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[Jun Uzuhashi](https://orcid.org/0000-0003-2023-8158), [Tadakatsu Ohkubo](https://orcid.org/0000-0003-3548-1951), [Kazuhiro Hono](https://orcid.org/0000-0001-7367-0193)

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[Development of automated tip preparation for atom probe tomography by using script-controlled FIB-SEM](https://mdr.nims.go.jp/datasets/f6f171ce-4744-4c99-8be7-2bb30613b383)

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1  Development of automated tip preparation for atom probe tomography by using script-controlled FIB-SEM  Jun Uzuhashi*, Tadakatsu Ohkubo and Kazuhiro Hono National Institute for Materials Science, Tsukuba, 305-0047, Japan *Corresponding author. E-mail: UZUHASHI.Jun@nims.go.jp  Keywords: APT; atom probe tomography, FIB; focused ion beam, SEM: scanning electron microscopy, automation, scripting language  Abstract Atom probe tomography (APT) has become a popular technique for microstructural analysis of a wide range of alloys and devices over the past two decades owing to the employment of laser-assisted field evaporation and the development of site-specific tip preparation using a focused ion beam (FIB) with a scanning electron microscopy (SEM) system. In laser-assisted field evaporation, laser irradiation conditions largely influence mass resolution; therefore, recent commercial APT instruments allow strict control of the analysis conditions. However, the mass resolution is affected not only by the laser condition but also by the thermal conductivity of the material and the tip shape. In addition, it is also important to keep the tip shape constant in order to obtain tomography data with good reproducibility since the analytical volume highly depends on the tip shape. In this study, we have developed a method to fabricate the tip with the desired shape automatically by using a script-controlled FIB-SEM system, which has traditionally depended on the skill of the FIB-SEM operator. The tip shape was then intentionally changed by using this method, and its effect on the APT data is also discussed.   Introduction Atom probe tomography (APT) is the only technique that can visualize the three-dimensional distribution of atoms in materials [1-4]. In APT analysis, laser pulses or voltage pulses are applied onto the needle-shaped specimen (tip) under a high electric field to ionize atoms from the tip surface while simultaneously measuring the mass and position of those ions by a position-sensitive detector. Although the volume size that can be analyzed is limited to the nanoscale, the technique has a high spatial resolution close to atomic resolution and high chemical sensitivity with quantitative analytical capability. Two major technological innovations in the past 20 years have contributed to the APT technique becoming a powerful tool for microstructural analysis; one is the development of a laser-assisted atom probe [5-13] and the other is the establishment of a tip preparation method using a focused ion beam (FIB) with a scanning electron microscopy (SEM) system [14-18], which has broadened the APT applications to insulators, semiconductors, and their devices [19-23]. Furthermore, laser-assisted field evaporation, which uses laser pulses instead of voltage pulses, has dramatically reduced the frequency of tip fracture during APT measurement, which has been a traditional problem in the APT analysis [2, 5, 7]. The laser-assisted field evaporation resulted in a mailto:UZUHASHI.Jun@nims.go.jp2  significant improvement in the analysis yield and measurable volume size. It has also been reported that the use of femtosecond laser pulses, instead of nanosecond voltage pulses, greatly improves the mass resolution [2, 5]. On the other hand, laser-assisted evaporation often causes a mass tail issue in mass spectra, which degrades mass resolution [8-13]. The mass tail was reported to depend on several factors, including the laser irradiation conditions [7, 8, 10, 12, 24], the thermal conductivity of the material, and tip shape [9, 10, 25]. The latest commercial instruments, i.e., CAMECA LEAP instruments, allow very precise control of measurement conditions such as laser power, wavelength, beam position, and evaporation rate. On the other hand, the tip fabrication for APT analysis still strongly depends on the skill and experience of the FIB-SEM operator. Since it is known that the tip shape strongly affects the mass resolution in the laser mode [2, 9, 10, 25], establishing a method to prepare tips reproducibly should make an important role to improve the reproducibility and reliability of APT data. In recent years, FIB-SEM systems can be automatically controlled by a scripting language, and an automated (or semi-automated) method of preparing samples for scanning transmission electron microscopy (S/TEM) has already been reported [26, 27]. In this study, we developed a method to fabricate tips in a specified shape automatically with high accuracy and reproducibility using a script-controlled FIB-SEM system. Automatically fabricated tips with intentionally different shapes were analyzed to study the effect of tip shape on APT data, and the underlying mechanism is also discussed in this paper.  