Spatial Resolutions of On-Axis and Off-Axis Transmission Kikuchi

applied sciences

Article Spatial Resolutions of On-Axis and Oﬀ-Axis Transmission Kikuchi Diﬀraction Methods

Yitian Shen 1,2 , Jingchao Xu 3, Yongsheng Zhang 1,2, Yongzhe Wang 1, Jimei Zhang 1, Baojun Yu 4, Yi Zeng 1,2,* and Hong Miao 3,* 1 The State Key Lab of High Performance Ceramics and Superﬁne Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Science, Shanghai 200050, China; [email protected] (Y.S.); [email protected] (Y.Z.); [email protected] (Y.W.); [email protected] (J.Z.) 2 Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China 3 CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China; [email protected] 4 Bruker (Beijing) Scientiﬁc Technology Co., Ltd., Shanghai 200233, China; [email protected] * Correspondence: [email protected] (Y.Z.); [email protected] (H.M.)

Received: 18 September 2019; Accepted: 19 October 2019; Published: 23 October 2019

Abstract: Spatial resolution is one of the key factors in orientation microscopy, as it determines the accuracy of grain size investigation and phase identification. We determined the spatial resolutions of on-axis and off-axis transmission Kikuchi diffraction (TKD) methods by calculating correlation coefficients using only the effective parts of on-axis and off-axis transmission Kikuchi patterns. During the calculation, we used average filtering to evaluate the spatial resolution more accurately. The spatial resolutions of both on-axis and off-axis TKD methods were determined in the same scanning electron microscope at different accelerating voltages and specimen thicknesses. The spatial resolution of the on-axis TKD was higher than that of the off-axis TKD at the same parameters. Furthermore, with an increase in accelerating voltage or a decrease in specimen thickness, the spatial resolutions of the two configurations could be significantly improved, from tens of nanometers to below 10 nm. At a voltage of 30 kV and sample thickness of 74 nm, both on-axis and off-axis TKD methods exhibited the highest resolutions of 6.2 and 9.7 nm, respectively.

Keywords: transmission Kikuchi diﬀraction (TKD); transmission electron back-scatter diﬀraction (t-EBSD); on-axis detector; spatial resolution

1. Introduction Electron back-scattering diffraction (EBSD) is a powerful technique in material science for microstructural analyses [1]. The use of nanomaterials has rapidly increased with the development of nanotechnologies. Nevertheless, the limited spatial resolution of the EBSD may not be sufficient to reveal the substructures and this may hamper its application in nanomaterial analyses. To improve the spatial resolution of the EBSD, Keller and Geiss changed the EBSD configuration so that the Kikuchi patterns formed by transmitted electrons can be acquired [2]. The resultant electron diffraction technique is referred to as transmission EBSD or off-axis transmission Kikuchi diffraction (off-axis TKD). However, the pattern center is distant from the center of the detector in the off-axis TKD method, which leads to a considerable distortion. In 2016, Fundenberger et al. proposed an on-axis TKD method, in which the incident beam, sample, and detector are collinear [3]. Compared to the off-axis TKD, the new configuration provides higher signal intensity and lower distortion. Furthermore, either the electron dose or acquisition time can be reduced 20 times to yield an equivalent pattern quality as that in the off-axis TKD method [4–6].

Appl. Sci. 2019, 9, 4478; doi:10.3390/app9214478 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 4478 2 of 8

