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Neutron depolarisation imaging: Stress measurements by magnetostriction effects in Ni foils
Physica B 406 (2011) 2412–2414
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Neutron depolarisation imaging: Stress measurements by magnetostriction effects in Ni foils Michael Schulz a,b,, Philipp Schmakat b, Christian Franz b, Andreas Neubauer b, Elbio Calzada a,b, ¨ b, Christian Pfleiderer b Burkhard Schillinger a,b, Peter Boni a b
Forschungsneutronenquelle FRM II, Technische Universit¨ at M¨ unchen, Lichtenbergstrasse 1, 85748 Garching, Germany Physik Department E21, Technische Universit¨ at M¨ unchen, James-Franck-Strasse, 85748 Garching, Germany
a r t i c l e i n f o
a b s t r a c t
Available online 5 November 2010
In this article we present first proof-of-principle neutron depolarization imaging measurements on Ni foils under mechanical stress. The magnetostrictive effect in Ni leads to a reorientation of the magnetic domains in the material depending on the applied force. This in turn leads to a change of the depolarization a neutron beam suffers from transmission of the sample. We propose to use this method as a new technique for the spatially resolved measurement of mechanical stress. & 2010 Elsevier B.V. All rights reserved.
Keywords: Radiography Polarized neutrons Magnetostriction
1. Introduction Imaging with polarized neutrons, is a new method which is increasingly being recognized as a powerful tool for the study of magnetic effects. The precession of the neutron spin in a magnetic field can i.e. be used to determine the field integral along the neutron flight path and thus to map out magnetic field arrangements [1]. Moreover, the method allows to probe internal magnetic fields in various materials which may for instance arise from superconducting vortices [1] or in magnetized thin ferromagnetic films [2]. Neutron depolarization imaging (NDI), which is based on the measurement of the depolarization of a neutron beam after transmission of unmagnetized samples has been used for the characterization and investigation of inhomogeneous ferromagnets [3,4]. Here we will present first proof-of-principle measurements of a further interesting application of neutron depolarization imaging. The magnetostriction effect leads to a change of the orientation of the domains within a sample, if a uniaxial force is applied on the sample. As a consequence, a change of the depolarization which a neutron beam suffers after transmission of the sample is observed. In our experiments we used this effect on high purity Ni foils as a method for the spatially resolved measurement of the mechanical stress in the material. Ni has a negative magnetostrictive constant of ls 37 106 [5], which results from averaging over the anisotropic values of 45:9 106 along the [1 0 0] axis and 24:3 106 along the [1 1 1] axis for a polycrystalline sample
Corresponding author at: Forschungsneutronenquelle FRM II, Technische ¨ Munchen, ¨ Universitat Lichtenbergstrasse 1, 85747 Garching, Germany. E-mail address: [email protected] (M. Schulz).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.10.079
[6]. Non-spatially resolved 3D neutron depolarization measurements of the magnetostrictive effect in Ni foils have already shown the possibility to use this effect as a measure of the stress applied to the foil [7]. In the future this technique might be used as a spatially resolved stress gauge.
2. Experimental techniques Our experiments were performed at the imaging beam line ANTARES at FRM II, Munich with a one dimensional polarization analysis setup shown in Fig. 1. The setup consists of a collimator (C), from which the neutron beam emerges and is monochromatized by a double crystal graphite monochromator (M) [8] to a wavelength ˚ After the monochromator the neutrons travel along an of 3.2 A. evacuated flight tube (FP) of approximately 12 m length to the sample area, where a 3He polarizer (P) and analyzer (A) were installed before and after the sample (S). The advantage of using 3 He polarizers is that the beam geometry is not altered by the polarizer and thus a good spatial resolution is achieved. For a detailed discussion of the different polarizing options for neutron imaging we refer to [3]. Additionally, a precession coil type spin flipper (F) was installed before the sample for selection of the desired polarization direction. As a detector (D) we used a thermoelectrically cooled 2048 2048 pixel CCD camera, which records the image of a LiF:ZnS scintillator with a thickness of 200 mm. The size of the polarized beam at the sample position was approximately 100 100 mm2 and the pixel size of the detector was 74 mm. High purity Ni foils (99+ %) with a thickness of 127 mm were cut to a concave shape as shown in Fig. 2 (right hand side) with a maximal width of 30 mm and a minimal width of 10 mm. After
M. Schulz et al. / Physica B 406 (2011) 2412–2414
cutting, the foils were annealed in vacuum at 900 1C for 8 h to remove any remaining strain from the samples and then mounted in a frame, which was fixed at the top end, while the bottom end could be loaded with weights up to 25 kg resulting in a maximum stress of s 200 MPa. For the experiment, the foil was placed in the polarized neutron beam between the 3He polarizer and analyzer of the setup shown above with the direction of the stress applied by the weights being parallel to the beam polarization. Spatially resolved measurements of the beam polarization after transmission of the Ni foils were performed with three different loads from 5 to 25 kg. A loading with 30 kg leads to the destruction of the sample, which is equivalent to an ultimate tensile strength of the material of 240 MPa.
