- Email: [email protected]
Scattering depth correction of evanescent waves in inelastic neutron scattering using a neutron prism
Nuclear Instruments and Methods in Physics Research A 686 (2012) 71–74
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Scattering depth correction of evanescent waves in inelastic neutron scattering using a neutron prism H. Frielinghaus a, O. Holderer a,n, F. Lipfert a, M. Monkenbusch b, N. Arend c, D. Richter a,b a
J¨ ulich Centre for Neutron Science (JCNS), Outstation at FRM II, D-85747 Garching, Germany J¨ ulich Centre for Neutron Science (JCNS) and Institute for Complex Systems, Forschungszentrum J¨ ulich, D-52425 J¨ ulich, Germany c J¨ ulich Centre for Neutron Science (JCNS), Outstation at SNS, Oak Ridge, USA b
a r t i c l e i n f o
abstract
Article history: Received 25 April 2012 Received in revised form 23 May 2012 Accepted 23 May 2012 Available online 1 June 2012
Grazing Incidence Neutron Spin Echo Spectroscopy (GINSES) has recently been applied to measure the dynamics of surfactant membranes close to a hydrophilic silicon wall. The scattering depth of the evanescent wave inside the microemulsion depends strongly on the angle of incidence and the wavelength. The inherently low scattering intensity of GINSES measurements, however, requires the integration over a rather broad wavelength band. In particular, at a pulsed source the instrument operates with a broad wavelength band covering all neutrons within one frame between two pulses. In order to yield viable counting statistics it is highly desirable to integrate data corresponding to significant fractions of the wavelength band. Therefore, in a normal reflectometry setup the penetration length would be smeared and blur the depth dependence of the experimental results. Here we describe a new method to strongly mitigate this effect and show its application in a GINSES experiment at the neutron spin echo instrument at the Spallation Neutron Source (SNS). A prism in front of the sample was introduced in order to adapt the angle of the incoming beam according to the wavelength by this optical component. As an example an experiment on a bicontinuous microemulsion using these neutron optics is presented. & 2012 Elsevier B.V. All rights reserved.
Keywords: Neutron spin echo Prism Grazing incidence
1. Introduction Neutron spin echo (NSE) spectroscopy achieves the highest resolution in inelastic neutron scattering [1–3]. The neutron velocity is encoded and decoded by a number of spin precessions in solenoids. The polarization of the neutron beam at the end of the decoding precession path is the intermediate scattering function Sðq, tÞ multiplied by a resolution function. In soft matter physics, the main fields of application are Brownian motion type processes, such as polymer chain dynamics in melts or membrane fluctuations in microemulsion systems [4]. Grazing incidence small angle neutron scattering (GISANS) is a technique which allows to study structural properties close to an interface. The incident neutron beam is strongly collimated in one direction and enters a silicon block from the side. It then hits the flat Si-liquid interface at a very small angle below the critical angle ac . Such studies allowed to resolve a lamellar structure close to the Si-interface of a bulk bicontinuous microemulsion [5]. The concept of probing the sample close to the interface has recently also been applied to studies of the dynamics of surfactant membranes in microemulsions as a function of scattering depth [6]. When transferring this technique to a spallation neutron source with a pulsed beam, the acquired data gain in complexity due to the time-of-flight nature of the measurement, hence the data
n
Corresponding author. Tel.: þ49 8928910707; fax: þ 49 8928910799. E-mail address: [email protected] (O. Holderer).
0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2012.05.064
reduction process is more elaborate. Due to the wavelength spread during the pulse, one naturally probes a certain q-range according to q ¼ 4p=l sinðy=2Þ and a Fourier time range, since the Fourier time tpl3 . Fortunately the approximate q3 dependence of the relaxation rates [7] implies a matching compensation of space and time scales and results in a remarkable independence of observed relaxation curves on wavelength width. For the GINSES experiment, however, the variation of the scattering depth into the sample adds additional complexity to the experiment. For intensity reasons it is absolutely necessary to integrate over the broad wavelength band. Regrouping of time tagged wavelength bins is difficult since the scattering vector q, the Fourier-time t and the scattering depth have different l dependences. This is different from a plain SANS experiment at a pulsed source where large sections of time bins and detector positions can be grouped to yield the same q value which in that case is the single parameter. Here we demonstrate that the wavelength-dependence of the scattering depth in a GINSES experiment can be corrected to a constant scattering depth for the whole wavelength band by using a neutron prism, which deflects the long wavelengths stronger than the short ones.
