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Near-grain-boundary characterization by atomic force microscopy
ARTICLE IN PRESS Ultramicroscopy 109 (2009) 741–747
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Near-grain-boundary characterization by atomic force microscopy A.K. Pramanick a,, A. Sinha a, G.V.S. Sastry b, R.N. Ghosh a a b
MST Division, National Metallurgical Laboratory, Jamshedpur 831007, India Centre of Advanced Study, Department of Metallurgical Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221005, India
a r t i c l e in fo
abstract
Article history: Received 5 September 2007 Received in revised form 12 January 2009 Accepted 20 January 2009
Characterization of near-grain boundary is carried out by atomic force microscopy (AFM). It has been observed to be the most suitable technique owing to its capability to investigate the surface at high resolution. Commercial purity-grade nickel processed under different conditions, viz., (i) cold-rolled and annealed and (ii) thermally etched condition without cold rolling, is considered in the present study. AFM crystallographic data match well with the standard data. Hence, it establishes two grain-boundary relations viz., plane matching and coincidence site lattice (CSL S ¼ 9) relation for the two different sample conditions. & 2009 Elsevier B.V. All rights reserved.
Keywords: Sigma relation Coincidence site lattice AFM Plane matching
1. Introduction In polycrystalline materials, the grain boundaries play a very important role in influencing the properties of a material [1]. Therefore, characterization of a grain boundary is crucial to the understanding of critical effects on the material properties. Studies on grain boundaries have reflected that a fraction of boundaries in the microstructure exhibits specific grain-boundary angles that have been well correlated with macroscopic properties [2,3] and are characterized by the coincident site lattice (CSL). Based on the angle between two grains, high-angle boundaries are variously modeled by coincidence site lattice (CSL), near coincidence (NC) and plane matching (PM) model. These models are geometric in origin and are referred to as special boundaries. Special boundaries are determined based on direct evidences or indirect evidences of grain boundary properties. Indirect methods are based on evidences like segregation, corrosion properties and diffusion of grain boundaries, presence of precipitates or from the mechanical properties such as low-temperature dislocation mobility near-grain boundaries. The direct method is to make energy measurements across grain boundaries. In the energy measurement method, both CSL and NC models predict energy cusps at a specific GB angle, while the PM model predicts energy valleys for all rotations about low-index axes [4]. Atomic force microscopy (AFM) has shown wide capability in the characterization of grain boundaries in recent studies, e.g., sliding of grain-boundary grooving [5], grain-boundary
Corresponding author.
E-mail address: [email protected] (A.K. Pramanick). 0304-3991/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2009.01.014
sliding and migration [6], identification of activated slip systems of the deformation process in a duplex stainless steel grains in polycrystalline material surfaces [7]. A study on nano-hardness while approaching a grain boundary from the interior has shown the importance of near-grain-boundary studies [8]. Due to the limitation of an AFM tip reaching inside the grooves of high-angle boundaries, it can only be used to study the grain interior and near-boundary regions. In this paper, we report the crystallographic orientational relationship obtained from the near-grain-boundary region of electrolytic-grade nickel through high-resolution AFM images operated in the contact mode at ambient conditions.
2. Experimental procedures An electrolytic-grade Ni plate (of purity 99.5%) is used for this experiment. The initial thickness of the plate is 4 mm, which is then cold-rolled to about 30%. Four pieces of size 20 mm 10 mm are cut and annealed at 900 1C for 30 h, followed by mechanical thinning to 2 mm. In the second stage of sample preparation, they are electropolished using methanol and nitric acid solution (3:1) at 10 1C and 10 V and electro-etched further using the same solution at 4 V. In the final stage, thermal etching is carried out in a graphite furnace in inert argon atmosphere at 1000 1C for 1 h. During thermal etching, nickel pieces were placed in a recrystallized alumina crucible and covered with another alumina crucible to reduce possible contamination from gaseous atmosphere at high temperature. Two sets of samples were prepared. The first set is the electroetched cold-rolled sample (sample-I). The second set of samples is
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not subjected to cold rolling and is thermally etched at 1000 1C for 1 h (sample-II). AFM (SPA400, Seiko, Japan) measures the dihedral angles between the nickel grains in contact mode. The cantilever tip diameter is less than 20 nm (SN-AF01). Since triple point junctions show good force balance in two dimensions, the initial scan is done for the highest permissible area of 100 mm2 (model SPA400PZT FS100N) with 0.5 Hz scanning frequency to locate a triple junction. The images are recorded in ambient condition. In the subsequent scan, the same area is rescanned with a triple junction centered to the area. The images in the nano-meter scale are
recorded with a 20 mm scanner (model SPA400-PZT FS20N). Experimental precautions considered for AFM imaging are further discussed in the following sections.
3. Results and discussion A representative AFM micrograph for each of sample-I and sample-II is shown in Figs. 1 and 4. The grain size for sample-I ranges in between 40 and 50 mm for few grains and the others range for more than 150 mm. Similarly in sample-II grain sizes
Fig. 1. AFM micrograph from sample-I, image is scanned for the 100 mm 100 mm area. The arrows show the positions where atomic resolution images are recorded for Fig. 3. (a) X-ray diffraction pattern of sample-I.
