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Microsc. Microanal., page 1 of 12doi:10.1017/S1431927616012605

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Correlating Atom Probe CrystallographicMeasurements with Transmission KikuchiDiffraction DataAndrew J. Breen,1,2,* Katharina Babinsky,3 Alec C. Day,1,2 K. Eder,1,2 Connor J. Oakman,1,2

Patrick W. Trimby,1 Sophie Primig,4 Julie M. Cairney,1 and Simon P. Ringer1,2,5*

1Australian Centre for Microscopy and Microanalysis, The University of Sydney, Sydney, NSW 2006, Australia2School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia3Department of Physical Metallurgy and Materials Testing, Montanuniversität Leoben, Franz-Josef Straße 18, 8700Leoben, Austria4School of Materials Science and Engineering, The University of New South Wales, Sydney, NSW 2052, Australia5Australian Institute for Nanoscale Science and Technology, School of Aerospace, Mechanical and Mechatronic Engineering,The University of Sydney, Sydney, NSW 2006, Australia

Abstract: Correlative microscopy approaches offer synergistic solutions to many research problems. One suchcombination, that has been studied in limited detail, is the use of atom probe tomography (APT) and transmissionKikuchi diffraction (TKD) on the same tip specimen. By combining these two powerful microscopy techniques,the microstructure of important engineering alloys can be studied in greater detail. For the first time, the accuracyof crystallographic measurements made using APT will be independently verified using TKD. Experimental datafrom two atom probe tips, one a nanocrystalline Al–0.5Ag alloy specimen collected on a straight flight-path atomprobe and the other a high purity Mo specimen collected on a reflectron-fitted instrument, will be compared. Wefind that the average minimum misorientation angle, calculated from calibrated atom probe reconstructions withtwo different pole combinations, deviate 0.7° and 1.4°, respectively, from the TKD results. The type of atom probeand experimental conditions appear to have some impact on this accuracy and the reconstruction andmeasurement procedures are likely to contribute further to degradation in angular resolution. The challenges andimplications of this correlative approach will also be discussed.

Key words: atom probe tomography, transmission Kikuchi diffraction, crystallography, misorientation,grain boundary

INTRODUCTIONAtom probe tomography (APT) enables the position andchemical identity of millions of individual atoms to bereconstructed in three dimensions (3D) and has one of thehighest analytical spatial resolutions of any microanalysistechnique currently available (Miller et al., 1996). It istherefore ideal for looking at the 3D nanostructure ofmaterials, such as studying the chemistry and topography ofindividual interfaces (Gault et al., 2012b; Larson et al., 2013;Miller & Forbes, 2014). A small, needle-shaped specimen,with an tip radius of

Transmission Kikuchi diffraction (TKD) in thescanning electron microscope (SEM) (Keller & Geiss, 2012;Trimby, 2012) offers a fast and convenient means of col-lecting complementary crystallographic information onatom probe specimens. Also known as transmission electronback-scattered diffraction (t-EBSD), it offers significantimprovements in lateral spatial resolution compared withconventional EBSD. The technique works by passing theprimary electron beam through the sample and analyzing thetransmitted diffracted electrons on a standard EBSD detec-tor. The lateral spatial resolution depends on a combinationof experimental parameters, including sample thickness, stepsize, and beam spot size, but is typically

to be 10 nm, with a pattern resolution of 168 × 128 pixels(8 × 8 binned from full resolution). The acquisition speedwas 67 points per second. The accelerating voltage was 30 kVand the probe current was ~15 nA. TKD maps were takenover a range of projections (0°, 90°, 180°, and 270°) bymanually rotating the sample in the holder and analyzedusing the Oxford Instruments® HKL® software.

