Data for: Correlative statistical microstructural assessment of precipitates and their distribution, with simultaneous electron backscatter diffraction and energy dispersive X-ray spectroscopy

Data bundle for “Correlative statistical microstructural assessment of precipitates and their distribution, with simultaneous electron backscatter diffraction and energy dispersive X-ray spectroscopy”

Chris Bilsland*, Andrew Barrow, and Ben Britton

*[e-mail]

This metadata file describes that data released to support the manuscript. The files descried below are organised principally into the figures they relate to however overlapping data is not copied and is just referred to.

Figures:

Figure 1: (a)The histograms for the pre and post processed Mo+Nb-Lα intensity map with the manually selected binarisation threshold. The pre-processing histogram shows the two intensities of the precipitates and the matrix regions. A programmatic method for threshold selection was trialled. Labelling of carbides using EDS based analysis (b) EDS spectra from a single point. (c) Reconstructed spatial map from the summed intensity of the Mo+Nb-Lα yellow window from the energy window from each point. (d) Binary particle map resulting from noise filtering and thresholding the image. (e) Red circles show where a circular Hough transform has detected a particle in the binary image.

Data_Package\MATLAB_FILES\ Figure1_Data

Figure1.BinaryMap

Figure1.ParticleData…

Figure1.IntensityFiltered

Figure1.RawMap

Figure1.RandSpectra

Histograms are plotted from the RawMap and IntensityFiltered files.

The random spectra is plotted as a random spectra selected from the raw EDS data, in the case RandSpectra.

The spatial map is an image plot of the RawMap.

The binary plot is BinaryMap.

The circle overlay is a plot of the BinaryMap with ParticleData.coords.x_um, ParticleData.coords.y_um and ParticleData.radii_um

Figure 2: Microstructure maps of HIP’ed Inconel 625 (a) crystal orientations. (b) Grain boundaries overlaid on a microstructure map, coloured by boundary type. The Σ3 and Σ9 are low energy ‘special’ CSL boundaries. Determining particle locations by combining EBSD and EDS data (c) Binary particle map with randomly orientated grain boundaries overlaid. (d) Binary particle map with Σ3 grain boundaries overlaid. (e) Microstructure map with identified particles separated and colour coded by location. Spectra are extracted from each point within each circle to enable comparison by precipitation location. (f) Cartoon of Euclidean distance calculation and threshold distance from circle to boundary for allocation of particle location. Distance is calculated from the central point of each circle.

Data_Package\MATLAB_FILES\ Figure2_Data

Figure2.EBSD…

Figure2.IQ

Figure2.GrainBoundaries… (in micrometres)

The EBSD map is plotted using MTEX from using EBSD

The Image Quality map with grain boundary overlay uses IQ and GrainBoundaries.parent, GrainBoundaries.Sig3 and GrainBoundaries.Sig9. Where column 1 is the x coordinates and column 2 is the y coordinates.

The Binary map overlaid with the parent Grainboundaries uses Figure1.BinaryMap with GrainBoundaries.parent.

The Binary map overlaid with the Σ3 boundaries uses Figure1.BinaryMap with Grainboundries.Sig3.

The image quality map overlaid with segmented circle data uses IQ with Figure1.ParticleData.(INSERTBOUNDARY).x_um, Figure1.ParticleData.( INSERTBOUNDARY).y_um and Figure1.ParticleData.( INSERTBOUNDARY).r_um. Boundaries are rand, s3, s9 and nb.

nb = noboundary.

Figure 3: Quantifying the effectiveness of the Hough  based circle detection approach. (a) The variation in the number of circles generated and detected over a series of trials at different generated normal distributions. Including the impact of a layer of gaussian noise. (b) Two different  corrections applied to the detected circles, a simple and barycentre approach to remove any excess incorrect labelling. (c) Comparing the empirical cumulative distribution functions (ECDF) for both generated and detected circle radii, with the normal CDF for the detected circles. The mean, standard deviation and result of a Kolmogorov-Smirnov test for similarity between the generated and detected ECDF’s is shown for each case.

Data_Package\MATLAB_FILES\ Figure3_Data

Figure3.QuantifyingCircles…

The data for the plot(a)

Figure3.QuantifyingCircles.(MEAN).gen_(RUN_NO) and Figure3.QuantifyingCircles.(MEAN).dec(RUN_NO) are used – these are the radii of indentified circles from the simulated data sets.

For the Kolmogorov-Smirnov test – the Emprical Cumulative Distribution Functions for both generated and detected radii and the Normal Cumulative Distribution Function for the detected radii were calculated using the Matlab Statistics tool box and the test applied.

Figure 4: The effect of sample tilt modelled by Monte-Carlo simulation with CASINO of increasing thickness of a surface of NbC with an infinite Ni layer beneath represented by taking the maximum generated X-ray intensity from the phi-rho-z curves.

