- Email: [email protected]
3D determination of grain shape in a FeAl-based nanocomposite by 3D FIB tomography
Scripta Materialia 45 (2001) 753±758
www.elsevier.com/locate/scriptamat
3D determination of grain shape in a FeAl-based nanocomposite by 3D FIB tomography B.J. Inksona*, M. Mulvihillb, and G. M obusa a
Department of Materials Science, University of Oxford, Parks Road, Oxford OX1 3PH, UK b Xinetics Inc., 37 MacArthur Avenue, Devens, MA 01432, USA
Received 6 April 2001; accepted 15 May 2001
Abstract The 3D shapes of individual grains in an extruded FeAl nanocomposite have been determined by a new method of 3D focused ion beam (FIB) tomographic analysis. Sequential 2D sectioning and imaging of grains using a FIB, and computer reconstruction can locate the grain boundaries with better than 100 nm precision. Ó 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: 3D; Focused ion beam microscopy; Grain shape; Intermetallics; Tomography
Introduction 3D analysis of inhomogeneous microstructures is of great importance in the development of successful structural materials. As microstructures increasingly become engineered at the sub-micron level, the ability to analyse structure and chemistry in 3D at speci®c sites chosen with high spatial resolution (<100 nm) is vital. At present there are a range of 3D analysis techniques available for determining grain morphology of individual grains, each with varying spatial and chemical resolution. For sub-micron resolution these include (i) secondary ion mass spectrometry for grains with a chemical variation at the grain boundaries and lateral width >200 nm [1,2], (ii) TEM tomography for particles <300 nm enveloped in a second phase matrix [3], and (iii) 3D ®eld ion microscopy for conducting grains <50 nm in size [4]. These three techniques however are not suitable for the 3D analysis of single-phase matrices with grains in the size range 300 nm to 2 lm, in which many modern nanoengineered materials lie.
*
Corresponding author. Fax: +44-1865-273789. E-mail address: [email protected] (B.J. Inkson).
1359-6462/01/$ - see front matter Ó 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 6 2 ( 0 1 ) 0 1 0 9 0 - 9
754
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
In this paper we present a new method for the 3D analysis of single-phase grains (also applicable to multiphase materials) in the size range 300 nm to 20 lm using a focused ion beam (FIB). The FIB is used as a `nanoknife', cutting slices through grains with a site-speci®c accuracy of <100 nm. The imaging and computer reconstruction of many parallel 2D slices through grains, enables the 3D morphology of individual grains with sub-micron grain size to be determined. 3D FIB analysis method The 3D FIB method used for 3D grain shape analysis is a modi®ed version of that used for the multiple 2D sectioning of chemically graded particles and multilayers [5±7], and the 3D analysis of cracks [8]. The FIB microscope used was a FEI FIB 200TEM workstation with Magnum column, which operates with a 30 kV Ga beam and ion currents 10 pA to 20 nA. The 3D analysis method is summarised as follows (Fig. 1): (i) Set-up: First a protective layer of Pt is deposited on the speci®c area to be sectioned, reference markers drilled into the surface and a deep trough drilled (Fig. 1(a)). The trough enables the sample to be rotated by h and a 2D cross-section of the surface to be imaged from the side (Fig. 1(b)). In this paper we will de®ne perpendicular axes (x; y; z) to be: z Ga beam direction used for milling, x specimen rotation axis (normal to z), and y direction perpendicular to x and z. h rotation of sample around x-axis away from the milling orientation (h 0°). If the small deviation from planarity of the milled plane is neglected, the z±x plane is eectively the milled surface, and the y-axis eectively the milled plane normal.
Fig. 1. Method of 3D FIB sectioning and grain morphology determination. (a) Set-up of protective Pt, reference markers, and imaging trough. (b) Rotation through angle h enables imaging of a 2D milled cross-section. (c) Sectioning a grain into many parallel 2D slices. (d) Alignment of sequential cross-sections O1 and O2 imaged at angle h. (e) Schematic of 3D reconstruction from aligned 2D sections through grains.