2. Experimental setup The spin echo spectrometer (SNS-NSE) at the Spallation Neutron Source (SNS) in Oak Ridge uses neutrons from the pulsed source with a repetition rate of 60 Hz. A chopper system selects a
72
H. Frielinghaus et al. / Nuclear Instruments and Methods in Physics Research A 686 (2012) 71–74
Fig. 1. Left: definition of the angles for the prism. The apex angle of the prism used in this experiment was 1701. Right: geometry of the experiment at the sample position. The beam is collimated in one direction and passes by the first NSE precession coil before hitting the prism. The scattered beam goes to the second precession coil of the spin echo setup.
wavelength band of about 3 A˚ for a moderator–detector distance of 21.3 m. In our case the band from 5 to 8 A˚ has been chosen. There the cold coupled moderator provides a high intensity and the needed Fourier time range of 0.1–30 ns can be reached. The effective sample volume under grazing incidence conditions is about five orders of magnitude smaller than in a conventional NSE experiments, which makes the choice of and integration over a high intensity wavelength band inevitable. The grazing incidence setup had been used to study the membrane dynamics close to an interface in a classical NSE setup [6]. In the present experiment an analogous setup has been used, extended by a prism just in front of the sample cell. Fig. 1 illustrates the geometry at the sample position. The grazing incidence cell including the prism is placed at the sample position of the SNS-NSE spectrometer, between the two velocity spin-encoding and -decoding main precession coils.
3. Prism layout Two main candidates for a material for neutron optical components are available: diamond and MgF2 [8]. The required size of a neutron prism can be achieved by the MgF2 prism. It has a scattering length density of r ¼ 5:16 1010 cm2 , with a refrac2 tive index of n ¼ 1l r=ð2pÞ with the neutron wavelength l. For small refractive index differences and small incident angles on the prism, the angle of refraction of such a prism is given by
dexit Cd þ l2 r=ðpEÞ:
ð1Þ
For a prism oriented as in Fig. 1, d and dexit are the deviations from the horizontal, E is the angle on the incident side. For an apex angle of 1701, E ¼ 51. The critical angle for the pffiffiffiffiffiffiffiffiffiffiffiffi ffi neutron wave hitting a planar surface is given by ac ¼ l Dr=p, with the difference in scattering length density between Si and the sample, Dr. The scattering depth Lin of the evanescent wave is
Lin ¼ ð4pDrð1a2in =a2c ÞÞ1=2
ð2Þ
where ain is the angle between the incoming neutron beam and the surface. The critical angle for the evanescent neutron wave depends linearly on the wavelength, whereas the wavelength correction dexit of the prism is proportional to l2 . By choosing an appropriate apex angle of the prism one obtains a variation of the incident angle in a given wavelength band which compensates very well the shift of the scattering depth with increasing wavelength. Fig. 2 compares the scattering depth with and without the ˚ The SNS-NSE spectroprism for the wavelength band l ¼ 4212 A. meter uses wavelength bands of 2.4–3.6 A˚ width, depending on the moderator–detector distance. The present experiment has been performed at the 21.3 m detector position with 5–8 A˚ neutrons. The scattering depth is almost constant in that region. Without the prism, Lin varies from 618 A˚ to 435 A˚ for an incident angle of 0.11. With the prism, a scattering depth Lin ¼ 4472455 A˚ is achieved. The incident angle on the prism in Fig. 2 is 0.041, resulting in the incident angle on the sample, ain , of 0.06–0.191.
Fig. 2. In the present experiment, a wavelength band of l ¼ 528 A˚ has been used. Without the prism, the scattering depth would vary according to the solid line, the prism shifts the incident angle in a way that the scattering depth is almost constant (dotted line).
