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Bragg diffraction optics for energy-dispersive neutron transmission diffraction
Physica B 283 (2000) 403}405
Bragg di!raction optics for energy-dispersive neutron transmission di!raction P. Mikula , M. VraH na , V. Wagner * Nuclear Physics Institute, 25068 R[ ez\ near Prague, Czech Republic Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
Abstract A new simple method to measure strains in a polycrystalline sample is reported. It is based on the shift of the Bragg di!raction edge, which can be observed in the wavelength-angle correlation of the transmitted neutrons by focusing techniques. 2000 Elsevier Science B.V. All rights reserved. Keywords: Energy-dispersive neutron transmission di!raction; Strain; Focusing
1. Introduction The energy-dispersive neutron transmission di!raction (EDNTD) method is based on the measurement of the decrease of beam intensity I(j) transmitted through a sample near the Bragg cuto!. A Bragg edge is observed when passing through the limit j"2d , (d is the lattice spacing), below FIJ FIJ which particular re#ection planes (hkl) begin to scatter neutrons. During the last few years we tested several modi"cations of the high-resolution EDNTD } based on Bragg di!raction optics, which were developed with the collaboration between NPI Rez and PTB Braunschweig [1}3]. All previous modi"cations used the dispersive setting of a double crystal diffractometer, where cylindrically bent perfect Sicrystals were used for a selection and analysis of * Corresponding author. Tel.: #49-531-5927400; fax: #49531-5927505. E-mail address: [email protected] (V. Wagner)
a quasi-monochromatic beam. The most e$cient modi"cation [3] employed a one-dimensional high-resolution position-sensitive detector (1dPSD) for data acquisition and has been routinely used in PTB and NPI for strain investigations as a technique complementary to the Bragg-di!raction-angle analysis (BDAA) method [4}7]. 2. Principal set-up The simplest EDNTD arrangement (see Fig. 1) exploiting Bragg di!raction optics is typically based on the following ideas [5,7]: a. Focusing in real space: The monochromator of horizontal bending radius R selects a mono+ chromatic beam and focuses the neutrons onto a narrow slit. The focal length of the bent crystal monochromator, generally cut asymmetrically at an angle W with respect to the re#ecting planes, equals f "R /2 sin(h !W). + + +
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 3 5 6 - 2
(1)
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P. Mikula et al. / Physica B 283 (2000) 403}405
Fig. 1. Schematic sketch of the simplest focusing set-up for energy dispersive neutron transmission di!ractometry (EDNTD).
b. Correlation angle-wavelength: There is a strong correlation h}j in the converging beam passing through the slit which is given by j"j [1!*h cot h (1!¸ /2f )], (2) + +1 + which can be easily manipulated by changing R + and/or the monochromator}sample distance ¸ . +1 No Soller collimators are used. c. Simultaneous data acquisition by a positionsensitive detector PSD at distance ¸ from the 1" sample, which measures I(*h) via *h"x/¸ . 1" The "nite thickness D of the monochromator + and the slit width = relax the strict correlation (2) and induce a blurring of the position x of the Bragg edge on the PSD by *x "= for D '=/cos h , (3a) + + + *x "=(1#2¸ /f ) for =(*h f /2, (3b) 5 1" + + respectively. In evaluating *x , only the curvature + of the lattice planes of the cylindrically bent crystal was considered. The parameters *x and *x , + 5 together with the spatial resolution of the detector *x , determine the instrumental resolution. " 3. Experimental results and discussion The test experiment was carried out on the diffractometer POLDI of PTB installed at the thermal neutron guide of the 5 MW research-reactor FRG1 in GKSS Geesthacht. As a monochromator, we
Fig. 2. Neutron spectrum registered by PSD (taken in the vicinity of j "0.153 nm). The empty slit spectrum (open symbols) show the distribution of neutrons in the neutron guide. The sample spectrum (full symbol) shows the edge e!ect of Bragg di!raction for the channel numbers lower than 300. Slit width ="2 mm.