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
755
(ii) 2D sectioning: A 2D cross-sectional surface through the sample is cut with the FIB. Here we used a milling current of 100 pA, as a compromise between a sharp section pro®le and reasonable milling time. An ion induced secondary electron image (ISE) is taken at h 0° to determine the milled plane position. A reduced ion current (here 30 pA) is used for imaging due to a smaller spot size (higher resolution) and reduced sputtering whilst imaging. The sample is then rotated by angle h about x, and ISE images recorded using at least two sample tilt angles h h1 ; h2 ; . . . ; in order to fully determine the grain boundary positions in single-phase material by changes in channelling contrast [9,10]. Multiphase material may require only a single tilt angle to determine phase boundaries [7]. (iii) Iterative 2D sectioning loop: The 2D sectioning and imaging sequence (ii) is then repeated with a dy increment in milled plane position (Fig. 1(c)). Each sequentially drilled 2D milled plane through the microstructure is imaged at h 0°; h1 ; h2 ; . . . ; from which the 3D positions of grain boundaries can be determined. The 2D images are aligned digitally as described elsewhere using cross-correlation of reference markers [7]. The relative y-coordinate for a given 2D milled plane (assumed to be eectively oriented in the z±x plane) is determined from the set of ISE images taken at h 0°. The ISE images taken at tilt angles h h1 ; h2 ; . . . ; (here h 30° and h 45°), are aligned with additional correction factors of y-axis origin shift O0 dy cos h and stretching along the z-axis by factor 1=sin (h) to compensate for the imaging angle (Fig. 1(d)). Note that there is no assumption that the specimen surface has been mounted in the x±y plane normal to the milling Ga beam. The grain boundaries are located by changes in ISE contrast between grains. In single-phase material we exploit the dierential contrast between grains of dierent orientation that occurs due to crystallographic channelling of the incident Ga ions which results in dierent secondary electron yields [9,10]. Since the ISE contrast value is not totally unique (several crystallographic orientations may have similar ion channelling), at least two tilt values h 30° and h 45° are used so that adjacent grains with similar contrast at one angle will be distinguished at another (Fig. 2). Mixtures of phases have additional contrast changes due to `material' dependant secondary electron yield. Once the grain boundary positions have been determined in the aligned
Fig. 2. Location of grain boundaries in the individual 2D ISE FIB images. (a) FeAl grains with imaging direction h 30°. (b) Same grains as (a) imaged down h 45°. As there is no compositional variation between grains, the contrast ¯uctuations between grains arise entirely from channelling contrast. The arrows indicate a grain whose upper boundary is visible in (b) but not in (a). A few Y2 O3 nanoparticles are visible as white ¯ecks inside the grains.
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B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
2D images, the grain boundary pro®les of individual grains can be extracted from each of the sequential 2D images, and trilinear interpolation carried out to generate a 3D reconstruction of grain shapes (Fig. 1(e)). All image processing was done with the voxel-based IDL image analysis package [11]. 