In recent years, both off-axis and on-axis TKD methods have been extensively used to analyze nanocrystalline and ultrafine-grain materials [6–11]. The spatial resolution is one of the key factors in the EBSD-based orientation microscopy, as it determines the accuracy of grain size investigations and phase identifications. Although Kikuchi patterns are commonly used to provide two-dimensional information about the microstructure of a material, they are a product of the three-dimensional electron interaction volume [12]. Consequently, when the electron beam is scanned across a grain boundary, the interaction volumes of both sides overlap, which leads to overlapping and unindexable Kikuchi patterns. Zaefferer defined two types of spatial resolution, physical spatial resolution (PSR) and effective spatial resolution (ESR) [13]. The PSR corresponds to the smallest distance from a large-angle grain boundary where the overlapping pattern of both crystals appears, while the ESR indicates the smallest distance across a boundary where the patterns are still indexable by a software algorithm [13,14]. Niessen et al. compared the on-axis and off-axis TKD methods in many aspects, including the spatial resolution [5]. They investigated the effect of working distance in spatial resolution at detector-typical microscope parameters and demonstrated that the PSR of the on-axis TKD was slightly improved compared to that of the off-axis TKD. However, no extensive studies have been carried out on the PSR changes with other microscope parameters and sample parameters for on-axis and off-axis TKDs in the same scanning electron microscope (SEM). In addition, the low signal-to-noise ratio of the TKD pattern leads to errors in the calculation of the PSR, which has been neglected in previous research. In this study, the evaluation method for the PSR was improved by considering only the effective parts of the patterns, while the noisy parts were eliminated during the calculation. Additionally, we introduced average filtering to remove low-frequency noise, and thus, precisely calculate the spatial resolution. Furthermore, the spatial resolution difference between the off-axis and on-axis TKDs was investigated at different accelerating voltages and specimen thicknesses. We aimed to analyze the limitations of the instruments for an optimal analysis of each sample.

2. Materials and Methods

2.1. Sample Preparation To measure the spatial resolutions of the on-axis and off-axis TKD methods, an electron-transparent sample containing twin boundaries is needed. Ferritic steel was used in this study for this purpose. The sample was polished with a 1200-grit abrasive paper. Subsequently, diamond suspensions were used for mechanical polishing. Afterwards smooth finishing was carried out by ion milling by using a LEICA EM TIC 3X system (Leica Mikrosysteme GmbH, Vienna, Austria). During the ion milling, voltages of 5.5 kV and 4.5 kV were used for polishing. The polished sample was cut using a dual focused ion beam system in FEI Versa™ 3D SEM (FEI, Brno, Czech Republic). Before cutting, platinum was deposited on the surface of the sample to protect it from damage. The grain boundary of the sample was identified in a back-scatter electron channeling image. Subsequently, an area with both grains and boundaries was selected and cut off from the matrix. The sample was welded onto a copper holder for further thinning. Three samples were cut from the same twin boundary to ensure that the boundary width was the same. They were thinned to three different thicknesses by a low Ga ion current of 100 pA and a low voltage of 3 kV, which was also applied to remove the amorphous layer. Finally, the thicknesses of the three samples were evaluated by the platinum layer deposited on the surface using a back-scatter electron image. Five measurements were taken for each sample to obtain an average thickness; these were 169 1 nm, 91 1 nm, 74 2 nm. ± ± ± 2.2. TKD Both on-axis and off-axis TKD spatial resolutions were measured by using a TESCAN MIRA3 SEM FS (TESCAN, Brno, Czech Republic) equipped with a Bruker e−Flash detector. For the off-axis TKD, the sample stage was tilted by 20 and the scintillator was set in the vertical position. For the on-axis − ◦ TKD, a Bruker OPTIMUS™ detector head (Bruker Nano GmbH, Berlin, Germany) was set horizontally, Appl. Sci. 2019, 9, 4478 3 of 8

and the tilt angle was set to 0◦. During the measurements in both conﬁgurations, the spot size was set to 4.8 nm. The operation and detector distances were 5 and 14.2 mm, respectively. The image resolution of all Kikuchi patterns was 640 480 pixels, while the contrast was 3%. To ensure a good × pattern quality, the beam current and exposure time in the on-axis and oﬀ-axis TKD measurements were set to 1 nA and 70 ms, and 2 nA and 150 ms, respectively. All samples were oriented so that their grain boundaries were parallel to the incident electron beam and perpendicular to the scanning direction. The Kikuchi pattern at each step was recorded while the beam was scanned across the grain boundary at accelerating voltages of 20–30 kV with increments of 5 kV and scanning step of 2 nm.

