- Email: [email protected]
EASYREF: Energy analysis system for reflectometers
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405 www.elsevier.com/locate/nima
EASYREF: Energy analysis system for reflectometers Fre´de´ric Ott Laboratoire Le´on Brillouin CEA/CNRS UM12, Centre d’Etudes de Saclay, 91191 Gif sur Yvette Cedex, France Received 2 August 2007; received in revised form 19 October 2007; accepted 25 October 2007 Available online 5 November 2007
Abstract We present a compact device, which can perform the energy analysis of a white neutron beam with an energy resolution of 5–10% for wavelengths l ranging between 0.2 and 2.5 nm. We propose that such a device could be used on neutron reflectometers in order to get rid of the disk chopper or the monochromator. Gains in flux of 1 to 2 orders of magnitude can be foreseen for specular reflectivity measurements. r 2007 Elsevier B.V. All rights reserved. PACS: 70.000 Keywords: Neutron; Energy analysis; Reflectivity; Reflectometry; Optics; Spectrometry
1. Introduction Neutron scattering offers a wealth of techniques to study solid state matter [1]. The flux on neutron spectrometers are, however, not comparable to what is available in synchrotron facilities. One of the limitations in thermal neutron scattering is that it is not possible to build detectors which can resolve the neutron energy. When a thermal neutron is detected, it is fully absorbed and its kinetic energy which is of the order of a few meV is negligible compared to its mass energy. Thus, when spectroscopic information is required, two different techniques can be implemented: (i) either use a diffracting crystal after the sample which analyzes a specific energy [2] or (ii) use a Time-of-Flight (ToF) technique which measures the neutron energy by measuring its travel time between the source and the detector [3]. In both cases, a lot of neutrons are wasted. In the first case, only a single energy can be analyzed at a time. In the second case, on continuous sources, the beam requires to be shaped into pulses by using choppers. This process also wastes a lot of neutrons. In order to improve the use of the neutron beams Tel.: +33 1 69 08 62 21; fax : +33 1 69 08 82 61.
E-mail address: [email protected] 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.10.042
on continuous sources, we propose an optical device which performs the equivalent of an energy analysis on a white neutron beam. Its characteristics make it ideal for specular reflectivity measurements. This idea was already proposed some time ago by C.F. Majkrzak [4].
2. Principle The possibility of illuminating the sample with a white beam and then directly measure the reflectivity at once is appealing since it means that the neutron flux on the sample can be multiplied by a factor 20–100 since no chopper or monochromator is required. Designs using refraction in prisms [5] and magnetic quadrupoles [6] have been proposed (Fig. 1). Both designs have limitations. We propose a new design based on reflective optics. The principle is based on the combination of multi-layer (ML) monochromator mirrors and a Position Sensitive Detector (PSD) (see Fig. 2). Ideally, each monochromator (index i) reflects a wavelength band {lidl/2; li+dl/2}. The diffracted beams are spatially spread on the PSD and the wavelength is directly determined by the position on the detector. The reflectivity is thus measured at once for all wavelengths.
ARTICLE IN PRESS Fre´de´ric Ott / Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405
402
White beam
In a typical neutron reflectivity experiment, the sample has a length of 40 mm; the incidence angle on the sample is of the order of 2.51 and the incident divergence is 0.061 (we consider the case of low resolution experiments). In this case, 200 mm after the sample, the beam width is
High res. detector
Energy analyzer
Spatial spread of the beam as a function of λ
Sample
Fig. 1. Principle of specular reflectivity measurements using an energy analysis device. A full white beam is sent onto a sample. After reflection, the different wavelengths are spatially spread in an energy analyzer. The reflectivity signal is measured at once for all wavelengths on a position sensitive detector.
w ¼ 40 mm sinð2:5o Þ þ 200 mm tanð0:06o Þ ¼ 2 mm: This means that in practical situations we have to analyze beams which have a size of several millimeters in width. 4. Geometrical arrangement of the mirrors
PSD White beam reflected from the sample
yn ¼ ln 4 ðdegree=nmÞ. 2
3
4
monochromators
Fig. 2. The reflected beam is sent on stacked monochromators. The incidence angle on each monochromator varies so that each monochromator diffracts a different wavelength band. The wavelength is directly determined by the position on the detector.