The same sample was then loaded into a CAMECA®LEAP® 4000X Si atom probe, which has a straight flight pathdesign. Data were collected at 40 K, using voltage pulsing(20% pulse fraction, 2000Hz, 0.5% evaporation rate). Datawere reconstructed using the commercially available IVAS®software. The mass spectrum and corresponding ranging canbe found in the Supplementary Material (Figure S1). Areconstruction calibration protocol, described by Gault et al.(2009), was also performed to ensure spatial integrity of thetomogram, as well accuracy in the subsequent crystal-lographic measurements. To mitigate changes in the imagecompression factor (ICF) and field factor (kf), which areknown to occur throughout the experiment (Gault et al.,2011), crystallographic calibration was performed within anapproximately one million atom slice in z, where crystal-lography was approximately constant. Any subsequentcrystallographic measurements were taken from this region.To determine the effect of crystallographic calibrationon the accuracy of the misorientation measurements, areconstruction that was not calibrated was also used forcomparison. MATLAB®was then used to further analyze thecrystallographic information in the detector hit maps andreconstruction from within the epos (extended pos) file thatcan be generated from IVAS®.

Supplementary Materials

Supplementary Materials can be found online. Please visitjournals.cambridge.org/jid_MAM.

Technically Pure Mo Sample Preparation andData AcquisitionThe technically pure Mo had a much larger grain size, sosamples were prepared using electropolishing, as well asadditional sharpening via a correlative TKD and FIB annularmilling procedure, to ensure a grain boundary was positionedclose to the apex of the specimen (Babinsky et al., 2014a). AnFEI® Versa® 3D DualBeam® (FIB/SEM) workstation equip-ped with an EDAX® Hikari® XP EBSD system was used forthis part of the study. The TKDmapping conditions were verysimilar to those used on the previous sample. An acceleratingvoltage of 30 kV and probe current of 11 nA were used. Thediffraction pattern resolution was 160 × 120 pixels with 4 × 4binning from full resolution, enabling an acquisition speed of40 frames/s. A 10nm step size was used. TKD maps for aseries of projections (0°, 90°, 180°, and 270°) were again taken.The EDAX® OIM® Analysis 7 software was then used for theanalysis of the EBSD data files.

The sample was then loaded into a CAMECA® LEAP®3000X HR atom probe, which has a reflectron design.A specimen temperature of 60K, target evaporation rate of 1%and laser pulsing with a green laser (λ = 532 nm), with 0.6 nJlaser energy at 250 kHz pulse frequency, were used duringexperimental acquisition. The conditions used were to helpwith specimen success rate, but are not ideal for the observa-tion of crystallographic information. The data collected weresubsequently reconstructed using IVAS® and calibrated simi-larly. One notable difference being the use of a 40mm virtualflight path length, rather than the physical 382mm. This wasfound to be a better representation of the flight displacementalong the z-direction from detector to specimen apex, andoffered improved convergence of calibration metrics. It wasdifficult to get enough crystallographic information to deter-mine misorientation between the two grains contained withinthe reconstruction from a single approximately one millionatom z-slice, so instead, two different regions, each containingenough information about one of the grains, were calibratedinstead. The calibration parameters were then averaged acrossthe whole reconstruction before misorientationmeasurementswere taken. A non-calibrated reconstruction was also used forcomparison. The resultant epos file was again used forsubsequent crystallographic analysis using MATLAB®. Themass spectrum and corresponding ranging can be found in theSupplementary Material (Figure S2).

RESULTSThe results from TKD and atom probe crystallographicmeasurements are presented for each material and atomprobe design. Mapping the grain orientation relative to thedetector and measuring the associated misorientationbetween grains is highly automated for the TKD analysiswhen using the commercially available EBSD software.However, making misorientation measurements in atomprobe reconstructions remains a very manual process, whichhas only been discussed in limited detail previously, so someattention is given here to the procedure undertaken.

Straight Flight Path Atom Probe Analyses VersusTKD Misorientation MeasurementsFigure 1a shows the calibrated tomographic reconstruction(ICF = 1.63, kf = 4, ε = 0.57, L = 90mm) and associatedcrystallographic measurements of the nanocrystalline sampleof the Al–0.5Ag alloy with Si impurities. The Si impurities, aswell as density fluctuations in the reconstruction, highlight thecaptured grain boundary. An approximately onemillion atomslice has been taken out of the centre of the reconstructionwhich, when viewed along the z-projection, clearly showszone line and poles (Fig. 1b). By comparing this to a stereo-graphic projection of the crystal structure of Al, the Millerindices corresponding to each pole can be determined.

