Analysis of Slip Systems in Nickel Superalloy by Micro Laue Diffraction

Project Advisor: Jennifer Carter | Author: Aaron Thompson Case Western Reserve University December 2015

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Summary The proposed project entails the analysis of slip systems in nickel superalloy via analysis of the shape of Laue diffraction peaks. The objective is to develop a process to measure the localization of deformation as well as the slip systems active.

It has been observed qualitatively that deformation is distributed according to the nature of grain boundaries as well as distance from grain boundaries through in-situ TEM analysis. Under elevated temperature creep conditions it was found that the areas of most significant deformation accumulation experienced slip along multiple planes. There were also grain boundaries that experienced grain boundary sliding (GBS) which were found to only experience single slip [1]. With both dislocation motion and grain boundary sliding contributing to creep in modern turbine disk alloys [2], a predictive model of grain boundary orientation and morphology would allow the engineering of grain boundaries to minimize creep.

Deformation and dislocation mechanisms will be determined from the shape and orientation of the peaks in Laue diffraction patterns. A 3D tomography of these Laue images will be obtained via a novel “Micro Laue” diffraction technique developed at Argonne National Lab’s Advanced Photon Source [3]. Deformation is indicated as elongated or split peaks in the diffraction patterns. This is caused by dislocations adding a slight rotation to the lattice about the dislocation line. Additionally the direction in which the peak is split or smeared can inform which slip planes are active [4].

The measurement of the deformation and slip systems will be conducted by fitting an ellipse to each peak in order to determine peak aspect ratio and orientation. The images will be filtered to reduce the impact of image noise. Ellipses will be fit to the filtered peaks by a moment of inertia based algorithm instead of a perimeter – based algorithm in order to take pixel intensity into account. Once the aspect ratio and orientation have been determined, the sensor geometry must be correlated to the crystalline orientation to relate the ellipse rotation angle to obtain slip plane activation. Once these parameters are measured for each peak, relations can be made given distance from grain boundaries, twin boundaries, etc.

The measured relationships between deformation and distance to grain boundaries is expected to validate what was observed with TEM analysis, as well as providing rudimentary quantitative results for the purpose of building a predictive model. A predictive model would allow grain boundary engineering to obtain optimized creep properties.

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Problem Statement The goal of this investigation is to determine the distance at which deformation within grains of polycrystalline nickel superalloy transitions from single slip system deformation to complex slip regimes. In crystalline plasticity simulations, the current assumption is that each grain only slips along one glide plane and in one direction. While this assumption is relatively accurate for the center of large grains, it has been previously observed via in-situ TEM analysis that slip systems become more complex at grain boundaries. This knowledge will allow more accurate plasticity models to be developed such that performance and lifetime of parts can be more accurately predicted.

Technical Background Nickel superalloys are extremely important to the aerospace industry, comprising the components that must endure the hottest regions of turbine engines. Failure of these parts occurs when they begin to deform appreciably, and it is of great importance to be able to predict failure as engine failure is costly and potentially life threatening. Previous work started with digital image correlation of a small region of a superalloy tensile specimen as it was deformed in-situ within a scanning electron microscope. By watching the motion of a random pattern of microscopic ceramic markers that were deposited on the surface of the tensile bar as it deformed, the localization of the deformation was determined (Figure 1)[5].

Figure 1 DIC strain map of nickel superalloy. Images were taken in-situ at regular time intervals as sample was deformed at 700°C. [5]

Attempts were made to correlate microstructural features to this deformation, including orientation mapping using electron backscatter diffraction, and indexing of grain boundary character (High angle vs. Σ3 vs. Σ4-29). These 2D techniques were found to not give enough information to provide the underlying mechanisms for the distribution of slip [6]. Given this, 3D analysis techniques were considered. One potential solution is EBSD combined with serial sectioning, where the a thin layer is

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sputtered away in between EBSD images [7]. Deformation information can be gleaned from the shape of the diffraction maxima [4], and the 2D raster combined with the “serial sectioning” gives a full 3D dataset. The benefit of this technique is that it has a relatively high spatial resolution (on the order of 250nm), as some of the microstructural features in this particular alloy are on the order of only several microns. The drawbacks, however, include the fact that this is a destructive test, as material must be etched away in-between every image taken. It is also incredibly time intensive both from a preparation, acquisition, and an image analysis standpoint [6]. Due to these limitations, another technique was explored, micro-Laue diffraction pioneered by the beamline scientists at the Advanced Photon Source at Argonne National Lab [3].