3D determination of grain shape in a FeAl nanocomposite We have applied the 3D FIB technique to the analysis of 3D grain shape in an FeAl intermetallic alloy. A FeAl±Y2 O3 nanocomposite was prepared by mechanical alloying FeAl and Y2 O3 powders, followed by compaction by extrusion in a steel sheath. A detailed characterisation of the mechanical properties and TEM microstructure of the as-extruded material has been previously carried out [12,13]. The nanocomposite microstructure consists of FeAl grains 0.5±5 lm in size, with a distribution of strengthening Y2 O3 nanoparticles 5±100 nm in size (Figs. 2 and 3). Only the largest Y2 O3 nanoparticles can be resolved as small ¯ecks in the ISE FIB images (Fig. 2). The 3D shape of the nanoparticles has been determined by a new high resolution method of 3D TEM EELS tomography [3]. The crystallographic orientation and texture of the FeAl grains were characterised by electron back-scattered diraction (EBSD) analysis of more than 3000 grains in the rods. EBSD scans were taken using a JEOL 6300 FEGSEM with TexSEM Lab (TSL) EBSD system, both with a 0.25 lm step size less than grain size to examine local texture and grain shape (Fig. 3(b) and (c)), and 4 lm step size for statistics from more grains for pole ®gure determination (Fig. 3(d)). The EBSD analyses show that there is only very limited crystallographic texture developed in the orientation of the FeAl grains within the as-extruded rods (Fig. 3(d)). 2D TEM, EBSD and optical sections carried out in two non-parallel directions across the rod and parallel to the rod axis show that on average the FeAl grains appear to be elongated along the extrusion axis and round the rod circumference (Fig. 3, Ref. [2]). From these 2D sections, it is not possible to determine the true 3D morphology and aspect ratios of individual grains, so the 3D FIB technique was applied to their analysis. Fig. 4 shows a representative 3D FIB reconstruction of two individual sub-surface grains in the as-extruded FeAl, determined from multiple parallel 2D FIB sections of dimensions 14 11 lm2 at 150±300 nm separation. The two sub-surface grains in Fig. 4 are located 4 mm from the centre of the rod, and have sizes in the middle of the grain size range 0.5±5 lm. The 3D reconstructions of these and other grains in the asextruded rod show that the individual FeAl grains are elongated in the rod both along the extrusion axis, and also round the extruded rod circumference. The grains have a maximum to minimum dimension aspect ratio of 2, which is consistent with that estimated previously from the 2D optical, TEM and EBSD cross-sections (Fig. 3, Ref. [2]). The errors in the location of the grain boundaries at 20 K magni®cation are estip mated as Dx 2 pixels 35 nm, Dz 2 2 pixels 50 nm in a given 2D slice, plus Dx; Dy; Dz 3 pixels 50 nm error alignment in the positions of the 2D slices,
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
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Fig. 3. FeAl nanocomposite microstructure in the as-extruded rods. (a, b) 2D sections parallel to the extrusion axis. (a) TEM image. (b) EBSD map, 0.25 lm step size. (c) EBSD map, 0.25 lm step size, from a 2D section perpendicular to the extrusion axis. (d) EBSD derived {1 0 0}, {1 1 0} and {1 1 1} pole ®gures (same orientation as (a, b), contour plot using gaussian function of half-width 5°), with maximum contour 2:52 random.
giving minimum errors of Dx 85 nm, Dy 50 nm and Dz 100 nm. The choice of imaging magni®cation, chosen here as 20 K to sample a 14 11 lm2 area, determines the absolute size of one pixel and thus the absolute error in nm [7]. Magni®cation is a trade-o between adequate ®eld of view and precision of grain boundary location. The FIB instrument resolution at about 10±15 nm is not limiting. The positions of the grain boundaries in the interpolated region between each slice have greater errors, with errors approximately distance from adjacent 2D slice. The discontinuous sampling in 3D space (2D data sets interpolation) results in some rounding of sharp corners in the reconstructed grain shapes visible in Fig. 4. Although ®ne boundary facets are missed, the grain aspect ratios and volumes are reliably estimated. The use of a voxel-based 3D
Fig. 4. 3D reconstruction of two grains in extruded FeAl, sectioned by FIB. (a) View along rod radius. (b)±(f) views rotated around the extrusion direction. (d) View along rod circumference. The two grains are plate-like, ¯attened along the extrusion direction and around the rod circumference.
