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A high resolution TOF diffractometer and spectrometer
Physica B 276}278 (2000) 116}117
A high resolution TOF di!ractometer and spectrometer F. Demmel *, Ph. Bernhardt , A. Magerl , E. Steichele Universita( t Erlangen-Nu( rnberg, Lehrstuhl fu( r Kristallographie und Strukturphysik, Bismarckstr. 10, D-91054 Erlangen, Germany TU Mu( nchen, Physikdepartment E21, 85747 Garching, Germany
Abstract We propose a combined high-resolution time-of-#ight (TOF) di!ractometer and spectrometer for the new Munich reactor FRM-II. The instrument uses a long #ight path and a fast "rst chopper for the primary spectrometer. The setup for the secondary spectrometer consists of a back scattering detector for the di!ractometer and analyser crystals on an arc around the sample position for the spectrometer. The relative resolution of the di!ractometer will be *d/d+2;10\ and the energy resolution of the spectrometer will be 2 leV with a silicon analyser system in near back scattering geometry. The dynamic range can be shifted with the chopper system by several meV, i.e. it exceeds a crystal back scattering spectrometer by a factor 50. 2000 Elsevier Science B.V. All rights reserved. Keywords: Backscattering; Neutron instruments; Time of #ight
1. Introduction Nearly 30 years ago the backscattering technique was developed at the Forschungsreaktor MuK nchen in Garching [1]. In addition a time of #ight di!ractometer in back scattering geometry with very long #ight path was built up at the same time [2]. For the new Munich reactor FRM-II we propose a combination of both types of instrument, to our knowledge for the "rst time at a reactor source. At pulsed sources it is in common use and others are to be built, e.g. IRIS and OSIRIS at RAL (Didcot) or HERMES at LANSCE (Los Alamos). To get highest resolution without losing intensity in di!ractometry it is wise to use a back scattering geometry. As further advantages of TOF di!ractometry we note, e.g. that entire Debye}Scherrer cones can be detected without degrading the resolution and also complicated sample environments can be used easier. For the spectrometer the main advantage is the wide dynamical range, which is a factor 50 enhanced as compared to a crystal back scattering spectrometer.
* Corresponding author. Fax.: #49-9131-852-2733. E-mail address: [email protected] (F. Demmel)
The instrument house will be built up in the old Atom-Ei at the end of a long guide (¸"80 m) from the cold source. The di!ractometer detectors are arranged in back-scattering geometry in a distance of about 2 m from the sample position for highest resolution, which provides di!raction angles up to 2h"1783. This geometry with nearly the same distances between end of the guide, sample and detector is a type of Bragg}Brentano geometry, which has the advantage that the resolution is in "rst order independent of the sample size. To reduce #ight path uncertainties a scintillation detector will be used. Around a second sample position (1 m position) analyser crystals are positioned on a part of a sphere. On one side silicon crystals (Si111) in 2 m distance are planned, while the other side will receive a crystal system for reduced resolution in a smaller distance, for example Pyrolytic Graphite.
2. Resolution We have calculated analytically the relative resolution of the di!ractometer *d/d (*d is the FWHM, Eq. (1)). Several parameters contribute to the resolution: the length of the pulses *t"10 ls, the path length uncertainty mainly due to the sample thickness *¸"10 mm, the angle contribution, which include the scattering angle
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 2 6 6 - 1
F. Demmel et al. / Physica B 276}278 (2000) 116}117
117
Fig. 1. The relative resolution of the TOF di!ractometer is compared with a high-resolution crystal di!ractometer.
Fig. 2. Energy resolution of the spectrometer for two di!erent analyser crystals.
h"88.63, and the divergence *h"0.0057, the quadratic sum of the in- and outgoing divergence.
great dynamical range of several meV with a resolution of about 2 leV.