The main concept of micro-Laue is very similar to traditional Laue diffraction, where white (polychromatic) x-rays illuminate a sample, and the beam diffracts in accordance with Bragg’s law to form patterns on an image sensor. The angles between peaks are measured and used to determine what crystalline planes they were reflected from. Knowing the plane indices, the rotational orientation of the lattice can then be determined [8].

The micro-Laue technique involves using the high brilliance synchrotron x-ray source in order to gather data up to roughly 100 microns deep into the sample. A pair of elliptic Kirkpatrick–Baez mirrors focus the beam to a sub-micron diameter by progressively reflecting the xray at incredibly shallow angles [9]. The sample is mounted on a motorized platform capable of sub-micron stepping in the x, y, and z axes where the z axis is parallel to the beam [10]. For each given X-Y position the image sensors then receive diffraction information from every point along the line at once. A thin platinum wire (referred to as a differential aperture) is used to block a small segment of angles at a time and is then scanned in the z direction along the surface of the sample in order to determine what diffraction peaks are being blocked at each depth of the wire (Figure 2).

Using the geometry of the sensor and the position of the wire, the image values of the pixels are subtracted from each other in order to extract images of only the diffraction peaks from each depth. The resultant data is a set of images representing the Laue diffraction patterns from each 3D position in the sample. From those patterns, the crystalline orientations are determined exactly as with traditional Laue backscatter diffraction [8], and also contain information about the residual strain and accumulated deformation [12]. This technique has several major benefits over EBSD combined with serial sectioning: micro-Laue imaging is non-destructive, involves much less sample preparation, as well as being much faster than the serial sectioning technique for image segmentation and alignment.

The strain data of interest is then contained within the shape of the peaks in the Laue patterns. As the crystal deforms, added dislocation content create sub-grains with slight rotations with respect to the average orientation of the whole grain. These slight rotations cause the peaks to smear or split slightly in the direction of the slip [13]. The direction and magnitude of this change of peak shape contains information regarding the amount and direction of slip, and is the main focus of this study. For example, if a material experiences single slip system activation, the peaks will elongate into ellipses along the direction of the burgers vector of the slip system. If multiple slip systems are

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activated the peak will first broaden more spherical in nature. When sub-grains are formed these elongated or broaden peaks subsequently split into sub peaks.

Figure 2 Diagram of the working principle of scanning the Pt wire across the surface of the sample in order to extract diffraction information from specific depths of the sample[11].

Technical Approach The primary goal of this investigation is to measure the shape of the diffraction

peaks, and use the orientation data provided from Argonne National Lab to correlate slip with grain boundaries and other meso-scale structures. Being a data-centric problem, the research will be conducted by writing code and scripts in Python in order to run computations on large amounts of data. Python was selected as a programming language for its forgiving learning curve, strong scientific community support, and open source licensing.

The data provided by Argonne comes in two primary forms that must be utilized in conjunction with each other. The first dataset is the diffraction images as reconstructed from each individual scan of the Pt wire. These images take the form of a 2D array of 16bit pixel intensity values representing the x-ray intensity at any given point on the detector. These images were then run through a set of algorithms to find peaks, as well as determine which planes of atoms those peaks were reflected from. Knowing which peaks correlate to which planes allows the orientation of the crystal to be determined within the lab space. These algorithms return data in the form of a large XML file, which contains a hierarchical representation of every peak forming every pattern for every image.

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Given these inputs, the project can be broken down into five main tasks:

Data munging: organizing the data so that it is possible to analyze peak shape on a per diffraction pattern basis instead of organized on a per-image basis.