central wavelength (nm)
2.5 2 1.5 1 0.5 0 5
10
15 20 25 monochromator index
30
The angle of incidence is then 101 for l ¼ 2.5 nm and 11 for l ¼ 0.25 nm neutrons. If we want to diffract a wavelength ln with a single mirror, its length is given by Ln ¼ w= tanðyn Þ. For the shortest wavelengths (l ¼ 0.2 nm), the monochromator length is 150 mm (see Fig. 4). The individual lengths of each monochromator are rather large and the mirrors cannot simply be put in line one after the other; otherwise the total length of the device would be close to 2 m. It is possible to consider a more compact arrangement of the mirrors (see Fig. 5). If we assume that the silicon wafers are e ¼ 0.25 mm thick, because of this finite thickness, some space is lost between each consecutive mirror and the mirrors must be slightly shifted one after the other. For each mirror, the lost space is equal to DXi ¼ e/sin yi. The total loss of space is equal to 240 mm when considering the set of 35 mirrors. An extra 150 mm must be added to account for the last
35
Fig. 3. Central wavelengths for a set of 35 monochromators. The wavelengths span from 0.2 to 2.5 nm. The band-pass of each mirror is set at 7%.
3. Requirements for a realistic device The central diffraction wavelengths of the different monochromators should follow the law: ln ¼ (1BW)n lmax where BW is the monochromator bandwidth. On typical ToF reflectometers, the available wavelength band ranges from 0.2 to 2.5 nm. The values of the central wavelength for the different monochromators are plotted on Fig. 3 in the case of a wavelength resolution of 7%. This is the typical wavelength resolution used on the ToF reflectometer EROS at the LLB [7]. In this case, it would be possible to measure 35 points at once in the reflectivity curve, which is sufficient for most applications where a high resolution is not required. This is typically the case of ultra-thin soft matter films.
10 9 8 7 6 5 4 3 2 1 0
150 125 100 75 50
length (mm)
1
tilt angle (°)
0
0
At the moment, it is possible to produce routinely m ¼ 4 high quality monochromators [8]. The incidence angle on an m ¼ 4 monochromator is given by
25 0 0
5
10 15 20 25 monochromator index
30
35
Fig. 4. Tilt angle and corresponding length of the different monochromators to analyze a 2 mm wide beam.
w
Δ Xi Fig. 5. Compact arrangement of the monochromator mirrors taking into account the finite thickness of the silicon substrates.
ARTICLE IN PRESS Fre´de´ric Ott / Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405
mirror length. The proposed device has nevertheless a reasonable size. 5. Modelling of the EASYREF set-up Monte Carlo simulations were performed on this design using SimulSpectro [9]. The monochromators were taken with a realistic reflectivity and a bandwidth of about 7% (Fig. 6a). The detector was set at 1500 mm after the device.
a Reflectivity
1
0 0
0.2
0.4
0.6 Q (nm -1)
0.8
1
1.2
b 2.5
B
Lambda (nm)
2.0
1.5 A 1.0
0.5
200
400
600
403
Fig. 6b represents the neutron position on the detector (X-axis) as a function of the wavelength (Y-axis). The signal of interest is along the region A. A wavelength can be associated to each position of the detector. Fig. 6c shows the raw reflectivity signal as measured for an Ni(10 nm)//Si film illuminated with the spectrum of the guide G3bis at the LLB at an incidence angle of 41. The finite size (2 mm) and divergence (0.061) of the incident beam are taken into account as well as the full reflectivity of the monochromator mirrors, including the total reflection region. In order to retrieve the actual reflectivity of the sample, it is necessary to divide the raw spectrum by the white incident spectrum. Experimentally, this signal is measured by sending the white beam through the device. After that, a wavelength must be attributed to each peak, which in practice can be calibrated by ToF. Fig. 7 compares the measured reflectivity in a classical ToF measurement, a raw integration of the Fig. 6c data and an integration after having filtered the parasitic neutrons from the region B on Fig. 6b which spoil the signal of the short wavelength neutrons. These parasitic neutrons come from the fact that: (i) the monochromators are not perfectly reflecting, (ii) that the overlap between the monochromators bands is not perfect, and (iii) that there are some total reflections below the Si critical edge. In practice, the filtering of these long wavelengths neutrons can be performed with a simple nickel mirror deposited on silicon. Without long wavelength filtering, the signal is spoiled above Q ¼ 3 nm1. And the lowest measurable reflectivity is around 106. If long wavelength neutrons are filtered out, signals down to a few 107 could be measured. Surprisingly, the oscillations in the EASYREF set-up are more pronounced than in the classical ToF measurement. This is due to the fact that in the case of the EASYREF setup, the 7% resolution distribution function is almost square. In the case of the ToF measurement, the resolution was taken as a Gaussian. These results are very satisfactory but they assume that the device described in Fig. 5 is properly built and that the mechanical alignments are good. This is not a trivial task.
