- Email: [email protected]
In situ determination of misorientation angle of grain boundary by field ion microscopy analysis
Ultramicroscopy 140 (2014) 20–25
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
In situ determination of misorientation angle of grain boundary by field ion microscopy analysis Jun Takahashi n, Kazuto Kawakami, Yukiko Kobayashi Advanced Technology Research Labs., Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu-City, Chiba 293-8511, Japan
art ic l e i nf o
a b s t r a c t
Available online 15 February 2014
We proposed an advanced analysis technique for characterizing a grain boundary using field ion microscopy (FIM) for atom probe analysis. The technique enables quick and precise estimation of the misorientation angle of the grain boundary by matching the calculated crystallographic pole positions with the actual FIM image including the grain boundary. We investigated the accuracy in estimation of the misorientation angle using target grain boundaries which had been analyzed by electron backscatter diffraction pattern (EBSD) analysis. From the comparison between EBSD and FIM analyses, we found that the technique enables the determination of the misorientation angle with a high accuracy of 70.41, which is comparable with that achieved by EBSD. & 2014 Elsevier B.V. All rights reserved.
Keywords: Field ion microscopy Grain boundary Misorientation angle Atom probe
1. Introduction Atom probe tomography (APT) is widely used for the quantitative observation of elements segregating at grain boundaries in materials, because atom probe can detect all elements from light to heavy with very high spatial resolution of atomic lattice size and sufficiently low detection limit of 10 at ppm level [1,2]. In particular, the application of steel materials requires to quantitatively observe light elements, such as hydrogen, boron, carbon, and nitrogen, that strongly influence the microstructure formation and mechanical property of steels. For example, boron and carbon segregation at the grain boundary decreases the ductilityembrittlement transition temperature (DBTT), while sulfur and phosphor increase it [3,4]. It should be noted that the amounts segregating at the grain boundary strongly depend on the character of the grain boundary in addition to the thermal history. The grain boundary character is described by five macroscopic degrees of freedom; a unit rotation vector (rotation direction), the rotation angle (misorientation angle) and the unit normal to the plane [5]. The misorientation angle of the grain boundary is the most important parameter to discuss the segregation and precipitation at the grain boundary. Therefore, the grain boundary in the needle tip must be characterized before atom probe measurements. Recently, analysis of 3D reconstruction data with the grain boundary using the five macroscopic degrees of freedom was attempted by electron backscatter diffraction (EBSD) analysis [6].
n
Corresponding author. Tel.: þ 81 439 80 2169; fax: þ81 439 80 2746. E-mail address: [email protected] (J. Takahashi).
http://dx.doi.org/10.1016/j.ultramic.2014.01.011 0304-3991 & 2014 Elsevier B.V. All rights reserved.
However, in most studies using atom probe, characterization of the observed grain boundaries has not been sufficiently performed because it needed much efforts [7]. In a few studies, it is reported that the grain boundary in the needle tip is characterized using Kikuchi pattern analysis with transmission electron microscope (TEM) before the atom probe measurement [8,9]. It is an appropriate method for grain boundary characterization, but requires much time and a high technique to estimate the misorientation angle. It is also reported as the method for characterizing the grain boundary from a field ion microscopic (FIM) image [10–13]; however, it cannot be applied easily and further cannot obtain the result with sufficient accuracy of less than 711. Recently, characterizations of grain boundary orientation using special distribution maps (SDMs) and 3D Hough transformation have been proposed in applications using local electrode atom probe (LEAP) [14,15]. However, the precision of these methods is limited primarily by the accuracy of APT reconstruction, which deteriorates by the uncertainty of the reconstruction parameters (detection efficiency, compression factor and geometric factor) based on a reconstruction protocol [1,16]. Further, these methods cannot be applied before atom probe measurement. In the grain boundary analysis, a quicker (in situ), easier, and more accurate technique before the atom probe measurement is required for long time. We propose an advanced technique for characterizing the grain boundary just before the atom probe measurement by using FIM. We have already applied this technique to the atom probe analysis of grain boundaries in ferritic steels [17]. However, the accuracy has not been quantitatively investigated. In this paper, the quantitative accuracy in the determination of the misorientation angle of the grain boundary is investigated using target grain boundaries,
J. Takahashi et al. / Ultramicroscopy 140 (2014) 20–25
which had been characterized by electron backscatter diffraction pattern (EBSD) analysis.