Methods and Materials  A FIB-SEM system, Thermo Fisher Scientific Helios 5UX, was used to prepare APT tips. The instrument is equipped with an "AutoScript 4" system that can control the FIB-SEM system with a Python-based scripting language [28]. Python 3.6-based scripting allows control of various FIB and SEM conditions, image acquisition, processing fabrications, stage movement, etc., without any operator interactions. In addition to the standard Python library [29], the following open-source Python libraries were used in our scripting; ConfigObj 5.0.6 for reading and writing of configuration files [30], NumPy 1.15.4 for the mathematical algorithms [31], tifffile 2020.9.3 for reading image and metadata [32], Pillow 5.2.0 for opening and saving images [33], scipy 1.2.1 [34] and openCV 4.0.1 for image processing [35]. Since the purpose of this study is to control the tip shape, the lift-out process was performed manually [16, 18]. Note that the semi-automatic lift-out method has already been demonstrated by Tsurusawa et al. for S/TEM sample preparation [27], and fully automated lift-out is another challenge.    APT analyses were carried out for the automatically fabricated tips in the laser mode to compare how the APT data differs depending on the tip shape. CAMECA LEAP 5000XS was used for APT analysis with a 355 nm wavelength picosecond laser pulsing mode at a repetition rate of 500 kHz with the laser pulse energy 100pJ at a specimen base temperature of 50 K. The detection rate was kept constant at 2.0 %, that is, one ion per 50 laser pulses. It should be noted that all the tips were mounted on silicon support with platinum FIB deposition, and the sample height, the distance from the tip apex to the Si support was 3  approximately 3.0 µm. The obtained APT data were analyzed by CAMECA AP Suite Software 6.1.  Three alloys were used in this experiment: Fe84.8B10.9P3.5Cu0.8 nanocrystalline soft magnetic material, Cu-2.5Ni-0.8Si (mass%) Corson alloy, and commercial SUS304 stainless steel. The Fe-based nanocrystalline soft magnetic material is a promising candidate as a potential substitute for electrical steel sheets to improve the iron loss of electric motors at high frequency ranges for automotive applications [36, 37]. The Corson alloy is used in most electric appliances due to its excellent electrical conductivity and strength; thus, the alloy is one of the key materials to realize an energy-efficient society [38]. Since the properties of these alloys highly depend on the nanoscale three-dimensional structure, APT is an ideal tool to understand the relationship between the properties and the microstructures. In addition, stainless steel contains several trace elements and is a suitable material for comparing differences in mass resolution and chemical sensitivity in APT analysis. Therefore, these three alloys were used as examples for the establishment of the automated APT tip fabrication method in this study.  Results and Discussions Figure 1 shows a schematic workflow of the automated tip fabrication process using a script-controlled FIB-SEM system. Once a Python-based program is executed, the FIB fabrication and monitoring of the tip shape from the SEM image is repeated automatically, until the tip shape becomes a set shape. The automated S/TEM sample fabrication method demonstrated by Tsurusawa et al. only performs the predefined FIB process [27]. However, since the sputtering yield by FIB varies depending on the material and crystal orientation [39, 40], it is impossible to maintain the reproducibility of the tip shape without sequentially acquiring SEM images and feeding the instantaneous tip shape back to the FIB process. The uniqueness of this study is that the FIB process is executed with active feedback from the SEM imaging, and this process flow improves the accuracy of fabrication.  Figure 1. Schematic workflow of an automated APT tip preparation using a FIB-SEM system. (a) Execute the program on a script-controlled FIB-SEM system, (b) FIB fabrication 4  is carried out for a few seconds, and (c) the tip shape is monitored by using an SEM image. Repeating (b) and (c) until the tip becomes (d) the desired shape.  