758
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
analysis package [11] enables grain volumes to be determined, and the grains in Fig. 4 have total volume 5:0 0:8 lm3 . As the errors are independent of the size of the grain, the relative volume error decreases with increasing grain size. Conclusions The 3D shapes of individual grains in an FeAl nanocomposite have been determined by a new method of 3D tomographic analysis using sequential 2D sectioning and imaging of grains using a FIB. Each 2D FIB cross-section through the microstructure is imaged at several angles to locate the grain boundary positions. Chemically identical grains are distinguished by dierential channelling contrast in the ISE images. From the multiple 2D aligned cross-sections, where grain boundary positions are located to better than 6 pixels (100 nm precision at 20 K magni®cation), computer reconstruction enables the 3D shape of individual grains to be determined. The 3D mapping technique is applicable to both single-phase and multiphase material, and has been applied to the analysis of the directional 3D microstructure of an extruded intermetallic FeAl nanocomposite. In the extruded rod, individual grains are observed to have 3D morphologies elongated parallel to the extrusion axis and round the rod circumference. Acknowledgements The authors gratefully acknowledge Dr. R. Baccino, CEREM who supplied the FeAl40 alloy as part of Brite Euram CEASI programme, Dr. E. Bischo, MPI f ur Metallforschung, Stuttgart for use of the FEG-SEM, Dr. A. Wilkinson for discussion, and funding from The Royal Society and the EPSRC, UK. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Patkin, A. J., & Morrison, G. H. (1982). Anal Chem 54(1), 2. Hutter, H., Wilhartitz, P., & Grasserbauer, M. (1993). Fres J Anal Chem 346, 66. M obus, G., & Inkson, B. J. Microscopy and Microanalysis Proc 2001. New York: Springer, in press. Cerezo, A., Godfrey, T. J., & Smith, G. D. W. (1988). Rev Sci Instrum 59(6), 862. Sakamoto, T., Cheng, Z., Takahashi, M., Owari, M., & Nihei, Y. (1998). Jpn J Appl Phys 37, 2051. Dunn, D. N., & Hull, R. (1999). Appl Phys Lett 75(21), 3414. Inkson, B. J., Steer, T., M obus, G., & Wagner, T. (2001). J Microsc 201(2), 256. Inkson, B. J., Wu, H., Steer, T., & M obus, G. Nanoindentation and Nanotribology. MRS Proc (Vol. 649). Pittsburgh, Pennsylvania: Materials Research Society, in press. Levi-Setti, R., Fox, T. R., & Lam, K. (1983). Nucl Instrum Meth 205, 299. Nikawa, K. (1991). J Vac Sci Technol B 9, 2566. IDL, Research Systems Inc., Boulder, Colorado, USA. Inkson, B. J., Threadgill, P. L. (1997). High Temperature Ordered Intermetallics VII. MRS Proc (Vol. 460, p. 767). Pittsburgh, Pennsylvania: Materials Research Society. Inkson, B. J., & Threadgill, P. L. (1998). Mat Sci Eng 258(1±2), 313.
www.elsevier.com/locate/scriptamat
3D determination of grain shape in a FeAl-based nanocomposite by 3D FIB tomography B.J. Inksona*, M. Mulvihillb, and G. M obusa a
Department of Materials Science, University of Oxford, Parks Road, Oxford OX1 3PH, UK b Xinetics Inc., 37 MacArthur Avenue, Devens, MA 01432, USA
Received 6 April 2001; accepted 15 May 2001
Abstract The 3D shapes of individual grains in an extruded FeAl nanocomposite have been determined by a new method of 3D focused ion beam (FIB) tomographic analysis. Sequential 2D sectioning and imaging of grains using a FIB, and computer reconstruction can locate the grain boundaries with better than 100 nm precision. Ó 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: 3D; Focused ion beam microscopy; Grain shape; Intermetallics; Tomography
Introduction 3D analysis of inhomogeneous microstructures is of great importance in the development of successful structural materials. As microstructures increasingly become engineered at the sub-micron level, the ability to analyse structure and chemistry in 3D at speci®c sites chosen with high spatial resolution (<100 nm) is vital. At present there are a range of 3D analysis techniques available for determining grain morphology of individual grains, each with varying spatial and chemical resolution. For sub-micron resolution these include (i) secondary ion mass spectrometry for grains with a chemical variation at the grain boundaries and lateral width >200 nm [1,2], (ii) TEM tomography for particles <300 nm enveloped in a second phase matrix [3], and (iii) 3D ®eld ion microscopy for conducting grains <50 nm in size [4]. These three techniques however are not suitable for the 3D analysis of single-phase matrices with grains in the size range 300 nm to 2 lm, in which many modern nanoengineered materials lie.
*
Corresponding author. Fax: +44-1865-273789. E-mail address: [email protected] (B.J. Inkson).