2. FIM analysis technique for grain boundary characterization 2.1. FIM projections Newman et al. reported that linear projection is a better approximate than geometric, stereographic, and orthographic projections to explain the positions of crystallographic poles in FIM images [18–21]. Fig. 1(a) shows the diagram of the FIM projections [19]. In the study, it is assumed that the center of the trajectory of ions O0 is fixed at one point on the straight line that connects the center of FIM screen O″ and that of the hemispherical cap of the needle tip O, where the distance between the hemispherical cap center O and trajectory center O0 is x and the radius of curvature of the hemisphere cap is r. The geometric and stereographic projections correspond to the cases of x¼0 and x¼r, respectively [18–20]. In this figure, the point P on the tip surface is projected to the point Q on the screen. Linear projection is described by the formula L¼kθ, where k is constant and L is the distance between the screen center O″ and projected point Q on the FIM screen. It should be noted that the trajectory center is not exactly fixed at one point for linear projection. Fig. 1(b) shows the relation between the distance L on the screen and the central angle θ under various positions of the trajectory center, where the projection factor is defined as x/r. To compare these projections in terms of linearity, the distance of the vertical axis is normalized by the slope at θ¼ 0, namely, ∂L=∂θjθ ¼ 0 in figure. In case the factor x/r is about 1.8, the relation is mostly approximate to the linear projection since the relation is given as a straight line in the angle range (o701). Calculated lines are deviated upward from the linear relation for projection factors smaller than 1.8, and downward for larger projection factors. Pole positions on the FIM image can be adjusted by the
21
scale factor as well as the projection factor. The scale factor controls the magnification of the FIM image, which is related to the distance between the screen and needle tip. 2.2. Pole-fitting method Fig. 2 shows the diagram of the coordinate system applied in this study. X, Y, and Z are the axes of the coordinate system fixed on the needle tip (the origin O). X0 , Y0 , and Z0 are the axes of the crystalline coordinate system (the origin O), which correspond to the [100], [010], and [001] axes in the bcc crystal. The Z-axis of the fixed axes is parallel to the direction of the needle specimen, and the X- and Y-axes are parallel to the directions of X″- and Y″-axes on the screen (the origin O ″), respectively. The misorientation angle between the two grains is estimated using the FIM image by the following three steps. The first step is to determine the direction matrix A of the first grain, which corresponds to the rotation from the fixed axes (X,Y,Z) on the needle tip to the crystal axes (X0 ,Y0 ,Z0 ) of the first grain. The picture of the actually observed FIM image and the positions of crystallographic poles calculated by the geometrical configuration shown in Fig. 1 are simultaneously displayed on a PC monitor. The pole positions on the monitor are determined by five parameters, namely three Euler angles (α,β,γ), the ion trajectory center O0 , and the screen center O″. The screen center O0 is related to the scale factor, while the position of O″ is related to the projection factor. These parameters can be estimated by matching the calculated positions of plural crystallographic poles with the actual FIM image. The parameters should be determined using at least three poles because a pole position has two information contents. The second step is to determine the direction matrix B about the other grain constructing the grain boundary in the same way as the first one. The third step is to estimate the misorientation angle of the grain boundary [6]. The direction matrices of the two grains are superimposed through rotation. The rotation matrix is given by M ¼ BA 1 ;
ð1Þ
Considering that a cubic crystal has three equivalent axes, the rotation matrix between two grains has 24 combinations. Transformation matrix of the coordinate axes is Rj. The 24 way rotation matrix Mj is obtained by Mj ¼ Rj BA 1 ;
ð2Þ
where j is the integer number from 1 to 24. The matrix elements of the rotation matrix are assumed as 0 1 a11 a12 a13 B C Mj ¼ @ a21 a22 a23 A: ð3Þ a31 a32 a33 The rotation angle and rotation axis are obtained by a11 þ a22 þ a33 1 φj ¼ cos 1 2 and
# a23 a12 a31 a13 a12 a21 lj ¼ ½lj 1 ; lj 2 ; lj 3 ¼ ; ; ; 2 sin φj 2 sin φj 2 sin φj
Fig. 1. (a) Schematic of FIM projections. P on the tip surface is projected at Q on the screen. (b) Relationship between central angle θ and normalized distance from the screen center L, calculated using various projection factors of x/r.
ð4Þ
"
ð5Þ
respectively. The misorientation angle of the grain boundary is defined as their minimum angle. Fig. 3 shows the result of fitting the calculated pole figure to the actual FIM image (8 kV, 70 K, Ne) in ferritic steel. The FIM image shows definite crystallographic poles of the bcc crystal and has the wide view angle corresponding to the full angle of about 1201. The red square marks in the figure represent the 002 pole family, the yellow circle marks represent the 011 family, the green diamond
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J. Takahashi et al. / Ultramicroscopy 140 (2014) 20–25
ones represent the 112 family, the orange triangular ones represent the 103 family, and the blue circle ones represent the 111 family. The red circle of the dotted line indicates the crystallographic directions inclined from the [001] axis by 451, which helps the fitting of the 011 pole family. Through fitting the calculated pole figure to the FIM image, the projection factor was preferably estimated to be 1.8. Pole-fitting is normally performed on the periphery of the FIM image including the grain boundary for the characterization. Therefore, the appropriate value of the projection factor must be chosen to match well with
Fig. 2. Schematic of the coordinate systems. X, Y, and Z are the axes of the coordinate system fixed on the needle tip (the origin O). X0 , Y0 , Z0 and are the axes of the crystalline coordinate system (the origin O). X″ and Y″ are the axes on the screen (the origin O″). O0 is the center of the trajectory of ions. P is the (l,m,n) pole.
the whole FIM image. It should be noted that good fitting is not obtained due to the position gap of poles in the tip with asymmetric shape, since the tip with symmetric shape is assumed in the calculation.