The experiments have then been performed with a MgF2 prism with a length of 70 mm and an apex angle of 1701, the projected height (from the tip to the base of the prism) measures 3 mm. The beam is collimated horizontally by a 2 mm slit at the beginning of the spectrometer and a 1 mm slit just in front of the prism. It is therefore easy to place the prism at the right position in the beam such that the beam passes through. The divergence of the beam can be derived from Fig. 3. The FWHM of the reflected peak without prism is 0.0241, which represents the divergence in the collimated direction. Without prism, the beam would hit the interface with an incident angle of 0.081, the prism bends then the beam to incident angles ranging from 0.11 to 0.151 for the ˚ wavelength band from 5 to 8 A. 3.1. Prism test The performance of the prism has been tested with the beam reflected at the Si block of the grazing incidence cell. For that purpose, the cell has been flooded with D2O to have sufficient contrast to the Si. The beam reflected at the surface has then been used to measure the exact orientation of the cell. A rough orientation could be seen already on the 2D detector of the NSE spectrometer. For the required resolution for an adjustment of the order of some 0.011, however, an image plate mounted about 3 m away from the sample has been used (between collimator and detector at the end of the second arm of the spectrometer). Image plate pictures of the reflected beam with and without the prism are shown in Fig. 3. The contrast has been enhanced for clarity. The wavelength band used in this experiment corresponds to angles of deflection from 0.061 to 0.141 (for 5–8 A˚ respectively), i.e. to a broadening of the peak by 70:041, which is about the broadening visible in the right picture of Fig. 3. The deflection is
H. Frielinghaus et al. / Nuclear Instruments and Methods in Physics Research A 686 (2012) 71–74
without prism
73
Direct beam
with prism
Fig. 3. Left: image plate pictures of the transmitted (direct) beam and the reflected beam. Without the prism, the reflected beam is much sharper, representing the collimation of the beam, whereas with the prism the reflection is spread due to the wavelength dependence of the deflection angle of the prism. Right: integrated line profile of the images on top. At 01, the direct beam is visible, the reflected beam is at 0.721 without the prism, and with the prism at 0.91, with a much broader peak. The sharp intensity dips visible in the peak regions stem from the shadows of the lamellae of the background reduction collimator, located just in front of the image plate.
slightly larger by 0.051, which is expected to be due to the mechanical uncertainty during the mounting of the prism into the holder. Once the prism is mounted, the cell stays in its position without mechanical forces acting on it, the adjustment is therefore preserved.
bulk 46.5 nm
1
4. GINSES on microemulsions As a first test of the setup, experiments on the same type of microemulsion as in Ref. [6] have been performed. A bicontinuous microemulsion with D2O, h-decane mixed with 12% d-decane, and the non-ionic surfactant C10E4 with a volume fraction of 17% has been measured. The time-of-flight mode of the SNS-NSE allows to choose the desired wavelength range for the evaluation after the experiment. Summing up over more time channels within the frame between consecutive pulses improves the statistics, at the expense of a smeared q-resolution. The targeted q-value was, as in the experiments in Ref. [6], q¼0.08 A˚ 1, a compromise between high intensity (at lower q) and probed length scale (local fluctuations are best observed at high q). Fig. 4 compares the dynamics under grazing incidence with that of the bulk microemulsion. The bulk sample has been measured in this case under the same conditions, only at an incident angle larger than the critical angle. It therefore reflects not the experimental statistics as obtained in a standard bulk measurement. The setup and operation of a NSE instrument at a pulsed source (i.e. a time-of-flight-NSE instrument) requires that one takes care of the q resolution not only in terms of detector region selected, but also in terms of the wavelength frames chosen for the evaluation. A too broad q-resolution results in an overestimation of the low-q regime with high scattering intensity from the microemulsion, where de Gennes-narrowing close to the correlation peak slows down the dynamics. A too small wavelength range spoils the statistics of this low-intensity experiment. The plot in Fig. 4 sums up a band of 20 out of 42 time channels in order to get sufficient intensity. The scattering depth of the experiment was 490 A˚ including the prism corrections. The relaxation times are 99 ns for the near interface measurement under grazing incidence, and 152 ns for the bulk microemulsion. The results in Ref. [6] were 133 ns for the bulk and 45 ns for the interface at 450 A˚ scattering depth at a q-value of 0.08 A˚ 1 with a 10% triangular wavelength spread due to the velocity selector. We judge the accuracy of adjusting the incident angle to be 7 0:011,
S(Q.t)/S(Q)
0.8
0.6 shifted by -0.3 0.4
0.2
q = 0.076 A-1
0 0
5
10
15 t [ns]
20
25
30
Fig. 4. Near-interface dynamics of a bicontinuous microemulsion measured under ˚ grazing incidence with the neutron prism with a scattering depth of 490 A, compared to the bulk microemulsion (measured at an incident angle significantly larger than the critical angle, in the same configuration). The data for the grazing incidence measurement are shifted down by 0.3 for clarity. As expected, the relaxation times of 152 ns for the bulk and 99 ns for the near interface sample show the faster dynamics close to the interface.