Position (mm)
1
c
normal TOF 7%
0.1
1 Intensity (a.u.)
Réflectivity
with EASYREF
0.01
EASYREF + filter
0.001 0.0001 0.00001 0.000001
0 150
250
350
450
550
Position (mm)
Fig. 6. (a) Reflectivity of the monochromator used for the simulations. (b) l vs. position on the detector. (c) Raw reflectivity signal as measured on the detector.
0.0000001 0
1
2
3
4
Q (nm−1) Fig. 7. Reflectivity on an Ni(10 nm)//Si sample. (Solid line) classical ToF measurement, (diamond) after integration of the signal of Fig. 6c, (square) after having filtered out the parasitic long wavelength neutrons.
ARTICLE IN PRESS Fre´de´ric Ott / Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405
404
6. Compact energy analyzer (CEA)
AðlÞð%=mmÞ ¼ 0:1 þ 0:4lðnmÞ.
Fig. 9. Template (gray part) for a compact energy analyzer. The wafers are stacked on the template, which defines the local curvature.
40 Absorption (%)
We propose another set-up, which consists of a stack of ML monochromators deposited on thin Si wafers (Fig. 8). The building bricks are thin silicon wafers (0.25 mm thick) on which an m ¼ 4 monochromator coating has been deposited. Instead of having individual mirrors diffracting a defined wavelength, we propose that the monochromators could be continuously bent. The Si wafers can be stacked so as to obtain a total thickness of several mm (typically 10 wafers). The stack is then bent so that at each position X, the incidence angle on the mirrors corresponds to the angular dependence calculated in Fig. 4. Thus the different wavelengths entering the device are continuously diffracted in different directions starting from long wavelengths to short wavelengths. The advantages of such a device are numerous. It can be considered as a bulk system. The neutrons enter by the side of the device and then simply travel inside bulk silicon. This avoids total reflection at the silicon critical edge. The second advantage is that the system is mechanically simpler to fabricate. A template following the required curvature (Fig. 9) can be machined using electro-erosion and then the silicon stack can be clamped on it. The length of the device is very reasonable (220 mm). The bending is 101 over 220 mm, which corresponds to a curvature radius of 1.3 m. If very high bending radius is required thinner silicon wafers could be used. The design can be scaled to wider beams since it only requires increasing the number of wafers in the stack. The absorption in the device can be easily calculated. The shorter the wavelength, the longer the travel path in silicon. Experimentally, we determined that the absorption in Si is given by
30 20 10 0 0
0.5
1
1.5
2
2.5
λ (nm) Fig. 10. Absorption of the device as a function of the wavelength.
The absorption in the CEA is represented on Fig. 10. The absorption remains limited below 25% for wavelengths above 0.5 nm. It, however, diverges for shorter wavelengths because we are working at constant dl/l resolution which means that the number of wafers increases significantly for shorter wavelengths. If the wavelength resolution would be relaxed to 10% for wavelengths below 0.5 nm, the absorption would remain below 30%. 7. Detection system
w δy
θi
X
δx
Y (mm)
0 −0.5 −1 −1.5 −2 0
80
160 X (mm)
Fig. 8. (a) Generation of the device geometry. (b) Realistic device. In order to catch a beam, which is 2 mm wide, with wavelengths ranging from 0.2 to 2.5 nm, a 220 mm device is required. A total of 40 wafers are required (not full length). On the drawing, the spacing between the mirrors does not appear constant. This is an artefact due to the fact that Y scale is strongly zoomed in.