A plane orientation extraction algorithm (POE), asdescribed previously (Araullo-Peters et al., 2015), has beenused to very precisely determine the normal to the sets of

Correlating Atom Probe Crystallographic Measurements 3

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planes detected within these pole regions of the reconstruc-tion (Fig. 1c–1f). The algorithm works by producing a 1Dspatial distribution map (SDM) along a range of differentdirections in 3D. A 1D SDM is a histogram of atomic dis-tances along a particular directional component, within agiven region of interest (ROI). A fast Fourier transform(FFT) is then applied to each SDM and the signal intensity isplotted over the range of directions, expressed in polarangles. The highest signal corresponds to the normal to thesets of detected planes. A clear maximum could be observedfor all families of planes. Finally, the SDMs corresponding tothe maximums in each pole region are provided, the peak-to-

peak distance of which should be close to the actual planespacings in the analyzed sample.

This information can then be used to determine theorientation of each grain relative to the detector and further,the misorientation between each of the grains. The polarangles can be converted to Cartesian unit vectors within thespecimen frame using the following sets of equations:

x= - sin θ;y= sinϕ cos θ;

z= cosϕ cos θ: ð1Þ

Figure 1. a: Nanocrystalline Al–0.5Ag atom probe reconstruction. b:Approximately one million atom slice from the region of interestmarked in (a) showing grain boundary and indexed pole information in each grain. c–f: The plane orientation extraction and spatial dis-tribution map results from each indexed pole.

4 Andrew J. Breen et al.



It should be noted that the convention used here, andthroughout the manuscript, is that previously defined byMoody et al., (2009) which differs from the typical sphericalco-ordinates definition.

The orientation matrix of each grain is defined using thefollowing equation:

Cc = g � Cs; (2)where Cc and Cs are the crystal frame and specimen frame,respectively, and g is the orientation matrix. g can be thoughtof as the rotation required to get the directions in Cs alignedwith Cc. However, as there are slight errors in themeasured orientation of directions in the Cs frame, due toinaccuracies in the tomographic reconstruction, Cs must becalibrated first. To do this, a new set of Cs directions werefitted to those measured within the reconstruction usingtwo restraints:

(1) The angles between the fitted directions are equal to thetheoretical angles between those crystallographicdirections.

(2) The residual sum of squares (RSS) of the angles (ϕ)between the measured and fitted directions in the Csframe was minimized:

RSS=Xni= 1

φ2i ; (3)

where n is the number of directions identified within theatom probe reconstruction and used in the calculation,typically n = 3 was used for the results in this manuscript.Such a calculation can be performed using the solverfunction in software such as Microsoft Excel® or MATLAB®.The misorientation, i.e., the transformation necessary torotate from one crystal orientation to the next, can then becalculated as

M12 = g1g - 12 : (4)

To determine the minimum misorientation, or disorienta-tion, between the grains, all orientation variants of one of thegrains must be considered. These variants can be found in tex-ture and crystallographic texts such as Randle & Engler (2000).

For a cubic system, 24 orientation variants exist. The minimummisorientation angle, i.e., the grain boundary angle, can be cal-culated from the following equation:

θ=min cos - 1tr M12ð Þ - 1

2

�� (5)

The misorientation axis is the real eigenvector of M12,a 3 × 1 column vector x, corresponding to the real eigenvalue λ:

M12x= λx: (6)

A worked example for calculating the disorientationbetween the grains in the nanocrystalline Al–0.5Ag atomprobe reconstruction shown in Figure 1 is provided in theSupplementary Material. For more information regardingthe mathematics of texture analysis the reader is referred toRandle & Engler (2000).

Supplementary Figure S1

Supplementary Figure S1 can be found online. Please visitjournals.cambridge.org/jid_MAM.

To further correlate the TKD and APT results, 3Dorientation mapping of the APT reconstruction was per-formed using MATLAB®. Due to the strong segregation ofthe Si impurities to the interface, filtering, based on a nearestneighbour (NN) distribution of the Si atoms, could be usedto define the grain boundary surface. Si–Si 50NN≤9 nm wasfound to work well (Figs. 2a, 2b). Additional filtering, using a3D point selection tool, enabled removal of any remainingatoms not belonging to the interface. Atoms on either side ofthe boundary were then defined. A boundary hull of eachgrain was 3D rendered and colored according to the verticalcrystallographic direction relative to the detector using theinverse pole figure (IPF) notation (Fig. 2c).