leading to an uncertainty of the scattering depth of 7 80 A˚ in the two experiments. The relaxation time in microemulsions goes with q3 , the difference in q would lead to an increase of the relaxation time by the factor ð0:08=0:076Þ3 ¼ 1:17 (i.e. from 45 ns to 53 ns). The relaxation time of 99 ns corresponds to a scattering depth of 600 A˚ in the experimental interpolation curve of our previous measurement, which is within the experimental errors in scattering depth of the two experiments. In order to utilize the ability to time-tag the different wavelengths in a frame of the SNS-NSE one would need experiments with very long counting times to obtain sufficient statistics in order to have the freedom to choose the desired wavelength- and hence q-t-range a posteriori. Since the small effective scattering volume largely obstructs this route the prism method is used to – at least – remove the variation of scattering depth within the wavelength frame width.
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H. Frielinghaus et al. / Nuclear Instruments and Methods in Physics Research A 686 (2012) 71–74
With sufficiently good counting statistics, it would be nonetheless possible to get a range of q values with the same scattering depth with a single scan.
5. Conclusion Neutron prisms are a suitable component to correct for differences in scattering depth, caused by different wavelengths within a pulse, for the evanescent wave in grazing incidence experiments. The results on a bicontinuous microemulsion measured with the prism under grazing incidence confirmed the applicability of this optical component to the grazing incidence setup by comparison with the previous experiment without prism. With a prism designed for the desired wavelength band, the scattering depth is almost constant during the pulse. The prism allows to vary the scattering depth more precisely, because very low angles and angles close to the critical angle can be approached more closely. Using the prism makes it possible to integrate over arbitrary broad wavelength bands in order to gain the desired statistics, without the penalty of smearing the scattering depth of the evanescent wave. Such corrections are even more important when thinking of a similar experiment at a long pulse source like the planned European Spallation Source ESS in Lund, Sweden, where a NSE experiment would have approximately an 8 A˚ wavelength band compared to the 3 A˚ wavelength band used at the SNS-NSE. Also for reactor based experiments using a continuous beam, the spread of scattering depths due to the 10–20% wavelength band typically cut out by the velocity selector might be sharpened. Additionally, it allows for changing
the wavelength during one scan without readjusting the sample cell and thus measuring always at the highest intensity possible for the desired Fourier time. More subtle effects concerning the distance of a fluctuating object to a hard wall can be studied in this way.
Acknowledgment This research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. References [1] F. Mezei (Ed.), Neutron Spin Echo. No. 128 Lecture Notes in Physics, vol. 128, Springer, Berlin, Heidelberg, New York, 1980. [2] F. Mezei, P.C. G.T. (Eds.), Neutron Spin Echo Spectroscopy. No. 601 in Lecture Notes in Physics, Springer, Berlin, Heidelberg, New York, 2003. [3] M. Monkenbusch, R. Schatzler, D. Richter, Nuclear Instruments & Methods In Physics Research. Section A: Accelerators Spectrometers Detectors and Associated Equipment 399 (1997) 301. [4] D. Richter, M. Monkenbusch, A. Arbe, J. Colmenero, Advances in Polymer Science 174 (2005) 1. [5] M. Kerscher, P. Busch, S. Mattauch, H. Frielinghaus, D. Richter, M. Belushkin, G. Gompper, Physical Review E 83 (2011) 030401(R). [6] H. Frielinghaus, M. Kerscher, O. Holderer, M. Monkenbusch, D. Richter, Physical Review E 85 (2012) 041408. [7] A.G. Zilman, R. Granek, Physical Review Letters 77 (1996) 4788. [8] H. Frielinghaus, V. Pipich, A. Radulescu, M. Heiderich, R. Hanslik, K. Dahlhoff, H. Iwase, S. Koizumi, D. Schwahn, Journal of Applied Crystallography 42 (2009) 681.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Scattering depth correction of evanescent waves in inelastic neutron scattering using a neutron prism H. Frielinghaus a, O. Holderer a,n, F. Lipfert a, M. Monkenbusch b, N. Arend c, D. Richter a,b a
J¨ ulich Centre for Neutron Science (JCNS), Outstation at FRM II, D-85747 Garching, Germany J¨ ulich Centre for Neutron Science (JCNS) and Institute for Complex Systems, Forschungszentrum J¨ ulich, D-52425 J¨ ulich, Germany c J¨ ulich Centre for Neutron Science (JCNS), Outstation at SNS, Oak Ridge, USA b