Image filtering: removing noise and irrelevant data

Peak shape analysis: ellipse fitting algorithm

Geometry correlation of slip systems: determine relation between ellipse long-axis measurements in diffractor space with slip systems in crystal space, and relate slip direction and magnitude to grain boundary proximity

Task 1: Data Munging The first challenge is to take the data collected about the peaks and diffraction

patterns provided in the XML and sort it into a native python object on a per-diffraction pattern basis rather than a per-image basis. It is not uncommon for a given image to contain an incomplete pattern that could not be fully indexed, in which case no orientation data can be obtained. These images are therefore not useful to the project, as correlations to orientation cannot be made. These images are therefore excluded from analysis. It is also common for images to contain multiple patterns, as with instances where a given measurement volume lies across a grain boundary, and the diffraction image is sampling multiple grains at the same time. In this case it is beneficial to the analysis of the data to treat the peaks on each of the patterns as unique, and as such the peaks are sorted on a per-pattern basis.

The XML file is first converted into a searchable python object called an element tree in order to facilitate the organization of the data [14]. When a pattern is found for a given image the hkl indices of the fitted peaks are rotated by the same rotation as the reciprocal lattice, and compared to the listed q-vectors of all the points found. This serves to extract the peaks from only that pattern in the event there are multiple patterns present in the same image, or there were peaks located but not attributed to a pattern.

Task 2: Image Filtering Once the peaks for each pattern are identified for analysis, a series of image filtering stages will be employed to ensure the accuracy of the ellipse fitting to follow. A simple blurring filter will be used to reduce low amplitude background noise by taking the median value of the 9 adjacent pixels [15]. A threshold is then applied to the image to select the bright peak from the dark background [16]. Successive minimum and maximum filters are applied in a similar way to the median filter, and have the effect of first reducing the radius of all peaks present, eliminating small peaks remaining from background noise, then increasing the radius of the desired peak back to its original size [17]. Finally unique indices are given to all connected regions and only the peak in center of the region of interest is selected Figure 3[18]. This accounts for the possibility of having two distinct peaks within close proximity to each other, by removing non-connected peaks from the region of interest.

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Figure 3

Task 3: Peak Shape Analysis After the peaks are sorted, their shape must be determined in order to analyze

the direction and magnitude of the deformation. An ellipse was chosen as a target shape to fit to each peak, as with the magnitude of the major axis, the minor axis, and the angle of inclination, many important features of the peak can be described. Many ellipse fitting algorithms rely on finding the shape of the perimeter of an object via a least-squares regression [19], however, this approach would not take into account the pixel values. Instead a moment of inertia based approach fits an ellipse to each peak based on the pixel intensity values [20]. Imagining the pixel values represent masses on a flat sheet, the first order moments are used to determine the center of mass and the second order moments are used to determine aspect ratio and angle of orientation. One small benefit of this approach is that the calculations involved are deterministic, and execute particularly fast; an important consideration when working with large datasets.

Task 4: Geometry Correlation of slip systems Once peak shapes have been determined, the crystalline orientation must be

related to the direction of peak elongation. This relation will be created by computing the sensor geometry in relation to the sample geometry all with respect to the lab coordinate system. From there the vectors must be normalized into crystalline direction components to account for the possibility of complicated slip systems [4], [13]. Additionally, sample points must be sorted by crystalline orientation and position to group data points into discreet grains. Once discreet grains are formed, grain boundaries can be defined and distance from any given point to a grain boundary can be calculated. This data will then be compared to the qualitative results found by Carter et al [1].

Risk Assessment and Mitigation See Appendix Figure 4

Unsupervised Computation(Figure 4 a)

Much of the processing of the data is done with no visual output, as there are tens of thousands of images to be considered with up to twenty or so peaks on some images. Manually looking over the results to confirm the validity of the computation is infeasible, however it is possible that the data will cause incorrect fitting of ellipses in some cases. In these cases data will still be recorded, and no errors will be thrown. One potential way to mitigate this risk is to determine analytical methods to identify poor

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ellipse fitting and generate visual representations of only those with poor fits. Given the visual representations decisions can be made on either how to re-fit the images or to exclude certain outliers in the data.

