- Email: [email protected]
Characterization of textured materials by TOF transmission
ARTICLE IN PRESS
Physica B 385–386 (2006) 636–638 www.elsevier.com/locate/physb
Characterization of textured materials by TOF transmission Javier R. Santistebana,, Lyndon Edwardsb, V. Stelmukhb a
Isis Facility, Rutherford Laboratory, CCLRC, Chilton, Oxfordshire OX11 0QX, UK Department of Materials Engineering, The Open University, Milton Keynes MK7 6AA, UK
b
Abstract Many materials are polycrystals with a non-random distribution of orientations. In these materials many physical properties are anisotropic. In particular, the transmission of thermal neutrons through textured materials is strongly dependent on the neutron wavelength and the specimen orientation. Here we show the large variation that exists in the neutron total cross-section of naturally occurring and manmade objects, as opposed to the simple behaviour expected for randomly oriented crystallites. We report time-of-flight transmission measurements along different sample orientations on a range of metal objects. We discuss the possibilities of the technique for the non-destructive characterization of the spatial variation of texture across macroscopic specimens. Finally, we provide an expression relating the orientation-dependent total cross-section with the pole figures measured on traditional diffraction experiments. r 2006 Elsevier B.V. All rights reserved. PACS: 61.12.Ld; 96.30.Za; 81.20.Vj; 81.40.Ef Keywords: Neutron transmission; Texture; Aluminium weld; Sikhote-Alin meteorite
1. Introduction Quantitative phase analysis by time-of-flight (TOF) neutron transmission has been used to study the kinetics of phase transformations in polycrystalline materials [1,2], and the spatial variation of phases across macroscopic objects [3]. However, a reliable analysis of the transmitted signal is sometimes prevented by the presence of preferred orientation or texture, which distorts the intensity and shape of the TOF transmission spectra from the simple behaviour observed for randomly oriented crystallites. Besides this, spatial variations in the neutron transmission of a specimen due to microstructural effects are important for a proper interpretation of radiography and tomography images produced using cold neutrons. Here we report experiments that illustrate the wide range of transmission spectra to be found in naturally occurring and manmade crystals. We have measured the TOF neutron transmission along several directions for: (i) a welded Al plate; and (ii) two Iron–Nickel meteorites from Corresponding author. Tel.: +44 1235 445434; fax: +44 1235 445720.
E-mail address: [email protected] (J.R. Santisteban). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.06.090
the Sikhote-Alin fall. The experiments were performed on the ENGIN-X beamline at the Isis Facility, UK [4]. The transmission of the samples was defined by measuring the direct neutron beam with and without the sample in front of a detector. The spatial variation of the TOF transmission across the specimens was defined with an array of 10 10 Li glass detectors covering an area of 25 25 mm2 with a spatial resoltion of 2 2 mm2 [5]. Excellent TOF resolution resulted from ENGIN-X 50 m flight path and methane moderator. In order to compare measurements made from different thicknesses the results are presented in terms of the total cross-section of the material, which is readily obtained from the measured transmission. 1.1. Welded aluminium plate Fig. 1(a) shows the total cross-section of a specimen taken from a rolled AA7150 aluminium plate. This material typically presents a strong texture in which the Brass /2 1 1S (1 0 0) is one of the main components [6]. The figure compares the curves measured along three different orientations to the theoretical values for a randomly oriented polycrystal. The theoretical curve
ARTICLE IN PRESS J.R. Santisteban et al. / Physica B 385–386 (2006) 636–638
637
Fig. 1. (a) Total cross-section of an AA7150 plate along different directions compared to prediction for an untextured sample (b) Schematic view of welded specimen (c) Total cross-section along LD measured at the points indicated in (b).