3. Results and discussion Five spin-up and spin-down images with an exposure time of 60 s each were acquired per applied load, from which the transmitted beam polarization was calculated. The beam polarization after transmission of the foil is plotted in the left panel of Fig. 2 along the yellow arrow shown in the right image. However, due to the strong depolarization of the beam by the Ni foil ðP 0Þ and the low neutron flux which results from using a monochromatic beam, the statistical error in these measurements is very large. To reduce the statistical error, the polarization was averaged over the horizontal extension of the arrow, as we expected the stress to be relatively constant along the x-direction. For better visibility, the red and blue curves were shifted by a value
Fig. 1. Experimental setup used for the experiments described in this article. The components include a collimator (C), double crystal monochromator (M), flight path (FP), polarizer (P), spin flipper (F), sample (S), polarization analyzer (A) and a CCD detector (D).
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of 0.02 with respect to each other along the y-axis as indicated by the dashed lines. It can be seen that the beam polarization increases with decreasing sample width and reaches its maximum at x 28 mm. The asymmetric shape of the curve might result from the clamps used to hold the sample which were mounted at different positions at the upper and lower end of the sample at y 10 mm and y 60 mm. The height of the peak in the beam polarization, which is located at the position where the sample has its smallest width (marked by the dashed green lines in Fig. 2) is plotted in Fig. 3 vs. the load. Even though the statistical errors in these measurements are very high, it is still visible that the peak height increases with increasing stress. The beam polarization increases due to the preferred alignment of the domains in the sample parallel to the direction of the applied mechanical stress and thus also parallel to the polarization of the beam. In general, the beam polarization after transmission of the sample also depends on the average domain size and the sample thickness, which were both assumed to be constant for these experiments. The latter assumption is justifiable due to the relatively small deformation of the sample by the applied stress.
Fig. 3. Beam polarization after transmission of the region where the sample has its smallest width as indicated by the green dashed line in Fig. 2. The transmitted beam polarization increases with increasing stress due to the preferred orientation of the domains in parallel to the direction of the incoming beam polarization.
Fig. 2. Beam polarization after transmission of a Ni foil along the line shown in the image on the right hand side (from top to bottom). The foil was loaded with different weights to modify the mechanical stress. Increasing stress leads to a reorientation of the domains and to increasing beam polarization. For better visibility, the curves are shifted by a value of 0.02 along the y-axis as indicated by the red and blue baselines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2414
M. Schulz et al. / Physica B 406 (2011) 2412–2414
To distinguish a change in the domain size from the formation of magnetic texture, a 3D depolarization analysis would be required which was not feasible with the current setup. A quantitative, spatially resolved evaluation of the mechanical stress in the foil from the presented experiment was not possible due to the large errors in the measurements. These errors could, however, be decreased in future measurements by acquiring more images and also by using a polychromatic beam in combination with an adiabatic fast passage (AFP) type spin flipper integrated in the 3He polarizer [9] giving much improved counting statistics.