Code Incompatibility(Figure 4 b)

Python was selected as a language among other things for it’s portability and

cross platform compatibility. The code may however depend on platform specific libraries that may not work on all machines. Mitigations for this include creating a virtual environment running Linux specifically for the computation of this data, as well as striving to preemptively code for multiple operating systems.

Data Loss (Figure 4 c)

The raw data takes up a large amount of storage, and is most efficiently stored

on physical hard drives. Physical hard drives have mechanical elements that can fail, and when that happens the data stored on the drive can sometimes become unrecoverable. This would have catastrophic consequences, as the data would be very difficult to re-collect. This risk can be mitigated by keeping redundant backups of the data in multiple locations.

Time Management (Figure 4 d)

As an undergraduate, I have a relatively busy schedule, and can fall prey to not managing my time efficiently. This can progressively delay the progress of the project as I have to dedicate more time catching up with other work. I will attempt to mitigate this risk by keeping a daily planner of assignments and updating my calendar regularly to help myself stay on schedule.

Results and Discussion The desired result of this investigation is to build data relating deformation accumulation and slip system activity to proximity and type of grain boundaries. A data model that retains information at multiple levels of complexity will be required to structure the results according to any desired parameters to facilitate the making of these relationships. Provided the results reinforce what was found with TEM analysis [1], quantitative results such as distributions of deformation can be correlated to parameters such as distance from grain boundaries. Models can be generated either manually based on measured values and prior knowledge of physical laws, or by data learning algorithms [21].

Conclusions/Summary Polycrystalline nickel superalloys are critical to the performance of turbine disks, and are subject to creep as they are under load at high temperature for prolonged periods of time. Dislocation movement as well as grain boundary sliding have been found to both contribute to creep, and be related to different dislocation mechanisms [1],

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[2]. With a better understanding of these mechanisms, and how they impact deformation, the models can be used to optimize the creep properties by engineering the grain boundaries to distribute deformation more evenly and reduce grain boundary sliding [22].

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References [1] J. l. w. Carter, N. Zhou, J. m. Sosa, P. a. Shade, A. l. Pilchak, M. w. Kuper, Y.

Wang, H. l. Fraser, M. d. Uchic, and M. j. Mills, “Characterization of Strain Accumulation at Grain Boundaries of Nickel-Based Superalloys,” in Superalloys 2012, E. S. Huron, R. C. Reed, rk C. Hardy, M. J. Mills, R. E. Montero, P. D. Portella, and J. Telesman, Eds. John Wiley & Sons, Inc., 2012, pp. 43–52.

[2] A. Soula, Y. Renollet, D. Boivin, J.-L. Pouchou, D. Locq, P. Caron, Breacute, and Y. Chet, “Analysis of high-temperature creep deformation in a polycrystalline nickel-base superalloy,” Mater. Sci. Amp Eng. A, vol. 510–511, pp. 301–306, 2009.

[3] B. C. Larson, W. Yang, G. E. Ice, J. D. Budai, and J. Z. Tischler, “Three-dimensional X-ray structural microscopy with submicrometre resolution,” Nature, vol. 415, no. 6874, pp. 887–890, Feb. 2002.

[4] R. Maaß, S. Van Petegem, C. N. Borca, and H. Van Swygenhoven, “In situ Laue diffraction of metallic micropillars,” Mater. Sci. Eng. A, vol. 524, no. 1–2, pp. 40–45, Oct. 2009.

[5] J. L. W. Carter, M. W. Kuper, M. D. Uchic, and M. J. Mills, “Characterization of Localized Deformation Near Grain Boundaries of Superalloy René-104 at Elevated Temperature,” Mater. Sci. Eng. A, vol. 605, pp. 127–136, 2014.