a r t i c l e i n f o
abstract
Article history: Received 25 April 2012 Received in revised form 23 May 2012 Accepted 23 May 2012 Available online 1 June 2012
Grazing Incidence Neutron Spin Echo Spectroscopy (GINSES) has recently been applied to measure the dynamics of surfactant membranes close to a hydrophilic silicon wall. The scattering depth of the evanescent wave inside the microemulsion depends strongly on the angle of incidence and the wavelength. The inherently low scattering intensity of GINSES measurements, however, requires the integration over a rather broad wavelength band. In particular, at a pulsed source the instrument operates with a broad wavelength band covering all neutrons within one frame between two pulses. In order to yield viable counting statistics it is highly desirable to integrate data corresponding to significant fractions of the wavelength band. Therefore, in a normal reflectometry setup the penetration length would be smeared and blur the depth dependence of the experimental results. Here we describe a new method to strongly mitigate this effect and show its application in a GINSES experiment at the neutron spin echo instrument at the Spallation Neutron Source (SNS). A prism in front of the sample was introduced in order to adapt the angle of the incoming beam according to the wavelength by this optical component. As an example an experiment on a bicontinuous microemulsion using these neutron optics is presented. & 2012 Elsevier B.V. All rights reserved.
Keywords: Neutron spin echo Prism Grazing incidence
1. Introduction Neutron spin echo (NSE) spectroscopy achieves the highest resolution in inelastic neutron scattering [1–3]. The neutron velocity is encoded and decoded by a number of spin precessions in solenoids. The polarization of the neutron beam at the end of the decoding precession path is the intermediate scattering function Sðq, tÞ multiplied by a resolution function. In soft matter physics, the main fields of application are Brownian motion type processes, such as polymer chain dynamics in melts or membrane fluctuations in microemulsion systems [4]. Grazing incidence small angle neutron scattering (GISANS) is a technique which allows to study structural properties close to an interface. The incident neutron beam is strongly collimated in one direction and enters a silicon block from the side. It then hits the flat Si-liquid interface at a very small angle below the critical angle ac . Such studies allowed to resolve a lamellar structure close to the Si-interface of a bulk bicontinuous microemulsion [5]. The concept of probing the sample close to the interface has recently also been applied to studies of the dynamics of surfactant membranes in microemulsions as a function of scattering depth [6]. When transferring this technique to a spallation neutron source with a pulsed beam, the acquired data gain in complexity due to the time-of-flight nature of the measurement, hence the data
n
Corresponding author. Tel.: þ49 8928910707; fax: þ 49 8928910799. E-mail address: [email protected] (O. Holderer).
0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2012.05.064
reduction process is more elaborate. Due to the wavelength spread during the pulse, one naturally probes a certain q-range according to q ¼ 4p=l sinðy=2Þ and a Fourier time range, since the Fourier time tpl3 . Fortunately the approximate q3 dependence of the relaxation rates [7] implies a matching compensation of space and time scales and results in a remarkable independence of observed relaxation curves on wavelength width. For the GINSES experiment, however, the variation of the scattering depth into the sample adds additional complexity to the experiment. For intensity reasons it is absolutely necessary to integrate over the broad wavelength band. Regrouping of time tagged wavelength bins is difficult since the scattering vector q, the Fourier-time t and the scattering depth have different l dependences. This is different from a plain SANS experiment at a pulsed source where large sections of time bins and detector positions can be grouped to yield the same q value which in that case is the single parameter. Here we demonstrate that the wavelength-dependence of the scattering depth in a GINSES experiment can be corrected to a constant scattering depth for the whole wavelength band by using a neutron prism, which deflects the long wavelengths stronger than the short ones.
