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Time of flight as a monochromatization technique for sans
Physica 136B (1986) 103-I05 North-Holland, Amsterdam
TIME OF FLIGHT AS A MONOCHROMATIZATION TECHNIQUE FOR SANS
J.P. COTTON and J. TEIXEIRA Laboratoire Ldon Brillouin*, CEN-Saclay, 91191 Gif-sur-Yvette, France
Replacing the mechanical selector by a chopper on a small angle scattering spectrometer we obtain a monochromatization technique with a very high resolution. The description of the set up is given. An example in the polymer field is shown.
1. Introduction
In a conventional small angle neutron scattering (SANS) experiment, a mechanical selector defines an incident wave length A from the polychromatic beam emerging from the reactor (4 < h < 20 A). The scattered intensity is measured simultaneously for different scattering angles with a multidetector. The range of scattering vector q (q = 27r0/A) is typically one decade. Another possibility consists of using all the wavelengths of the incident beam by using a time of flight technique. The advantages of this method are well known since they are those of a pulsed neutron source [1]. The q range is enlarged typically by a factor 10. The goal of the experiment described here is to test the method with a steady state reactor (Orph6e LLB. Saclay) and with neutrons of very large wavelengths (up to 20 A). In fact this example is chosen in order to emphasize another advantage; the power of the method for having an excellent resolution.
2. Experimental set up and data analysis
The experimental set-up is obtained from the small angle spectrometer PACE which uses the cold neutrons of the guide G1 (wavelength cut-off of about 6 A) of the reactor Orph6e at Saclay. For * Laboratoire commun CEA-CNRS.
the experiment the mechanical selector is replaced by an element of neutron guide. The incident collimation is achieved by two circular slits (12 and 7 mm diameter) at a distance of 5 m apart (under vacuum). The sample was placed beyond the smaller aperture. The scattered intensity is measured with a multidetector composed of 30 concentric rings with radius p ( 3 < p < 3 2 c m ; A p = l c m ) . The sample detector distance is 5 m (under vacuum). The chopper is placed just before the sample. It is a disk with two slits on the same 30 cm diameter. Each one is 20 mm high and 2 mm wide. The rotation speed of the chopper gives a time of 28400/zs between two successive pulses and the width of each of the 200 channels of analysis is 90/zs. A delay time of 10 000/xs for the optical pulse allows the analysis of h in the range 7.39
AA/A< 0.02.
The data are treated using the quasistatic approximation. Under this condition the scattering law is proportional to I(q) [2] Is°(A) I(q)-= I o (A) = lOs(A)
I°(A) I°(A) '
where IT(A) are the intensity values for a wavelength A at angle 0 and I°(A) is the transmitted intensity through the sample i; the subcripts S and T stand for the sample and the background sample, respectively.
0378-4363/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
104
J.P. Cotton and J. Teixeira / T O F as a monochromatization technique f o r S A N S
3. E x a m p l e o f a diblock c o p o l y m e r in the bulk state
The sample is a solid made from a diblock copolymer (polystyrenepolyisoprene) [3]. The molecular weight of each branch is around 500 000. This sample is a mesomorphic phase of cylinders containing polymers of one species inside an amorphous bulk of the other species. This ordered phase is characterized by a Bragg peak of spacing 2300A [3]. With a classical technique (A = 8 A, D = 5 m), the measured scattering law S(q) shows the Bragg peak (fig. 1) but only the first point determined from the first ring proves the presence of this peak. The lower q points in a small angle experiment being normally poorly defined, this result is not really convincing. The case of the time of flight monochromatization clarifies the situation. Fig. 2 shows the spectrum obtained at 0 = 19' as a function of q, after the data treatment. The peak appears now clearly in spite of the statistical dispersion; there are actually 200 points defining the peak. Statistical accuracy is substantially increased when the points are grouped at constant AA/A = 0.1 (fig. 3), a value chosen by analogy to that imposed by the mechanical selector of the spectrometer D l l at I.L.L. or PACE at LLB. Even with this rather poor A resolution, the peak appears clearly on fig. 3 and the ambiguity found on fig. 1 disappears. 3
I
...