3. Results and Discussion

3.1. Quantitative Evaluation of the Spatial Resolution In this study, the digital image correlation (DIC) technique [15–17] was used to investigate the effects of the accelerating voltage and specimen thickness. The DIC method can be used to quantitatively evaluate small variations between patterns by calculating their correlation coefficient. As the electron beam is scanned close to a grain boundary, the interaction volumes of both sides overlap, which leads to overlapping Kikuchi patterns, and thus to a decreased correlation coefficient. Therefore, this method can be used to determine the spatial resolution. It has been extensively used to evaluate the physical resolutions of the EBSD [14,18] and off-axis TKD methods [19–21]. The correlation coefficient can be P gij gij expressed as r = q , where g and g denote the grey scale of the reference and sampling ij P 2 P 2 ij ij gij gij pattern at each position (i,j), respectively. The middle part of the on-axis and off-axis Kikuchi patterns have good qualities; however, the boundaries of the patterns contain considerable noise. Moreover, a bright spot is generated by the transmitted beam in the center of the on-axis Kikuchi pattern. The size and shape of the bright spot can change during the scanning. Thus, if the whole pattern (640 480 pixels) is considered, the correlation × coefficient would deviate and the results would be inaccurate. Therefore, regions of interest (ROIs) have to be selected to increase the precision. Wang et al. used this method to determine the resolution of the off-axis TKD [19]. In this study, we have used a similar approach. Circular ROIs were chosen for the off-axis TKD, which contained the overlapping region, as shown in Figure1C. On the other hand, annular ROIs were selected in the on-axis TKD to ensure that the boundaries and bright spots were eliminated while retaining the overlapping regions (Figure1B). In addition, the chosen ROIs should be as large as possible to ensure representativity. The calculated correlation coefficients at a voltage of 30 kV and specimen thickness of 91 nm are presented in Figure2. Chen et al. [ 14] and Shih et al. [20] applied a fast Fourier transform (FFT) filter to reduce the noise, while FFT followed by inverse FFT were applied by Wang et al. [19] to obtain smooth curves. FFT is commonly used for filtering in the frequency domain; if a smooth profile is needed, the peak may be broadened. Therefore, an average filtering algorithm is introduced to avoid the deviation in the correlation coefficient, which can smooth profiles in the spatial domain. As it does not affect the profile width, it is commonly used to filter out Gaussian noise. In Figure2B, the low-frequency noise was removed and the whole curve became smoother after filtering. The smooth profiles of the correlation coefficients were summed and normalized. The procedure is presented in previous reports [14,19,20]. With this approach, we can obtain the sum of the normalized correlation coefficients as a function of the distance (Figure2C) and the full width at half maximum can be easily calculated, which is defined as the PSR [14]. Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 8

Appl. Sci. 2019, 9, 4478 4 of 8 Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 8

FigureFigureFigure 1. 1. (A( A1.) )Schematic(A Schematic) Schematic of of ofthe the the ferritic ferriticferritic steel steel steel lamella lamella used used used for for forthe the thedetermination determination determination of the of ofspatial the the spatial spatialresolutions resolutions resolutions of the on-axis and off-axis transmission Kikuchi diffraction (TKD). Kikuchi patterns across the grain ofof the the on on-axis-axis and and off off--axisaxis transmission transmission Kikuchi Kikuchi diffraction diffraction ( (TKD).TKD). Kikuchi Kikuchi patterns patterns across across the the grain grain boundary at an accelerating voltage of 30 kV and thickness of 91 nm, acquired by (B) on-axis TKD boundaryboundary at an acceleratingaccelerating voltagevoltage of of 30 30 kV kV and and thickness thickness of of 91 91 nm, nm, acquired acquired by (byB) ( on-axisB) on-axis TKD TKD (the regions(the ofregions interest of interest (ROIs) (ROIs are outlined) are outlined by theby the red red annular annular rings) rings) and ( (CC) )off off-axis-axis TKD TKD (the (the ROIs ROIs are (the regionsare outlined of interest by the red (ROIs circles).) are outlined by the red annular rings) and (C) off-axis TKD (the ROIs outlined by the red circles). are outlined by the red circles).