Figure 2(a) shows SEM images of the same silicon tip by an Everhart-Thornley detector (ETD), through-the-lens detector (TLD), and ion conversion and electron (ICE) detector (5kV, WD: 4mm) [41-43]. Fig. 2(b) shows the normalized intensity profiles from the arrows in Fig. 2(a). The secondary electron images acquired with the out-lens type detectors (ETD and ICED) show left-right asymmetric contrasts. On the other hand, the intensity of secondary electron images acquired with through-the-lens detectors (TLD) is relatively symmetrical. The asymmetry of the intensity acquired with an out-lens type detector can be understood from the geometry of the detectors in the chamber as illustrated in Fig. 2(c). Unlike judgment by the human eye, asymmetric contrast causes misrecognition by the boundary extraction program for monitoring the instantaneous change of the tip shape, so we have concluded that a through-the-lens SEM image is appropriate for monitoring the tip shape. A through-the-lens secondary electron image will henceforth be referred to as an "SEM image”.  Figure 2. (a) Secondary electrons SEM images of the same silicon tip by using Everhart-Thornley detector (ETD), through-the-lens detector (TLD), and ion conversion and electron 5  (ICE) detectors. (b) Normalized SEM intensity line profiles from the arrows indicated in the SEM images. (c) Schematic of detectors geometry.  Figure 3(a) shows the definition of the tip shape and Fig. 3(b) shows an example of the tip observed by the SEM. A boundary extraction method called "canny edge detection" was applied to the SEM image for monitoring the tip shape [44]. Boundary extraction determines the position of the tip apex indicated by the yellow arrow in Fig. 3(a). At the same time, the position where the width of the tip ("width: W1" in Fig. 3(a)) is twice the radius of the tip curvature ("r (nm)" in Fig. 3(a)), i.e., W1=2r, is determined. In Fig. 3(b), W1 is 5.8×10-7 m, so the radius of this tip curvature is 1/2 of the value, i.e., 290 nm. From the values of W1~n with constant interval "d (nm)" in the depth direction, the shank angle is calculated by linear approximation as illustrated in Fig. 3(a). Based on the typical observing magnification when an operator performs APT tip preparation manually, “d” was set to 300~500 nm for rough fabrication and 200 nm for later FIB process. The “n”, the number of measuring positions, was set as 5 in this study. The shank angle is 35.9° by linear approximation in the SEM image shown in Fig. 3(b). In this way, the tip shape defined by the radius of the tip curvature and the shank angle can be monitored by the program.  Figure 3. (a) Schematic of tip shape definition by the radius of the tip curvature and the shank angle. (b) Example of calculating the radius of the tip curvature and the shank angle by using the SEM image.  The next issue is the FIB fabrication conditions. In general, the APT tip fabrication is performed at 30 keV, followed by a cleaning process to remove Ga ion damage at 2~5 keV [2, 16]. Based on the typical FIB processes of manual APT tip preparation, three different fabrication conditions were set as shown in Table 1. The outer diameter of the donut-shaped sputtering mask was kept constant at 3~4 µm, and the inner diameter was gradually decreased according to the desired tip shape. The processing duration depends on the FIB sputtering 6  yield of the target material and the desired tip shape. In conventional operator-dependent processing, the operator must determine the size of the sputtering mask and processing duration based on his/her experience. In the automated fabrication method, on the other hand, if the tip shape does not meet the conditions specified in Table 1, the same process is repeated, and if the set conditions are satisfied, the next process is automatically started. During the process, SEM images are acquired every 5~10 seconds in the rough fabrication process, and every 2~3 seconds in the middle and later stages of the process. In addition, SEM images are acquired at a higher resolution than during rough milling so that monitoring the tip shape can be performed with high accuracy at the latter stages. This has made it possible to prepare the tip with high precision and reproducibility regardless of differences in sputtering yields of materials and crystal orientations. Figure 4 shows automatically fabricated tips of nanocrystalline soft magnetic material using the three different conditions shown in Table 1. Shapes A and B have the same radius of tip curvature but different shank angles. Shape C has twice the radius of tip curvature as B. Although the images are not shown here, we were also able to fabricate tips with high precision in the case of the stainless steel and the Corson alloy. We analyzed these tips under the same APT measurement conditions to verify how the tip shape affects the APT data.  