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vary in between 100 and 150 mm and others are approximately 200 mm. The X-ray diffraction pattern (Fig. 1a) of sample-I shows the most of the grains are aligned for 111 texture after annealing at 900 1C for 30 h. A comparative X-ray diffraction study of sample-II shows more number of peaks [(111), (2 0 0), (3 11), (2 2 2), (4 0 0), (3 3 1) and (4 2 0)] (see Fig. 1a). Fig. 1 is recorded around a triple point of grain boundary. It shows clear grooves of the boundary besides pits at a few places along the grain boundary. The sample plane, as seen by AFM, depicts steps along the z-direction. The steps in surface are produced at the time of electro polishing of the sample and pitting occurs along the grain boundary during the electro-etching process, since the rate of attack of the solution is higher for high-energy regions. The dihedral angle is measured by first putting a straight line perpendicular to the grain-boundary groove. The dihedral angle is then obtained by putting pointers in slopes of adjacent grain boundaries of the scanned micrograph when viewed cross-sectionally. This facility is provided with AFM software. The dihedral angles are measured from different points along the grain boundaries and different grain boundaries at a triple point junction. The frequency of distribution of dihedral angles is plotted in Fig. 2. From the plot, it is evident that most of the grain boundaries are of the high-angle type. To establish grain-boundary correlations, atomic resolution images are recorded from 3nm 3 nm regions on both sides of grain boundaries marked as GB-1, GB-2 and GB-3. The appropriate positions from both sides of grain boundaries are marked as left (L) and right (R) in Fig. 4. The left hand and right hand sides are decided
Frequency
40
30
743
by looking down the boundary from the triple point. Due to positional problem of the AFM tip on the sample surface, no proper characterization was feasible for GB-2. The crystallographic planes corresponding to both sides of GB-1 and GB-3 are obtained as ð1 1¯ 0Þ and (0 0 1). Details of calculation for the planes are shown in Table 1. The first column mentions the point from where atomic resolution images are taken. Column 2 lists experimentally measured distances in two different directions ‘p’ and ‘q’. Column 3 tabulates the standard ‘d-values’ nearest to the experimentally measured values and the corresponding crystallographic directions are assigned in Column 4. By knowing two crystallographic directions, the corresponding planes are calculated for that image plane. The last column tabulates the corresponding planes. Due to space limitations associated with a grooved high-angle boundary and the width of the cantilever, it is not possible to scan the groove. Therefore, atomic resolution images are recorded from a 3 nm 3 nm area and are from the marked portions adjacent to the sides of the grain boundary (Fig. 3). The marked directions show interplanar spacings as 1.211 and 0.987 A˚ for both the images scanned. These are, respectively, 2.8% and 2.2% less than the nearest interplanar spacings of [2 2 0] and [2 2 2]. On defining both directions, the corresponding plane works out to be ð1 1¯ 0Þ, which is one of the planes from the {2 2 0} family. On superpositioning both the lattice images, one can observe the grain orientation from both sides of the grain boundary to be the same (see Fig. 3a) [8]. This type of matching in grain-boundary engineering is referred to as the plane matching model. In the PM model, low-index planes of low energy are continuous across a high-angle grain boundary. This effect can occur in any crystal system where atoms are sufficiently closely packed; in FCC crystals these planes are {2 0 0}, {2 2 0} and {111}. Thus, our results for nickel are consistent with the findings of Pumphrey [4] and it demonstrates the feasibility of such grain-boundary characterization by AFM.
3.1. Errors associated with the measurements
20
10
0 0
10
20 30 40 Misorientation angle
50
60
Fig. 2. Plot of frequency distribution of grain-boundary angle in sample-II. The total numbers of grain-boundary angles measured are 200.
Before discussing CSL determination at grain boundary-1 (Figs. 4 and 5), errors associated with AFM imaging will be considered in the following section. Table 2 shows the percentage of error in measuring the distances along [2 0 0] and [111] directions with reference to Fig. 5. Maximum errors of 9.6% and 4.23% in [111] are encountered for grain boundaries 3 and 1, respectively. These deviations are expected as the sample is thermally etched. In such conditions, nucleation and growth of grains readily occur. For minimization of energy, grain boundaries do migrate. Since the above processes occurred for stability of the system, lattice distortions do take place by the compression or the elongation of the lattice on either
Table 1 Experimentally measured distances (A˚)
Standard ‘d’ values (A˚)
Direction
p
q
p
q
p
q
Grain boundary-1 Left Right
1.76 2.12
2.08 1.763
1.762 2.034
2.034 1.762
/2 0 0S /111S
/111S /2 0 0S
ð1 1¯ 0Þ ð1 1¯ 0Þ
Grain boundary-3 Left Right
1.82 1.86
1.36 2.01
1.762 1.762
1.24 2.034
/2 0 0S /2 0 0S
/2 2 0S /111S
(0 0 1) (0 0 1)
Features in the image
Plane
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Right side GB
Left side GB
[222]
[222]
[220]
[220]
Fig. 3. Lattice resolution images are recorded from left and right side of the grain boundary as marked in Fig. 1. (a) Lattice resolution images as in Fig. 3 are matched with plane matching.
Fig. 4. Triple point junction in sample-II. Atomic resolution images are recorded on both sides of grain boundary and from the position as marked in the figure.
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Left GB 1
(011)
745
Right GB 1
(011)
p
[111]
p
[200]
[200] [111] q
q
Fig. 5. Lattice resolution images at grain boundary-1, reference to Fig. 3.