Figure 2. Correlation coefficient profiles at the accelerating voltage of 30 kV and thickness of 91 nm (A) determined by using the digital image correlation (DIC) technique by comparing the sampling patterns with the left (blue curve) and right patterns (red curve) in order and (B) after average FigureFigure 2. 2. CorrelationCorrelation coefficient coefficient profiles profiles at at the the accelerating accelerating voltage voltage of of 30 30 kV kV and and thickness thickness of of 91 91 nm nm filtering. (C) Sum of the normalized correlation coefficients as a function of the distance. ((AA)) determined determined by by using using the the digital image correlation ( (DIC)DIC) technique technique by comparing the the sampling patterns3.2.patterns Difference with with in the the Spatial left left (blue Resolution (blue curve) curve) between and and right the right patternsOn - patternsAxis (redand Off (redcurve)-Axis curve) in TKD order in Methods andorder (B and) after (B average) after average filtering. filtering.(C) Sum of(C) the Sum normalized of the normalized correlation correlation coefficients coefficients as a function as a offunction the distance. of the distance. By using the above method, the spatial resolutions of the on-axis and off-axis TKD methods were 3.2. Dimeasuredfference in the Spatial same Resolution SEM at the between same sample the On-Axis position. and The O dataff-Axis obtained TKD Methodsat different voltages and 3.2. Differencesample thicknesses in Spatial are Resolution presented between in Figure the 3. On The-Axis intensity and Off and-Axis contrast TKD of Methods the pattern for the 169- By using the above method, the spatial resolutions of the on-axis and off-axis TKD methods Bynm -usingthick samplethe above were method, too low theto identify spatial atresolutions the same parameters of the on- axisused and for theoff -othaxiser TKDtwo samples. methods were wereTherefore, measured results in the are same presented SEM atonly the for same the two sample samples. position. The data obtained at different voltages measured in the same SEM at the same sample position. The data obtained at different voltages and and sample thicknesses are presented in Figure3. The intensity and contrast of the pattern for the sample thicknesses are presented in Figure 3. The intensity and contrast of the pattern for the 169- 169-nm-thick sample were too low to identify at the same parameters used for the other two samples. nm-thick sample were too low to identify at the same parameters used for the other two samples. Therefore, results are presented only for the two samples. Therefore, results are presented only for the two samples. Appl. Sci. 2019, 9, 4478 5 of 8 Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 8