3. Experimental results and discussions 3.1. Target grain boundary The material used in this investigation was a low-carbon ferrite steel of the composition Fe–0.03C–0.50Mn–3.0%Al mass%. Aluminum addition was applied to obtain large grains by increasing the transformation temperature of ferrite to austenite. The hot-rolled plate was annealed at 1300 1C for 15 min in the ferrite region and quenched into water. The diameter of ferritic grains was in the submillimeter range. In this study, both EBSD and FIM analyses of the same grain boundaries are performed, and thus, the sample steel composed of large grains of low dislocation density is suitable for this experiment. First, triangular indenters were marked for the identification of the target grain boundaries. Then, the grain boundaries were characterized with EBSD analysis. Dual FIB–SEM (Quanta 3D FEG, FEI) was employed for EBSD measurement (HIKARI, EDAX). Fig. 4 shows the example of grain boundary characterization with EBSD. The optical micrograph of Fig. 4(a) shows the target grain boundary (GB-1) marked by triangular indenters, where the EBSD analyzed region across the boundary is represented as a rectangular area (12 μm 5 μm). Fig. 4(b) shows an inverse pole figure (IPF) map obtained by the EBSD analysis under the condition of 0.04 μm step. The border between the different contrast regions is the target grain boundary. Fig. 4(c) shows the misorientation angle of the line profile across the grain boundary in the IPF map. This figure indicates that the analyzed points have a deviation ranging 0.1–0.51 within each grain, which results from the ambiguity in the identification of Kikuchi band. Therefore, the misorientation angle of the grain boundary was determined as the difference between the averaged values of a sequence of 10 point data adjacent to the grain boundary in the two grains. The misorientation angle of the grain boundary (GB-1) was estimated to be 38.8170.21, where the error is given as standard deviation (1s) of each 10 point data. 3.2. Needle specimen preparation for FIM analysis
Fig. 3. Result of pole-fitting of calculated pole positions to the actual FIM image of ferritic steel. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Focused ion beam (FIB) fabrication with the lift-out method has been widely used for the sampling of site-specific region of interest for atom probe analysis [22,23]. In this experiment, a FIB with a microsampling system (HF2000A, Hitachi) was employed for needle
Fig. 4. (a) Optical micrograph of the target grain boundary (GB-1) marked by triangular indenters. (b) IPF map obtained by EBSD analysis. (c) Misorientation angle obtained by the line analysis in the IPF map.
J. Takahashi et al. / Ultramicroscopy 140 (2014) 20–25
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Fig. 5. (a) Preparation process of the needle specimen tip including the target grain boundary by FIM milling with lift-out method. (b) TEM micrograph of the needle tip. The arrows indicate the position of the grain boundary. (c) Optical micrograph of the sample steel surface after lift-out of the blocks across the grain boundaries.
specimen fabrication. Fig. 5(a) shows the fabrication process of the needle specimen including the target grain boundary whose misorientation angle had been examined with EBSD analysis (Fig. 4). A small pillar block (10 μm 10 μm 60 μm) across the grain boundary was cut out by FIB milling. The block was carried to the needle stage (post) by a micromanipulator of a tungsten wire and was fixed there by tungsten deposition. Then, a sharp tip containing the grain boundary was fabricated by FIB milling with rectangular and annular patterns [23]. The grain boundary was positioned within 200 nm from the tip apex. Fig. 5(b) shows a TEM micrograph of the needle tip, which indicates that the grain boundary was located at 150 nm from the tip apex. Fig. 5(c) shows an optical micrograph of the target grain boundaries (GB-1, 2, 3, 4) in the lightly etched surface of the sample steel. Small, dark rectangular portions are the marks where the pillar blocks across the grain boundaries were taken out by the lift-out method. Repolishing and reetching were conducted after the blocks of the grain boundaries of GB-1 and GB-2 were taken out, and thus the marks (#1, #2, #3) are blurred and enlarged as compared to the marks (#4, #5) of GB-3 and GB-4. In this study, five needle specimens were produced from the four target grain boundaries by the identical preparation process (Figs. 4 and 5). 3.3. Grain boundary characterization using FIM We employed an energy-compensated three-dimensional atom probe (3DAP, Oxford Nanoscience Ltd.) with a FIM system in this study. The distance between the tip and the FIM screen was 58 mm, and the screen diameter was about 73 mm. The FIM has the full angle of about 1201 (solid angle of π sr). FIM images were observed using neon as an imaging gas (1–2 10 5 Torr) at 60–90 K. The misorientation angle and the rotation axis of the grain boundary were estimated using our proposed pole-fitting method
(Section 2.2). With observing the FIM image, continuous field evaporation is carried out by gradually increasing DC voltage until the grain boundary appears on the image. The grain boundary is identified as a dark band with the discontinuous FIM pattern in the sample steel. Fig. 6 shows the characterization of the grain boundary (GB-1) using the FIM pole-fitting method. In figure, the grain boundary is represented by a dashed line. The blurred feature at the right-hand side is a precipitated particle at the grain boundary, which has a different evaporation field. The grain boundary appeared from the upper side of the image and reached the center during the continuous field evaporation. The grains of the tip apex side and bottom side are named as grain-A and grainB, respectively. Pole-fitting using more than two crystallographic poles was individually conducted in grains-A and -B. Euler angles and scale factor of the two grains are shown in figure. The scale factors of the two grains were set to the same value because the two grains simultaneously appeared in the FIM image. By the polefitting method, the misorientation angle and rotation axis were determined to be 38.47 0.41 and [0.075, 0.114, 0.991], respectively. The estimated value of the misorientation angle was mostly coincident with that estimated by the EBSD analysis (Fig. 4) with the difference of 0.41 in this experiment. Fig. 7 shows the comparison of pole positions calculated with different misorientation angles and the actual FIM image (grain-B in Fig. 6), where the misorientation angle was changed at the step of 0.41. The figures show that the difference of 0.41 was sufficiently recognized as the definite change in positions of some poles. Therefore, the error of the determination of the misorientation angle in the FIM analysis is estimated as 70.41. In the experiment, the best pole-fitting was obtained at α¼38.41. The influence of the pole position shifts to the misorientation angle α depends on the types of crystallographic poles. Therefore, it is important for this method to choose the appropriate poles that are sensitive to the
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J. Takahashi et al. / Ultramicroscopy 140 (2014) 20–25
Fig. 6. Characterization of the target grain boundary (GB-1) using our proposed FIM pole-fitting method.