displays a series of Bragg edges at specific wavelengths lhkl ¼ 2dhkl, which correspond with the neutrons being back reflected at 2y ¼ p. The height of each edge is proportional to the number of crystallites having directions from the (h k l) family along the direction of the incident beam. The graph reveals large variations in edge height between different directions. In particular, the absence of the (1 1 1) edge along the normal direction (ND) means that no crystallite has directions from this family aligned to ND. On the other hand, the existence of a texture at least 6 random is revealed by a six-fold increase in intensity along the transverse direction (TD). Moreover, the value of the coherent total cross-section at a wavelength l to the left of a Bragg edge is proportional to the number of crystallites having their (h k l) directions making an angle bhkl ¼ (p/2)arcsin(l/2dhkl) with the incident beam. Along ND the total cross-section only starts increasing at lo4.37 A˚, indicating that no (1 1 1) crystal directions are found within a cone of 401 around ND. Even larger anomalies are found at intermediate directions, as is exemplified by the large peak observed at the left of the (2 0 0) direction. Two 12.5 mm thick AA7150 plates were joined together along the longitudinal (or rolling) direction (LD) by friction stir welding, a relatively new joining process of great interest in the aerospace industry, see Fig. 1(b). The figure also shows a macrograph of the weld, where different regions can be identified. We mapped the variation of the total cross-section along LD over an area of 25 12.5 mm2. Fig. 1(c) shows typical curves measured for the parent plate (10 mm), the transition zone (2.5 mm) and at the weld centre (0 mm). The graph shows that the strong texture found in the parent plate becomes an almost perfectly random distribution at the weld centre. These changes in total cross-section appear as variations in the transmission of the sample, which can be easily resolved on a neutron radiography experiment. 1.2. Iron–nickel meteorite We measured the total cross-sections of two meteorites from the Sikhote-Alin fall. In this fall a meteorite of an
Fig. 2. Total cross-section of (a) a complete specimen and, (b) a fragment from the Sikhote-Alin fall. The former displays diffraction peaks characteristic of a single crystal, whilst the latter corresponds to a ‘‘cold-worked’’ specimen.
estimated mass of 1000 tonnes exploded at an altitude of 6000 m [7]. These meteorites are composed mostly of Kamacite (BCC FeNi) with a small quantity of Taenite (FCC NiFe). Specimens from this fall are of two types. Those commonly called complete individuals, showing ablation and a fusion crust (Fig. 2(a)), which are probably the ones that broke off from the main mass early in the decent. They are characterized by regmaglypts on their surface, i.e., ablation cavities resembling thumbprints. The second type of Sikhote-Alin specimen is the fragment (Fig. 2(b)), which shows the effects of being torn apart from the explosion or on impact with the ground. They look like shrapnel from violent explosions. Fig. 2(a) shows the total cross-section of a 10 mm thick complete individual, together with the theoretical curve for a random FeNi specimen. Bragg edges are absent from the curve because the specimen is essentially a single crystal.
ARTICLE IN PRESS J.R. Santisteban et al. / Physica B 385–386 (2006) 636–638
638
For this case, the reflection of neutrons is concentrated into Laue spots which manifest as peaks in the total crosssection. For this extreme texture, the crystal orientation and mosaicity of the specimen can be easily extracted from the position and width of the peaks appearing in the figure, as explained in Ref. [8]. We must note that this specimen completely reflects all the neutrons in the (1.97, 1.99) A˚ range for the direction explored by the experiment. Fig. 2(b) shows the total cross-section for one of the fragments. The shape of the specimen can be approximated by an 8 mm thick plate, slightly bent around an axis identified by striations seen on the concave or inner surface. The presence of Bragg edges reveals the pollycrystalline nature of the specimen, presumably resulting after severe plastic deformation during the explosion. The presence of texture is also evident in this case. As the figures show, the (2 0 0) Bragg edge dissappears at an angle of 451 from ND, accompanied by a 3 random increase of the (1 1 0) edge. For both specimens the results were found to be nearly uniform over the 10 10 mm2 area covered by the pixellated detector.
So for a textured material the expresion for selcoh becomes selcoh ðlÞ ¼
hkl ol l2 2dX jF hkl j2 d hkl Rðl; d hkl Þ. 4V 0 hkl
(3)
In order to calculate the transmission along a different sample direction the pole figures need to be transformed accordingly. This is not a difficult task for modern texture analysis programs which produce a model of the full orientation distribution function of the crystallites (ODF) [11]. Provided the wealth of information available to a single transmission spectrum, it is in principle possible to define the ODF of high-symmetry materials from the analysis of TOF spectra recorded at different orientations. As a final comment about the angular resolution of the TOF transmission technique, we note that from Bragg law Dy ¼ (Dl/l)cot y. So for the transmission detector on ENGIN-X where (Dl/l0.001), we see that for y ¼ 451 the diffracted signal comes from a cone with a width of approximately 4 min of arc. This justifies the use of a line integral over the pole figure in the calculation of the texture correction for the total cross-section.