2. Experimental setup The spin echo spectrometer (SNS-NSE) at the Spallation Neutron Source (SNS) in Oak Ridge uses neutrons from the pulsed source with a repetition rate of 60 Hz. A chopper system selects a
72
H. Frielinghaus et al. / Nuclear Instruments and Methods in Physics Research A 686 (2012) 71–74
Fig. 1. Left: definition of the angles for the prism. The apex angle of the prism used in this experiment was 1701. Right: geometry of the experiment at the sample position. The beam is collimated in one direction and passes by the first NSE precession coil before hitting the prism. The scattered beam goes to the second precession coil of the spin echo setup.
wavelength band of about 3 A˚ for a moderator–detector distance of 21.3 m. In our case the band from 5 to 8 A˚ has been chosen. There the cold coupled moderator provides a high intensity and the needed Fourier time range of 0.1–30 ns can be reached. The effective sample volume under grazing incidence conditions is about five orders of magnitude smaller than in a conventional NSE experiments, which makes the choice of and integration over a high intensity wavelength band inevitable. The grazing incidence setup had been used to study the membrane dynamics close to an interface in a classical NSE setup [6]. In the present experiment an analogous setup has been used, extended by a prism just in front of the sample cell. Fig. 1 illustrates the geometry at the sample position. The grazing incidence cell including the prism is placed at the sample position of the SNS-NSE spectrometer, between the two velocity spin-encoding and -decoding main precession coils.
3. Prism layout Two main candidates for a material for neutron optical components are available: diamond and MgF2 [8]. The required size of a neutron prism can be achieved by the MgF2 prism. It has a scattering length density of r ¼ 5:16 1010 cm2 , with a refrac2 tive index of n ¼ 1l r=ð2pÞ with the neutron wavelength l. For small refractive index differences and small incident angles on the prism, the angle of refraction of such a prism is given by
dexit Cd þ l2 r=ðpEÞ:
ð1Þ
For a prism oriented as in Fig. 1, d and dexit are the deviations from the horizontal, E is the angle on the incident side. For an apex angle of 1701, E ¼ 51. The critical angle for the pffiffiffiffiffiffiffiffiffiffiffiffi ffi neutron wave hitting a planar surface is given by ac ¼ l Dr=p, with the difference in scattering length density between Si and the sample, Dr. The scattering depth Lin of the evanescent wave is
Lin ¼ ð4pDrð1a2in =a2c ÞÞ1=2
ð2Þ
where ain is the angle between the incoming neutron beam and the surface. The critical angle for the evanescent neutron wave depends linearly on the wavelength, whereas the wavelength correction dexit of the prism is proportional to l2 . By choosing an appropriate apex angle of the prism one obtains a variation of the incident angle in a given wavelength band which compensates very well the shift of the scattering depth with increasing wavelength. Fig. 2 compares the scattering depth with and without the ˚ The SNS-NSE spectroprism for the wavelength band l ¼ 4212 A. meter uses wavelength bands of 2.4–3.6 A˚ width, depending on the moderator–detector distance. The present experiment has been performed at the 21.3 m detector position with 5–8 A˚ neutrons. The scattering depth is almost constant in that region. Without the prism, Lin varies from 618 A˚ to 435 A˚ for an incident angle of 0.11. With the prism, a scattering depth Lin ¼ 4472455 A˚ is achieved. The incident angle on the prism in Fig. 2 is 0.041, resulting in the incident angle on the sample, ain , of 0.06–0.191.
Fig. 2. In the present experiment, a wavelength band of l ¼ 528 A˚ has been used. Without the prism, the scattering depth would vary according to the solid line, the prism shifts the incident angle in a way that the scattering depth is almost constant (dotted line).