Table 2 Grain boundary plane
% of error in d-values on left side
ð1 1¯ 0Þ (0 0 1)
/2 0 0S0.11 /2 0 0S+3.40
% of error in d-values on right side /111S+2.26 /111S+9.67
side of the boundary. Since, in the present case, the grainboundary plane is obtained by AFM, imaging takes place by force interactions between the tip and the sample and images are rendered with the aid of electronics. At this length scale, thermal vibration is also an important factor. Therefore, a compound effect of image shift takes place during AFM imaging. It is also important to recall that drift in atomic planes will also be seen in the AFM imaging due to movement of atoms on the sample surface. These factors will appear as drift in atomic positions from top left to bottom right side of the image. Keeping all these points in view, atomic resolution AFM images were investigated for an image shift. By drawing diagonal lines in the 3 nm 3 nm (Fig. 5) region, a shift in atomic position is estimated to be approximately 0.5 A˚ (in q direction of Fig. 5), which amounts to less than 2% error. This degree of error may be assumed to arise from thermal vibration at room temperature and is a limitation of the experiment. In a similar fashion, a systematic error in the horizontal direction of the image due to small electronic phase lag between scanning of the sample and creation of the image on the display screen also occurs. However, any such effect is neglected here. Thus in a complex fashion, scanning conditions for atomic resolution will vary within a certain degree. Other possible artifacts in contact mode are discussed and justified in a separate communication [9]. 3.2. CSL determination Since the sample is a single-phase metal and is thermally etched at 1000 1C for 1 h, in the present case of sample-II, one can assume that near-grain-boundary planes are continuous up to grain boundary, which is at a distance of 1 mm. In addition, it is difficult to find grain-boundary axis for a high-angle boundary by AFM tip. In such condition, the question may arise as to how it is possible to determine the CSL relationship from the results of two-dimensional maps. This question has two aspects to it, viz., How do grain boundaries orient themselves at the sample surface? and How to validate the data collected by the AFM?
/2 0 0S +0.06 /2 0 0S+5.6
/111S+4.23 /111S1.18
The strategy adopted in the present study is explained in the following. During annealing, the growth of grain boundaries near the free metallic surface tends to lie perpendicular by reducing net curvature of the boundaries next to the surface. Hence, curvatures of the grains become cylindrical on the sample surface and thus terminate normal to the surface [10]. Therefore, crystallographic information just beside the grain boundary and its neighborhood will be equivalent. To verify the effect on grain orientation, a series of atomic resolution images are recorded away from the grain boundary, which will be discussed in the next section. In AFM imaging, one plane of sample surface is exposed for the study. The atomic resolution image of this experimental plane is in real space. According to the atomic packing for a particular material, a limited set of planes crossing the experimental plane is in the image. Therefore, measurements of interplanar spacings from these images can be compared with those obtained from phase contrast images in high-resolution electron microscopy or those from the reciprocal space information from X-ray diffraction studies. Many such comparisons of the AFM data with particularly X-ray diffraction data are made in different studies [11–13]. Moreover, AFM data in the present study match well with crystallographic planes for nickel. Therefore, with the above analogies CSL can be determined using AFM. Experimental procedures for the study are discussed in the following section. Atomic resolution images are recorded from a selected scan area of 3 nm 3 nm (Fig. 5) from both sides of grain boundary-1. The selected areas are marked by ‘L’ and ‘R’ as shown in Fig. 4. The details of directions and corresponding planes for both the boundaries are shown in Fig. 5. Therefore, the grain-boundary axis is determined to be ½1 1¯ 0. As the AFM study does not distinguish positive or negative direction of any crystallographic direction, the ½1 1¯ 0 direction can be considered as [11 0]. Fig. 6 shows sigma matching for grain boundary-1 (GB-1). On rotating the lattice by an angle of 401 over the left side of lattices for GB-1, a matching for sigma relation is obtained. Matching of the points is in agreement with the experimental condition. A deviation in measurement of d-values is summarized in Table 2. The rotation angle is matched with the known rotational angle and axis [11 0]
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Fig. 6. CSL is determined to be S ¼ 9 for grain boundary-1.
pair in the FCC material. Based on the above angle/axis pair, the CSL value is compared with the work of Pumphrey [4] and the CSL is determined as S ¼ 9 for GB-1 [4]. Since the above atomic resolution images are recorded near the grain boundary, it is in our general interest to know how the orientations of the atomic planes vary as a function of distance from the grain boundary. For this reason, a series of atomic resolution images are recorded from boundary positions (GB-1).
(110) p [111]
[100] 3.3. Plane orientation away from GB The positions from the grain boundary are marked into three regions by alphabets ‘a’, ‘b’, and ‘c’ according to the features (Fig. 4). Among the different marked regions and between regions, atomic resolution images are recorded. A representative atomic resolution AFM image from ‘a–b region’ is shown in (Fig. 7). All measurements on AFM images are tabulated in Table 3. The last column of Table 3 depicts same plane orientation ð1 1¯ 0Þ when experiments were conducted up to 4–5 mm distances away from a GB-1. In Fig. 7, the angle measurement between [1 0 0] and [111] is seen to be 561, which is very close to its theoretical value of 54.71. However, angle measurements between two directions for left and right sides of GB-1 (Fig. 5) show a maximum difference of approximately 61. This discrepancy could be arising due to local rearrangement of the planes beside the grain boundary. 3.4. Effect of cold rolling and grain boundary crystallography The effect of heat treatment at 1000 1C for 1 h for cold-rolled nickel has changed the grain structure of the sample, where the average grain size is found to vary between 100 and 150 mm. The primary crystallization of cold worked FCC metals such as nickel results in a marked change. In the present study, texture has been developed in the ð1 1¯ 0Þ direction with 391 angle. Grainboundary texture is a subject of study for a number of researchers. In the view of the present work, few important aspects can
q
Fig. 7. Lattice resolution images in between ‘a–b’ region away from grain boundary-1.