2. Discussion
3. Conclusion
A quantitive texture analysis from neutron transmission experiments requires the calculation of the effect of preferred orientation on the neutron total cross-section. Along this line, Vogel has developed a model to account for fibre textures in phase analysis by TOF neutron transmission [9]. The wavelength dependence of the elastic coherent total cross-section sel coh for random polycrystalline materials was first measured by Fermi and collaborators [10]. Neutrons of wavelength l can be diffracted by any lattice planes having 2dhkl4l:
The thermal neutron transmission of manmade and naturally occuring materials departs strongly from the behaviour observed for specimens composed of randomly oriented crystallites. Such differences are easily resolved by TOF experiments. A qualitative analysis of the transmitted TOF spectra can give basic information about the microstructure of unknown samples. When a pixellated array of TOF detectors is used, it provides a fast tool for the non-destructive investigation of macroscopic spatial variations in the microstructure of bulk specimens. Finally, it is in principle possible to define the orientation distribution function of crystallites from a quantitative analysis of the transmitted spectra recorded at several orientations.
selcoh ðlÞ ¼
2d hkl ol l2 X jF hkl j2 d hkl , 4V 0 hkl
(1)
where V0 is the volume of the unit cell and Fhkl is the structure factor. Each term of the series is represented by a Bragg edge in the total cross-section. However, as the present experiments have shown, the total cross-section of textured materials departs considerably from the isotropic case. The value of sel coh along the sample direction t can be directly calculated from the pole figures Phkl(a, b) around t. To do so, we note that for the wavelength l we need to count all the crystallites making the angle bhkl with the incident beam. This corresponds exactly to the integral of the pole figure Phkl(a, b) around a ring of radius bhkl: Z 2p l Rðl; d hkl Þ ¼ Phkl a; p=2 arcsin da. (2) 2d hkl 0
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
K. Meggers, et al., Mater. Sci. Eng. A 188 (1994) 301. S. Vogel, et al., Mater. Sci. Eng. A 333 (2002) 1. A. Steuwer, et al., J. Appl. Phys. 97 (2005) 074903. J.A. Dann, et al., Physica B (2004) e511. J.R. Santisteban, et al., Nucl. Instr. Meth. A 481 (2002) 765. S.C. Chang, et al., Scr. Mater. 39 (1998) 583. V. Buchwald, Handbook of Iron Meteorites, University of California Press, CA, USA, 1976. J.R. Santisteban, J. Appl. Crystallogr. 38 (2005) 934. S. Vogel, Ph.D. Thesis, Kiel University, 2000. E. Fermi, et al., Phys. Rev. 71 (1947) 589. U.F. Kocks, C.N. Tome, H.R. Wenk, Texture and Anisotropy, Cambridge University Press, Cambridge, 1998.
Physica B 385–386 (2006) 636–638 www.elsevier.com/locate/physb
Characterization of textured materials by TOF transmission Javier R. Santistebana,, Lyndon Edwardsb, V. Stelmukhb a
Isis Facility, Rutherford Laboratory, CCLRC, Chilton, Oxfordshire OX11 0QX, UK Department of Materials Engineering, The Open University, Milton Keynes MK7 6AA, UK
b
Abstract Many materials are polycrystals with a non-random distribution of orientations. In these materials many physical properties are anisotropic. In particular, the transmission of thermal neutrons through textured materials is strongly dependent on the neutron wavelength and the specimen orientation. Here we show the large variation that exists in the neutron total cross-section of naturally occurring and manmade objects, as opposed to the simple behaviour expected for randomly oriented crystallites. We report time-of-flight transmission measurements along different sample orientations on a range of metal objects. We discuss the possibilities of the technique for the non-destructive characterization of the spatial variation of texture across macroscopic specimens. Finally, we provide an expression relating the orientation-dependent total cross-section with the pole figures measured on traditional diffraction experiments. r 2006 Elsevier B.V. All rights reserved. PACS: 61.12.Ld; 96.30.Za; 81.20.Vj; 81.40.Ef Keywords: Neutron transmission; Texture; Aluminium weld; Sikhote-Alin meteorite
1. Introduction Quantitative phase analysis by time-of-flight (TOF) neutron transmission has been used to study the kinetics of phase transformations in polycrystalline materials [1,2], and the spatial variation of phases across macroscopic objects [3]. However, a reliable analysis of the transmitted signal is sometimes prevented by the presence of preferred orientation or texture, which distorts the intensity and shape of the TOF transmission spectra from the simple behaviour observed for randomly oriented crystallites. Besides this, spatial variations in the neutron transmission of a specimen due to microstructural effects are important for a proper interpretation of radiography and tomography images produced using cold neutrons. Here we report experiments that illustrate the wide range of transmission spectra to be found in naturally occurring and manmade crystals. We have measured the TOF neutron transmission along several directions for: (i) a welded Al plate; and (ii) two Iron–Nickel meteorites from Corresponding author. Tel.: +44 1235 445434; fax: +44 1235 445720.
