was employed in the preparation of this reconstruction; manual segmentation was the primary method used. After adequate segmentation, datasets were converted to three-dimensional (3-D) arrays for visualization and evaluation of the dendritic structure using IDL.


…describe the overall significance of this paper?
Traditionally, investigation of the solidification process in cast structures is performed by examination of various twodimensional sections throughout the casting. Here, an experimental method for the characterization of the full three-dimensional dendritic substructure at the solid–liquid interface in a directionally solidified superalloy is presented and discussed.

…describe this work to a materials science and engineering professional with no experience in your technical specialty?
Understanding the microstructure of directionally cast superalloys plays a pivotal role in the ability to estimate not only the quality of these components but also the reliability, lifetime, and any potential processing defects within them. Here an experimental method for capturing and characterizing the three-dimensional microstructure present during directional solidification is shown.

…describe this work to a layperson?
The overall effectiveness of turbine blades for aircraft engines and industrial gas turbines is very sensitive to the presence of defects, which can occur during casting. The most common of these defects are called “freckles.” This work employs three-dimensional reconstructions of the casting event at the physical location of transition from molten liquid to solid. This reconstruction can be used to more accurately predict the occurrence of freckles.

The fully reconstructed volume measures 2.3 mm × 2.3 mm × 1.5 mm and is shown in Figure 2. The sectioning and imaging orientations are the xy plane, which is parallel to the primary growth direction denoted by the green arrow. Secondary and tertiary arms are observable in the reconstruction as shown in Figure 3.

Dentrite Arm Spacing
Since decanting was employed to isolate dendritic structures at the solidification front, the degree of departure from typical solidification behavior is a reasonable concern. To address this, dendrite arm spacings at the solidification front were quantified in the 3-D section in comparison to conventional 2-D measures. Primary and secondary dendrite arm spacings (PDAS and SDAS) vary in a predictable manner with thermal gradients and withdrawal rates during solidification18–24 and these parameters are well characterized for the present experiments. Three independent methods were used to measure and compare dendrite arm spacings.

Traditional planar metallography was employed to polish, image, and measure material from regions near the vicinity of the reconstruction to measure PDAS and SDAS. In this way, over 1,400 dendrite cores were counted and more than 30 independent measures of SDAS were made. In accordance with the method previously discussed by A.J. Elliott,25 following PDAS measurement, a select number of cores were identifi ed and cut along their growth direction, providing surfaces for SDAS measurement. Figures 4 and 5 show two representative optical micrographs showing primary and secondary arms from which measurements were made according to Equations 1 and 2. (All equations are given in the table.) Here np is the number of cores counted per cross-sectional area, L is a predetermined line length located along the growth direction of a primary dendrite arm, and n is the number of secondary dendrite arms intersecting the line.

Using these 2-D measures, a PDAS of 560 + 27.5 μm and an SDAS of 82 + 6.9 μm were obtained.

Taking a similar approach with planar sections of the reconstruction, PDAS and SDAS were approximated using the same relationships as above. Representative images of these planar cross sections are shown in Figures 6 and 7. Although the reconstructed volume was somewhat less than the equivalent 2-D volume sampled for PDAS, measurements taken suggest an average PDAS of 480 ± 28.6 μm and an average SDAS of 86 ± 6.8 μm. Graphical comparisons of the 2-D and 3-D measurements are shown in Figures 8 and 9.

The casting under investigation was grown under a thermal gradient (G) of 40°C/cm and a growth rate (V) of 2.5 mm/min. Based upon the relationships between G and V, the expected spacing of primary and secondary dendrite arms has been shown to vary according to the two relationships shown in Equations 3 and 4.26

γ1 = np -1/2
γ2 = L/(n-1)
γ3 ∞ (G-1/2 * V-1/4)
γ2 = (G * V)-1/3

Collections of measurements from castings produced within the University of Michigan’s Bridgman furnace under similar withdrawal rates with and without liquid-tin enhanced cooling were investigated and compared using the relationship shown in Equations 3 and 4.14 Only in cases of extreme transverse growth at solidification growth rates beyond 8.5 mm/min. with liquidtin coolant did the approximation fail to correctly predict the dendrite spacing. Consequently, based upon the processing conditions, it would be expected that the PDAS in the sample under investigation would be in the range of 450–600 μm while the SDAS should be in the range of 60–80 μm. These values indicate good agreement between not only the 2-D and 3-D measures but also the expected range based upon G and V. This suggests that no irregular artifacts in the dendritic structure have been introduced as a result of decanting liquid from the solidification front.