Fig. 7. Comparison of actual FIM image (grain-B in Fig. 6) and pole figures calculated with different misorientation angles of (a) 38.41, (b) 38.81, (c) 39.21, and (d) 39.61.
Table 1 Comparison of misorientation angles estimated by EBSD and FIM analyses. No.
#1 #2 #3 #4 #5
Grain boundary
GB-1 GB-1 GB-2 GB-3 GB-4
Estimated misorientation angle EBSD
FIM
38.8 70.2 38.8 70.2 37.0 70.2 42.9 70.2 28.3 70.2
38.4 7 0.4 38.2 7 0.4 37.2 7 0.4 42.7 7 0.4 28.2 7 0.4
misorientation angle, and to use poles as much as possible in the FIM image. The FIM analysis did not need 10 min, and was rather accomplished in only a few minutes. After the analysis of the
grain boundary, atom probe measurement can be performed by selecting the analysis region of interest. Such procedure means mostly “in situ” characterization of the grain boundary in atom probe. Table 1 shows the comparison of the misorientation angles estimated by EBSD and FIM analyses in five needle specimens. In the grain boundary of GB-1, the results of two needle specimens produced from the slightly different positions of the same grain boundary were shown. In this study, the difference in the values estimated by EBSD and FIM analyses was 0.61 at the maximum. In case of the needle tip with slightly asymmetric shape, the accuracy in the determination of the misorientation angle is decreased because of the difficulty in pole-fitting. FIB milling with annular patterns easily creates the symmetric shape tips, but the electropolishing occasionally makes the asymmetric tips. The needle shape should be noticed in the pole-fitting method.
J. Takahashi et al. / Ultramicroscopy 140 (2014) 20–25
This study indicates that our proposed FIM analysis has high accuracy in the determination of the misorientation angle when the needle tip has an ideal symmetric shape. The performance in the crystallographic direction analysis is sufficiently comparable to the EBSD analysis. EBSD analysis had a deviation ranging from 0.11 to 0.51 because of the uncertainty in the identification of Kikuchi patterns. In contrast, the FIM method enables the accurate estimation even at a position adjacent to the boundary. In case that the steel has microstructures such as martensite and bainite, which contain inner strains and local misorientation, the FIM polefitting method might be better than the EBSD analysis since the former can give local information at a position adjacent to the grain boundary. Our proposed FIB pole-fitting method enabled rapid and precise characterization of the grain boundary before atom probe measurement. However, it should be noted that the accuracy of the method significantly depends on the shape of the needle tip and the quality of the FIM images. 4. Conclusion We proposed a grain boundary characterization technique based on FIM pole-fitting, and investigated the accuracy of the technique by applying actual grain boundaries in ferritic steel, whose misorientation angles had been investigated by EBSD analysis. (1) In this experiment, the technique could determine the misorientation angle with a high accuracy of 70.41 and the difference in the values estimated by EBSD and FIM analyses was 0.61 at the maximum.