1359-6462/01/$ - see front matter Ó 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 6 2 ( 0 1 ) 0 1 0 9 0 - 9
754
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
In this paper we present a new method for the 3D analysis of single-phase grains (also applicable to multiphase materials) in the size range 300 nm to 20 lm using a focused ion beam (FIB). The FIB is used as a `nanoknife', cutting slices through grains with a site-speci®c accuracy of <100 nm. The imaging and computer reconstruction of many parallel 2D slices through grains, enables the 3D morphology of individual grains with sub-micron grain size to be determined. 3D FIB analysis method The 3D FIB method used for 3D grain shape analysis is a modi®ed version of that used for the multiple 2D sectioning of chemically graded particles and multilayers [5±7], and the 3D analysis of cracks [8]. The FIB microscope used was a FEI FIB 200TEM workstation with Magnum column, which operates with a 30 kV Ga beam and ion currents 10 pA to 20 nA. The 3D analysis method is summarised as follows (Fig. 1): (i) Set-up: First a protective layer of Pt is deposited on the speci®c area to be sectioned, reference markers drilled into the surface and a deep trough drilled (Fig. 1(a)). The trough enables the sample to be rotated by h and a 2D cross-section of the surface to be imaged from the side (Fig. 1(b)). In this paper we will de®ne perpendicular axes (x; y; z) to be: z Ga beam direction used for milling, x specimen rotation axis (normal to z), and y direction perpendicular to x and z. h rotation of sample around x-axis away from the milling orientation (h 0°). If the small deviation from planarity of the milled plane is neglected, the z±x plane is eectively the milled surface, and the y-axis eectively the milled plane normal.
Fig. 1. Method of 3D FIB sectioning and grain morphology determination. (a) Set-up of protective Pt, reference markers, and imaging trough. (b) Rotation through angle h enables imaging of a 2D milled cross-section. (c) Sectioning a grain into many parallel 2D slices. (d) Alignment of sequential cross-sections O1 and O2 imaged at angle h. (e) Schematic of 3D reconstruction from aligned 2D sections through grains.
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
755
(ii) 2D sectioning: A 2D cross-sectional surface through the sample is cut with the FIB. Here we used a milling current of 100 pA, as a compromise between a sharp section pro®le and reasonable milling time. An ion induced secondary electron image (ISE) is taken at h 0° to determine the milled plane position. A reduced ion current (here 30 pA) is used for imaging due to a smaller spot size (higher resolution) and reduced sputtering whilst imaging. The sample is then rotated by angle h about x, and ISE images recorded using at least two sample tilt angles h h1 ; h2 ; . . . ; in order to fully determine the grain boundary positions in single-phase material by changes in channelling contrast [9,10]. Multiphase material may require only a single tilt angle to determine phase boundaries [7]. (iii) Iterative 2D sectioning loop: The 2D sectioning and imaging sequence (ii) is then repeated with a dy increment in milled plane position (Fig. 1(c)). Each sequentially drilled 2D milled plane through the microstructure is imaged at h 0°; h1 ; h2 ; . . . ; from which the 3D positions of grain boundaries can be determined. The 2D images are aligned digitally as described elsewhere using cross-correlation of reference markers [7]. The relative y-coordinate for a given 2D milled plane (assumed to be eectively oriented in the z±x plane) is determined from the set of ISE images taken at h 0°. The ISE images taken at tilt angles h h1 ; h2 ; . . . ; (here h 30° and h 45°), are aligned with additional correction factors of y-axis origin shift O0 dy cos h and stretching along the z-axis by factor 1=sin (h) to compensate for the imaging angle (Fig. 1(d)). Note that there is no assumption that the specimen surface has been mounted in the x±y plane normal to the milling Ga beam. The grain boundaries are located by changes in ISE contrast between grains. In single-phase material we exploit the dierential contrast between grains of dierent orientation that occurs due to crystallographic channelling of the incident Ga ions which results in dierent secondary electron yields [9,10]. Since the ISE contrast value is not totally unique (several crystallographic orientations may have similar ion channelling), at least two tilt values h 30° and h 45° are used so that adjacent grains with similar contrast at one angle will be distinguished at another (Fig. 2). Mixtures of phases have additional contrast changes due to `material' dependant secondary electron yield. Once the grain boundary positions have been determined in the aligned
Fig. 2. Location of grain boundaries in the individual 2D ISE FIB images. (a) FeAl grains with imaging direction h 30°. (b) Same grains as (a) imaged down h 45°. As there is no compositional variation between grains, the contrast ¯uctuations between grains arise entirely from channelling contrast. The arrows indicate a grain whose upper boundary is visible in (b) but not in (a). A few Y2 O3 nanoparticles are visible as white ¯ecks inside the grains.