used a cylindrically bent Si(1 1 1) crystal slab of the dimensions of 1;30;200 mm (thickness; width;length) at a take-o! angle of 2h "28.323 + (j"0.1534 nm). Owing to a remote control of the bending device the optimum focusing conditions could be easily set, practically for any distance ¸ . +1 The EDNTD pro"les of the neutron beam passing through the slit and the polycrystalline samples were scanned by a linear position-sensitive detector ORDELA having a channel width of about 0.35 mm and spatial resolution of about 1 mm. In our test experiment we observed the (321)-Bragg edge of a-Fe using the following parameters: ¸ "1 m, ¸ "1.775 m, R "8.2 m, and +1 1" + 1;20 mm or 2;20 mm slits. Fig. 2 shows two spectra of neutrons passing through the 2;20 mm slit without and with the sample situated behind it. After substraction and normalization of intensities we obtain the amplitude of the Bragg edge. It is clear that the amplitude of the edge corresponding to j"2d depends on the thickness t of FIJ the sample (cf. Fig. 3). However, the most important parameter of the set-up is the resolution dd/d"dj/j, which is mainly determined by the width of the slit = (see formulae (3a) and (3b) in conjunction with Eq. (2)). In our case ¸ "f , dj/j"(1/2)dh cot h . +1 + +
P. Mikula et al. / Physica B 283 (2000) 403}405
Fig. 3. Bragg di!raction edge amplitude of Fe(3 2 1) for di!erent thickness t of the sample. Slit width ="2 mm.
Fig. 4 shows the edge pro"le of plastically deformed ARMCO steel after cold rolling (reduction factor 80%). It demonstrates that the new modi"cation of the EDNTD method can also be used for evaluation of microstrains. The novel EDNTD set-up can be easily adapted to any di!ractometer providing the appropriate wavelength. Only one di!raction axis is needed. Su$ciently high-resolution dd/d } even for evaluation of microstrains in plastically deformed polycrystalline samples [8,9] } is obtained, when both a narrow sample slit and thin monochromator ()1 mm) and a large monochromator take-o! angle are used. Depending on the reactor power, the area of the sample slit can be reduced to less than 10 mm (virtually to less than 1 mm for high #ux neutron sources) and the sample thickness up to 40 mm and reasonable counting times. Finally it should be pointed out that the EDNTD techniques are limited to measurements of only one strain component parallel to the axis of the incident monochromatized beam, a feature it has in common with similar TOF techniques used at pulsed neutron sources [10], which, however, observe more than one lattice plane.
Acknowledgements This work has been supported in part by the Grant Agency of the Czech Republic under con-
405
Fig. 4. Bragg di!raction edge of plastically deformed ARMCO steel (dh "0.57 mrad) and, for comparison, of an 8 mm $5&+ thick standard sample (dh "0.72 mrad). A Gaussian $5&+ cumulative function was "tted to edge pro"les. The inset displaying the derivative of the amplitude shows the broadening of the edge more clearly. Slit width ="1 mm.
tract No. 202/97/K038 and the TMR-Network ERB FMR XCT 96-0057.
References [1] M. VraH na, P. Mikula, P. LukaH s\ , J. S[ aroun, P. Strunz, Acta Physica Hungarica 75 (1994) 305. [2] P. Mikula, M. VraH na, P. LukaH s\ , J. S[ aroun, P. Strunz, V. Wagner, B. Alefeld, Physica B 213&214 (1995) 845. [3] V. Wagner, Z. Kour\ il, P. LukaH s\ , P. Mikula, M. VraH na, SPIE 2867 (1997) 168. [4] P. Mikula, P. LukaH s\ , M. VraH na, P. Klimanek, T. Kschidock, K. Macek, J. Janovec, J.C. Osborn, G.M. Swallowe, J. Physique IV, Colloque C7 3 (1993) 2183. [5] M. VraH na, P. LukaH s\ , P. Mikula, J. Kulda, Nucl. and Instr. Meth. A 338 (1994) 125. [6] P. Mikula, M. VraH na, P. LukaH s\ , J. S[ aroun, P. Strunz, V. Wagner, B. Alefeld, Physica B 213&214 (1995) 845. [7] P. Mikula, M. VraH na, P. LukaH s, J. S[ aroun, P. Strunz, H.J. Ullrich, V. Wagner, in: T. Ericsson, M. OdeH n, A. Andersson (Eds.), Proceedings of the Fifth International Conference on Residual Stresses, LinkoK ping (S), Vol. 2, pp. 721}725. [8] P. Strunz, P. LukaH s\ , P. Mikula, V. Wagner, Z. Kour\ il, M. VraH na, in: T. Ericsson, M. OdeH n, A. Andersson (Eds.), Proceedings of the Fifth International Conference on Residual Stresses, LinkoK ping (S), Vol. 2, pp. 688}693. [9] P. LukaH s\ , Z. Kour\ il, P. Strunz, P. Mikula, M. VraH na, V. Wagner, Physica B 234}236 (1997) 956. [10] H.G. Priesmeyer, J. Larsen, K. Meggers, J. Neutron Res. 2 (1994) 31.