Data_Package\Figure 4\

Contains excel files for both the peak intensity generated for tilted and untitled simulations.

Figure 5: Segmented EDS spectra by boundary category compared as raw spectra, quantified atomic % and statistically compared through ANOVA. (a) Mean EDS spectra across each boundary. (b) Radar plot of the atomic % of element present by boundary category from the marked particles. (c) Comparison of the calculated mean, with 95% confidence intervals for Nb content, compared by boundary type. (d)The quantification metrics for precipitate distributions in size range, location, boundary content and particle distribution along each boundary.

Data_Package\MATLAB_FILES\ Figure5_Data

Figure5.SegmentedEDS

Figure5.Radii (in um)

Figure5.Num_Particles

Figure5.BoundaryProportions

Figure5.BoundaryLenghts

Data_Package\Quantified_Spectra\HIP\Atomic_percent_tilt_corrected\ebsd_inconel_625…

The relative intensity plot takes the SegmentedEDS data

[Sigma3, Sigma9, NoBoundary, Random, Matrix] columns

The atomic percent radar plot uses the average quantified data from the segmented quantifed data in Data_Package\Quantified_Spectra\HIP\Atomic_percent_tilt_corrected\ebsd_inconel_625…

The Anova plot uses the same quantified data and plots the output of the matlab ANOVA between the Σ3, random and internal quantified data for Niobium.

The precipitation distribution plot is a histogram of Radii.

The boundary proportion plot is a bar chart from BoundaryProportions.

The Precipitation distributions plot uses the Num_Particles [Random, Sigma3, Sigma9, No boundary].

The inter-particle distance calculates the average distance between particles using Num_Paritlces/BoundaryLenghts for each boundary.

Figure 6: The microstructure of a sample HIP and Wrought microstructures (top) with the accompanying binary particle map and overlaid grain boundary structure (bottom).

Data_Package\MATLAB_FILES\Figure6_data

Figure6.HIP.Radon

Figure6.HIP.GrainBoundaries… (both pixels and um - labelled)

Figure6.HIP.BinaryMap

Figure6.WR.Radon

Figure6.WR.GrainBoundaries… (both pixels and um - labelled)

Figure6.WR.BinaryMap

The image quality map overlaid with grain boundaries uses Figure6.(INSERT HIP/WR).Radon with Figure6.(INSERT HIP/WR).GrainBoundaries.(INSERT TYPE) which contains x,y coordinates in um.

The binary maps use Figure6.(INSERT HIP/WR).BinaryMap with Figure6.(INSERT HIP/WR).GrainBoundaries.(INSERT TYPE).

Figure 7: Quantitative particle and boundary analysis comparing the HIP and wrought (WR) microstructures. (a) The mean chemical spectra for particles identified along each boundary highlighting the difference in the particle compositions and the similarity in the matrix compositions. (b) Quantified mean spectra in Atomic %. (c) Resulting P-Values of ANOVA for each individual element compared between each segment. (d) Proportion of the total grain boundary length that is each of Σ3, Σ9 (special boundaries) and randomly misoriented grain boundaries. The proportion of total identified particle compared by precipitation location identified and the mean spacing of the particles along each of the boundary types.

Data_Package\MATLAB_FILES\Figure7_data

Figure7.HIP_Spectra

Figure7.WR_Spectra

Figure7.HIP.BoundaryLength (in um)

Figure7.HIP.NumParticles

Figure7.WR.BoundaryLength (in um)

Figure7.WR.NumParticles

Data_Package\Quantified_Spectra\HIP\Atomic_percent_tilt_corrected…

Data_Package\Quantified_Spectra\WR\Atomic_percent_tilt_corrected…

The averga spectra plot for HIP and WR spectra use Figure7.(INSERT HIP/WR)_Spectra [Simga3, Sigma9, NoBoundary, Random, Matrix]

The Radar plots use the average quantifed data from all three regions for the HIP and WR samples from Data_Package\Quantified_Spectra\HIP\Atomic_percent_tilt_corrected… and Data_Package\Quantified_Spectra\WR\Atomic_percent_tilt_corrected…

The P-vales are extracted from ANOVA run for this quantified data.

The precipitation by location uses Figure7.(INSERT HIP/WR).NumParticles [Random, Sigma3, Sigma 9, Internal].

Mean inter-particle spacing uses Figure7.(INSERT HIP/WR).BoundaryLength [Total, Sigma3, Sigma 9, Random]/ Figure7.(INSERT HIP/WR).NumParticles [Random, Sigma3, Sigma 9, Internal].

Total Boundary length is a plot of Figure7.(INSERT HIP/WR).BoundaryLength [Total, Sigma3, Sigma 9, Random].