A comparison of the TKD and APT orientation maps isshown in Figure 3. TKD maps are shown at four differentprojections at ~90° intervals in Figure 3a, the red box on thefinal map indicates the approximate region of the corre-sponding APT reconstruction. Grains in the TKDmaps were

Figure 2. a: Si–Si 50 NN histogram. b: Si–Si 50 NN ≤9 nm is used to filter out atoms at interface and define boundary. c: The interfaceand boundary atoms of reconstruction are used to define hulls of each grain colored according to the vertical crystallographic orientation.




colored according to the crystallographic direction in thevertical direction, i.e., the direction close to the vertical axisof the tip, so that the coloring would be similar to thatobserved in the APT orientation maps. The relative crystalorientation of each grain is also provided. The corresponding3D orientation maps of the APT reconstruction are shown inFigure 3b at four projections, also at ~90° intervals, and aclear correlation between the crystallographic informationfor the two techniques can be obtained. A movie of the APTorientation map can be found in the Supplementary Material(movie file 1). Figure 3c is a 1D concentration profile of theimpurity species along the direction approximately normalto the grain boundary, which was measured from the APT

reconstruction. It has been included to demonstrate how thechemical information contained within the APT data can becompared directly with the crystallographic information forprecise chemical and structural analysis of grain boundariesin these materials.

A summary of the measurements from each technique isgiven in Table 1. From the TKD results, the averageorientation of each grain was calculated using the HKL®software and the minimum misorientation between the twograins was measured. From the APT data, three separatemeasurements of the same grain boundary are given. Thefirst one is for the calibrated reconstruction. The secondis a measurement using the default or non-calibrated IVAS®

Figure 3. a: Transmission Kikuchi diffraction maps of the Al–0.5Ag sample at four different projections. b: Three dimensional(3D) orientation maps of atom probe tomographic reconstruction. c: 1D concentration profile perpendicular to grain boundary (shownin inset).

Table 1. Misorientation Measurements of Al–0.5Ag: Transmission Kikuchi Diffraction (TKD) Versus Atom Probe Tomography (APT)(Straight Flight Path)

Calibration Parameters Poles g1 Poles g2

ICF kf L (mm) ε 1 2 3 1 2 3 Angle (°) Axis [h k l]

TKD – – – – – – – – – – 41.4 [0.003 0.197 0.980]APT 1 1.63 4 90 0.57 1 1 2 1 1 2 39.9 [0.054 0.168 0.984]

1 1 0 1 1 21 3 2 1 3 0a

APT 2 1.65 3.3 90 0.50 1 1 2 1 1 2 39.3 [0.028 0.277 0.960]1 1 0 1 1 21 3 2 1 3 0a

APT 3 1.63 4 90 0.57 2 1 2 1 1 4 41.5 [0.035 0.228 0.973]1 1 5 3 1 21 3 1a 5 3 2a

ICF, image compression factor.Three different APT measurements of the same grain boundary are provided varying reconstruction parameters and pole selection.aDirection calculated from cross-product of the other two.




reconstruction parameters and same pole selection.The third measurement is for the calibrated reconstructionusing a different selection of poles. The average minimummisorientation angle/axis pair calculated from the calibratedreconstruction with different pole selections, is 40.7°/[0.0450.198 0.979]. The misorientation angle and axis deviate 0.7°and 2.6°, respectively, from the TKD results.

Reflectron Fitted Atom Probe Analyses Versus TKDMisorientation Measurements

A similar crystallographic analysis procedure was thenundertaken for the technically pure Mo specimen. Figure 4ashows the calibrated atom probe reconstruction collected forthe sample (ICF = 1.28, kf = 2.56, ε = 0.37, L = 40mm).Strong segregation of the N and P impurity species can be seenat the grain boundary running down the centre of the recon-struction. Once again, pole and zone line structure could beobserved throughout the reconstruction, although this wasweaker than in the previous example (Figs. 4b, 4f). Densitymaps from approximately one million atom slices of tworegions within the reconstruction have been used. It was stillpossible to index individual poles and clear periodicity of lat-tice planes was observed within these regions as indicated bythe POE and SDMs (Figs. 4c–4e, 4g–4i). Using this informa-tion, the orientation of each grain, as well as the misorienta-tion between them, could be calculated using the methoddescribed in the previous section. These measurements couldthen be compared directly to those from the TKDmaps takenof the tip before the atom probe experiment.