*d " d
*¸ *t # #(cot h *h). ¸ t
(1)
Fig. 1 shows the resolution of the TOF di!ractometer compared with a planned high-resolution crystal di!ractometer with a Ge 551 monochromator at a thermal beam tube. Although the resolution values are nearly the same in a small range of d-values the behaviour of the resolution functions is totally di!erent. The TOF di!ractometer has a very smooth function over a wide range of d-values, which is only limited due to the characteristics of the cold source. The energy resolution of the spectrometer is calculated with Eq. (2) using *t"30 ls, *¸"0.03 m, *E "2 E
*t *¸ *q # # #(cot h *h), t ¸ q
(2)
¸"80 m, *q/q+2;10\ with the reciprocal lattice vector q of Si (1 1 1), h"893 and *h"0.02. The expected gradient in d-spacing of the silicon analyser system is due to elastic deformation of the glued wafers. A value of *q/q+1;10\ has been achieved until now at crystal back scattering spectrometers with a very favourable Gaussian line shape [3]. With relaxed parameters and Pyrolytic Graphite crystals the energy resolution can be changed by a factor of 10 in the secondary spectrometer at the same momentum transfer vector. Fig. 2 shows the analytical calculated energy resolution for two di!erent crystal systems and pulse lengths. Remarkable is the
3. Intensity With the parametrized brilliance from the cold source we have calculated the spectral continuous #ux at the sample position to 1.5;10 n/cm s As at j"6 As [4]. For an aluminium powder sample we calculated in the highest resolution mode the count rate for the (1 1 1) peak (j"4.68 As ) using the scattering formula for TOF powder di!ractometry from Buras [5]. The sample area was a square with 20 mm side length and with a thickness of 8 mm. The chosen dynamic range was about 0.1 As , which implies a repetition rate of 500 pulses/s. We expect an integrated count rate of about 3600 n/min in six 20 mm wide detector rings. MC simulations with optimized parameters have shown even higher count rates. For the spectrometer the pulsed #ux at the sample position will be about 2;10 n/cm s at 6 As . This value is calculated for a dynamic range of about 100 leV, 300 pulses/s and a pulse length of *t"30 ls. References [1] [2] [3] [4]
B. Alefeld, Bay. Akad. Wiss. Math.-Nat. Kl. 11 (1967) 109. E. Steichele, P. Arnold, Phys. Lett. A 3 (1973) 165. B. Frick, Physica B 234}236 (1997) 1177. W. Gaubatz, J. Felber, 2. Arbeitstre!en zur Instrumentierung, TUM, 1998. [5] B. Buras, Nukleonika 8 (1963) 259.
A high resolution TOF di!ractometer and spectrometer F. Demmel *, Ph. Bernhardt , A. Magerl , E. Steichele Universita( t Erlangen-Nu( rnberg, Lehrstuhl fu( r Kristallographie und Strukturphysik, Bismarckstr. 10, D-91054 Erlangen, Germany TU Mu( nchen, Physikdepartment E21, 85747 Garching, Germany
Abstract We propose a combined high-resolution time-of-#ight (TOF) di!ractometer and spectrometer for the new Munich reactor FRM-II. The instrument uses a long #ight path and a fast "rst chopper for the primary spectrometer. The setup for the secondary spectrometer consists of a back scattering detector for the di!ractometer and analyser crystals on an arc around the sample position for the spectrometer. The relative resolution of the di!ractometer will be *d/d+2;10\ and the energy resolution of the spectrometer will be 2 leV with a silicon analyser system in near back scattering geometry. The dynamic range can be shifted with the chopper system by several meV, i.e. it exceeds a crystal back scattering spectrometer by a factor 50. 2000 Elsevier Science B.V. All rights reserved. Keywords: Backscattering; Neutron instruments; Time of #ight
1. Introduction Nearly 30 years ago the backscattering technique was developed at the Forschungsreaktor MuK nchen in Garching [1]. In addition a time of #ight di!ractometer in back scattering geometry with very long #ight path was built up at the same time [2]. For the new Munich reactor FRM-II we propose a combination of both types of instrument, to our knowledge for the "rst time at a reactor source. At pulsed sources it is in common use and others are to be built, e.g. IRIS and OSIRIS at RAL (Didcot) or HERMES at LANSCE (Los Alamos). To get highest resolution without losing intensity in di!ractometry it is wise to use a back scattering geometry. As further advantages of TOF di!ractometry we note, e.g. that entire Debye}Scherrer cones can be detected without degrading the resolution and also complicated sample environments can be used easier. For the spectrometer the main advantage is the wide dynamical range, which is a factor 50 enhanced as compared to a crystal back scattering spectrometer.