25
(2) The pole-fitting method enabled quick and precise estimation of the misorientation angle of the grain boundary before atom probe measurement, which means mostly in situ characterization of grain boundaries. References [1] M.K. Miller, Atom Probe Tomography: Analysis at the Atomic Level, Kluwer Academic/Plenum Publishers, New York (2000) p51. [2] M. Thuvander, H.-O. Andren, Mater. Charact. 44 (2000) 87–100. [3] H. Kimura, Tetsu-to-Hagané 79 (1993) N754–N760. [4] E. Wachowicz, A. Kiejna, Model. Simul. Mater. Sci. Eng. 19 (2011) 025001. [5] J.W. Cahn, J. Phys.—Paris 43 (1982) 199–213. [6] S. Baik, M.J. Olszta, S.M. Bruemmer, D.N. Seidman, Scr. Mater. 66 (2012) 809–812. [7] V. Randle, B. Ralph, J. Mater. Sci. 21 (1986) 3823–3828. [8] D.N. Seidman, in: D. Wulf, S Yip (Eds.), Materials Interfaces (Chapter 2), Chapman & Hall, London, 1992. [9] N. Maruyama, G.D.W. Smith, A. Cerezo, Mater. Sci. Eng. A353 (2003) 126–132. [10] R. Morgan, B. Ralph, Acta Metall. 15 (1967) 341–349. [11] S. Ranganathan, Ph.D. thesis, Cambridge University, 1965. [12] D.A. Smith, M.J. Goringe, Philos. Mag. 25 (1972) 1505–1509. [13] P.L. Bolin, R.J. Bayuzick, B.N. Ranganathan, Philos. Mag. 32 (1975) 895–908. [14] M.P. Moody, F. Tang, G. Gault, S.P. Ringer, J.M. Cairney, Ultramicroscopy 111 (2011) 493–499. [15] L. Yao, M.P. Moody, J.M. Cairney, D. Haley, A.V. Ceguerra, C. Zhu, S.P. Ringer, Ultramicroscopy 111 (2011) 458–463. [16] B. Gault, D. Haley, F. de Geuser, M.P. Moody, E.A. Marquis, D.J. Larson, B.P. Geiser, Ultramicroscopy 111 (2011) 448–457. [17] J. Takahashi, K. Kawakami, K. Ushioda, S. Takaki, N Nakada, T. Tsuchiyama, Scr. Mater. 66 (2012) 207–210. [18] D.G. Brandon, J. Sci. Instrum. 41 (1964) 373–375. [19] R.W. Newman, R.C. Sanwald, J.J. Hren, J. Sci. Instrum. 44 (1967) 828–830. [20] T.I. Wilkes, G.D.W. Smith, D.A. Smith, Metallography 7 (1974) 403–430. [21] A. Cerezo, P.J. Warren, G.D.W. Smith, Ultramicroscopy 79 (1999) 251–257. [22] M.K. Miller, K.F. Russell, G.B. Thompson, Ultramicroscopy 102 (2005) 287–298. [23] J. Takahashi, K. Kawakami, Y. Yamaguchi, M. Sugiyama, Ultramicroscopy 107 (2007) 744–749.
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
In situ determination of misorientation angle of grain boundary by field ion microscopy analysis Jun Takahashi n, Kazuto Kawakami, Yukiko Kobayashi Advanced Technology Research Labs., Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu-City, Chiba 293-8511, Japan
art ic l e i nf o
a b s t r a c t
Available online 15 February 2014
We proposed an advanced analysis technique for characterizing a grain boundary using field ion microscopy (FIM) for atom probe analysis. The technique enables quick and precise estimation of the misorientation angle of the grain boundary by matching the calculated crystallographic pole positions with the actual FIM image including the grain boundary. We investigated the accuracy in estimation of the misorientation angle using target grain boundaries which had been analyzed by electron backscatter diffraction pattern (EBSD) analysis. From the comparison between EBSD and FIM analyses, we found that the technique enables the determination of the misorientation angle with a high accuracy of 70.41, which is comparable with that achieved by EBSD. & 2014 Elsevier B.V. All rights reserved.
Keywords: Field ion microscopy Grain boundary Misorientation angle Atom probe
1. Introduction Atom probe tomography (APT) is widely used for the quantitative observation of elements segregating at grain boundaries in materials, because atom probe can detect all elements from light to heavy with very high spatial resolution of atomic lattice size and sufficiently low detection limit of 10 at ppm level [1,2]. In particular, the application of steel materials requires to quantitatively observe light elements, such as hydrogen, boron, carbon, and nitrogen, that strongly influence the microstructure formation and mechanical property of steels. For example, boron and carbon segregation at the grain boundary decreases the ductilityembrittlement transition temperature (DBTT), while sulfur and phosphor increase it [3,4]. It should be noted that the amounts segregating at the grain boundary strongly depend on the character of the grain boundary in addition to the thermal history. The grain boundary character is described by five macroscopic degrees of freedom; a unit rotation vector (rotation direction), the rotation angle (misorientation angle) and the unit normal to the plane [5]. The misorientation angle of the grain boundary is the most important parameter to discuss the segregation and precipitation at the grain boundary. Therefore, the grain boundary in the needle tip must be characterized before atom probe measurements. Recently, analysis of 3D reconstruction data with the grain boundary using the five macroscopic degrees of freedom was attempted by electron backscatter diffraction (EBSD) analysis [6].
n
Corresponding author. Tel.: þ 81 439 80 2169; fax: þ81 439 80 2746. E-mail address: [email protected] (J. Takahashi).
http://dx.doi.org/10.1016/j.ultramic.2014.01.011 0304-3991 & 2014 Elsevier B.V. All rights reserved.
However, in most studies using atom probe, characterization of the observed grain boundaries has not been sufficiently performed because it needed much efforts [7]. In a few studies, it is reported that the grain boundary in the needle tip is characterized using Kikuchi pattern analysis with transmission electron microscope (TEM) before the atom probe measurement [8,9]. It is an appropriate method for grain boundary characterization, but requires much time and a high technique to estimate the misorientation angle. It is also reported as the method for characterizing the grain boundary from a field ion microscopic (FIM) image [10–13]; however, it cannot be applied easily and further cannot obtain the result with sufficient accuracy of less than 711. Recently, characterizations of grain boundary orientation using special distribution maps (SDMs) and 3D Hough transformation have been proposed in applications using local electrode atom probe (LEAP) [14,15]. However, the precision of these methods is limited primarily by the accuracy of APT reconstruction, which deteriorates by the uncertainty of the reconstruction parameters (detection efficiency, compression factor and geometric factor) based on a reconstruction protocol [1,16]. Further, these methods cannot be applied before atom probe measurement. In the grain boundary analysis, a quicker (in situ), easier, and more accurate technique before the atom probe measurement is required for long time. We propose an advanced technique for characterizing the grain boundary just before the atom probe measurement by using FIM. We have already applied this technique to the atom probe analysis of grain boundaries in ferritic steels [17]. However, the accuracy has not been quantitatively investigated. In this paper, the quantitative accuracy in the determination of the misorientation angle of the grain boundary is investigated using target grain boundaries,
J. Takahashi et al. / Ultramicroscopy 140 (2014) 20–25
which had been characterized by electron backscatter diffraction pattern (EBSD) analysis.