Figure 5 shows a comparison between the TKD and APTanalyses of the same grain boundary region. Once again, thegrains have been colored according to the crystallographicdirection in the vertical direction, as measured from bothtechniques. Figure 5a shows four TKD maps of the specimenat projections spaced ~90° apart, the relative measuredorientation of each grain is also provided. Figure 5b shows thecorresponding 3D orientation maps of the APT reconstruc-tion, also at four projections spaced ~90° apart. A movie of the3D orientation map of the reconstruction can be found in theSupplementary Material (movie file 2). The coloring fromeach technique is very similar, indicating close agreement inthe crystallographic measurements and facilitates easy com-parison between the two results. A 1D concentration profile ofthe impurity elements along the direction normal to the grainboundary is also provided, which again highlights the abilityto combine very precise atomic chemical and crystallographicinformation of individual grain boundaries with this analysisapproach.

A summary of the minimum misorientation measure-ments is given in Table 2. As done earlier, the averageorientation of each grain was calculated and a minimummisorientation was measured using these values. Threeseparate measurements of the same boundary in the atomprobe data were conducted from the calibrated reconstruc-tion, non-calibrated reconstruction, and the calibrated

reconstruction with a different selection of poles. The aver-age minimum misorientation angle, calculated from themeasurements taken on the calibrated reconstruction withdifferent pole selections, is 33.4°/[0.099 0.640 0.761]. Themisorientation angle and axis deviate 1.4° and 5.7°, respec-tively, from the TKD result.

DISCUSSIONAngular ResolutionFrom the presented results, it was possible to gain insight intothe angular resolution of orientation and misorientation mea-surements made directly from APT reconstructions throughthe use of complementary TKD results on the same tip speci-men. Such information is useful, because APT crystallographicstudies are starting to become popular as a means of combiningatomic scale chemical and crystallographic measurementsacross individual grain boundaries, yet there has been limitedinvestigation into the accuracy of such measurements. It isimportant to point out that the angular resolution of TKD,while significantly high, still has a margin of error. A quick wayto estimate this error is to perform a transect across a defor-mation free grain and view the pixel to pixel misorientationdata. For the data presented, this was found to be on averageapproximately ±0.3°. When measuring the misorientationbetween two separate grains, the margin of error is double thisvalue or ±0.6°. Higher angular resolutions would be possiblewith higher diffraction pattern resolutions but this wouldincrease the time required to generate the TKD maps.

An accurate estimate of the true angular resolution usingAPT is difficult due to the time each individual measurementtakes, the influence of so many variables, including thereconstruction calibration, and the protocols used to makethe measurement itself and falls outside the scope of thismanuscript. However, to gain some insight into the effect ofreconstruction calibration and pole selection, three separatemeasurements were taken changing these parameters on eachsample. It was presumed that the carefully calibrated recon-structions would result in significantly more accurate mis-orientation measurements, but based on themeasurements inTables 1 and 2, this could not be substantiated and is perhapsan indication of the robustness in making misorientationmeasurements from APT reconstructions. Nevertheless,some variance in the results, depending on parameter selec-tion, was observed. For the calibrated atom probe recon-structions, the maximum deviation of misorientation angle is2°. However, when the measurements using different poleselection are averaged, this falls to 1.4° and suggests that theaccuracy can be improved by averaging multiple measure-ments using a different selection of poles. The deviation in themisorientation axis is larger, i.e., on average ~4°. This was tobe expected as the nature of the misorientation axis calcula-tion is even more sensitive to variation in the orientationof each grain. The same compounding error is also seen incalculations from EBSD and TKD data. It is also worthpointing out that this is particularly the case when low angle




Figure 4. a: Technically pure Mo atom probe reconstruction. b,f: Density maps of top and bottom grains, respectively, with indexed polestructure. c–e, g–i: Plane orientation extractions and spatial distribution maps of indexed families of planes.




grain boundaries are being studied (Prior, 1999), but in thepresented study only high angle grain boundaries wereconsidered. These errors must be a significant considerationwhen observing changes in segregation behavior withmisorientation across interfaces, because even small devia-tions from special crystallographic arrangements at grainboundaries can have a strong effect on segregation behavior(Rohrer, 2011; Herbig et al., 2014).