be noted from the results of Baker and Li [14]. In this paper, the authors have summarized results obtained by different researchers. Lejcˇek and Sˇı´ma [15] have observed 191//1 0 0S orientation relation between primary recrystallization texture and secondary grain grown during unidirectional annealing for heavily deformed nickel. The same authors have noted that a change in rotation axis may arise if the activation energy for grain-boundary migration is higher for twist boundary than tilt boundary. Makita et al. [16] have observed that orientation relations in statically annealed nickel are 191//1 0 0S, 221//111S and 381//111S for large grains. The /111S or /1 0 0S preferential rotation direction can be controlled by rolling procedure. Makita et al. [16] and other workers [14] have emphasized the role of CSL that CSL boundaries
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Table 3 Features in a region
Experimentally measured distances (A˚)
Correlation with standard ‘d’ values (A˚)
Direction
‘a’ Rods Between rods Between ‘a’ and ‘b’ regions
1.248 2.496 1.08
1.010 3.48 1.239
1.246 2.034 1.017
1.0172 3.529 1.247
/2 2 0S /111S /2 2 2S
/2 2 2S /1 0 0S /2 2 0S
ð1 1¯ 0Þ ð1 1¯ 0Þ ð1¯ 1 0Þ
‘b’ Round regions Between ‘b’ and ‘c’ regions
1.436 1.43
1.003 1.014
1.438 1.438
1.017 1.017
/11 2S /11 2S
/2 2 2S /2 2 2S
ð1 1¯ 0Þ ð1 1¯ 0Þ
‘c’ Wavy surface Away from ‘c’
0.72 1.431
2.037 0.994
0.722 1.438
2.034 1.017
/4 4 2S /11 2S
/111S /2 2 2S
ð1 1¯ 0Þ ð1 1¯ 0Þ
around large grains have higher mobility than other boundaries. They have also noted {11 0} /11 2S orientation relationship and explained it as related to twin orientation. These orientational relationships are governed by a complex process of primary and even secondary crystallization according to the congenial conditions prevailing. In primary recrystallization, the cubic texture in FCC materials gets sharpened and strengthened by increasing the annealing temperature and time [14]. Lejcˇek and Sˇı´ma [15] have noted secondary crystallization being activated at temperatures greater than the critical temperature of 777 1C for 90% cold-rolled nickel. Therefore, in the present case, 30% cold-rolled nickel will have higher secondary recrystallization temperature than 777 1C. However, secondary crystallization is mainly responsible for growth of larger grain sizes and develops another set of texture. Therefore, annealing at 1000 1C for 1 h and the grain sizes observed in the present case indicate that secondary recrystallization has taken place. Baker and Li [14] have observed that annealing at 1000 1C for 90% coldrolled nickel left small cube-oriented grains along with a larger ¯ orientations and few proportion of non-cubic {1 2 4}h2 1 1i random textures. Lee and Richards [17] have recorded special boundary fraction (3pSp29) for commercial pure nickel annealed at 900 1C for 10 min. Note S ¼ 3 boundary is a twin. Therefore, occurrence of a texture of (11 0) [14,15,17] cannot be ruled out in cold-rolled and annealed sample of nickel. Retention of cubic rotational axis indicates that the occurrence is due to primary crystallization. In contrast, larger grain size reveals that secondary crystallization has occurred. But secondary recrystallization process also retains few cubic orientations [14]. Hence for the present study, it can be concluded that secondary crystallization has already set in and the AFM study around a triple point junction mapped an orientation, which is due to primary crystallization. The mapped orientation (for grain boundary-1) shows a CSL S ¼ 9 relation, and high mobility within grains around triple point junction can be marked by its surface morphology (see Fig. 4). From morphological appearance in Fig. 4, it can be said that mobility has been locked for grain boundary-1. Grain boundary-3 is a moving boundary with the (1 0 0) direction from both sides. The last grain boundary-2 is complicated where lattice imaging revealed only a complicated pattern.
annealed nickel and (ii) thermally etched condition without cold rolling. On cold rolling, the first sample has generated maximum numbers of grains along 111. In the second sample, annealing has generated recrystallization. Both the samples are characterised by AFM in contact mode. Atomic resolution images are recorded in the near-grain-boundary regions and detailed crystallographic measurements are consistent with standard data. The feasibility of obtaining accurate crystallographic information by AFM images is demonstrated. In the case of cold-rolled and annealed Ni, the plane matching model for the grain-boundary structure and a CSL boundary with S ¼ 9 in the case of thermally etched condition without any cold rolling could be established.
Acknowledgements The authors extend their sincere thanks to Prof. S.P. Mehrotra, Director, NML, for supporting the above study under an in-house research scheme. They also thank Prof. Subra Suresh (MIT, USA) and Dr. S. Nayar (NML, Jamshedpur) for their kind suggestions and interest in the present work.
References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12]
4. Conclusion Near-grain-boundary characterization is carried out for commercial purity-grade nickel in two conditions: (i) cold-rolled and
Plane
[13] [14] [15] [16] [17]
L.S. Shvindlerman, B.B. Straumal, Acta Metall. 33 (1985) 1735. G. Palumbo, E.M. Lehockey, P. Lin, J. Met. 50 (1998) 40. V. Randle, Acta Mater. 52 (2004) 4067. P.H. Pumphrey, in: G.A. Chadwick, D. Smith (Eds.), Grain Boundary Structure and Properties, Academic Press, New York (Orlando,Fl/London/San Diego,CA), 1976, p. 139 (Chapter V). E. Rabkin, L. Klinger, T. Izyumova, A. Berner, V. Semenov, Acta Mater. 49 (2001) 1429. H. Yoshida, K. Yokoyama, N. Shibata, Y. Ikuhara, T. Sakuma, Acta Mater. 52 (2004) 2349. S. Fre´chard, F. Martin, C. Cle´ment, J. Cousty, Mater. Sci. Eng. A 418 (2006) 312. Ya.M. Soifer, A. Verdyan, M. Kazakevich, E. Rabkin, Scr. Mater. 47 (2002) 799. A.K. Pramanick, A. Sinha, In communication. Robert E. Reed-Hill, Reza Abbaschian, Physical Metallurgy Principles, 3rd ed., PWS Publishing Company, Boston, 1994, pp. 256 Chapter 8.26. E. Grotenhuis, J.P. Eerden Van der, F.J. Hoogesteger, L.W. Jenneskens, Chem. Phys. Lett. 250 (1996) 549. R. Stammer, A.R. Martin, Th. Geue, H. Gobel, W. Hub, U. Pietsch, JCPDS Int. Centre Diffr. Data (1999) 101. J.E. Oh, M.D. Kim, J. Semicond. Technol. Sci. 6 (2006) 131. I. Baker, J. Li, Microsc. Res. Tech. 63 (2004) 289. P. Lejcˇek, V. Sˇı´ma, Mater. Sci. Eng. A 60 (1988) 121. H. Makita, S. Hanada, O. Izumi, Acta Met. 36 (1988) 403. S.L. Lee, N.L. Richards, Mater. Sci. Eng. A 390 (2005) 81.