The experiments have then been performed with a MgF2 prism with a length of 70 mm and an apex angle of 1701, the projected height (from the tip to the base of the prism) measures 3 mm. The beam is collimated horizontally by a 2 mm slit at the beginning of the spectrometer and a 1 mm slit just in front of the prism. It is therefore easy to place the prism at the right position in the beam such that the beam passes through. The divergence of the beam can be derived from Fig. 3. The FWHM of the reflected peak without prism is 0.0241, which represents the divergence in the collimated direction. Without prism, the beam would hit the interface with an incident angle of 0.081, the prism bends then the beam to incident angles ranging from 0.11 to 0.151 for the ˚ wavelength band from 5 to 8 A. 3.1. Prism test The performance of the prism has been tested with the beam reflected at the Si block of the grazing incidence cell. For that purpose, the cell has been flooded with D2O to have sufficient contrast to the Si. The beam reflected at the surface has then been used to measure the exact orientation of the cell. A rough orientation could be seen already on the 2D detector of the NSE spectrometer. For the required resolution for an adjustment of the order of some 0.011, however, an image plate mounted about 3 m away from the sample has been used (between collimator and detector at the end of the second arm of the spectrometer). Image plate pictures of the reflected beam with and without the prism are shown in Fig. 3. The contrast has been enhanced for clarity. The wavelength band used in this experiment corresponds to angles of deflection from 0.061 to 0.141 (for 5–8 A˚ respectively), i.e. to a broadening of the peak by 70:041, which is about the broadening visible in the right picture of Fig. 3. The deflection is
H. Frielinghaus et al. / Nuclear Instruments and Methods in Physics Research A 686 (2012) 71–74
without prism
73
Direct beam
with prism
Fig. 3. Left: image plate pictures of the transmitted (direct) beam and the reflected beam. Without the prism, the reflected beam is much sharper, representing the collimation of the beam, whereas with the prism the reflection is spread due to the wavelength dependence of the deflection angle of the prism. Right: integrated line profile of the images on top. At 01, the direct beam is visible, the reflected beam is at 0.721 without the prism, and with the prism at 0.91, with a much broader peak. The sharp intensity dips visible in the peak regions stem from the shadows of the lamellae of the background reduction collimator, located just in front of the image plate.
slightly larger by 0.051, which is expected to be due to the mechanical uncertainty during the mounting of the prism into the holder. Once the prism is mounted, the cell stays in its position without mechanical forces acting on it, the adjustment is therefore preserved.
bulk 46.5 nm
1
4. GINSES on microemulsions As a first test of the setup, experiments on the same type of microemulsion as in Ref. [6] have been performed. A bicontinuous microemulsion with D2O, h-decane mixed with 12% d-decane, and the non-ionic surfactant C10E4 with a volume fraction of 17% has been measured. The time-of-flight mode of the SNS-NSE allows to choose the desired wavelength range for the evaluation after the experiment. Summing up over more time channels within the frame between consecutive pulses improves the statistics, at the expense of a smeared q-resolution. The targeted q-value was, as in the experiments in Ref. [6], q¼0.08 A˚ 1, a compromise between high intensity (at lower q) and probed length scale (local fluctuations are best observed at high q). Fig. 4 compares the dynamics under grazing incidence with that of the bulk microemulsion. The bulk sample has been measured in this case under the same conditions, only at an incident angle larger than the critical angle. It therefore reflects not the experimental statistics as obtained in a standard bulk measurement. The setup and operation of a NSE instrument at a pulsed source (i.e. a time-of-flight-NSE instrument) requires that one takes care of the q resolution not only in terms of detector region selected, but also in terms of the wavelength frames chosen for the evaluation. A too broad q-resolution results in an overestimation of the low-q regime with high scattering intensity from the microemulsion, where de Gennes-narrowing close to the correlation peak slows down the dynamics. A too small wavelength range spoils the statistics of this low-intensity experiment. The plot in Fig. 4 sums up a band of 20 out of 42 time channels in order to get sufficient intensity. The scattering depth of the experiment was 490 A˚ including the prism corrections. The relaxation times are 99 ns for the near interface measurement under grazing incidence, and 152 ns for the bulk microemulsion. The results in Ref. [6] were 133 ns for the bulk and 45 ns for the interface at 450 A˚ scattering depth at a q-value of 0.08 A˚ 1 with a 10% triangular wavelength spread due to the velocity selector. We judge the accuracy of adjusting the incident angle to be 7 0:011,
S(Q.t)/S(Q)
0.8
0.6 shifted by -0.3 0.4
0.2
q = 0.076 A-1
0 0
5
10
15 t [ns]
20
25
30
Fig. 4. Near-interface dynamics of a bicontinuous microemulsion measured under ˚ grazing incidence with the neutron prism with a scattering depth of 490 A, compared to the bulk microemulsion (measured at an incident angle significantly larger than the critical angle, in the same configuration). The data for the grazing incidence measurement are shifted down by 0.3 for clarity. As expected, the relaxation times of 152 ns for the bulk and 99 ns for the near interface sample show the faster dynamics close to the interface.