Figure 3. Spatial resolution of the on-axis and off-axis TKD methods as functions of the accelerating voltageFigure 3. at Spatial thicknesses resolution of 91 andof the 74 on nm.-axis and off-axis TKD methods as functions of the accelerating voltage at thicknesses of 91 and 74 nm. The spatial resolution of the on-axis TKD was better than that of the off-axis TKD at the same acceleratingThe spatial voltage resolution and thickness; of the on the-axi largests TKD gapwas wasbetter 8 nm.than The that only of the di ffofference-axis betweenTKD at the the same two configurationsaccelerating voltage was theand intersection thickness; the angle largest between gap was the phosphor8 nm. The screen only difference and incident between beam the (α)[ two5]. Inconfigurations the off-axis TKD,was the the intersection intersection angle angle between had a magnitude the phosphor of onlyscreen a fewand degrees,incident beam which (α) led [5] to. In a highthe off gnomonic-axis TKD, distortion the intersection and low angle diffraction had a magnitude intensity. On of only the contrary, a few degrees, no pattern which distortion led to a high and gnomonic distortion and low diffraction intensity. On the contrary, no pattern distortion and high high diffraction intensity were observed in the on-axis TKD because the angle α was close to 90◦. Consequently,diffraction intensity in the owereff-axis observed TKD, the in probe the on current-axis TKD and/or because exposure the time angle have α towas be close increased to 90°. to produceConsequently, an equivalent in the off pattern-axis TKD, quality. the Inprobe this current study, weand/or increased exposure both time current have and to be exposure increased time. to Nonetheless,produce an equivalent the increase pattern in current quality leads. In to this larger study, probe we size increased and interaction both current volume, and which exposure inevitably time. increaseNonetheless, the spatial the increase resolution. in current Therefore, leads at their to larger optimal probe parameters, size and the interaction beam current volume, used which in the oinevitablyff-axis TKD increase method the should spatial be resolution. higher than Therefore, that in the at on-axis their optimal TKD method, parameters, which the leads beam to acurrent larger spatialused in resolution. the off-axis Similarly, TKD method if we should set equal be parametershigher than forthat both in the TKD on- methods,axis TKD themethod, pattern which quality leads in theto a o largerff-axis spatial TKD method resolution. would Similarly, be worse if owingwe set toequal its lower parameters intensity. for Therefore,both TKD themethods, spatial the resolution pattern ofquality the o ffin-axis the off TKD-axis would TKD stillmethod be worse would than be worse that of owi theng on-axis to its lower TKD. intensity. Therefore, the spatial resolutionAnother of reasonthe off- foraxis the TKD diff woulderence still is the be smaller worse netthan scattering that of the angle on-axis in the TKD. on-axis TKD because of the detectorAnother geometry. reason for At the a given difference depth, is thethe path smaller length net throughscattering the angle sample in the is smaller on-axis for TKD the because on-axis TKD,of the whichdetector implies geometry. that fewerAt a given scattering depth, events the path may length occur through before the sample electrons is reachsmaller the for detector. the on- Therefore,axis TKD, the which on-axis implies TKD thathas a fewer thicker scattering source region events of detected may occur intensity, before which the electrons is beneficial reach to the the lateraldetector. spatial Therefore, resolution, the buton-axis detrimental TKD has to athe thicker depth sourcespatial resolution region of [detected5,22]. intensity, which is beneficial to the lateral spatial resolution, but detrimental to the depth spatial resolution [5,22]. 3.3. Effects of the Accelerating Voltage and Specimen Thickness on the On-Axis and Off-Axis TKDs 3.3. Effects of the Accelerating Voltage and Specimen Thickness on the On-Axis and Off-Axis TKDs As shown in Figure3, the spatial resolutions of both configurations were improved, from tens of nanometersAs shown to below in Figure 10 nm, 3, the with spatial the increase resolutions in accelerating of both configurations voltage or decrease were improved, in sample from thickness. tens Atof the nanometers voltage of to 30 below kV and 10 sample nm, with thickness the increase of 74 nm, in the accelerating on-axis and voltage off-axis TKD or decrease methods in achieved sample thethickness. lowest resolutions At the volta ofge 6.2 of and 30 9.7 kV nm, and respectively. sample thickness of 74nm, the on-axis and off-axis TKD methodsWith achieved the increase the lowest in thickness, resolutions the Kikuchiof 6.2 and bands 9.7 nm, became respectively. less sharp and higher noises were observedWith at the the increase boundaries in thickness, of the patterns. the Kikuchi For the bands on-axis became TKD, the less size sharp of the and direct higher beam noises decreased were withobserved the increase at the bound in thickness,aries of the which patterns. indicates For the a larger on-axis energy TKD, loss the beforesize of thethe electronsdirect beam emerge decreased from thewith sample the increase (Figure in4 ).thickness, The results which also indicates demonstrate a larger that energy a thinner loss before sample the leads electrons to a better emerge spatial from resolution.the sample If(Figure the thickness 4). The isresults reduced also by demonstrate only tens of that nanometers, a thinner thesampl spatiale leads resolution to a better would spatial be significantlyresolution. If improved.the thickness This is canreduced be explained by only bytens the of scattering nanometers, events the ofspatial diffracted resolution electrons would along be thesignificantly crystal plane improved. [19,21, 23This,24 ].can For be the explained same material by the scattering at the same events accelerating of diffracted voltage, electrons the electron along penetrationthe crystal plane depth [19,21,23,24] is the same.. If For the the sample same is material thicker, the at electronthe same point accelerating source would voltage, be furtherthe electron from thepenetration emergence depth surface. is the This same. increases If the sample the likelihood is thicker, of the incoherent electron scattering point source along would the emergence be further from the emergence surface. This increases the likelihood of incoherent scattering along the emergence path, which leads to a larger energy loss and reduced pattern contrast [8,25]. On the other hand, less scattering events lead to a smaller electron beam broadening, and thus to a lower spatial Appl. Sci. 2019, 9, 4478 6 of 8 path,Appl. which Sci. 2019 leads, 9, x FOR to aPEER larger REVIEW energy loss and reduced pattern contrast [8,25]. On the other hand,6 of less8 scatteringAppl. Sci. 2019 events, 9, x FOR lead PEER toa REVIEW smaller electron beam broadening, and thus to a lower spatial resolution.6 of 8 resolution. Usually, the thickness of the TKD sample should be 1.5 times the grain size. If the Usually, the thickness of the TKD sample should be 1.5 times the grain size. If the specimen thickness resolution.specimen thickness Usually, is the more thickness than two of times the TKDthe grain sample size, shouldthe Kikuchi be 1.5 patterns times of the the grain top and size. bottom If the is more than two times the grain size, the Kikuchi patterns of the top and bottom layers would overlap. specimenlayers would thickness overlap. is more This than would two lead times to the a significantlygrain size, the reduced Kikuchi pattern patterns quality. of the top The and minimum bottom This would lead to a significantly reduced pattern quality. The minimum thickness for TKD is a quarter layersthickness would for TKD overlap. is a quarter This would of the leadextinction to a significantlydistance, according reduced to patternRice et al. quality. [24], because The minimum the total of the extinction distance, according to Rice et al. [24], because the total number of scattering events thnumberickness of for scat TKDtering is a events quarter will of bethe rapidly extinction reduced distance, and theaccording scattering to Rice angle et wal.ill [24] be ,very because small, the below total willnumberthe be threshold. rapidly of scat reduced tering events and the will scattering be rapidly angle reduced will and be the very scattering small, below angle thewill threshold. be very small, below the threshold.