2. FIM analysis technique for grain boundary characterization 2.1. FIM projections Newman et al. reported that linear projection is a better approximate than geometric, stereographic, and orthographic projections to explain the positions of crystallographic poles in FIM images [18–21]. Fig. 1(a) shows the diagram of the FIM projections [19]. In the study, it is assumed that the center of the trajectory of ions O0 is fixed at one point on the straight line that connects the center of FIM screen O″ and that of the hemispherical cap of the needle tip O, where the distance between the hemispherical cap center O and trajectory center O0 is x and the radius of curvature of the hemisphere cap is r. The geometric and stereographic projections correspond to the cases of x¼0 and x¼r, respectively [18–20]. In this figure, the point P on the tip surface is projected to the point Q on the screen. Linear projection is described by the formula L¼kθ, where k is constant and L is the distance between the screen center O″ and projected point Q on the FIM screen. It should be noted that the trajectory center is not exactly fixed at one point for linear projection. Fig. 1(b) shows the relation between the distance L on the screen and the central angle θ under various positions of the trajectory center, where the projection factor is defined as x/r. To compare these projections in terms of linearity, the distance of the vertical axis is normalized by the slope at θ¼ 0, namely, ∂L=∂θjθ ¼ 0 in figure. In case the factor x/r is about 1.8, the relation is mostly approximate to the linear projection since the relation is given as a straight line in the angle range (o701). Calculated lines are deviated upward from the linear relation for projection factors smaller than 1.8, and downward for larger projection factors. Pole positions on the FIM image can be adjusted by the
21
scale factor as well as the projection factor. The scale factor controls the magnification of the FIM image, which is related to the distance between the screen and needle tip. 2.2. Pole-fitting method Fig. 2 shows the diagram of the coordinate system applied in this study. X, Y, and Z are the axes of the coordinate system fixed on the needle tip (the origin O). X0 , Y0 , and Z0 are the axes of the crystalline coordinate system (the origin O), which correspond to the [100], [010], and [001] axes in the bcc crystal. The Z-axis of the fixed axes is parallel to the direction of the needle specimen, and the X- and Y-axes are parallel to the directions of X″- and Y″-axes on the screen (the origin O ″), respectively. The misorientation angle between the two grains is estimated using the FIM image by the following three steps. The first step is to determine the direction matrix A of the first grain, which corresponds to the rotation from the fixed axes (X,Y,Z) on the needle tip to the crystal axes (X0 ,Y0 ,Z0 ) of the first grain. The picture of the actually observed FIM image and the positions of crystallographic poles calculated by the geometrical configuration shown in Fig. 1 are simultaneously displayed on a PC monitor. The pole positions on the monitor are determined by five parameters, namely three Euler angles (α,β,γ), the ion trajectory center O0 , and the screen center O″. The screen center O0 is related to the scale factor, while the position of O″ is related to the projection factor. These parameters can be estimated by matching the calculated positions of plural crystallographic poles with the actual FIM image. The parameters should be determined using at least three poles because a pole position has two information contents. The second step is to determine the direction matrix B about the other grain constructing the grain boundary in the same way as the first one. The third step is to estimate the misorientation angle of the grain boundary [6]. The direction matrices of the two grains are superimposed through rotation. The rotation matrix is given by M ¼ BA 1 ;
ð1Þ
Considering that a cubic crystal has three equivalent axes, the rotation matrix between two grains has 24 combinations. Transformation matrix of the coordinate axes is Rj. The 24 way rotation matrix Mj is obtained by Mj ¼ Rj BA 1 ;
ð2Þ
where j is the integer number from 1 to 24. The matrix elements of the rotation matrix are assumed as 0 1 a11 a12 a13 B C Mj ¼ @ a21 a22 a23 A: ð3Þ a31 a32 a33 The rotation angle and rotation axis are obtained by a11 þ a22 þ a33 1 φj ¼ cos 1 2 and
# a23 a12 a31 a13 a12 a21 lj ¼ ½lj 1 ; lj 2 ; lj 3 ¼ ; ; ; 2 sin φj 2 sin φj 2 sin φj
Fig. 1. (a) Schematic of FIM projections. P on the tip surface is projected at Q on the screen. (b) Relationship between central angle θ and normalized distance from the screen center L, calculated using various projection factors of x/r.