leading to an uncertainty of the scattering depth of 7 80 A˚ in the two experiments. The relaxation time in microemulsions goes with q3 , the difference in q would lead to an increase of the relaxation time by the factor ð0:08=0:076Þ3 ¼ 1:17 (i.e. from 45 ns to 53 ns). The relaxation time of 99 ns corresponds to a scattering depth of 600 A˚ in the experimental interpolation curve of our previous measurement, which is within the experimental errors in scattering depth of the two experiments. In order to utilize the ability to time-tag the different wavelengths in a frame of the SNS-NSE one would need experiments with very long counting times to obtain sufficient statistics in order to have the freedom to choose the desired wavelength- and hence q-t-range a posteriori. Since the small effective scattering volume largely obstructs this route the prism method is used to – at least – remove the variation of scattering depth within the wavelength frame width.
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With sufficiently good counting statistics, it would be nonetheless possible to get a range of q values with the same scattering depth with a single scan.
5. Conclusion Neutron prisms are a suitable component to correct for differences in scattering depth, caused by different wavelengths within a pulse, for the evanescent wave in grazing incidence experiments. The results on a bicontinuous microemulsion measured with the prism under grazing incidence confirmed the applicability of this optical component to the grazing incidence setup by comparison with the previous experiment without prism. With a prism designed for the desired wavelength band, the scattering depth is almost constant during the pulse. The prism allows to vary the scattering depth more precisely, because very low angles and angles close to the critical angle can be approached more closely. Using the prism makes it possible to integrate over arbitrary broad wavelength bands in order to gain the desired statistics, without the penalty of smearing the scattering depth of the evanescent wave. Such corrections are even more important when thinking of a similar experiment at a long pulse source like the planned European Spallation Source ESS in Lund, Sweden, where a NSE experiment would have approximately an 8 A˚ wavelength band compared to the 3 A˚ wavelength band used at the SNS-NSE. Also for reactor based experiments using a continuous beam, the spread of scattering depths due to the 10–20% wavelength band typically cut out by the velocity selector might be sharpened. Additionally, it allows for changing
the wavelength during one scan without readjusting the sample cell and thus measuring always at the highest intensity possible for the desired Fourier time. More subtle effects concerning the distance of a fluctuating object to a hard wall can be studied in this way.
Acknowledgment This research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. References [1] F. Mezei (Ed.), Neutron Spin Echo. No. 128 Lecture Notes in Physics, vol. 128, Springer, Berlin, Heidelberg, New York, 1980. [2] F. Mezei, P.C. G.T. (Eds.), Neutron Spin Echo Spectroscopy. No. 601 in Lecture Notes in Physics, Springer, Berlin, Heidelberg, New York, 2003. [3] M. Monkenbusch, R. Schatzler, D. Richter, Nuclear Instruments & Methods In Physics Research. Section A: Accelerators Spectrometers Detectors and Associated Equipment 399 (1997) 301. [4] D. Richter, M. Monkenbusch, A. Arbe, J. Colmenero, Advances in Polymer Science 174 (2005) 1. [5] M. Kerscher, P. Busch, S. Mattauch, H. Frielinghaus, D. Richter, M. Belushkin, G. Gompper, Physical Review E 83 (2011) 030401(R). [6] H. Frielinghaus, M. Kerscher, O. Holderer, M. Monkenbusch, D. Richter, Physical Review E 85 (2012) 041408. [7] A.G. Zilman, R. Granek, Physical Review Letters 77 (1996) 4788. [8] H. Frielinghaus, V. Pipich, A. Radulescu, M. Heiderich, R. Hanslik, K. Dahlhoff, H. Iwase, S. Koizumi, D. Schwahn, Journal of Applied Crystallography 42 (2009) 681.