After passing through the CEA, the neutrons must be measured on a PSD. The detector should be positioned approximately at 1000 mm from the CEA and have a size of 500 mm with a resolution of the order of 3 mm (see Fig. 6c). The detector must be able to handle a very high flux. Such detectors are readily available. The flux on the detector will be rather large, of the order of 1 MHz. A first choice could be a delay line detector. Otherwise, a set of PSD tubes could also be used. 8. Simplified version of the EASYREF set-up As a first step before a full-scale implementation, we propose that a simplified version of the device could be implemented. It follows the idea proposed in Ref. [6] which consists in combining fast ToF and energy analysis. Since most of the technical issues arise from short wavelength neutrons, we propose to use a very fast ToF chopper
ARTICLE IN PRESS Fre´de´ric Ott / Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405
operating at 300 Hz so that all neutrons below 0.4 nm can be analyzed using classical ToF. Such a chopper can be built by simply multiplying the number of holes in the disk (from 1 to 20 typically). However, in order to avoid frame overlap problems (and waste of neutrons), the longer wavelengths would be analyzed using the EASYREF device. However, since only longer wavelengths need to be analyzed, the requirements on the device are relaxed. The longest mirror would be only 70 mm, the total length of monochromator coating would be reduced to 370 mm (making the device rather cheap) and the total length of the device would be 220 mm. This would also significantly reduce the absorption and diffuse scattering issues. Since the chopper is rotating at a high speed (300 Hz compared to 20 Hz on the reflectometer EROS), a typical gain in flux of the order of 15 would be obtained.
405
We should mention that the idea of maximizing the use of the neutron beam is presently being implemented at NIST by combining multiple graphite crystals to select multiple energies in the beam [11]. The CEA could also be used for other purposes. Instead of using it to perform only specular reflectivity, it could be used to perform inelastic measurements. One of the drawbacks of the device is that its angular acceptance is small which limits its general use on other spectrometers. However, as the samples studied by neutron scattering are getting smaller and smaller, the small size of the device could turn into advantages since it would be perfectly suited for studying samples which are smaller than 1 mm. The device could be used to perform inelastic measurements on very small samples almost as efficiently as on regular ToF spectrometers since the chopper system would not be required anymore.
9. Conclusion and perspectives We have presented a device, which could boost the performances of neutron reflectometers for specular reflectivity measurements by a factor of 20–100. For a first practical implementation, we suggest that a simplified hybrid set-up combining ToF and energy analysis could already boost the performances by a factor 15 on most ToF reflectometers. The device would be quite simple and cheap. The EASYREF device is technically simpler to setup and cheaper than other solutions proposed to take benefit of the whole white beam in neutron reflectometry experiments [5,6,10]. The most critical issue is the diffuse scattering from the mirrors, which needs to be assessed experimentally. Note that the device can easily be upgraded into a polarized version.
References [1] G.L. Squires, Introduction to the Theory of Thermal Neutron Scattering, Dover Publications, New York, 1997. [2] G. Shirane, S.M. Shapiro, J.M. Tranquada, Neutron Scattering with a Triple-Axis Spectrometer, Cambridge University Press, Cambridge, 2002. [3] J.R.D. Copley, T.J. Udovic, J. Res. Natl. Inst. Stand. Technol. 98 (1993) 71. [4] C.F. Majkrzak, Physica B 173 (1991) 75. [5] R. Cubitt, et al., Nucl. Instr. and Meth. A 558 (2006) 547. [6] F. Ott, A. de Vismes, Physica B 397 (2007) 153. [7] /www-llb.cea.fr/spectros/pdf/eros-llb.pdfS. [8] /www.swissneutronics.chS. [9] /www-llb.cea.fr/prism/programs/simulspectro/simulspectro2D.htmlS. [10] F. Ott, A. Menelle, Physica B 385–386 (2006) 985. [11] /http://www.ncnr.nist.gov/expansion/CANDOR053007.htmlS.
Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405 www.elsevier.com/locate/nima
EASYREF: Energy analysis system for reflectometers Fre´de´ric Ott Laboratoire Le´on Brillouin CEA/CNRS UM12, Centre d’Etudes de Saclay, 91191 Gif sur Yvette Cedex, France Received 2 August 2007; received in revised form 19 October 2007; accepted 25 October 2007 Available online 5 November 2007
Abstract We present a compact device, which can perform the energy analysis of a white neutron beam with an energy resolution of 5–10% for wavelengths l ranging between 0.2 and 2.5 nm. We propose that such a device could be used on neutron reflectometers in order to get rid of the disk chopper or the monochromator. Gains in flux of 1 to 2 orders of magnitude can be foreseen for specular reflectivity measurements. r 2007 Elsevier B.V. All rights reserved. PACS: 70.000 Keywords: Neutron; Energy analysis; Reflectivity; Reflectometry; Optics; Spectrometry
1. Introduction Neutron scattering offers a wealth of techniques to study solid state matter [1]. The flux on neutron spectrometers are, however, not comparable to what is available in synchrotron facilities. One of the limitations in thermal neutron scattering is that it is not possible to build detectors which can resolve the neutron energy. When a thermal neutron is detected, it is fully absorbed and its kinetic energy which is of the order of a few meV is negligible compared to its mass energy. Thus, when spectroscopic information is required, two different techniques can be implemented: (i) either use a diffracting crystal after the sample which analyzes a specific energy [2] or (ii) use a Time-of-Flight (ToF) technique which measures the neutron energy by measuring its travel time between the source and the detector [3]. In both cases, a lot of neutrons are wasted. In the first case, only a single energy can be analyzed at a time. In the second case, on continuous sources, the beam requires to be shaped into pulses by using choppers. This process also wastes a lot of neutrons. In order to improve the use of the neutron beams Tel.: +33 1 69 08 62 21; fax : +33 1 69 08 82 61.
E-mail address: [email protected] 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.10.042
on continuous sources, we propose an optical device which performs the equivalent of an energy analysis on a white neutron beam. Its characteristics make it ideal for specular reflectivity measurements. This idea was already proposed some time ago by C.F. Majkrzak [4].
2. Principle The possibility of illuminating the sample with a white beam and then directly measure the reflectivity at once is appealing since it means that the neutron flux on the sample can be multiplied by a factor 20–100 since no chopper or monochromator is required. Designs using refraction in prisms [5] and magnetic quadrupoles [6] have been proposed (Fig. 1). Both designs have limitations. We propose a new design based on reflective optics. The principle is based on the combination of multi-layer (ML) monochromator mirrors and a Position Sensitive Detector (PSD) (see Fig. 2). Ideally, each monochromator (index i) reflects a wavelength band {lidl/2; li+dl/2}. The diffracted beams are spatially spread on the PSD and the wavelength is directly determined by the position on the detector. The reflectivity is thus measured at once for all wavelengths.
ARTICLE IN PRESS Fre´de´ric Ott / Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405
402
White beam
In a typical neutron reflectivity experiment, the sample has a length of 40 mm; the incidence angle on the sample is of the order of 2.51 and the incident divergence is 0.061 (we consider the case of low resolution experiments). In this case, 200 mm after the sample, the beam width is
High res. detector
Energy analyzer
Spatial spread of the beam as a function of λ
Sample
Fig. 1. Principle of specular reflectivity measurements using an energy analysis device. A full white beam is sent onto a sample. After reflection, the different wavelengths are spatially spread in an energy analyzer. The reflectivity signal is measured at once for all wavelengths on a position sensitive detector.
w ¼ 40 mm sinð2:5o Þ þ 200 mm tanð0:06o Þ ¼ 2 mm: This means that in practical situations we have to analyze beams which have a size of several millimeters in width. 4. Geometrical arrangement of the mirrors
PSD White beam reflected from the sample
yn ¼ ln 4 ðdegree=nmÞ. 2
3
4
monochromators
Fig. 2. The reflected beam is sent on stacked monochromators. The incidence angle on each monochromator varies so that each monochromator diffracts a different wavelength band. The wavelength is directly determined by the position on the detector.