FIB Donut-shaped Mask (nm) Parameters Outer Diameter A B C Tip radius (nm) Shank angle (degrees) Inner Diameter A B C A B C 1 30 keV 0.26 nA 4000 1200 650 25 35 2 3000 700 400 15 30 3 30keV 90 pA 3000 300 400 200 250 13 25 4 3000 170 200 60 125 10 25 5 5 keV 21 pA 3000 0 50 100 10 25 Table 1. Detailed fabrication steps and conditions for automated fabrications based on typical APT tips fabrication process. “Shape A, B, and C” are written as just “A”, “B”, and “C” in the table.  7  Figure 4. Automatically prepared APT tips from Fe-based nanocrystalline soft magnetic material with different conditions.  Figure 5 shows (a) a bright-field TEM image of the nanocrystalline soft magnetic material, (b) 2-nm-sliced elemental maps from the first 10 million atoms, and (c) mass spectra. As described in the previous report, the alloy has an amorphous phase surrounding bcc-Fe crystal grains of about 25 nm as shown in Fig. 5(a) [45]. In Fig. 5(b), the Fe grains are visualized using an iso-concentrated surface with Fe=95 at%. Since the electric field on the tip surface is 𝐹𝐹 = 𝑉𝑉𝑘𝑘𝑘𝑘, where V is the applied DC voltage, k is a constant called the field factor and r is the tip radius, shapes A and B have the same field of view (FOV) immediately after the measurement starts, but the FOV of shape A hardly changes during measurement, while the FOV of shape B becomes larger. Shape C, on the other hand, has a radius of curvature twice that of A and B, so the FOV at the start of measurement is four times larger. The obtained 3D elemental maps reflect the shape of each tip. The difference in the mass spectrum shown in Fig. 5(c) is noteworthy. Comparing the mass resolution m/∆m defined as the full width at half-maximum (FWHM), shape A is 185, B is 619, and C has 890. Shape A in particular shows a serious degradation in mass resolution; therefore, the 57Fe++ and 58Fe++ peaks are buried in the mass tail and barely discernible. This result is consistent with previous reports on the effect of tip shape on a mass resolution [9, 10]. That is, if the shank angle is small, the dissipation of the heat at the tip apex is reduced. Then, it leads to an increase in the unsynchronized evaporations with the laser pulses, resulting in an increase of the mass tail. 8   Figure 5. (a) Bright-field TEM image. (b) 2-nm-thick sliced 3D elemental maps reconstructed from the initial 10 million ions, and (c) mass spectra for Fe-B-P-Cu alloy. Iso-concentration surfaces at Fe of 95 at% are drawn to visualize Fe grains.  Figure 6 shows the APT mass spectra of (a) the stainless steel and (b) the Corson alloy. The m/∆m value at FWHM of the stainless steel, which is a Fe-based alloy, is 191 for shape A, 534 for B, and 855 for C. The m/∆m of Fig. 6(a) and Fig. 5(c) are in good agreement because both alloys are Fe-based materials. It is particularly noteworthy that the atom probe data of the stainless steel clearly shows differences in the detection sensitivity of trace elements, i.e., 55Mn++ and 59Co++, due to differences in the magnitude of the mass tail. Copper alloys are a typical example known for frequent tip fractures during APT measurements in the voltage mode. We analyzed several tens of copper alloys in the voltage mode, but it was not possible to obtain APT data with a large volume due to frequent tip fractures. Thus, it can be adequately analyzed with a larger volume size in the laser mode. The mass resolution m/∆m at FWHM of the Corson alloy shown in Fig. 6(b) was 476, 824, and 793 for shapes A, B, and C, respectively. The m/∆m values for Fe-based nanocrystalline soft magnetic materials and stainless steels were in the order of C > B > A, whereas for Cu-based Corson alloy shows in the order of B~C > A (the difference between shape B and C is very slight). This difference may be due to the thermal conductivity of each alloy as discussed below. 9    Figure 6. APT mass spectra for (a) stainless steel and (b) a Cu-Ni-Si Corson alloy.   