756
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
2D images, the grain boundary pro®les of individual grains can be extracted from each of the sequential 2D images, and trilinear interpolation carried out to generate a 3D reconstruction of grain shapes (Fig. 1(e)). All image processing was done with the voxel-based IDL image analysis package [11]. 3D determination of grain shape in a FeAl nanocomposite We have applied the 3D FIB technique to the analysis of 3D grain shape in an FeAl intermetallic alloy. A FeAl±Y2 O3 nanocomposite was prepared by mechanical alloying FeAl and Y2 O3 powders, followed by compaction by extrusion in a steel sheath. A detailed characterisation of the mechanical properties and TEM microstructure of the as-extruded material has been previously carried out [12,13]. The nanocomposite microstructure consists of FeAl grains 0.5±5 lm in size, with a distribution of strengthening Y2 O3 nanoparticles 5±100 nm in size (Figs. 2 and 3). Only the largest Y2 O3 nanoparticles can be resolved as small ¯ecks in the ISE FIB images (Fig. 2). The 3D shape of the nanoparticles has been determined by a new high resolution method of 3D TEM EELS tomography [3]. The crystallographic orientation and texture of the FeAl grains were characterised by electron back-scattered diraction (EBSD) analysis of more than 3000 grains in the rods. EBSD scans were taken using a JEOL 6300 FEGSEM with TexSEM Lab (TSL) EBSD system, both with a 0.25 lm step size less than grain size to examine local texture and grain shape (Fig. 3(b) and (c)), and 4 lm step size for statistics from more grains for pole ®gure determination (Fig. 3(d)). The EBSD analyses show that there is only very limited crystallographic texture developed in the orientation of the FeAl grains within the as-extruded rods (Fig. 3(d)). 2D TEM, EBSD and optical sections carried out in two non-parallel directions across the rod and parallel to the rod axis show that on average the FeAl grains appear to be elongated along the extrusion axis and round the rod circumference (Fig. 3, Ref. [2]). From these 2D sections, it is not possible to determine the true 3D morphology and aspect ratios of individual grains, so the 3D FIB technique was applied to their analysis. Fig. 4 shows a representative 3D FIB reconstruction of two individual sub-surface grains in the as-extruded FeAl, determined from multiple parallel 2D FIB sections of dimensions 14 11 lm2 at 150±300 nm separation. The two sub-surface grains in Fig. 4 are located 4 mm from the centre of the rod, and have sizes in the middle of the grain size range 0.5±5 lm. The 3D reconstructions of these and other grains in the asextruded rod show that the individual FeAl grains are elongated in the rod both along the extrusion axis, and also round the extruded rod circumference. The grains have a maximum to minimum dimension aspect ratio of 2, which is consistent with that estimated previously from the 2D optical, TEM and EBSD cross-sections (Fig. 3, Ref. [2]). The errors in the location of the grain boundaries at 20 K magni®cation are estip mated as Dx 2 pixels 35 nm, Dz 2 2 pixels 50 nm in a given 2D slice, plus Dx; Dy; Dz 3 pixels 50 nm error alignment in the positions of the 2D slices,
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
757
Fig. 3. FeAl nanocomposite microstructure in the as-extruded rods. (a, b) 2D sections parallel to the extrusion axis. (a) TEM image. (b) EBSD map, 0.25 lm step size. (c) EBSD map, 0.25 lm step size, from a 2D section perpendicular to the extrusion axis. (d) EBSD derived {1 0 0}, {1 1 0} and {1 1 1} pole ®gures (same orientation as (a, b), contour plot using gaussian function of half-width 5°), with maximum contour 2:52 random.