central wavelength (nm)
2.5 2 1.5 1 0.5 0 5
10
15 20 25 monochromator index
30
The angle of incidence is then 101 for l ¼ 2.5 nm and 11 for l ¼ 0.25 nm neutrons. If we want to diffract a wavelength ln with a single mirror, its length is given by Ln ¼ w= tanðyn Þ. For the shortest wavelengths (l ¼ 0.2 nm), the monochromator length is 150 mm (see Fig. 4). The individual lengths of each monochromator are rather large and the mirrors cannot simply be put in line one after the other; otherwise the total length of the device would be close to 2 m. It is possible to consider a more compact arrangement of the mirrors (see Fig. 5). If we assume that the silicon wafers are e ¼ 0.25 mm thick, because of this finite thickness, some space is lost between each consecutive mirror and the mirrors must be slightly shifted one after the other. For each mirror, the lost space is equal to DXi ¼ e/sin yi. The total loss of space is equal to 240 mm when considering the set of 35 mirrors. An extra 150 mm must be added to account for the last
35
Fig. 3. Central wavelengths for a set of 35 monochromators. The wavelengths span from 0.2 to 2.5 nm. The band-pass of each mirror is set at 7%.
3. Requirements for a realistic device The central diffraction wavelengths of the different monochromators should follow the law: ln ¼ (1BW)n lmax where BW is the monochromator bandwidth. On typical ToF reflectometers, the available wavelength band ranges from 0.2 to 2.5 nm. The values of the central wavelength for the different monochromators are plotted on Fig. 3 in the case of a wavelength resolution of 7%. This is the typical wavelength resolution used on the ToF reflectometer EROS at the LLB [7]. In this case, it would be possible to measure 35 points at once in the reflectivity curve, which is sufficient for most applications where a high resolution is not required. This is typically the case of ultra-thin soft matter films.
10 9 8 7 6 5 4 3 2 1 0
150 125 100 75 50
length (mm)
1
tilt angle (°)
0
0
At the moment, it is possible to produce routinely m ¼ 4 high quality monochromators [8]. The incidence angle on an m ¼ 4 monochromator is given by
25 0 0
5
10 15 20 25 monochromator index
30
35
Fig. 4. Tilt angle and corresponding length of the different monochromators to analyze a 2 mm wide beam.
w
Δ Xi Fig. 5. Compact arrangement of the monochromator mirrors taking into account the finite thickness of the silicon substrates.
ARTICLE IN PRESS Fre´de´ric Ott / Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405
mirror length. The proposed device has nevertheless a reasonable size. 5. Modelling of the EASYREF set-up Monte Carlo simulations were performed on this design using SimulSpectro [9]. The monochromators were taken with a realistic reflectivity and a bandwidth of about 7% (Fig. 6a). The detector was set at 1500 mm after the device.
a Reflectivity
1
0 0
0.2
0.4
0.6 Q (nm -1)
0.8
1
1.2
b 2.5
B
Lambda (nm)
2.0
1.5 A 1.0
0.5
200
400
600
403
Fig. 6b represents the neutron position on the detector (X-axis) as a function of the wavelength (Y-axis). The signal of interest is along the region A. A wavelength can be associated to each position of the detector. Fig. 6c shows the raw reflectivity signal as measured for an Ni(10 nm)//Si film illuminated with the spectrum of the guide G3bis at the LLB at an incidence angle of 41. The finite size (2 mm) and divergence (0.061) of the incident beam are taken into account as well as the full reflectivity of the monochromator mirrors, including the total reflection region. In order to retrieve the actual reflectivity of the sample, it is necessary to divide the raw spectrum by the white incident spectrum. Experimentally, this signal is measured by sending the white beam through the device. After that, a wavelength must be attributed to each peak, which in practice can be calibrated by ToF. Fig. 7 compares the measured reflectivity in a classical ToF measurement, a raw integration of the Fig. 6c data and an integration after having filtered the parasitic neutrons from the region B on Fig. 6b which spoil the signal of the short wavelength neutrons. These parasitic neutrons come from the fact that: (i) the monochromators are not perfectly reflecting, (ii) that the overlap between the monochromators bands is not perfect, and (iii) that there are some total reflections below the Si critical edge. In practice, the filtering of these long wavelengths neutrons can be performed with a simple nickel mirror deposited on silicon. Without long wavelength filtering, the signal is spoiled above Q ¼ 3 nm1. And the lowest measurable reflectivity is around 106. If long wavelength neutrons are filtered out, signals down to a few 107 could be measured. Surprisingly, the oscillations in the EASYREF set-up are more pronounced than in the classical ToF measurement. This is due to the fact that in the case of the EASYREF setup, the 7% resolution distribution function is almost square. In the case of the ToF measurement, the resolution was taken as a Gaussian. These results are very satisfactory but they assume that the device described in Fig. 5 is properly built and that the mechanical alignments are good. This is not a trivial task.