The laser-assisted field evaporation is thought to be primarily triggered by the temperature rise due to laser irradiation, and if the temperature of the tip apex takes a longer time to cool down, the mass tail will appear and degrade mass resolution as a result [2, 8-10, 12, 13]. The quality of APT data depends not only on the tip shape but also on a complex combination of various factors such as the laser wavelength, beam spot size, pulse width, repetition rate, the materials absorption efficiency of the laser light, and so on [6-10, 12, 13], however, a simplified one-dimensional model is used here to discuss the effect of tip shape. According to previous studies [2, 46, 47], the APT tip can be considered as a stack of cylinders with different cross-sectional areas as schematically shown in Fig. 7(a). Here, models with radii of tip curvature and shank angles corresponding to shapes A, B, and C were made for discussion. The laser spot size of LEAP5000XS is about 2.5 µm [48], thus, the Gaussian laser intensity profile along the tip can be drawn as Fig. 7(b). The UV laser penetration depth is reported as 10 to 15 nm for Fe, Cu, and Si [49], thus, the absorbed energy is approximately proportional to the laser-illuminated area size (m2). The laser-illuminated area along the tip direction can be calculated by considering the APT tip as a stack of cylinders. The Δ z is set as 100 nm in this calculation, and z0 indicates the tip apex. Therefore, 10  the absorption distribution of the laser along the tip was calculated as Fig. 7(c) by multiplication of the laser light intensity with the corresponding cylinder depth. By taking the cylinder volume size into account, the absorbed laser energy per unit volume was calculated in Fig. 7(d). The absorbed laser energy will be exchanged to the heat in each cylinder. In other words, the profiles shown in Fig. 7(d) indicate the initial temperature distributions by laser illumination in the tip shape A, B, and C. Due to a relatively larger volume size of tips with larger tip radius or shank angle, the order of temperature rises is C<B<A.  Figure 7. (a) Schematic illustration of a simplified model for the APT tip as a stack of cylinders with different cross-sectional areas. (b) The normalized intensity of illuminated laser with a spot size of 2.5 µm and (c) the absorption distribution of the laser along the tip. (d) The absorbed laser energy per unit volume. 11   When the laser irradiation is stopped, the tip immediately starts cooling down. The heat transfer in the APT tip should be complex, however, we treat the heat transfer problem by reducing it to a one-dimensional heat conduction equation to simplify the problem. That is, the heat generated by laser illumination is one-dimensionally transferred from the tip apex toward Si support through the cylinders with the different cross-sectional areas. The heat conduction equation is described as 𝛥𝛥𝑇𝑇 = 𝑄𝑄𝜆𝜆𝐴𝐴, where ΔT is the temperature gradient (K/m), Q is the amount of the heat (W), λ is the thermal conductivity of the material (W/mK), A is cross-sectional area (m2) [50]. The temperature gradient at depth “zn” (zn =n×Δ z; n=0, 1, 2, 3…) is described as 𝑇𝑇𝑛𝑛 − 𝑇𝑇𝑛𝑛+1 = 𝛥𝛥𝑧𝑧𝑄𝑄𝑛𝑛𝜆𝜆𝐴𝐴. Since there is no heat generation without laser irradiation, the total amount of heat (W) is constant. Although the thermal conductivity of a material varies by temperature, the calculations here were performed using values at 50 K, which is generally set as the base temperature for APT measurements. The thermal conductivity of Cu is extremely high at 800 W/mK, while stainless steel is only 15 W/mK, and silicon used as support is 200 W/mK [50-54]. The thermal conductivities of a material are temperature dependent, but in this case, the order of values doesn’t change in the range of 50 to 300 K [50-54]. Therefore, the calculations shown in Fig. 8 were performed using constant thermal conductivities at 50 K. Note that the tip and Si support are bonded by Pt deposition; however, it was ignored in the calculations here. We assumed the temperature at 5 µm depth, far away from the tip apex, is well cold at 50 K in the model. Then, the one-dimensional temperature distributions after stopping the laser irradiation for stainless steel and Cu tips were calculated as Fig. 8(a) and (b). A determination of the actual peak temperature is hard since it depends on too many factors [55, 56]; hence, Fig. 8(a) and (b) show the normalized temperature distributions along the tip after stopping laser irradiation. The thermal conductivity of Cu is so high that the heat should be dissipated faster from the tip apex; however, the calculated temperature distributions of the Cu tips (Fig. 8(b)) show gentle ones compared to the stainless steel (Fig. 8(a)). This tendency is due to the Si support having a much lower thermal conductivity (200 W/mK) than that of Cu (800 W/mK). 12   Figure 8. The normalized temperature distributions along the tip after stopping laser irradiation for (a) stainless steel tips and (b) Cu tips on Si support.    