E-mail address: [email protected] (J.R. Santisteban). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.06.090
the Sikhote-Alin fall. The experiments were performed on the ENGIN-X beamline at the Isis Facility, UK [4]. The transmission of the samples was defined by measuring the direct neutron beam with and without the sample in front of a detector. The spatial variation of the TOF transmission across the specimens was defined with an array of 10 10 Li glass detectors covering an area of 25 25 mm2 with a spatial resoltion of 2 2 mm2 [5]. Excellent TOF resolution resulted from ENGIN-X 50 m flight path and methane moderator. In order to compare measurements made from different thicknesses the results are presented in terms of the total cross-section of the material, which is readily obtained from the measured transmission. 1.1. Welded aluminium plate Fig. 1(a) shows the total cross-section of a specimen taken from a rolled AA7150 aluminium plate. This material typically presents a strong texture in which the Brass /2 1 1S (1 0 0) is one of the main components [6]. The figure compares the curves measured along three different orientations to the theoretical values for a randomly oriented polycrystal. The theoretical curve
ARTICLE IN PRESS J.R. Santisteban et al. / Physica B 385–386 (2006) 636–638
637
Fig. 1. (a) Total cross-section of an AA7150 plate along different directions compared to prediction for an untextured sample (b) Schematic view of welded specimen (c) Total cross-section along LD measured at the points indicated in (b).
displays a series of Bragg edges at specific wavelengths lhkl ¼ 2dhkl, which correspond with the neutrons being back reflected at 2y ¼ p. The height of each edge is proportional to the number of crystallites having directions from the (h k l) family along the direction of the incident beam. The graph reveals large variations in edge height between different directions. In particular, the absence of the (1 1 1) edge along the normal direction (ND) means that no crystallite has directions from this family aligned to ND. On the other hand, the existence of a texture at least 6 random is revealed by a six-fold increase in intensity along the transverse direction (TD). Moreover, the value of the coherent total cross-section at a wavelength l to the left of a Bragg edge is proportional to the number of crystallites having their (h k l) directions making an angle bhkl ¼ (p/2)arcsin(l/2dhkl) with the incident beam. Along ND the total cross-section only starts increasing at lo4.37 A˚, indicating that no (1 1 1) crystal directions are found within a cone of 401 around ND. Even larger anomalies are found at intermediate directions, as is exemplified by the large peak observed at the left of the (2 0 0) direction. Two 12.5 mm thick AA7150 plates were joined together along the longitudinal (or rolling) direction (LD) by friction stir welding, a relatively new joining process of great interest in the aerospace industry, see Fig. 1(b). The figure also shows a macrograph of the weld, where different regions can be identified. We mapped the variation of the total cross-section along LD over an area of 25 12.5 mm2. Fig. 1(c) shows typical curves measured for the parent plate (10 mm), the transition zone (2.5 mm) and at the weld centre (0 mm). The graph shows that the strong texture found in the parent plate becomes an almost perfectly random distribution at the weld centre. These changes in total cross-section appear as variations in the transmission of the sample, which can be easily resolved on a neutron radiography experiment. 1.2. Iron–nickel meteorite We measured the total cross-sections of two meteorites from the Sikhote-Alin fall. In this fall a meteorite of an
Fig. 2. Total cross-section of (a) a complete specimen and, (b) a fragment from the Sikhote-Alin fall. The former displays diffraction peaks characteristic of a single crystal, whilst the latter corresponds to a ‘‘cold-worked’’ specimen.
estimated mass of 1000 tonnes exploded at an altitude of 6000 m [7]. These meteorites are composed mostly of Kamacite (BCC FeNi) with a small quantity of Taenite (FCC NiFe). Specimens from this fall are of two types. Those commonly called complete individuals, showing ablation and a fusion crust (Fig. 2(a)), which are probably the ones that broke off from the main mass early in the decent. They are characterized by regmaglypts on their surface, i.e., ablation cavities resembling thumbprints. The second type of Sikhote-Alin specimen is the fragment (Fig. 2(b)), which shows the effects of being torn apart from the explosion or on impact with the ground. They look like shrapnel from violent explosions. Fig. 2(a) shows the total cross-section of a 10 mm thick complete individual, together with the theoretical curve for a random FeNi specimen. Bragg edges are absent from the curve because the specimen is essentially a single crystal.