ð4Þ
"
ð5Þ
respectively. The misorientation angle of the grain boundary is defined as their minimum angle. Fig. 3 shows the result of fitting the calculated pole figure to the actual FIM image (8 kV, 70 K, Ne) in ferritic steel. The FIM image shows definite crystallographic poles of the bcc crystal and has the wide view angle corresponding to the full angle of about 1201. The red square marks in the figure represent the 002 pole family, the yellow circle marks represent the 011 family, the green diamond
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ones represent the 112 family, the orange triangular ones represent the 103 family, and the blue circle ones represent the 111 family. The red circle of the dotted line indicates the crystallographic directions inclined from the [001] axis by 451, which helps the fitting of the 011 pole family. Through fitting the calculated pole figure to the FIM image, the projection factor was preferably estimated to be 1.8. Pole-fitting is normally performed on the periphery of the FIM image including the grain boundary for the characterization. Therefore, the appropriate value of the projection factor must be chosen to match well with
Fig. 2. Schematic of the coordinate systems. X, Y, and Z are the axes of the coordinate system fixed on the needle tip (the origin O). X0 , Y0 , Z0 and are the axes of the crystalline coordinate system (the origin O). X″ and Y″ are the axes on the screen (the origin O″). O0 is the center of the trajectory of ions. P is the (l,m,n) pole.
the whole FIM image. It should be noted that good fitting is not obtained due to the position gap of poles in the tip with asymmetric shape, since the tip with symmetric shape is assumed in the calculation.
3. Experimental results and discussions 3.1. Target grain boundary The material used in this investigation was a low-carbon ferrite steel of the composition Fe–0.03C–0.50Mn–3.0%Al mass%. Aluminum addition was applied to obtain large grains by increasing the transformation temperature of ferrite to austenite. The hot-rolled plate was annealed at 1300 1C for 15 min in the ferrite region and quenched into water. The diameter of ferritic grains was in the submillimeter range. In this study, both EBSD and FIM analyses of the same grain boundaries are performed, and thus, the sample steel composed of large grains of low dislocation density is suitable for this experiment. First, triangular indenters were marked for the identification of the target grain boundaries. Then, the grain boundaries were characterized with EBSD analysis. Dual FIB–SEM (Quanta 3D FEG, FEI) was employed for EBSD measurement (HIKARI, EDAX). Fig. 4 shows the example of grain boundary characterization with EBSD. The optical micrograph of Fig. 4(a) shows the target grain boundary (GB-1) marked by triangular indenters, where the EBSD analyzed region across the boundary is represented as a rectangular area (12 μm 5 μm). Fig. 4(b) shows an inverse pole figure (IPF) map obtained by the EBSD analysis under the condition of 0.04 μm step. The border between the different contrast regions is the target grain boundary. Fig. 4(c) shows the misorientation angle of the line profile across the grain boundary in the IPF map. This figure indicates that the analyzed points have a deviation ranging 0.1–0.51 within each grain, which results from the ambiguity in the identification of Kikuchi band. Therefore, the misorientation angle of the grain boundary was determined as the difference between the averaged values of a sequence of 10 point data adjacent to the grain boundary in the two grains. The misorientation angle of the grain boundary (GB-1) was estimated to be 38.8170.21, where the error is given as standard deviation (1s) of each 10 point data. 3.2. Needle specimen preparation for FIM analysis
Fig. 3. Result of pole-fitting of calculated pole positions to the actual FIM image of ferritic steel. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Focused ion beam (FIB) fabrication with the lift-out method has been widely used for the sampling of site-specific region of interest for atom probe analysis [22,23]. In this experiment, a FIB with a microsampling system (HF2000A, Hitachi) was employed for needle
Fig. 4. (a) Optical micrograph of the target grain boundary (GB-1) marked by triangular indenters. (b) IPF map obtained by EBSD analysis. (c) Misorientation angle obtained by the line analysis in the IPF map.
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Fig. 5. (a) Preparation process of the needle specimen tip including the target grain boundary by FIM milling with lift-out method. (b) TEM micrograph of the needle tip. The arrows indicate the position of the grain boundary. (c) Optical micrograph of the sample steel surface after lift-out of the blocks across the grain boundaries.