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Near-grain-boundary characterization by atomic force microscopy A.K. Pramanick a,, A. Sinha a, G.V.S. Sastry b, R.N. Ghosh a a b
MST Division, National Metallurgical Laboratory, Jamshedpur 831007, India Centre of Advanced Study, Department of Metallurgical Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221005, India
a r t i c l e in fo
abstract
Article history: Received 5 September 2007 Received in revised form 12 January 2009 Accepted 20 January 2009
Characterization of near-grain boundary is carried out by atomic force microscopy (AFM). It has been observed to be the most suitable technique owing to its capability to investigate the surface at high resolution. Commercial purity-grade nickel processed under different conditions, viz., (i) cold-rolled and annealed and (ii) thermally etched condition without cold rolling, is considered in the present study. AFM crystallographic data match well with the standard data. Hence, it establishes two grain-boundary relations viz., plane matching and coincidence site lattice (CSL S ¼ 9) relation for the two different sample conditions. & 2009 Elsevier B.V. All rights reserved.
Keywords: Sigma relation Coincidence site lattice AFM Plane matching
1. Introduction In polycrystalline materials, the grain boundaries play a very important role in influencing the properties of a material [1]. Therefore, characterization of a grain boundary is crucial to the understanding of critical effects on the material properties. Studies on grain boundaries have reflected that a fraction of boundaries in the microstructure exhibits specific grain-boundary angles that have been well correlated with macroscopic properties [2,3] and are characterized by the coincident site lattice (CSL). Based on the angle between two grains, high-angle boundaries are variously modeled by coincidence site lattice (CSL), near coincidence (NC) and plane matching (PM) model. These models are geometric in origin and are referred to as special boundaries. Special boundaries are determined based on direct evidences or indirect evidences of grain boundary properties. Indirect methods are based on evidences like segregation, corrosion properties and diffusion of grain boundaries, presence of precipitates or from the mechanical properties such as low-temperature dislocation mobility near-grain boundaries. The direct method is to make energy measurements across grain boundaries. In the energy measurement method, both CSL and NC models predict energy cusps at a specific GB angle, while the PM model predicts energy valleys for all rotations about low-index axes [4]. Atomic force microscopy (AFM) has shown wide capability in the characterization of grain boundaries in recent studies, e.g., sliding of grain-boundary grooving [5], grain-boundary
Corresponding author.
E-mail address: [email protected] (A.K. Pramanick). 0304-3991/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2009.01.014
sliding and migration [6], identification of activated slip systems of the deformation process in a duplex stainless steel grains in polycrystalline material surfaces [7]. A study on nano-hardness while approaching a grain boundary from the interior has shown the importance of near-grain-boundary studies [8]. Due to the limitation of an AFM tip reaching inside the grooves of high-angle boundaries, it can only be used to study the grain interior and near-boundary regions. In this paper, we report the crystallographic orientational relationship obtained from the near-grain-boundary region of electrolytic-grade nickel through high-resolution AFM images operated in the contact mode at ambient conditions.
2. Experimental procedures An electrolytic-grade Ni plate (of purity 99.5%) is used for this experiment. The initial thickness of the plate is 4 mm, which is then cold-rolled to about 30%. Four pieces of size 20 mm 10 mm are cut and annealed at 900 1C for 30 h, followed by mechanical thinning to 2 mm. In the second stage of sample preparation, they are electropolished using methanol and nitric acid solution (3:1) at 10 1C and 10 V and electro-etched further using the same solution at 4 V. In the final stage, thermal etching is carried out in a graphite furnace in inert argon atmosphere at 1000 1C for 1 h. During thermal etching, nickel pieces were placed in a recrystallized alumina crucible and covered with another alumina crucible to reduce possible contamination from gaseous atmosphere at high temperature. Two sets of samples were prepared. The first set is the electroetched cold-rolled sample (sample-I). The second set of samples is
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not subjected to cold rolling and is thermally etched at 1000 1C for 1 h (sample-II). AFM (SPA400, Seiko, Japan) measures the dihedral angles between the nickel grains in contact mode. The cantilever tip diameter is less than 20 nm (SN-AF01). Since triple point junctions show good force balance in two dimensions, the initial scan is done for the highest permissible area of 100 mm2 (model SPA400PZT FS100N) with 0.5 Hz scanning frequency to locate a triple junction. The images are recorded in ambient condition. In the subsequent scan, the same area is rescanned with a triple junction centered to the area. The images in the nano-meter scale are
recorded with a 20 mm scanner (model SPA400-PZT FS20N). Experimental precautions considered for AFM imaging are further discussed in the following sections.