The unsteady-heat conduction is stated as: 𝜕𝜕𝑇𝑇𝜕𝜕𝑡𝑡= 𝛼𝛼 𝜕𝜕2𝑇𝑇𝜕𝜕𝑧𝑧2 (1) , where α is the thermal diffusivity of the materials (m2/s) according to previous studies on heat conduction problem [46, 50]. If “T(n, i)“ is defined as the temperature at depth “zn” and at duration “ti” (ti=i×Δt; i=0, 1, 2, 3…), then, the following equation can be obtained by using a finite-difference method; 𝑇𝑇(𝑛𝑛,   𝑖𝑖+1) = 𝛩𝛩𝑧𝑧𝑇𝑇(𝑛𝑛+1,   𝑖𝑖) + (1 − 2𝛩𝛩𝑧𝑧)𝑇𝑇(𝑛𝑛,   𝑖𝑖) + 𝛩𝛩𝑧𝑧𝑇𝑇(𝑛𝑛−1,   𝑖𝑖)  (2) , where 𝛩𝛩𝑧𝑧 is 𝛼𝛼 𝛥𝛥𝑡𝑡(𝛥𝛥𝑧𝑧)2 [57, 58]. The Eq. (2) is called Forward Time Centered Space (FTCS) approximation and detailed method can be found at [57, 58]. As the boundary condition, Eq. (2) can be applied if 0＜zn＜5 µm. For the zn=0, Eq. (2) is described as: 𝑇𝑇(0,   𝑖𝑖+1) = 2𝛩𝛩𝑧𝑧𝑇𝑇(1,   𝑖𝑖) + (1 − 2𝛩𝛩𝑧𝑧)𝑇𝑇(0,   𝑖𝑖)  (3) The temperature is always kept at 50 K for zn=5 µm (n=50). The thermal diffusivities of stainless steel, Cu, and Si are about 1~2×10-3, 1~2×10-5, and 1~2×10-4 (m2/s) at 50 K, respectively [54]. The thermal diffusivities are also temperature dependent, the values keep in 13  order of Cu＞Si＞stainless steel in a temperature range of 50 to 300 K. The temperature changes of the tip apex as the function of time were calculated in Fig. 9(a) and (b) for initial 20 ns by using the Eq. (2) and (3). As mentioned earlier, the cooling rate of the tip apex is considered to determine the magnitude of the mass tail [2, 8-10, 12, 13, 46, 47, 55, 56]. In the case of stainless steel, the temperatures are in the order of C<B<A, whereas the temperatures in the case of Cu are in the order of B<C<A (B is very slightly lower than C). However, the difference in this model calculation is much smaller than the experimental APT results. Although several unconsidered parameters should influence the cooling rate complicatedly, the calculation was carried out using a simplified one-dimensional model in this study; hence, the temperature changes in Fig. 9 indicate the qualitative tendency. The model for close-to-reality calculation is required, however, it would be another challenge. Here, the tendency of calculated cooling rates of the tip apex is in good agreement with the APT mass tails shown in Figs. 5(c) and 6. Therefore, the calculations indicate that the thermal conductivity of the material and the tip shape affect the cooling rate of the tip apex after laser irradiation, which in turn affects the APT mass resolution.  Figure 9. Calculated temperature changes of the tip apex as a function of the time for (a) stainless steel tips and (b) Cu tips on Si support.  As shown in the results above, the APT mass resolution in the laser mode differs even on the same alloy under the same measurement condition depending on tip shape. Hence, the 14  tip shape must be optimized according to the purpose of the APT analysis, so that the data quality can be kept the same. For example, if one wants to quantitatively compare microstructural differences in a series of the same alloy with different heat treatment conditions, it is important to maintain the same APT data quality. For this purpose, it is indispensable to have a method to fabricate tips with the same shape to improve the quantitative performance and reliability of APT data.   Conclusion In summary, we have established a method to prepare APT tips with a specified shape by using a script-controllable FIB-SEM system. Using this method, tips with three different shapes were fabricated from a nanocrystalline soft magnetic material, stainless steel, and Corson alloy, and their APT results were compared. In the laser mode, there is a clear difference in the mass resolution depending on the tip shape even with the same alloy under the same measurement condition. The mechanism behind the difference in the APT data can be explained by the thermal conductivities of the materials and the tip shape using a simplified heat conduction model. Both experimental and calculation results strongly indicate that the automated tip fabrication method has a significant role to improve the reproducibility and reliability of the APT technique.   Acknowledgments The authors thank Smart Solutions Inc. for supporting the writing of the scripting for the FIB-SEM dual beam system, Tohoku Magnet Institute Inc. for providing us with Fe-based nanocrystalline soft magnetic material, and Furukawa Electric Inc. for providing Corson alloy, and Kyoko Suzuki for technical support.  References 1. M.K. Miller, Atom Probe Tomography: Analysis at the Atomic Level, Kluwer Academic, New York, 2000. https://doi.org/10.1007/978-1-4615-4281-0 2. B. Gault, M. P. Moody, J.M. Cairney, S.P. 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