The type of APT instrument (straight flight path versusreflectron) appears to have some impact on angular resolu-tion of misorientation measurements. It was assumed that

measurements from a reflectron fitted instrument would beworse, due to distortions in the reconstruction caused by thecurved flight path of the ions, and indeed, even after carefulcalibration and incorporating the 40mm flight path,approximately twice the level of deviation in the mis-orientation angle/axis pair was observed. Interestingly, thebest result came from the non-calibrated reconstruction.More measurements would be needed to further confirm thisobservation and perhaps the calibration methods used forthese reconstructions needs further development. Even so,misorientation measurements were still possible to within an

Figure 5. a: Transmission Kikuchi diffraction maps of technically pure Mo sample at different projections. b: Three dimensionalorientation maps of atom probe tomographic reconstruction. c: 1D concentration profile in direction perpendicular to grain boundary(shown in inset).

Table 2. Crystallographic Measurements of Technically Pure Mo: Transmission Kikuchi Diffraction (TKD) Versus Atom ProbeTomography (APT) (Reflectron).

Calibration Parameters Poles g1 Poles g2

ICF kf L (mm) ε 1 2 3 1 2 3 Angle (°) Axis [h k l]

TKD – – – – – – – – – – 32.0 [0.196 0.640 0.743]APT 1 1.28 2.56 40 0.37 0 1 1 2 1 1 34.0 [0.148 0.627 0.765]

1 1 2 1 1 11 2 1 3 2 1a

APT 2 1.65 3.3 382 0.37 0 1 1 2 1 1 32.7 [0.186 0.679 0.710]1 1 2 1 1 11 2 1 3 2 1a

APT 3 1.28 2.56 40 0.37 0 1 1 1 1 1 32.8 [0.050 0.652 0.757]1 1 1 2 1 11 2 1a 3 2 1a

ICF, image compression factor.Three different APT measurements of the same grain boundary are provided varying reconstruction parameters and pole selection.aDirection calculated from cross-product of the other two.




accuracy of several degrees and there is significant scope forimprovement. It is also worth noting that pole and zone linestructure is often less clear on reflectron instruments, eventhough lattice planes may still be conserved within theresultant reconstructions. Crystallographic signal intensitymapping approaches (Araullo-Peters et al., 2015) would beuseful to enhance this information, particularly in situationswhere zone and pole line signal is too poor to index.

The reason for the discrepancy is likely to be causedpredominantly from inaccuracies in the reconstruction cali-bration and measurement itself. A likely source of error iscaused from the imperfectly reconstructed atom probe dataand the requirement to fit the Cs frame to this structure. It isworth noting that the image compression factor (ICF) and kf,which are used in the typical reconstruction protocol, changethroughout the atom probe experiment (Gault et al., 2011)and may have added to measurement error. Some effort wasmade to mitigate this effect. For the nanocrystallineAl–0.5Ag dataset, it was possible tomeasure the orientation ofeach grain from a single calibrated slice within the recon-struction, thereby avoiding any change in crystallography indepth. For the technically pure Mo, it was difficult to obtainsufficient crystallographic information of each grain within asingle slice in depth. Consequently, an average ICF and kffrom two slices, that contained sufficient crystallographicinformation about each grain, was calculated and applied tothe entire reconstruction. The orientation of each grain wasthen measured at each slice. A dynamic reconstructionapproach as proposed by (Gault et al., 2011), would haveenabled the observed crystal structure in each grain to remainapproximately constant in depth and hence would haveprobably improved the accuracy of the measurement further.However, this reconstruction calibration protocol takes muchlonger to implement for a small gain in accuracy.