ARTICLE IN PRESS J.R. Santisteban et al. / Physica B 385–386 (2006) 636–638
638
For this case, the reflection of neutrons is concentrated into Laue spots which manifest as peaks in the total crosssection. For this extreme texture, the crystal orientation and mosaicity of the specimen can be easily extracted from the position and width of the peaks appearing in the figure, as explained in Ref. [8]. We must note that this specimen completely reflects all the neutrons in the (1.97, 1.99) A˚ range for the direction explored by the experiment. Fig. 2(b) shows the total cross-section for one of the fragments. The shape of the specimen can be approximated by an 8 mm thick plate, slightly bent around an axis identified by striations seen on the concave or inner surface. The presence of Bragg edges reveals the pollycrystalline nature of the specimen, presumably resulting after severe plastic deformation during the explosion. The presence of texture is also evident in this case. As the figures show, the (2 0 0) Bragg edge dissappears at an angle of 451 from ND, accompanied by a 3 random increase of the (1 1 0) edge. For both specimens the results were found to be nearly uniform over the 10 10 mm2 area covered by the pixellated detector.
So for a textured material the expresion for selcoh becomes selcoh ðlÞ ¼
hkl ol l2 2dX jF hkl j2 d hkl Rðl; d hkl Þ. 4V 0 hkl
(3)
In order to calculate the transmission along a different sample direction the pole figures need to be transformed accordingly. This is not a difficult task for modern texture analysis programs which produce a model of the full orientation distribution function of the crystallites (ODF) [11]. Provided the wealth of information available to a single transmission spectrum, it is in principle possible to define the ODF of high-symmetry materials from the analysis of TOF spectra recorded at different orientations. As a final comment about the angular resolution of the TOF transmission technique, we note that from Bragg law Dy ¼ (Dl/l)cot y. So for the transmission detector on ENGIN-X where (Dl/l0.001), we see that for y ¼ 451 the diffracted signal comes from a cone with a width of approximately 4 min of arc. This justifies the use of a line integral over the pole figure in the calculation of the texture correction for the total cross-section.
2. Discussion
3. Conclusion
A quantitive texture analysis from neutron transmission experiments requires the calculation of the effect of preferred orientation on the neutron total cross-section. Along this line, Vogel has developed a model to account for fibre textures in phase analysis by TOF neutron transmission [9]. The wavelength dependence of the elastic coherent total cross-section sel coh for random polycrystalline materials was first measured by Fermi and collaborators [10]. Neutrons of wavelength l can be diffracted by any lattice planes having 2dhkl4l:
The thermal neutron transmission of manmade and naturally occuring materials departs strongly from the behaviour observed for specimens composed of randomly oriented crystallites. Such differences are easily resolved by TOF experiments. A qualitative analysis of the transmitted TOF spectra can give basic information about the microstructure of unknown samples. When a pixellated array of TOF detectors is used, it provides a fast tool for the non-destructive investigation of macroscopic spatial variations in the microstructure of bulk specimens. Finally, it is in principle possible to define the orientation distribution function of crystallites from a quantitative analysis of the transmitted spectra recorded at several orientations.
selcoh ðlÞ ¼
2d hkl ol l2 X jF hkl j2 d hkl , 4V 0 hkl
(1)
where V0 is the volume of the unit cell and Fhkl is the structure factor. Each term of the series is represented by a Bragg edge in the total cross-section. However, as the present experiments have shown, the total cross-section of textured materials departs considerably from the isotropic case. The value of sel coh along the sample direction t can be directly calculated from the pole figures Phkl(a, b) around t. To do so, we note that for the wavelength l we need to count all the crystallites making the angle bhkl with the incident beam. This corresponds exactly to the integral of the pole figure Phkl(a, b) around a ring of radius bhkl: Z 2p l Rðl; d hkl Þ ¼ Phkl a; p=2 arcsin da. (2) 2d hkl 0
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
K. Meggers, et al., Mater. Sci. Eng. A 188 (1994) 301. S. Vogel, et al., Mater. Sci. Eng. A 333 (2002) 1. A. Steuwer, et al., J. Appl. Phys. 97 (2005) 074903. J.A. Dann, et al., Physica B (2004) e511. J.R. Santisteban, et al., Nucl. Instr. Meth. A 481 (2002) 765. S.C. Chang, et al., Scr. Mater. 39 (1998) 583. V. Buchwald, Handbook of Iron Meteorites, University of California Press, CA, USA, 1976. J.R. Santisteban, J. Appl. Crystallogr. 38 (2005) 934. S. Vogel, Ph.D. Thesis, Kiel University, 2000. E. Fermi, et al., Phys. Rev. 71 (1947) 589. U.F. Kocks, C.N. Tome, H.R. Wenk, Texture and Anisotropy, Cambridge University Press, Cambridge, 1998.