specimen fabrication. Fig. 5(a) shows the fabrication process of the needle specimen including the target grain boundary whose misorientation angle had been examined with EBSD analysis (Fig. 4). A small pillar block (10 μm 10 μm 60 μm) across the grain boundary was cut out by FIB milling. The block was carried to the needle stage (post) by a micromanipulator of a tungsten wire and was fixed there by tungsten deposition. Then, a sharp tip containing the grain boundary was fabricated by FIB milling with rectangular and annular patterns [23]. The grain boundary was positioned within 200 nm from the tip apex. Fig. 5(b) shows a TEM micrograph of the needle tip, which indicates that the grain boundary was located at 150 nm from the tip apex. Fig. 5(c) shows an optical micrograph of the target grain boundaries (GB-1, 2, 3, 4) in the lightly etched surface of the sample steel. Small, dark rectangular portions are the marks where the pillar blocks across the grain boundaries were taken out by the lift-out method. Repolishing and reetching were conducted after the blocks of the grain boundaries of GB-1 and GB-2 were taken out, and thus the marks (#1, #2, #3) are blurred and enlarged as compared to the marks (#4, #5) of GB-3 and GB-4. In this study, five needle specimens were produced from the four target grain boundaries by the identical preparation process (Figs. 4 and 5). 3.3. Grain boundary characterization using FIM We employed an energy-compensated three-dimensional atom probe (3DAP, Oxford Nanoscience Ltd.) with a FIM system in this study. The distance between the tip and the FIM screen was 58 mm, and the screen diameter was about 73 mm. The FIM has the full angle of about 1201 (solid angle of π sr). FIM images were observed using neon as an imaging gas (1–2 10 5 Torr) at 60–90 K. The misorientation angle and the rotation axis of the grain boundary were estimated using our proposed pole-fitting method
(Section 2.2). With observing the FIM image, continuous field evaporation is carried out by gradually increasing DC voltage until the grain boundary appears on the image. The grain boundary is identified as a dark band with the discontinuous FIM pattern in the sample steel. Fig. 6 shows the characterization of the grain boundary (GB-1) using the FIM pole-fitting method. In figure, the grain boundary is represented by a dashed line. The blurred feature at the right-hand side is a precipitated particle at the grain boundary, which has a different evaporation field. The grain boundary appeared from the upper side of the image and reached the center during the continuous field evaporation. The grains of the tip apex side and bottom side are named as grain-A and grainB, respectively. Pole-fitting using more than two crystallographic poles was individually conducted in grains-A and -B. Euler angles and scale factor of the two grains are shown in figure. The scale factors of the two grains were set to the same value because the two grains simultaneously appeared in the FIM image. By the polefitting method, the misorientation angle and rotation axis were determined to be 38.47 0.41 and [0.075, 0.114, 0.991], respectively. The estimated value of the misorientation angle was mostly coincident with that estimated by the EBSD analysis (Fig. 4) with the difference of 0.41 in this experiment. Fig. 7 shows the comparison of pole positions calculated with different misorientation angles and the actual FIM image (grain-B in Fig. 6), where the misorientation angle was changed at the step of 0.41. The figures show that the difference of 0.41 was sufficiently recognized as the definite change in positions of some poles. Therefore, the error of the determination of the misorientation angle in the FIM analysis is estimated as 70.41. In the experiment, the best pole-fitting was obtained at α¼38.41. The influence of the pole position shifts to the misorientation angle α depends on the types of crystallographic poles. Therefore, it is important for this method to choose the appropriate poles that are sensitive to the
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Fig. 6. Characterization of the target grain boundary (GB-1) using our proposed FIM pole-fitting method.
Fig. 7. Comparison of actual FIM image (grain-B in Fig. 6) and pole figures calculated with different misorientation angles of (a) 38.41, (b) 38.81, (c) 39.21, and (d) 39.61.
Table 1 Comparison of misorientation angles estimated by EBSD and FIM analyses. No.
#1 #2 #3 #4 #5
Grain boundary
GB-1 GB-1 GB-2 GB-3 GB-4
Estimated misorientation angle EBSD
FIM
38.8 70.2 38.8 70.2 37.0 70.2 42.9 70.2 28.3 70.2
38.4 7 0.4 38.2 7 0.4 37.2 7 0.4 42.7 7 0.4 28.2 7 0.4
misorientation angle, and to use poles as much as possible in the FIM image. The FIM analysis did not need 10 min, and was rather accomplished in only a few minutes. After the analysis of the
grain boundary, atom probe measurement can be performed by selecting the analysis region of interest. Such procedure means mostly “in situ” characterization of the grain boundary in atom probe. Table 1 shows the comparison of the misorientation angles estimated by EBSD and FIM analyses in five needle specimens. In the grain boundary of GB-1, the results of two needle specimens produced from the slightly different positions of the same grain boundary were shown. In this study, the difference in the values estimated by EBSD and FIM analyses was 0.61 at the maximum. In case of the needle tip with slightly asymmetric shape, the accuracy in the determination of the misorientation angle is decreased because of the difficulty in pole-fitting. FIB milling with annular patterns easily creates the symmetric shape tips, but the electropolishing occasionally makes the asymmetric tips. The needle shape should be noticed in the pole-fitting method.
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This study indicates that our proposed FIM analysis has high accuracy in the determination of the misorientation angle when the needle tip has an ideal symmetric shape. The performance in the crystallographic direction analysis is sufficiently comparable to the EBSD analysis. EBSD analysis had a deviation ranging from 0.11 to 0.51 because of the uncertainty in the identification of Kikuchi patterns. In contrast, the FIM method enables the accurate estimation even at a position adjacent to the boundary. In case that the steel has microstructures such as martensite and bainite, which contain inner strains and local misorientation, the FIM polefitting method might be better than the EBSD analysis since the former can give local information at a position adjacent to the grain boundary. Our proposed FIB pole-fitting method enabled rapid and precise characterization of the grain boundary before atom probe measurement. However, it should be noted that the accuracy of the method significantly depends on the shape of the needle tip and the quality of the FIM images. 4. Conclusion We proposed a grain boundary characterization technique based on FIM pole-fitting, and investigated the accuracy of the technique by applying actual grain boundaries in ferritic steel, whose misorientation angles had been investigated by EBSD analysis. (1) In this experiment, the technique could determine the misorientation angle with a high accuracy of 70.41 and the difference in the values estimated by EBSD and FIM analyses was 0.61 at the maximum.
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