giving minimum errors of Dx 85 nm, Dy 50 nm and Dz 100 nm. The choice of imaging magni®cation, chosen here as 20 K to sample a 14 11 lm2 area, determines the absolute size of one pixel and thus the absolute error in nm [7]. Magni®cation is a trade-o between adequate ®eld of view and precision of grain boundary location. The FIB instrument resolution at about 10±15 nm is not limiting. The positions of the grain boundaries in the interpolated region between each slice have greater errors, with errors approximately distance from adjacent 2D slice. The discontinuous sampling in 3D space (2D data sets interpolation) results in some rounding of sharp corners in the reconstructed grain shapes visible in Fig. 4. Although ®ne boundary facets are missed, the grain aspect ratios and volumes are reliably estimated. The use of a voxel-based 3D
Fig. 4. 3D reconstruction of two grains in extruded FeAl, sectioned by FIB. (a) View along rod radius. (b)±(f) views rotated around the extrusion direction. (d) View along rod circumference. The two grains are plate-like, ¯attened along the extrusion direction and around the rod circumference.
758
B.J. Inkson et al./Scripta Materialia 45 (2001) 753±758
analysis package [11] enables grain volumes to be determined, and the grains in Fig. 4 have total volume 5:0 0:8 lm3 . As the errors are independent of the size of the grain, the relative volume error decreases with increasing grain size. Conclusions The 3D shapes of individual grains in an FeAl nanocomposite have been determined by a new method of 3D tomographic analysis using sequential 2D sectioning and imaging of grains using a FIB. Each 2D FIB cross-section through the microstructure is imaged at several angles to locate the grain boundary positions. Chemically identical grains are distinguished by dierential channelling contrast in the ISE images. From the multiple 2D aligned cross-sections, where grain boundary positions are located to better than 6 pixels (100 nm precision at 20 K magni®cation), computer reconstruction enables the 3D shape of individual grains to be determined. The 3D mapping technique is applicable to both single-phase and multiphase material, and has been applied to the analysis of the directional 3D microstructure of an extruded intermetallic FeAl nanocomposite. In the extruded rod, individual grains are observed to have 3D morphologies elongated parallel to the extrusion axis and round the rod circumference. Acknowledgements The authors gratefully acknowledge Dr. R. Baccino, CEREM who supplied the FeAl40 alloy as part of Brite Euram CEASI programme, Dr. E. Bischo, MPI f ur Metallforschung, Stuttgart for use of the FEG-SEM, Dr. A. Wilkinson for discussion, and funding from The Royal Society and the EPSRC, UK. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Patkin, A. J., & Morrison, G. H. (1982). Anal Chem 54(1), 2. Hutter, H., Wilhartitz, P., & Grasserbauer, M. (1993). Fres J Anal Chem 346, 66. M obus, G., & Inkson, B. J. Microscopy and Microanalysis Proc 2001. New York: Springer, in press. Cerezo, A., Godfrey, T. J., & Smith, G. D. W. (1988). Rev Sci Instrum 59(6), 862. Sakamoto, T., Cheng, Z., Takahashi, M., Owari, M., & Nihei, Y. (1998). Jpn J Appl Phys 37, 2051. Dunn, D. N., & Hull, R. (1999). Appl Phys Lett 75(21), 3414. Inkson, B. J., Steer, T., M obus, G., & Wagner, T. (2001). J Microsc 201(2), 256. Inkson, B. J., Wu, H., Steer, T., & M obus, G. Nanoindentation and Nanotribology. MRS Proc (Vol. 649). Pittsburgh, Pennsylvania: Materials Research Society, in press. Levi-Setti, R., Fox, T. R., & Lam, K. (1983). Nucl Instrum Meth 205, 299. Nikawa, K. (1991). J Vac Sci Technol B 9, 2566. IDL, Research Systems Inc., Boulder, Colorado, USA. Inkson, B. J., Threadgill, P. L. (1997). High Temperature Ordered Intermetallics VII. MRS Proc (Vol. 460, p. 767). Pittsburgh, Pennsylvania: Materials Research Society. Inkson, B. J., & Threadgill, P. L. (1998). Mat Sci Eng 258(1±2), 313.