* Corresponding author. Fax.: #49-9131-852-2733. E-mail address: [email protected] (F. Demmel)
The instrument house will be built up in the old Atom-Ei at the end of a long guide (¸"80 m) from the cold source. The di!ractometer detectors are arranged in back-scattering geometry in a distance of about 2 m from the sample position for highest resolution, which provides di!raction angles up to 2h"1783. This geometry with nearly the same distances between end of the guide, sample and detector is a type of Bragg}Brentano geometry, which has the advantage that the resolution is in "rst order independent of the sample size. To reduce #ight path uncertainties a scintillation detector will be used. Around a second sample position (1 m position) analyser crystals are positioned on a part of a sphere. On one side silicon crystals (Si111) in 2 m distance are planned, while the other side will receive a crystal system for reduced resolution in a smaller distance, for example Pyrolytic Graphite.
2. Resolution We have calculated analytically the relative resolution of the di!ractometer *d/d (*d is the FWHM, Eq. (1)). Several parameters contribute to the resolution: the length of the pulses *t"10 ls, the path length uncertainty mainly due to the sample thickness *¸"10 mm, the angle contribution, which include the scattering angle
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 2 6 6 - 1
F. Demmel et al. / Physica B 276}278 (2000) 116}117
117
Fig. 1. The relative resolution of the TOF di!ractometer is compared with a high-resolution crystal di!ractometer.
Fig. 2. Energy resolution of the spectrometer for two di!erent analyser crystals.
h"88.63, and the divergence *h"0.0057, the quadratic sum of the in- and outgoing divergence.
great dynamical range of several meV with a resolution of about 2 leV.
*d " d
*¸ *t # #(cot h *h). ¸ t
(1)
Fig. 1 shows the resolution of the TOF di!ractometer compared with a planned high-resolution crystal di!ractometer with a Ge 551 monochromator at a thermal beam tube. Although the resolution values are nearly the same in a small range of d-values the behaviour of the resolution functions is totally di!erent. The TOF di!ractometer has a very smooth function over a wide range of d-values, which is only limited due to the characteristics of the cold source. The energy resolution of the spectrometer is calculated with Eq. (2) using *t"30 ls, *¸"0.03 m, *E "2 E
*t *¸ *q # # #(cot h *h), t ¸ q
(2)
¸"80 m, *q/q+2;10\ with the reciprocal lattice vector q of Si (1 1 1), h"893 and *h"0.02. The expected gradient in d-spacing of the silicon analyser system is due to elastic deformation of the glued wafers. A value of *q/q+1;10\ has been achieved until now at crystal back scattering spectrometers with a very favourable Gaussian line shape [3]. With relaxed parameters and Pyrolytic Graphite crystals the energy resolution can be changed by a factor of 10 in the secondary spectrometer at the same momentum transfer vector. Fig. 2 shows the analytical calculated energy resolution for two di!erent crystal systems and pulse lengths. Remarkable is the
3. Intensity With the parametrized brilliance from the cold source we have calculated the spectral continuous #ux at the sample position to 1.5;10 n/cm s As at j"6 As [4]. For an aluminium powder sample we calculated in the highest resolution mode the count rate for the (1 1 1) peak (j"4.68 As ) using the scattering formula for TOF powder di!ractometry from Buras [5]. The sample area was a square with 20 mm side length and with a thickness of 8 mm. The chosen dynamic range was about 0.1 As , which implies a repetition rate of 500 pulses/s. We expect an integrated count rate of about 3600 n/min in six 20 mm wide detector rings. MC simulations with optimized parameters have shown even higher count rates. For the spectrometer the pulsed #ux at the sample position will be about 2;10 n/cm s at 6 As . This value is calculated for a dynamic range of about 100 leV, 300 pulses/s and a pulse length of *t"30 ls. References [1] [2] [3] [4]
B. Alefeld, Bay. Akad. Wiss. Math.-Nat. Kl. 11 (1967) 109. E. Steichele, P. Arnold, Phys. Lett. A 3 (1973) 165. B. Frick, Physica B 234}236 (1997) 1177. W. Gaubatz, J. Felber, 2. Arbeitstre!en zur Instrumentierung, TUM, 1998. [5] B. Buras, Nukleonika 8 (1963) 259.