3. Results and discussion A representative AFM micrograph for each of sample-I and sample-II is shown in Figs. 1 and 4. The grain size for sample-I ranges in between 40 and 50 mm for few grains and the others range for more than 150 mm. Similarly in sample-II grain sizes
Fig. 1. AFM micrograph from sample-I, image is scanned for the 100 mm 100 mm area. The arrows show the positions where atomic resolution images are recorded for Fig. 3. (a) X-ray diffraction pattern of sample-I.
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vary in between 100 and 150 mm and others are approximately 200 mm. The X-ray diffraction pattern (Fig. 1a) of sample-I shows the most of the grains are aligned for 111 texture after annealing at 900 1C for 30 h. A comparative X-ray diffraction study of sample-II shows more number of peaks [(111), (2 0 0), (3 11), (2 2 2), (4 0 0), (3 3 1) and (4 2 0)] (see Fig. 1a). Fig. 1 is recorded around a triple point of grain boundary. It shows clear grooves of the boundary besides pits at a few places along the grain boundary. The sample plane, as seen by AFM, depicts steps along the z-direction. The steps in surface are produced at the time of electro polishing of the sample and pitting occurs along the grain boundary during the electro-etching process, since the rate of attack of the solution is higher for high-energy regions. The dihedral angle is measured by first putting a straight line perpendicular to the grain-boundary groove. The dihedral angle is then obtained by putting pointers in slopes of adjacent grain boundaries of the scanned micrograph when viewed cross-sectionally. This facility is provided with AFM software. The dihedral angles are measured from different points along the grain boundaries and different grain boundaries at a triple point junction. The frequency of distribution of dihedral angles is plotted in Fig. 2. From the plot, it is evident that most of the grain boundaries are of the high-angle type. To establish grain-boundary correlations, atomic resolution images are recorded from 3nm 3 nm regions on both sides of grain boundaries marked as GB-1, GB-2 and GB-3. The appropriate positions from both sides of grain boundaries are marked as left (L) and right (R) in Fig. 4. The left hand and right hand sides are decided
Frequency
40
30
743
by looking down the boundary from the triple point. Due to positional problem of the AFM tip on the sample surface, no proper characterization was feasible for GB-2. The crystallographic planes corresponding to both sides of GB-1 and GB-3 are obtained as ð1 1¯ 0Þ and (0 0 1). Details of calculation for the planes are shown in Table 1. The first column mentions the point from where atomic resolution images are taken. Column 2 lists experimentally measured distances in two different directions ‘p’ and ‘q’. Column 3 tabulates the standard ‘d-values’ nearest to the experimentally measured values and the corresponding crystallographic directions are assigned in Column 4. By knowing two crystallographic directions, the corresponding planes are calculated for that image plane. The last column tabulates the corresponding planes. Due to space limitations associated with a grooved high-angle boundary and the width of the cantilever, it is not possible to scan the groove. Therefore, atomic resolution images are recorded from a 3 nm 3 nm area and are from the marked portions adjacent to the sides of the grain boundary (Fig. 3). The marked directions show interplanar spacings as 1.211 and 0.987 A˚ for both the images scanned. These are, respectively, 2.8% and 2.2% less than the nearest interplanar spacings of [2 2 0] and [2 2 2]. On defining both directions, the corresponding plane works out to be ð1 1¯ 0Þ, which is one of the planes from the {2 2 0} family. On superpositioning both the lattice images, one can observe the grain orientation from both sides of the grain boundary to be the same (see Fig. 3a) [8]. This type of matching in grain-boundary engineering is referred to as the plane matching model. In the PM model, low-index planes of low energy are continuous across a high-angle grain boundary. This effect can occur in any crystal system where atoms are sufficiently closely packed; in FCC crystals these planes are {2 0 0}, {2 2 0} and {111}. Thus, our results for nickel are consistent with the findings of Pumphrey [4] and it demonstrates the feasibility of such grain-boundary characterization by AFM.
3.1. Errors associated with the measurements
20
10
0 0
10
20 30 40 Misorientation angle
50
60
Fig. 2. Plot of frequency distribution of grain-boundary angle in sample-II. The total numbers of grain-boundary angles measured are 200.
Before discussing CSL determination at grain boundary-1 (Figs. 4 and 5), errors associated with AFM imaging will be considered in the following section. Table 2 shows the percentage of error in measuring the distances along [2 0 0] and [111] directions with reference to Fig. 5. Maximum errors of 9.6% and 4.23% in [111] are encountered for grain boundaries 3 and 1, respectively. These deviations are expected as the sample is thermally etched. In such conditions, nucleation and growth of grains readily occur. For minimization of energy, grain boundaries do migrate. Since the above processes occurred for stability of the system, lattice distortions do take place by the compression or the elongation of the lattice on either
Table 1 Experimentally measured distances (A˚)
Standard ‘d’ values (A˚)
Direction
p
q
p
q
p
q
Grain boundary-1 Left Right
1.76 2.12
2.08 1.763
1.762 2.034
2.034 1.762
/2 0 0S /111S
/111S /2 0 0S
ð1 1¯ 0Þ ð1 1¯ 0Þ
Grain boundary-3 Left Right
1.82 1.86
1.36 2.01
1.762 1.762
1.24 2.034
/2 0 0S /2 0 0S
/2 2 0S /111S
(0 0 1) (0 0 1)
Features in the image
Plane
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Right side GB
Left side GB
[222]
[222]
[220]
[220]
Fig. 3. Lattice resolution images are recorded from left and right side of the grain boundary as marked in Fig. 1. (a) Lattice resolution images as in Fig. 3 are matched with plane matching.