4. Conclusion and outlook These proof-of-principle measurements have shown the possibility to use ferromagnetic foils with a large magnetostrictive constant as stress gauges for the spatially resolved determination of mechanical stress. The sensitivity of the method could be further improved by using foils with a larger magnetostrictive constant, e.g. FeCoV, for which the magnitude of the magnetostrictive constant ls 83:4 106 is approximately twice as high as for Ni [10,6]. Moreover, the use of a polychromatic neutron beam would lead to a large increase in the neutron flux and thus improve the counting statistics. Stress sensors could be built by mounting annealed Ni foils on the surface of a (nonmagnetic) sample and measuring the depolarization of the beam after transmission of the foil as a spatially resolved replacement of standard resistance strain
gauges. More detailed calibration measurements in a dedicated setup would have to be performed to determine the dependence of the beam polarization on the applied stress more accurately. Furthermore, 3D depolarization analysis experiments are planned with a modified setup which will allow to distinguish between changes of the domain size and the introduction of magnetic texture by the applied stress. References [1] N. Kardjilov, I. Manke, M. Strobl, A. Hilger, W. Treimer, M. Meissner, T. Krist, J. Banhart, Nature Physics 4 (5) (2008) 399. [2] F. Piegsa, B. van den Brandt, P. Hautle, J. Kohlbrecher, J. Konter, Physical Review Letters 102 (14) (2009) 145501. ¨ ¨ [3] M. Schulz, P. Boni, C. Franz, A. Neubauer, E. Calzada, M. Muhlbauer, B. Schillinger, C. Pfleiderer, A. Hilger, N. Kardjilov, Comparison of Polarizers for Neutron Radiography, Journal of Physics—Conference Series, in press. [4] M. Schulz, Radiography with polarized neutrons, Ph.D. Thesis, Technische ¨ ¨ Universitat Munchen, 2010 /http://nbn-resolving.de/urn/resolver. pl?urn:nbn:de:bvb:91-diss-20100824-963430-1-2S. [5] G. Matsumoto, M. Kato, A. Tasaki, Journal of the Physical Society of Japan 21 (5) (1966) 882. [6] S. Chikazumi, C. Graham, Physics of Ferromagnetism, Oxford University Press, USA, 1997. ¨ Physik A Hadrons and Nuclei 259 (5) (1973) 391. [7] M. Rekveldt, Zeitschrift fur ¨ E. Calzada, M. Muhlbauer, ¨ [8] M. Schulz, P. Boni, B. Schillinger, Nuclear Instruments and Methods in Physics Research, A 605 (1–2) (2009) 33. [9] E. Babcock, A. Petoukhov, J. Chastagnier, D. Jullien, E. Lelie vre-Berna, K. Andersen, R. Georgii, S. Masalovich, S. Boag, C. Frost, S. Parnell, Physica B: Condensed Matter 397 (1–2) (2007) 172. ¨ [10] M.S. Kumar, P. Boni, Journal of Applied Physics 91 (6) (2002) 3750.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Neutron depolarisation imaging: Stress measurements by magnetostriction effects in Ni foils Michael Schulz a,b,, Philipp Schmakat b, Christian Franz b, Andreas Neubauer b, Elbio Calzada a,b, ¨ b, Christian Pfleiderer b Burkhard Schillinger a,b, Peter Boni a b
Forschungsneutronenquelle FRM II, Technische Universit¨ at M¨ unchen, Lichtenbergstrasse 1, 85748 Garching, Germany Physik Department E21, Technische Universit¨ at M¨ unchen, James-Franck-Strasse, 85748 Garching, Germany
a r t i c l e i n f o
a b s t r a c t
Available online 5 November 2010
In this article we present first proof-of-principle neutron depolarization imaging measurements on Ni foils under mechanical stress. The magnetostrictive effect in Ni leads to a reorientation of the magnetic domains in the material depending on the applied force. This in turn leads to a change of the depolarization a neutron beam suffers from transmission of the sample. We propose to use this method as a new technique for the spatially resolved measurement of mechanical stress. & 2010 Elsevier B.V. All rights reserved.
Keywords: Radiography Polarized neutrons Magnetostriction
1. Introduction Imaging with polarized neutrons, is a new method which is increasingly being recognized as a powerful tool for the study of magnetic effects. The precession of the neutron spin in a magnetic field can i.e. be used to determine the field integral along the neutron flight path and thus to map out magnetic field arrangements [1]. Moreover, the method allows to probe internal magnetic fields in various materials which may for instance arise from superconducting vortices [1] or in magnetized thin ferromagnetic films [2]. Neutron depolarization imaging (NDI), which is based on the measurement of the depolarization of a neutron beam after transmission of unmagnetized samples has been used for the characterization and investigation of inhomogeneous ferromagnets [3,4]. Here we will present first proof-of-principle measurements of a further interesting application of neutron depolarization imaging. The magnetostriction effect leads to a change of the orientation of the domains within a sample, if a uniaxial force is applied on the sample. As a consequence, a change of the depolarization which a neutron beam suffers after transmission of the sample is observed. In our experiments we used this effect on high purity Ni foils as a method for the spatially resolved measurement of the mechanical stress in the material. Ni has a negative magnetostrictive constant of ls 37 106 [5], which results from averaging over the anisotropic values of 45:9 106 along the [1 0 0] axis and 24:3 106 along the [1 1 1] axis for a polycrystalline sample
Corresponding author at: Forschungsneutronenquelle FRM II, Technische ¨ Munchen, ¨ Universitat Lichtenbergstrasse 1, 85747 Garching, Germany. E-mail address: [email protected] (M. Schulz).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.10.079
[6]. Non-spatially resolved 3D neutron depolarization measurements of the magnetostrictive effect in Ni foils have already shown the possibility to use this effect as a measure of the stress applied to the foil [7]. In the future this technique might be used as a spatially resolved stress gauge.