Position (mm)
1
c
normal TOF 7%
0.1
1 Intensity (a.u.)
Réflectivity
with EASYREF
0.01
EASYREF + filter
0.001 0.0001 0.00001 0.000001
0 150
250
350
450
550
Position (mm)
Fig. 6. (a) Reflectivity of the monochromator used for the simulations. (b) l vs. position on the detector. (c) Raw reflectivity signal as measured on the detector.
0.0000001 0
1
2
3
4
Q (nm−1) Fig. 7. Reflectivity on an Ni(10 nm)//Si sample. (Solid line) classical ToF measurement, (diamond) after integration of the signal of Fig. 6c, (square) after having filtered out the parasitic long wavelength neutrons.
ARTICLE IN PRESS Fre´de´ric Ott / Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405
404
6. Compact energy analyzer (CEA)
AðlÞð%=mmÞ ¼ 0:1 þ 0:4lðnmÞ.
Fig. 9. Template (gray part) for a compact energy analyzer. The wafers are stacked on the template, which defines the local curvature.
40 Absorption (%)
We propose another set-up, which consists of a stack of ML monochromators deposited on thin Si wafers (Fig. 8). The building bricks are thin silicon wafers (0.25 mm thick) on which an m ¼ 4 monochromator coating has been deposited. Instead of having individual mirrors diffracting a defined wavelength, we propose that the monochromators could be continuously bent. The Si wafers can be stacked so as to obtain a total thickness of several mm (typically 10 wafers). The stack is then bent so that at each position X, the incidence angle on the mirrors corresponds to the angular dependence calculated in Fig. 4. Thus the different wavelengths entering the device are continuously diffracted in different directions starting from long wavelengths to short wavelengths. The advantages of such a device are numerous. It can be considered as a bulk system. The neutrons enter by the side of the device and then simply travel inside bulk silicon. This avoids total reflection at the silicon critical edge. The second advantage is that the system is mechanically simpler to fabricate. A template following the required curvature (Fig. 9) can be machined using electro-erosion and then the silicon stack can be clamped on it. The length of the device is very reasonable (220 mm). The bending is 101 over 220 mm, which corresponds to a curvature radius of 1.3 m. If very high bending radius is required thinner silicon wafers could be used. The design can be scaled to wider beams since it only requires increasing the number of wafers in the stack. The absorption in the device can be easily calculated. The shorter the wavelength, the longer the travel path in silicon. Experimentally, we determined that the absorption in Si is given by
30 20 10 0 0
0.5
1
1.5
2
2.5
λ (nm) Fig. 10. Absorption of the device as a function of the wavelength.
The absorption in the CEA is represented on Fig. 10. The absorption remains limited below 25% for wavelengths above 0.5 nm. It, however, diverges for shorter wavelengths because we are working at constant dl/l resolution which means that the number of wafers increases significantly for shorter wavelengths. If the wavelength resolution would be relaxed to 10% for wavelengths below 0.5 nm, the absorption would remain below 30%. 7. Detection system
w δy
θi
X
δx
Y (mm)
0 −0.5 −1 −1.5 −2 0
80
160 X (mm)
Fig. 8. (a) Generation of the device geometry. (b) Realistic device. In order to catch a beam, which is 2 mm wide, with wavelengths ranging from 0.2 to 2.5 nm, a 220 mm device is required. A total of 40 wafers are required (not full length). On the drawing, the spacing between the mirrors does not appear constant. This is an artefact due to the fact that Y scale is strongly zoomed in.