I
:."
• +
I
.~'...
,~:..~'Vo..
• .. C ~/:'_'~..." ."~.S'_
-..-,e
+
l 2
L 3
[ t~ q 10-3 A -~
Fig. 2. Intensity scattered by the same sample of fig. 1 but obtained using the time-of-flight technique.
I
I
I
I
[
I
5-
t+
3
2
q
1
I 2
l 3
I
I
/+
5
q 10-3,,~-1
Fig. 3. The same result as in fig. 2 after a grouping of the data at constant AA/h = 0.1. l
I
I
I
4. Discussion
05
1
1.5
q IO-Z.A -1
Fig. 1. Scattered intensity from a diblock copolymer as a function of the scattering vector q, with the classical set-up (A = 18/~). Notice that the peak is defined by a unique point.
For this example the method seems very expensive in intensity since the chopper reduces it by a factor 125 for each A value (with a resolution AA/A < 0.02). However all values are measured simultaneously and the results show that it can be used even on a medium flux reactor. Finally it is worth noting that the analyzed q range with a sufficient number of data of fig. 3 would be accessible only with a spectrometer having a sample to detector distance of 20 m (as
J.P. Cotton and J. Teixeira / TOF as a monochromatization technique for SANS
o p p o s e d to 5 m here) and with e v e n fewer experim e n t a l points, then a lower resolution.
Acknowledgement We wish to t h a n k Dr. D. Mildner for m a n y helpful discussions.
105
References [1] See for instance G.S. Windsor, Pulsed Neutron Scattering (Taylor and Francis, London, 1981) p. 150. [2] C.S. Borso et al., J. Appl. Cryst. 15 (1982) 443. D.F.R. Mildner, J. Appl. Cryst. 17 (1984) 293. [3] J.P. Cotton, Thesis, Note CEA No. 1743 (1974) 25.
TIME OF FLIGHT AS A MONOCHROMATIZATION TECHNIQUE FOR SANS
J.P. COTTON and J. TEIXEIRA Laboratoire Ldon Brillouin*, CEN-Saclay, 91191 Gif-sur-Yvette, France
Replacing the mechanical selector by a chopper on a small angle scattering spectrometer we obtain a monochromatization technique with a very high resolution. The description of the set up is given. An example in the polymer field is shown.
1. Introduction
In a conventional small angle neutron scattering (SANS) experiment, a mechanical selector defines an incident wave length A from the polychromatic beam emerging from the reactor (4 < h < 20 A). The scattered intensity is measured simultaneously for different scattering angles with a multidetector. The range of scattering vector q (q = 27r0/A) is typically one decade. Another possibility consists of using all the wavelengths of the incident beam by using a time of flight technique. The advantages of this method are well known since they are those of a pulsed neutron source [1]. The q range is enlarged typically by a factor 10. The goal of the experiment described here is to test the method with a steady state reactor (Orph6e LLB. Saclay) and with neutrons of very large wavelengths (up to 20 A). In fact this example is chosen in order to emphasize another advantage; the power of the method for having an excellent resolution.
2. Experimental set up and data analysis
The experimental set-up is obtained from the small angle spectrometer PACE which uses the cold neutrons of the guide G1 (wavelength cut-off of about 6 A) of the reactor Orph6e at Saclay. For * Laboratoire commun CEA-CNRS.
the experiment the mechanical selector is replaced by an element of neutron guide. The incident collimation is achieved by two circular slits (12 and 7 mm diameter) at a distance of 5 m apart (under vacuum). The sample was placed beyond the smaller aperture. The scattered intensity is measured with a multidetector composed of 30 concentric rings with radius p ( 3 < p < 3 2 c m ; A p = l c m ) . The sample detector distance is 5 m (under vacuum). The chopper is placed just before the sample. It is a disk with two slits on the same 30 cm diameter. Each one is 20 mm high and 2 mm wide. The rotation speed of the chopper gives a time of 28400/zs between two successive pulses and the width of each of the 200 channels of analysis is 90/zs. A delay time of 10 000/xs for the optical pulse allows the analysis of h in the range 7.39
AA/A< 0.02.