[6] T. J. Turner, P. A. Shade, J. Schuren, M. A. Groeber, M. Miller, and M. D. Uchic, “Two Integrated Experimental and Modeling Approaches to Study Strain Distributions in Nickel and Nickel-Base Superalloy Polycrystals,” in Superalloys 2012, John Wiley & Sons, Inc., 2012, pp. 643–652.

[7] M. A. Groeber, B. K. Haley, M. D. Uchic, D. M. Dimiduk, and S. Ghosh, “3D reconstruction and characterization of polycrystalline microstructures using a FIB–SEM system,” Mater. Charact., vol. 57, no. 4–5, pp. 259–273, Dec. 2006.

[8] M. Graef, Structure of materials : an introduction to crystallography, diffraction, and symmetry. New York: Cambridge University Press, 2012.

[9] H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics, vol. 7, no. 1, pp. 43–47, Jan. 2013.

[10] United States D.O.E., “Experimental Setup: Sample Coordinates,” X-ray Laue Diffraction Microscopy in 3D at 34-ID-E, APS, 25-May-2010. [Online]. Available:

http://www.aps.anl.gov/Sectors/33_34/microdiff/. [11] “Image Reconstruction,” Argonne National Laboratory. [Online]. Available:

http://www.aps.anl.gov/Sectors/33_34/microdiff/. [12] “Data Analysis flow chart,” Argonne National Laboratory. [Online]. Available:

http://www.aps.anl.gov/Sectors/33_34/microdiff/. [13] L. Wang, R. I. Barabash, Y. Yang, T. R. Bieler, M. A. Crimp, P. Eisenlohr, W. Liu,

and G. E. Ice, “Experimental Characterization and Crystal Plasticity Modeling of

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Heterogeneous Deformation in Polycrystalline α-Ti,” Metall. Mater. Trans. A, vol. 42,

no. 3, pp. 626–635, Mar. 2011. [14] “XML tree,” Wikipedia, the free encyclopedia. 29-Jun-2015. [15] “Median filter,” Wikipedia, the free encyclopedia. 21-Apr-2015. [16] “Thresholding (image processing),” Wikipedia, the free encyclopedia. 17-Nov-

2015. [17] “Rank Value Filter,” Wikipedia. 11-Jul-2015. [18] “Connected-component labeling,” Wikipedia, the free encyclopedia. 25-Aug-

2015. [19] A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,”

IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 5, pp. 476–480, May 1999. [20] L. Rocha, L. Velho, and P. C. P. Carvalho, “Image moments-based structuring

and tracking of objects,” in Computer Graphics and Image Processing, 2002. Proceedings. XV Brazilian Symposium on, 2002, pp. 99–105.

[21] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res., vol. 12, pp. 2825–2830, 2011.

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Appendices

Risk Assessment

Figure 4

a) Unsupervised computations could potentially return incorrect results silently b) Code may be incompatible on non Unix based computers c) Hard disk drives may fail mechanically and incur data loss d) Poor time management may lead to project delays

d).

b).

c).

a).

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Budget

SALARY:

Senior Project

Faculty

4,800

Undergraduate Student

1,440

SUB-TOTAL

6,240

FRINGE BENEFITS 27.00%

1,296

SALARY & FRINGE BENEFITS TOTAL 7,536

NON-SALARY:

Consumables

500

Internal Services

1,000

SUB-TOTAL 1,500

Total Direct Costs

9,036

Indirect Costs 58.50% 5,286

Total

14,322

Budget Justification Faculty salary is billed at $50 per hour for a total of 96 hours over the course of a

year, totaling $4,800. Student salary is billed at $10 per hour for a total of 144 hours over the course of a year, totaling $1,440. Accommodation for benefits brings the salary sub total to $7,536. An allotment for $400 in additional hard drives (for data storage) is made along with an allotment of $100 for shipping costs for a total of $500 in the consumables category. The indirect costs of $1,000 account for charges associated with network and technological resources such as network storage and server usage. The total direct costs amount to $9,036 with an additional 58.5% in indirect costs, bringing the total project budget to a total of $14,32200.