After passing through the CEA, the neutrons must be measured on a PSD. The detector should be positioned approximately at 1000 mm from the CEA and have a size of 500 mm with a resolution of the order of 3 mm (see Fig. 6c). The detector must be able to handle a very high flux. Such detectors are readily available. The flux on the detector will be rather large, of the order of 1 MHz. A first choice could be a delay line detector. Otherwise, a set of PSD tubes could also be used. 8. Simplified version of the EASYREF set-up As a first step before a full-scale implementation, we propose that a simplified version of the device could be implemented. It follows the idea proposed in Ref. [6] which consists in combining fast ToF and energy analysis. Since most of the technical issues arise from short wavelength neutrons, we propose to use a very fast ToF chopper
ARTICLE IN PRESS Fre´de´ric Ott / Nuclear Instruments and Methods in Physics Research A 584 (2008) 401–405
operating at 300 Hz so that all neutrons below 0.4 nm can be analyzed using classical ToF. Such a chopper can be built by simply multiplying the number of holes in the disk (from 1 to 20 typically). However, in order to avoid frame overlap problems (and waste of neutrons), the longer wavelengths would be analyzed using the EASYREF device. However, since only longer wavelengths need to be analyzed, the requirements on the device are relaxed. The longest mirror would be only 70 mm, the total length of monochromator coating would be reduced to 370 mm (making the device rather cheap) and the total length of the device would be 220 mm. This would also significantly reduce the absorption and diffuse scattering issues. Since the chopper is rotating at a high speed (300 Hz compared to 20 Hz on the reflectometer EROS), a typical gain in flux of the order of 15 would be obtained.
405
We should mention that the idea of maximizing the use of the neutron beam is presently being implemented at NIST by combining multiple graphite crystals to select multiple energies in the beam [11]. The CEA could also be used for other purposes. Instead of using it to perform only specular reflectivity, it could be used to perform inelastic measurements. One of the drawbacks of the device is that its angular acceptance is small which limits its general use on other spectrometers. However, as the samples studied by neutron scattering are getting smaller and smaller, the small size of the device could turn into advantages since it would be perfectly suited for studying samples which are smaller than 1 mm. The device could be used to perform inelastic measurements on very small samples almost as efficiently as on regular ToF spectrometers since the chopper system would not be required anymore.
9. Conclusion and perspectives We have presented a device, which could boost the performances of neutron reflectometers for specular reflectivity measurements by a factor of 20–100. For a first practical implementation, we suggest that a simplified hybrid set-up combining ToF and energy analysis could already boost the performances by a factor 15 on most ToF reflectometers. The device would be quite simple and cheap. The EASYREF device is technically simpler to setup and cheaper than other solutions proposed to take benefit of the whole white beam in neutron reflectometry experiments [5,6,10]. The most critical issue is the diffuse scattering from the mirrors, which needs to be assessed experimentally. Note that the device can easily be upgraded into a polarized version.
References [1] G.L. Squires, Introduction to the Theory of Thermal Neutron Scattering, Dover Publications, New York, 1997. [2] G. Shirane, S.M. Shapiro, J.M. Tranquada, Neutron Scattering with a Triple-Axis Spectrometer, Cambridge University Press, Cambridge, 2002. [3] J.R.D. Copley, T.J. Udovic, J. Res. Natl. Inst. Stand. Technol. 98 (1993) 71. [4] C.F. Majkrzak, Physica B 173 (1991) 75. [5] R. Cubitt, et al., Nucl. Instr. and Meth. A 558 (2006) 547. [6] F. Ott, A. de Vismes, Physica B 397 (2007) 153. [7] /www-llb.cea.fr/spectros/pdf/eros-llb.pdfS. [8] /www.swissneutronics.chS. [9] /www-llb.cea.fr/prism/programs/simulspectro/simulspectro2D.htmlS. [10] F. Ott, A. Menelle, Physica B 385–386 (2006) 985. [11] /http://www.ncnr.nist.gov/expansion/CANDOR053007.htmlS.