FigureFigure 4. 4.Kikuchi Kikuchi patterns patterns atat thethe acceleratingaccelerating voltage of of 30 30 kV kV and and thicknesses thicknesses of of(A (,AC),C 91) 91and and (B, (DB), D) 169Figure169 nm nm for 4.for theKikuchi the on-axis on -patternsaxis and and o atoffff -axisthe-axis accelerating TKDs,TKDs, respectively.respec voltagetively. of These These30 kV two twoand samples samplesthicknesses are are presented of presented (A,C) 91 because and because (B ,theD) the diff169differenceerence nm for in in theirthe their on thickness- axisthickness and isoff is larger. -larger.axis TKDs, respectively. These two samples are presented because the difference in their thickness is larger. WithWith the the increase increase in in accelerating accelerating voltage, voltage, the width width of of the the Kikuchi Kikuchi band band decreases decreases and and the the boundaryboundaryWith becomes becomes the increase clearer.clearer. in acceleratingFor For the the on on-axis-axis voltage, TKD, TKD, the thetransmitted width transmitted-beam of the-beam Kikuchi diam bandeter diameter and decreases diffraction and di andff ractionspot the spotboundarybrightness brightness becomes are are increased increased clearer. ( FigureFor (Figure the 5).on5 -axis). The The TKD, spatial spatial the resolution transmitted resolution can-beam can be be improveddiam improvedeter and by by diffraction increasing increasing spot the the acceleratingbrightnessaccelerating voltage; are voltage; increased however, however, (Figure the the influenceinfluence5). The spatial ofof the voltage resolution on on the the can spatial spatial be improved resolution resolution by is isreduced increasing reduced above above the 25accelerating25 kV. kV. In In other other voltage; words, words, however, ifif the acc accelerating theelerating influence voltage voltage of the is voltage issufficiently suffi onciently the high spatial high so that soresolution thatmost mostelectrons is reduced electrons reach above the reach the25detector, detector, kV. In other the the spatial spatialwords, resolution resolutionif the acc elerating w willill be be minimallyvoltage minimally is sufficiently affected affected by by high the the voltage.so voltage. that most When When electrons the the acceleration accelerationreach the voltagedetector,voltage is is 30 the30 kV, kV, spatial the the spatial spatial resolution resolution resolution will be isis minimally optimal,optimal, which affected can can byalso also the be be voltage.explained explained When by by sc theattering scattering acceleration events. events. voltageAccording is 30 to kV,a Monte the spatial Carlo simulation,resolution is the optimal, electron which penetration can also depth be explained increases bywith sc theattering accelerating events. According to a Monte Carlo simulation, the electron penetration depth increases with the accelerating Accordingvoltage [20] to. Therefore,a Monte Carlo for asimulation, material with the electronthe same penetration thickness, thedepth point increases source with will thebe closeraccelerating to the voltage [20]. Therefore, for a material with the same thickness, the point source will be closer to voltageemergence [20] surface.. Therefore, This for indicates a material fewer with scattering the same events thickness, will happen the point before source the w electronsill be closer leave to the the emergence surface. This indicates fewer scattering events will happen before the electrons leave emergencesample because surface. of This the shorterindicates path, fewer which scattering leads events to better will spatialhappen resolution. before the electrons However, leave in both the the sample because of the shorter path, which leads to better spatial resolution. However, in both sampleconfigurations, because the of accelerating the shorter voltagepath, which has a minor leads role to better in the spatialspatial resolution.resolution compared However, to in that both of configurations,configurations,the specimen thickness. the the accelerating accelerating voltage voltage hashas a minor role role in in the the spatial spatial resolution resolution compared compared to tothat that of of thethe specimen specimen thickness. thickness.