The data are treated using the quasistatic approximation. Under this condition the scattering law is proportional to I(q) [2] Is°(A) I(q)-= I o (A) = lOs(A)
I°(A) I°(A) '
where IT(A) are the intensity values for a wavelength A at angle 0 and I°(A) is the transmitted intensity through the sample i; the subcripts S and T stand for the sample and the background sample, respectively.
0378-4363/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
104
J.P. Cotton and J. Teixeira / T O F as a monochromatization technique f o r S A N S
3. E x a m p l e o f a diblock c o p o l y m e r in the bulk state
The sample is a solid made from a diblock copolymer (polystyrenepolyisoprene) [3]. The molecular weight of each branch is around 500 000. This sample is a mesomorphic phase of cylinders containing polymers of one species inside an amorphous bulk of the other species. This ordered phase is characterized by a Bragg peak of spacing 2300A [3]. With a classical technique (A = 8 A, D = 5 m), the measured scattering law S(q) shows the Bragg peak (fig. 1) but only the first point determined from the first ring proves the presence of this peak. The lower q points in a small angle experiment being normally poorly defined, this result is not really convincing. The case of the time of flight monochromatization clarifies the situation. Fig. 2 shows the spectrum obtained at 0 = 19' as a function of q, after the data treatment. The peak appears now clearly in spite of the statistical dispersion; there are actually 200 points defining the peak. Statistical accuracy is substantially increased when the points are grouped at constant AA/A = 0.1 (fig. 3), a value chosen by analogy to that imposed by the mechanical selector of the spectrometer D l l at I.L.L. or PACE at LLB. Even with this rather poor A resolution, the peak appears clearly on fig. 3 and the ambiguity found on fig. 1 disappears. 3
I
...
I
:."
• +
I
.~'...
,~:..~'Vo..
• .. C ~/:'_'~..." ."~.S'_
-..-,e
+
l 2
L 3
[ t~ q 10-3 A -~
Fig. 2. Intensity scattered by the same sample of fig. 1 but obtained using the time-of-flight technique.
I
I
I
I
[
I
5-
t+
3
2
q
1
I 2
l 3
I
I
/+
5
q 10-3,,~-1
Fig. 3. The same result as in fig. 2 after a grouping of the data at constant AA/h = 0.1. l
I
I
I
4. Discussion
05
1
1.5
q IO-Z.A -1
Fig. 1. Scattered intensity from a diblock copolymer as a function of the scattering vector q, with the classical set-up (A = 18/~). Notice that the peak is defined by a unique point.
For this example the method seems very expensive in intensity since the chopper reduces it by a factor 125 for each A value (with a resolution AA/A < 0.02). However all values are measured simultaneously and the results show that it can be used even on a medium flux reactor. Finally it is worth noting that the analyzed q range with a sufficient number of data of fig. 3 would be accessible only with a spectrometer having a sample to detector distance of 20 m (as
J.P. Cotton and J. Teixeira / TOF as a monochromatization technique for SANS
o p p o s e d to 5 m here) and with e v e n fewer experim e n t a l points, then a lower resolution.
Acknowledgement We wish to t h a n k Dr. D. Mildner for m a n y helpful discussions.
105
References [1] See for instance G.S. Windsor, Pulsed Neutron Scattering (Taylor and Francis, London, 1981) p. 150. [2] C.S. Borso et al., J. Appl. Cryst. 15 (1982) 443. D.F.R. Mildner, J. Appl. Cryst. 17 (1984) 293. [3] J.P. Cotton, Thesis, Note CEA No. 1743 (1974) 25.