Perhaps a more accurate approach for future workwould be to measure the orientation directly from the poleand zone lines observed in the detector hit map, therebyalleviating any need to interrogate the tomographic recon-struction directly. Such an approach should achieve similaraccuracy to that reported by Takahashi et al. (2014) (± 0.4°),with the added benefit that the APT experiments couldcontinue without the time consuming process of a FIMexperiment, which would require large changes to thevacuum within the analysis chamber. Further improvementscould also be possible with improved reconstruction meth-ods and measurement protocols, such as improved indexingand interpretation of spacing between observed zone lineand pole patterns, as well as averaging multiple measure-ments based on a different selection of poles.

Correlating the TKD and APT Orientation MapsFigure 2 outlines the process used to filter out the boundaryusing a NN analysis, which worked well due to the strongsegregation of impurity species in both examples. In caseswhere this type of segregation is not observed, density fluc-tuations within the reconstruction could be used instead to

highlight the boundaries using techniques such as the inter-face detection method proposed by (Liddicoat et al., 2010).

Figures 3 and 5 are useful for directly comparing thecrystallographic information each technique provides. Inboth samples, the calculated color of the grains, based on theIPF, was very similar between the two techniques, indicatingthat crystallographic alignment was very close in the verticaldirection. The 3D orientation maps from the atom probereconstructions highlight the unique ability of APT to giveadditional information about grain morphology and com-pletely describe the boundary to 5 degrees of freedom,including the boundary plane orientation if desired. It shouldbe noted that the 3D APT orientation maps only show theglobal orientation average of each grain, whereas the TKDorientation maps can show local changes in crystallographywithin the grains themselves due to strain or dislocations.However, all misorientation measurements in the presentedstudy were based on average grain orientation. Althoughlocal changes in crystallography can be observed in APT, thisis generally only in the pole and zone line regions and itis difficult to determine whether this change is due toinaccuracies in the reconstruction or true changes in localcrystallography.

Alignment between the TKD and APT results is animportant consideration. It is interesting to note that thelonger TKD maps in Figure 3 demonstrate clearly that,depending on orientation, the grain structure can appearquite different as only 2D crystallographic information in thebottom 10–20 nm of the sample, relative to the detector, isbeing displayed. This potentially adds a level of complexity toworking out corresponding grains between the two techni-ques, and may even render some grains invisible to TKD ifthey are buried within the centre of the atom probe tip.However, this was not an issue for the examples shown asonly a single boundary was captured in each APT recon-struction. Due to the angular field-of-view of APT beinglimited to ~30–40° because of the electrode and detectorconfiguration, ions on the periphery of most tips are notdetected and so what is reconstructed is a conical sub-volume of the original specimen. It is therefore difficult toprecisely align the location of the APT reconstruction to theTKD map without multiple boundaries being captured ineach. In cases where sufficient crystallographic informationis present within the atom probe reconstructions to deter-mine grain orientation, this information can be used to helpmatch up individual grains, otherwise density fluctuationsand atomic segregation to the interfaces can be a usefulmeans for grain alignment. TKD could also potentially guidereconstructions of these materials, if changes in grain mor-phology and boundary orientation are identified, however,this process would currently be challenging.

Efficiency and Future OutlooksAlthough APT crystallography is important for reasonsoutlined previously, it is also time consuming, particularlyfor the non-expert with limited programming experience. In




cases where only a misorientation value across a grainboundary is required, TKD may currently be the ideal choiceto get these measurements as it is convenient, rapid, andcurrently more accurate. However, APT crystallography willcontinue to be important for reconstruction calibration andfull crystallographic quantification of nanocrystalline grains,including the boundary plane orientations. What is requiredis development very similar to that observed with EBSDtechnology, whereby the process becomes much moreautomated. With improvements to the reconstructionalgorithm, signal detection algorithms and modification ofsoftware to automatically index patterns, perhaps throughutilization of the Hough transform, this could one day be areality. TKD can be a very useful metric to guide this process.