Fig. 4. Triple point junction in sample-II. Atomic resolution images are recorded on both sides of grain boundary and from the position as marked in the figure.
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Left GB 1
(011)
745
Right GB 1
(011)
p
[111]
p
[200]
[200] [111] q
q
Fig. 5. Lattice resolution images at grain boundary-1, reference to Fig. 3.
Table 2 Grain boundary plane
% of error in d-values on left side
ð1 1¯ 0Þ (0 0 1)
/2 0 0S0.11 /2 0 0S+3.40
% of error in d-values on right side /111S+2.26 /111S+9.67
side of the boundary. Since, in the present case, the grainboundary plane is obtained by AFM, imaging takes place by force interactions between the tip and the sample and images are rendered with the aid of electronics. At this length scale, thermal vibration is also an important factor. Therefore, a compound effect of image shift takes place during AFM imaging. It is also important to recall that drift in atomic planes will also be seen in the AFM imaging due to movement of atoms on the sample surface. These factors will appear as drift in atomic positions from top left to bottom right side of the image. Keeping all these points in view, atomic resolution AFM images were investigated for an image shift. By drawing diagonal lines in the 3 nm 3 nm (Fig. 5) region, a shift in atomic position is estimated to be approximately 0.5 A˚ (in q direction of Fig. 5), which amounts to less than 2% error. This degree of error may be assumed to arise from thermal vibration at room temperature and is a limitation of the experiment. In a similar fashion, a systematic error in the horizontal direction of the image due to small electronic phase lag between scanning of the sample and creation of the image on the display screen also occurs. However, any such effect is neglected here. Thus in a complex fashion, scanning conditions for atomic resolution will vary within a certain degree. Other possible artifacts in contact mode are discussed and justified in a separate communication [9]. 3.2. CSL determination Since the sample is a single-phase metal and is thermally etched at 1000 1C for 1 h, in the present case of sample-II, one can assume that near-grain-boundary planes are continuous up to grain boundary, which is at a distance of 1 mm. In addition, it is difficult to find grain-boundary axis for a high-angle boundary by AFM tip. In such condition, the question may arise as to how it is possible to determine the CSL relationship from the results of two-dimensional maps. This question has two aspects to it, viz., How do grain boundaries orient themselves at the sample surface? and How to validate the data collected by the AFM?
/2 0 0S +0.06 /2 0 0S+5.6
/111S+4.23 /111S1.18
The strategy adopted in the present study is explained in the following. During annealing, the growth of grain boundaries near the free metallic surface tends to lie perpendicular by reducing net curvature of the boundaries next to the surface. Hence, curvatures of the grains become cylindrical on the sample surface and thus terminate normal to the surface [10]. Therefore, crystallographic information just beside the grain boundary and its neighborhood will be equivalent. To verify the effect on grain orientation, a series of atomic resolution images are recorded away from the grain boundary, which will be discussed in the next section. In AFM imaging, one plane of sample surface is exposed for the study. The atomic resolution image of this experimental plane is in real space. According to the atomic packing for a particular material, a limited set of planes crossing the experimental plane is in the image. Therefore, measurements of interplanar spacings from these images can be compared with those obtained from phase contrast images in high-resolution electron microscopy or those from the reciprocal space information from X-ray diffraction studies. Many such comparisons of the AFM data with particularly X-ray diffraction data are made in different studies [11–13]. Moreover, AFM data in the present study match well with crystallographic planes for nickel. Therefore, with the above analogies CSL can be determined using AFM. Experimental procedures for the study are discussed in the following section. Atomic resolution images are recorded from a selected scan area of 3 nm 3 nm (Fig. 5) from both sides of grain boundary-1. The selected areas are marked by ‘L’ and ‘R’ as shown in Fig. 4. The details of directions and corresponding planes for both the boundaries are shown in Fig. 5. Therefore, the grain-boundary axis is determined to be ½1 1¯ 0. As the AFM study does not distinguish positive or negative direction of any crystallographic direction, the ½1 1¯ 0 direction can be considered as [11 0]. Fig. 6 shows sigma matching for grain boundary-1 (GB-1). On rotating the lattice by an angle of 401 over the left side of lattices for GB-1, a matching for sigma relation is obtained. Matching of the points is in agreement with the experimental condition. A deviation in measurement of d-values is summarized in Table 2. The rotation angle is matched with the known rotational angle and axis [11 0]
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Fig. 6. CSL is determined to be S ¼ 9 for grain boundary-1.
pair in the FCC material. Based on the above angle/axis pair, the CSL value is compared with the work of Pumphrey [4] and the CSL is determined as S ¼ 9 for GB-1 [4]. Since the above atomic resolution images are recorded near the grain boundary, it is in our general interest to know how the orientations of the atomic planes vary as a function of distance from the grain boundary. For this reason, a series of atomic resolution images are recorded from boundary positions (GB-1).