2. Experimental techniques Our experiments were performed at the imaging beam line ANTARES at FRM II, Munich with a one dimensional polarization analysis setup shown in Fig. 1. The setup consists of a collimator (C), from which the neutron beam emerges and is monochromatized by a double crystal graphite monochromator (M) [8] to a wavelength ˚ After the monochromator the neutrons travel along an of 3.2 A. evacuated flight tube (FP) of approximately 12 m length to the sample area, where a 3He polarizer (P) and analyzer (A) were installed before and after the sample (S). The advantage of using 3 He polarizers is that the beam geometry is not altered by the polarizer and thus a good spatial resolution is achieved. For a detailed discussion of the different polarizing options for neutron imaging we refer to [3]. Additionally, a precession coil type spin flipper (F) was installed before the sample for selection of the desired polarization direction. As a detector (D) we used a thermoelectrically cooled 2048 2048 pixel CCD camera, which records the image of a LiF:ZnS scintillator with a thickness of 200 mm. The size of the polarized beam at the sample position was approximately 100 100 mm2 and the pixel size of the detector was 74 mm. High purity Ni foils (99+ %) with a thickness of 127 mm were cut to a concave shape as shown in Fig. 2 (right hand side) with a maximal width of 30 mm and a minimal width of 10 mm. After
M. Schulz et al. / Physica B 406 (2011) 2412–2414
cutting, the foils were annealed in vacuum at 900 1C for 8 h to remove any remaining strain from the samples and then mounted in a frame, which was fixed at the top end, while the bottom end could be loaded with weights up to 25 kg resulting in a maximum stress of s 200 MPa. For the experiment, the foil was placed in the polarized neutron beam between the 3He polarizer and analyzer of the setup shown above with the direction of the stress applied by the weights being parallel to the beam polarization. Spatially resolved measurements of the beam polarization after transmission of the Ni foils were performed with three different loads from 5 to 25 kg. A loading with 30 kg leads to the destruction of the sample, which is equivalent to an ultimate tensile strength of the material of 240 MPa.
3. Results and discussion Five spin-up and spin-down images with an exposure time of 60 s each were acquired per applied load, from which the transmitted beam polarization was calculated. The beam polarization after transmission of the foil is plotted in the left panel of Fig. 2 along the yellow arrow shown in the right image. However, due to the strong depolarization of the beam by the Ni foil ðP 0Þ and the low neutron flux which results from using a monochromatic beam, the statistical error in these measurements is very large. To reduce the statistical error, the polarization was averaged over the horizontal extension of the arrow, as we expected the stress to be relatively constant along the x-direction. For better visibility, the red and blue curves were shifted by a value
Fig. 1. Experimental setup used for the experiments described in this article. The components include a collimator (C), double crystal monochromator (M), flight path (FP), polarizer (P), spin flipper (F), sample (S), polarization analyzer (A) and a CCD detector (D).
2413
of 0.02 with respect to each other along the y-axis as indicated by the dashed lines. It can be seen that the beam polarization increases with decreasing sample width and reaches its maximum at x 28 mm. The asymmetric shape of the curve might result from the clamps used to hold the sample which were mounted at different positions at the upper and lower end of the sample at y 10 mm and y 60 mm. The height of the peak in the beam polarization, which is located at the position where the sample has its smallest width (marked by the dashed green lines in Fig. 2) is plotted in Fig. 3 vs. the load. Even though the statistical errors in these measurements are very high, it is still visible that the peak height increases with increasing stress. The beam polarization increases due to the preferred alignment of the domains in the sample parallel to the direction of the applied mechanical stress and thus also parallel to the polarization of the beam. In general, the beam polarization after transmission of the sample also depends on the average domain size and the sample thickness, which were both assumed to be constant for these experiments. The latter assumption is justifiable due to the relatively small deformation of the sample by the applied stress.