CONCLUSIONThe highly accurate crystallographic measurements thatTKD provides can be useful for atom probe specimenpreparation procedures as well as complementing the che-mical, structural, and morphological information that APTprovides in 3D at the atomic level. Atom probe crystal-lographic studies, whereby lattice information is directlyobserved from within the atom probe data, are particularlyuseful for reconstruction calibration and enabling chemico-textural orientation mapping in 3D at resolutions otherwiseunavailable.

Here we have used TKD to independently verify atomprobe crystallographic measurements for the very first time.Two grain boundaries, one in a nanocrystalline Al–0.5Agalloy and the other in technically pure Mo, have been studiedusing complementary TKD and APT. We found that for thetwo grain boundaries, measurements of the minimum mis-orientation angle from the calibrated atom probe recon-structions was at most only 2.0° different from the TKDmeasurements. The minimum misorientation angle, calcu-lated from calibrated atom probe reconstructions with twodifferent pole combinations, deviate 0.7° and 1.4°, respec-tively, from the TKD results. Also interesting to note was thatthe measurements from the straight flight path instrumenthad approximately half the deviation of the reflectioninstrument (2.4° and 5.7° on average, respectively). Theaccuracy of the APT measurement appears to be dependenton inaccuracies in the reconstruction, as well as calculationerrors from the misorientation measurement itself.

The results have significant implications to the struc-tural analysis of individual grain boundaries at the atomiclevel, which plays a critical role in the understanding ofstructure-property relationships in polycrystalline materials.Regardless of the atom probe instrument used and thematerial being analyzed, it appears that crystallographicmeasurements to within several degrees of accuracy arecurrently possible, so long as enough crystallographic infor-mation can be detected, and efforts are being made toimprove crystallographic signal detection for non-idealspecimens (Araullo-Peters et al., 2015; Yao, 2016).

With improved reconstruction and measurement protocols,this accuracy could also be improved in the future. TKD willnot entirely supersede APT for crystallographic measure-ments, since APT crystallography will, for example, alwaysbe useful for reconstruction calibration and measuring the3D crystallographic orientation of grain boundary planes.But it will be invaluable as a tool to guide these measure-ments, as well as providing a convenient, accurate, and morerapid means of directly correlative grain texture informationof atom probe specimens.

ACKNOWLEDGMENTSThe authors acknowledge the scientific and technical sup-port of the Australian Microscopy and MicroanalysisResearch Facility (AMMRF—ammrf.org.au) node at theAustralian Centre for Microscopy and Microanalysis(ACMM) at the University of Sydney, as well as at theDepartment of Physical Metallurgy and Materials Testing,Montanuniversität Leoben. The nanocrystalline Al wasfabricated by Oliver Renk at the Erich Schmidt institute inLeoben. The technically pure Mo was supplied by Plansee SE,Austria. The authors are particularly grateful to Dr. AnnaCeguerra and Dr. Peter Felfer for fruitful discussion, ThomasHartley for assistance with graphic design of figures andrelated presentations, Dr. Takanori Sato for experimentalatom probe support and Nathan Wallace and Dr. BaptisteGault for assistance with crystallographic analysis.

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Correlating Atom Probe Crystallographic Measurements with Transmission Kikuchi DiffractionDataIntroductionMaterials and MethodsNanocrystalline Al–0.5Ag Sample Preparation and Data AcquisitionSupplementary Materials

Technically Pure Mo Sample Preparation and Data Acquisition

ResultsStraight Flight Path Atom Probe Analyses Versus TKD Misorientation Measurements

Figure 1a: Nanocrystalline Al–0.5Ag atom probe reconstruction.Outline placeholderSupplementary Figure S1

Figure 2a: Si–Si 50 NN histogram.Figure 3a: Transmission Kikuchi diffraction maps of the Al–0.5Ag sample at four different projections.Table tab1 Reflectron Fitted Atom Probe Analyses Versus TKD Misorientation Measurements

DiscussionAngular Resolution

Figure 4a: Technically pure Mo atom probe reconstruction.Figure 5a: Transmission Kikuchi diffraction maps of technically pure Mo sample at different projections.Table tab2 Correlating the TKD and APT Orientation MapsEfficiency and Future Outlooks

ConclusionAcknowledgmentsACKNOWLEDGEMENTSReferences

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