(110) p [111]
[100] 3.3. Plane orientation away from GB The positions from the grain boundary are marked into three regions by alphabets ‘a’, ‘b’, and ‘c’ according to the features (Fig. 4). Among the different marked regions and between regions, atomic resolution images are recorded. A representative atomic resolution AFM image from ‘a–b region’ is shown in (Fig. 7). All measurements on AFM images are tabulated in Table 3. The last column of Table 3 depicts same plane orientation ð1 1¯ 0Þ when experiments were conducted up to 4–5 mm distances away from a GB-1. In Fig. 7, the angle measurement between [1 0 0] and [111] is seen to be 561, which is very close to its theoretical value of 54.71. However, angle measurements between two directions for left and right sides of GB-1 (Fig. 5) show a maximum difference of approximately 61. This discrepancy could be arising due to local rearrangement of the planes beside the grain boundary. 3.4. Effect of cold rolling and grain boundary crystallography The effect of heat treatment at 1000 1C for 1 h for cold-rolled nickel has changed the grain structure of the sample, where the average grain size is found to vary between 100 and 150 mm. The primary crystallization of cold worked FCC metals such as nickel results in a marked change. In the present study, texture has been developed in the ð1 1¯ 0Þ direction with 391 angle. Grainboundary texture is a subject of study for a number of researchers. In the view of the present work, few important aspects can
q
Fig. 7. Lattice resolution images in between ‘a–b’ region away from grain boundary-1.
be noted from the results of Baker and Li [14]. In this paper, the authors have summarized results obtained by different researchers. Lejcˇek and Sˇı´ma [15] have observed 191//1 0 0S orientation relation between primary recrystallization texture and secondary grain grown during unidirectional annealing for heavily deformed nickel. The same authors have noted that a change in rotation axis may arise if the activation energy for grain-boundary migration is higher for twist boundary than tilt boundary. Makita et al. [16] have observed that orientation relations in statically annealed nickel are 191//1 0 0S, 221//111S and 381//111S for large grains. The /111S or /1 0 0S preferential rotation direction can be controlled by rolling procedure. Makita et al. [16] and other workers [14] have emphasized the role of CSL that CSL boundaries
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Table 3 Features in a region
Experimentally measured distances (A˚)
Correlation with standard ‘d’ values (A˚)
Direction
‘a’ Rods Between rods Between ‘a’ and ‘b’ regions
1.248 2.496 1.08
1.010 3.48 1.239
1.246 2.034 1.017
1.0172 3.529 1.247
/2 2 0S /111S /2 2 2S
/2 2 2S /1 0 0S /2 2 0S
ð1 1¯ 0Þ ð1 1¯ 0Þ ð1¯ 1 0Þ
‘b’ Round regions Between ‘b’ and ‘c’ regions
1.436 1.43
1.003 1.014
1.438 1.438
1.017 1.017
/11 2S /11 2S
/2 2 2S /2 2 2S
ð1 1¯ 0Þ ð1 1¯ 0Þ
‘c’ Wavy surface Away from ‘c’
0.72 1.431
2.037 0.994
0.722 1.438
2.034 1.017
/4 4 2S /11 2S
/111S /2 2 2S
ð1 1¯ 0Þ ð1 1¯ 0Þ
around large grains have higher mobility than other boundaries. They have also noted {11 0} /11 2S orientation relationship and explained it as related to twin orientation. These orientational relationships are governed by a complex process of primary and even secondary crystallization according to the congenial conditions prevailing. In primary recrystallization, the cubic texture in FCC materials gets sharpened and strengthened by increasing the annealing temperature and time [14]. Lejcˇek and Sˇı´ma [15] have noted secondary crystallization being activated at temperatures greater than the critical temperature of 777 1C for 90% cold-rolled nickel. Therefore, in the present case, 30% cold-rolled nickel will have higher secondary recrystallization temperature than 777 1C. However, secondary crystallization is mainly responsible for growth of larger grain sizes and develops another set of texture. Therefore, annealing at 1000 1C for 1 h and the grain sizes observed in the present case indicate that secondary recrystallization has taken place. Baker and Li [14] have observed that annealing at 1000 1C for 90% coldrolled nickel left small cube-oriented grains along with a larger ¯ orientations and few proportion of non-cubic {1 2 4}h2 1 1i random textures. Lee and Richards [17] have recorded special boundary fraction (3pSp29) for commercial pure nickel annealed at 900 1C for 10 min. Note S ¼ 3 boundary is a twin. Therefore, occurrence of a texture of (11 0) [14,15,17] cannot be ruled out in cold-rolled and annealed sample of nickel. Retention of cubic rotational axis indicates that the occurrence is due to primary crystallization. In contrast, larger grain size reveals that secondary crystallization has occurred. But secondary recrystallization process also retains few cubic orientations [14]. Hence for the present study, it can be concluded that secondary crystallization has already set in and the AFM study around a triple point junction mapped an orientation, which is due to primary crystallization. The mapped orientation (for grain boundary-1) shows a CSL S ¼ 9 relation, and high mobility within grains around triple point junction can be marked by its surface morphology (see Fig. 4). From morphological appearance in Fig. 4, it can be said that mobility has been locked for grain boundary-1. Grain boundary-3 is a moving boundary with the (1 0 0) direction from both sides. The last grain boundary-2 is complicated where lattice imaging revealed only a complicated pattern.
annealed nickel and (ii) thermally etched condition without cold rolling. On cold rolling, the first sample has generated maximum numbers of grains along 111. In the second sample, annealing has generated recrystallization. Both the samples are characterised by AFM in contact mode. Atomic resolution images are recorded in the near-grain-boundary regions and detailed crystallographic measurements are consistent with standard data. The feasibility of obtaining accurate crystallographic information by AFM images is demonstrated. In the case of cold-rolled and annealed Ni, the plane matching model for the grain-boundary structure and a CSL boundary with S ¼ 9 in the case of thermally etched condition without any cold rolling could be established.
Acknowledgements The authors extend their sincere thanks to Prof. S.P. Mehrotra, Director, NML, for supporting the above study under an in-house research scheme. They also thank Prof. Subra Suresh (MIT, USA) and Dr. S. Nayar (NML, Jamshedpur) for their kind suggestions and interest in the present work.
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[5] [6] [7] [8] [9] [10] [11] [12]
4. Conclusion Near-grain-boundary characterization is carried out for commercial purity-grade nickel in two conditions: (i) cold-rolled and
Plane
[13] [14] [15] [16] [17]
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