Bragg di!raction optics for energy-dispersive neutron transmission di!raction P. Mikula , M. VraH na , V. Wagner * Nuclear Physics Institute, 25068 R[ ez\ near Prague, Czech Republic Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
Abstract A new simple method to measure strains in a polycrystalline sample is reported. It is based on the shift of the Bragg di!raction edge, which can be observed in the wavelength-angle correlation of the transmitted neutrons by focusing techniques. 2000 Elsevier Science B.V. All rights reserved. Keywords: Energy-dispersive neutron transmission di!raction; Strain; Focusing
1. Introduction The energy-dispersive neutron transmission di!raction (EDNTD) method is based on the measurement of the decrease of beam intensity I(j) transmitted through a sample near the Bragg cuto!. A Bragg edge is observed when passing through the limit j"2d , (d is the lattice spacing), below FIJ FIJ which particular re#ection planes (hkl) begin to scatter neutrons. During the last few years we tested several modi"cations of the high-resolution EDNTD } based on Bragg di!raction optics, which were developed with the collaboration between NPI Rez and PTB Braunschweig [1}3]. All previous modi"cations used the dispersive setting of a double crystal diffractometer, where cylindrically bent perfect Sicrystals were used for a selection and analysis of * Corresponding author. Tel.: #49-531-5927400; fax: #49531-5927505. E-mail address: [email protected] (V. Wagner)
a quasi-monochromatic beam. The most e$cient modi"cation [3] employed a one-dimensional high-resolution position-sensitive detector (1dPSD) for data acquisition and has been routinely used in PTB and NPI for strain investigations as a technique complementary to the Bragg-di!raction-angle analysis (BDAA) method [4}7]. 2. Principal set-up The simplest EDNTD arrangement (see Fig. 1) exploiting Bragg di!raction optics is typically based on the following ideas [5,7]: a. Focusing in real space: The monochromator of horizontal bending radius R selects a mono+ chromatic beam and focuses the neutrons onto a narrow slit. The focal length of the bent crystal monochromator, generally cut asymmetrically at an angle W with respect to the re#ecting planes, equals f "R /2 sin(h !W). + + +
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 3 5 6 - 2
(1)
404
P. Mikula et al. / Physica B 283 (2000) 403}405
Fig. 1. Schematic sketch of the simplest focusing set-up for energy dispersive neutron transmission di!ractometry (EDNTD).
b. Correlation angle-wavelength: There is a strong correlation h}j in the converging beam passing through the slit which is given by j"j [1!*h cot h (1!¸ /2f )], (2) + +1 + which can be easily manipulated by changing R + and/or the monochromator}sample distance ¸ . +1 No Soller collimators are used. c. Simultaneous data acquisition by a positionsensitive detector PSD at distance ¸ from the 1" sample, which measures I(*h) via *h"x/¸ . 1" The "nite thickness D of the monochromator + and the slit width = relax the strict correlation (2) and induce a blurring of the position x of the Bragg edge on the PSD by *x "= for D '=/cos h , (3a) + + + *x "=(1#2¸ /f ) for =(*h f /2, (3b) 5 1" + + respectively. In evaluating *x , only the curvature + of the lattice planes of the cylindrically bent crystal was considered. The parameters *x and *x , + 5 together with the spatial resolution of the detector *x , determine the instrumental resolution. " 3. Experimental results and discussion The test experiment was carried out on the diffractometer POLDI of PTB installed at the thermal neutron guide of the 5 MW research-reactor FRG1 in GKSS Geesthacht. As a monochromator, we
Fig. 2. Neutron spectrum registered by PSD (taken in the vicinity of j "0.153 nm). The empty slit spectrum (open symbols) show the distribution of neutrons in the neutron guide. The sample spectrum (full symbol) shows the edge e!ect of Bragg di!raction for the channel numbers lower than 300. Slit width ="2 mm.