Fig. 3. Beam polarization after transmission of the region where the sample has its smallest width as indicated by the green dashed line in Fig. 2. The transmitted beam polarization increases with increasing stress due to the preferred orientation of the domains in parallel to the direction of the incoming beam polarization.
Fig. 2. Beam polarization after transmission of a Ni foil along the line shown in the image on the right hand side (from top to bottom). The foil was loaded with different weights to modify the mechanical stress. Increasing stress leads to a reorientation of the domains and to increasing beam polarization. For better visibility, the curves are shifted by a value of 0.02 along the y-axis as indicated by the red and blue baselines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2414
M. Schulz et al. / Physica B 406 (2011) 2412–2414
To distinguish a change in the domain size from the formation of magnetic texture, a 3D depolarization analysis would be required which was not feasible with the current setup. A quantitative, spatially resolved evaluation of the mechanical stress in the foil from the presented experiment was not possible due to the large errors in the measurements. These errors could, however, be decreased in future measurements by acquiring more images and also by using a polychromatic beam in combination with an adiabatic fast passage (AFP) type spin flipper integrated in the 3He polarizer [9] giving much improved counting statistics.
4. Conclusion and outlook These proof-of-principle measurements have shown the possibility to use ferromagnetic foils with a large magnetostrictive constant as stress gauges for the spatially resolved determination of mechanical stress. The sensitivity of the method could be further improved by using foils with a larger magnetostrictive constant, e.g. FeCoV, for which the magnitude of the magnetostrictive constant ls 83:4 106 is approximately twice as high as for Ni [10,6]. Moreover, the use of a polychromatic neutron beam would lead to a large increase in the neutron flux and thus improve the counting statistics. Stress sensors could be built by mounting annealed Ni foils on the surface of a (nonmagnetic) sample and measuring the depolarization of the beam after transmission of the foil as a spatially resolved replacement of standard resistance strain
gauges. More detailed calibration measurements in a dedicated setup would have to be performed to determine the dependence of the beam polarization on the applied stress more accurately. Furthermore, 3D depolarization analysis experiments are planned with a modified setup which will allow to distinguish between changes of the domain size and the introduction of magnetic texture by the applied stress. References [1] N. Kardjilov, I. Manke, M. Strobl, A. Hilger, W. Treimer, M. Meissner, T. Krist, J. Banhart, Nature Physics 4 (5) (2008) 399. [2] F. Piegsa, B. van den Brandt, P. Hautle, J. Kohlbrecher, J. Konter, Physical Review Letters 102 (14) (2009) 145501. ¨ ¨ [3] M. Schulz, P. Boni, C. Franz, A. Neubauer, E. Calzada, M. Muhlbauer, B. Schillinger, C. Pfleiderer, A. Hilger, N. Kardjilov, Comparison of Polarizers for Neutron Radiography, Journal of Physics—Conference Series, in press. [4] M. Schulz, Radiography with polarized neutrons, Ph.D. Thesis, Technische ¨ ¨ Universitat Munchen, 2010 /http://nbn-resolving.de/urn/resolver. pl?urn:nbn:de:bvb:91-diss-20100824-963430-1-2S. [5] G. Matsumoto, M. Kato, A. Tasaki, Journal of the Physical Society of Japan 21 (5) (1966) 882. [6] S. Chikazumi, C. Graham, Physics of Ferromagnetism, Oxford University Press, USA, 1997. ¨ Physik A Hadrons and Nuclei 259 (5) (1973) 391. [7] M. Rekveldt, Zeitschrift fur ¨ E. Calzada, M. Muhlbauer, ¨ [8] M. Schulz, P. Boni, B. Schillinger, Nuclear Instruments and Methods in Physics Research, A 605 (1–2) (2009) 33. [9] E. Babcock, A. Petoukhov, J. Chastagnier, D. Jullien, E. Lelie vre-Berna, K. Andersen, R. Georgii, S. Masalovich, S. Boag, C. Frost, S. Parnell, Physica B: Condensed Matter 397 (1–2) (2007) 172. ¨ [10] M.S. Kumar, P. Boni, Journal of Applied Physics 91 (6) (2002) 3750.