Volume Fraction
The 3-D dataset allows for a direct measure of the local volume fraction as a function of height in the mushy zone; this is shown in Figure 10. While small fluctuations of solid fraction are indicative of the local volume fluctuations due to secondary dendrite arms, the global trend exhibits a near-parabolic decrease in volume fraction with an approximately 80% decrease in volume fraction to zero over the upper 500 μm of the mushy zone. This is important since models for convection in the mushy zone often infer a linear change in volume fraction as a function of temperature or height in the mushy zone during solidification. Additionally, any property exhibiting a dependence on volume fraction may in fact vary drastically over small intervals of height in the mushy zone. This may have significant implications for local fluid flow in these structures.

Interdendritic Connectivity
In addition to understanding the gradient associated with the solid-to-liquid transition, the degree to which interdendritic regions are connected to one another is critical to understanding the paths for convective flow. Table I shows an analysis of the interconnectivity of the voids in the mushy zone, which quantifies the volumes of interconnected regions available for fluid flow during solidification. Independent interdendritic voids are grouped by descending volume. This was measured by reconstructing all non-solid regions in the reconstruction as shown in Figure 11. It is interesting to note that the uppermost region is a single interconnected body that accounts for roughly 98% of the total voided regions and reaches down some 900 μm into the mushy zone.


Models for defect formation during directional solidification typically rely on Rayleigh criteria to assess the onset of convective instabilities at the solidliquid interface during solidification. 1–5,7,27 The permeability of the mushy zone, which is sensitive to the volume fraction of fluid in the mushy zone, is a parameter that is difficult to assess but has a strong influence on the Rayleigh number. The present serial sectioning and reconstruction method for characterization of the dendritic structure provides a path for direct assessment of permeability. The 3-D data can be utilized to extend prior 2-D numerical approaches10,11 to a full 3-D analysis of the fluid flow; this will be discussed in future publications.

The automated serial sectioning approach provided by RoboMET.3D produces very stringent user repeatability. Under typical working conditions, variations in sectioning height are only produced by irregularity in lapping films or alterations to user-input polishing offset height. In this work, the standard deviation associated with the 2.2 µm/slice sectioning height was s = + 0.3 µm. Additionally, while the 3-D PDAS measures appear slightly lower than the 2-D measures for PDAS, this is likely a result of the limited cross section available for examination from the reconstruction.

The more localized SDAS measurements show a closer agreement, likely due to similar length scales in the measurements field of view in both the 2-D and 3-D approach. Volume fraction measurements in this René N4 superalloy tend to suggest the overall height of the mushy zone that could contribute to convective flow is much shorter than typical estimates based upon linear variations in liquid fraction for the given imposed thermal gradient. This could be due to the thermodynamics of the multi-component alloy in this temperature range or the complex heat flow in the mushy zone, or both. Finally, further analysis of liquid connectivity and fluid flow in the mushy zone over a wider range of solidification conditions could give new insight to defect formation processes as well as a better understanding of porosity formation in these single crystal microstructures.


This research has been supported by and is in contribution to the Air Force Offi ce of Scientific Research MEANSII Program, Grant No. FA9550-05-1- 0104. The authors also acknowledge useful technical discussions with P. Voorhees, S. Roper, and S. Davis of Northwestern University.


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J. Madison, graduate student research assistant, and T.M. Pollock, professor, are in the Materials Science and Engineering Department, University of Michigan, Ann Arbor, MI 48109; J.E. Spowart, senior materials research engineer, is with the Air Force Research Laboratory/RXLM, Wright-Patterson AFB, OH 45433-7817; and D.J. Rowenhorst, metallurgist, is with Naval Research Laboratory, Washington, DC 20375. Mr. Madison can be reached at (734) 615-5163; e-mail .