used a cylindrically bent Si(1 1 1) crystal slab of the dimensions of 1;30;200 mm (thickness; width;length) at a take-o! angle of 2h "28.323 + (j"0.1534 nm). Owing to a remote control of the bending device the optimum focusing conditions could be easily set, practically for any distance ¸ . +1 The EDNTD pro"les of the neutron beam passing through the slit and the polycrystalline samples were scanned by a linear position-sensitive detector ORDELA having a channel width of about 0.35 mm and spatial resolution of about 1 mm. In our test experiment we observed the (321)-Bragg edge of a-Fe using the following parameters: ¸ "1 m, ¸ "1.775 m, R "8.2 m, and +1 1" + 1;20 mm or 2;20 mm slits. Fig. 2 shows two spectra of neutrons passing through the 2;20 mm slit without and with the sample situated behind it. After substraction and normalization of intensities we obtain the amplitude of the Bragg edge. It is clear that the amplitude of the edge corresponding to j"2d depends on the thickness t of FIJ the sample (cf. Fig. 3). However, the most important parameter of the set-up is the resolution dd/d"dj/j, which is mainly determined by the width of the slit = (see formulae (3a) and (3b) in conjunction with Eq. (2)). In our case ¸ "f , dj/j"(1/2)dh cot h . +1 + +
P. Mikula et al. / Physica B 283 (2000) 403}405
Fig. 3. Bragg di!raction edge amplitude of Fe(3 2 1) for di!erent thickness t of the sample. Slit width ="2 mm.
Fig. 4 shows the edge pro"le of plastically deformed ARMCO steel after cold rolling (reduction factor 80%). It demonstrates that the new modi"cation of the EDNTD method can also be used for evaluation of microstrains. The novel EDNTD set-up can be easily adapted to any di!ractometer providing the appropriate wavelength. Only one di!raction axis is needed. Su$ciently high-resolution dd/d } even for evaluation of microstrains in plastically deformed polycrystalline samples [8,9] } is obtained, when both a narrow sample slit and thin monochromator ()1 mm) and a large monochromator take-o! angle are used. Depending on the reactor power, the area of the sample slit can be reduced to less than 10 mm (virtually to less than 1 mm for high #ux neutron sources) and the sample thickness up to 40 mm and reasonable counting times. Finally it should be pointed out that the EDNTD techniques are limited to measurements of only one strain component parallel to the axis of the incident monochromatized beam, a feature it has in common with similar TOF techniques used at pulsed neutron sources [10], which, however, observe more than one lattice plane.
Acknowledgements This work has been supported in part by the Grant Agency of the Czech Republic under con-
405
Fig. 4. Bragg di!raction edge of plastically deformed ARMCO steel (dh "0.57 mrad) and, for comparison, of an 8 mm $5&+ thick standard sample (dh "0.72 mrad). A Gaussian $5&+ cumulative function was "tted to edge pro"les. The inset displaying the derivative of the amplitude shows the broadening of the edge more clearly. Slit width ="1 mm.
tract No. 202/97/K038 and the TMR-Network ERB FMR XCT 96-0057.
References [1] M. VraH na, P. Mikula, P. LukaH s\ , J. S[ aroun, P. Strunz, Acta Physica Hungarica 75 (1994) 305. [2] P. Mikula, M. VraH na, P. LukaH s\ , J. S[ aroun, P. Strunz, V. Wagner, B. Alefeld, Physica B 213&214 (1995) 845. [3] V. Wagner, Z. Kour\ il, P. LukaH s\ , P. Mikula, M. VraH na, SPIE 2867 (1997) 168. [4] P. Mikula, P. LukaH s\ , M. VraH na, P. Klimanek, T. Kschidock, K. Macek, J. Janovec, J.C. Osborn, G.M. Swallowe, J. Physique IV, Colloque C7 3 (1993) 2183. [5] M. VraH na, P. LukaH s\ , P. Mikula, J. Kulda, Nucl. and Instr. Meth. A 338 (1994) 125. [6] P. Mikula, M. VraH na, P. LukaH s\ , J. S[ aroun, P. Strunz, V. Wagner, B. Alefeld, Physica B 213&214 (1995) 845. [7] P. Mikula, M. VraH na, P. LukaH s, J. S[ aroun, P. Strunz, H.J. Ullrich, V. Wagner, in: T. Ericsson, M. OdeH n, A. Andersson (Eds.), Proceedings of the Fifth International Conference on Residual Stresses, LinkoK ping (S), Vol. 2, pp. 721}725. [8] P. Strunz, P. LukaH s\ , P. Mikula, V. Wagner, Z. Kour\ il, M. VraH na, in: T. Ericsson, M. OdeH n, A. Andersson (Eds.), Proceedings of the Fifth International Conference on Residual Stresses, LinkoK ping (S), Vol. 2, pp. 688}693. [9] P. LukaH s\ , Z. Kour\ il, P. Strunz, P. Mikula, M. VraH na, V. Wagner, Physica B 234}236 (1997) 956. [10] H.G. Priesmeyer, J. Larsen, K. Meggers, J. Neutron Res. 2 (1994) 31.