Figure 5. Kikuchi patterns of the 91-nm-thick sample at the voltages of (A,C ) 20 and (B,D) 30 kV for FigureFigurethe on 5.- axis5.Kikuchi Kikuchi and off patterns patterns-axis TKDs, of of thethe respectively. 91-nm-thick91-nm-thick sample at at the the voltages voltages of of (A (A,C,)C 20) 20 and and (B (,DB,)D 30) 30kV kV for for thethe on-axis on-axis and and o ﬀoff-axis-axis TKDs, TKDs, respectively. respectively. Appl. Sci. 2019, 9, 4478 7 of 8

The results are in agreement with our previous study on the spatial resolutions of the off-axis TKD method for 41-, 69-, and 91-nm-thick austenitic steel samples [19]. Nevertheless, the spatial resolution measured in this study is considerably lower for the samples with a similar thickness, mainly because of the improved filtering algorithm. Furthermore, the density of the ferritic steel is lower than that of the austenitic steel. According to van Bremen et al., TKD is more effective in the analyses of less dense samples [23]. Additionally, Wang et al. reported that the spatial resolution at a voltage of 20 kV and thickness of 91 nm could not be calculated owing to the low intensity. In contrast, we evaluated the resolution under the same conditions, because the current in the off-axis TKD was 2 nA, instead of 1.6 nA, as used by Wang et al.

4. Conclusions The spatial resolutions of the on-axis and off-axis TKD methods were investigated by the improved DIC technique. We considered only the effective parts of the patterns and eliminated the noisy parts during the calculation to reduce the deviation. Moreover, average filtering was used to remove the low-frequency noise. The spatial resolution of the on-axis TKD was better than that of the off-axis TKD at the same accelerating voltage and sample thickness, which was attributed mainly to the high intensity and thick source region in the on-axis TKD. Furthermore, the spatial resolutions of both configurations were improved with an increase in accelerating voltage or a decrease in sample thickness. The optimal resolutions were achieved at the voltage of 30 kV and sample thickness of 74 nm, 6.2 nm for the on-axis TKD and 9.7 nm for the off-axis TKD.

Author Contributions: Conceptualization, Y.Z.; methodology, Y.S., Y.Z., Y.W., J.Z. and B.Y.; software, J.X.; formal analysis, Y.S.; investigation, Y.S.; writing—original draft preparation, Y.S.; writing—review and editing, Y.S.; supervision, Y.Z. and Hong Miao; project administration, Y.Z.; funding acquisition, Y.Z. Funding: This research was funded by the National Key R&D Program of China (2018YFB0704400), CAS Key Foundation for Exploring Scientific Instrument (YJKYYQ20170041), International Partnership Program of Science (GJH21721), Shanghai Technical Platform for testing on inorganic materials (19DZ2290700), and Shanghai Action Projects for Scientific and Technological Innovation (17142201500). Acknowledgments: The authors are grateful for the technical assistance provided by Xuemei Song, Ziwei Liu, Chucheng Lin, Wei Zheng, Caifen Jiang and Henghui Cai. Conflicts of Interest: The authors declare no conflict of interest.

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