Small angle neutron scattering (SANS) instruments typically cover a q (scattering vector) range from 0.001 to 0.6Å1. This range in q is achieved through a combination of cold neutrons (λ>4Å) and a highly collimated beam. However, as a direct result of the unavailability of a cold source at the Canadian Neutron Beam Centre (CNBC), we have resorted to adapting a triple-axis spectrometer to perform SANS measurements. This is achieved through the use of multiple converging incident beams which enhance the neutron flux on the sample by a factor of 20, compared to a single beam of the same spot size. Furthermore, smearing effects due to vertical divergence from the slit geometry are reduced through the use of horizontal Soller collimators. As a result, this modified triple-axis spectrometer enables SANS measurements to a minimum q value (qmin) of 0.006Å1. Data obtained from the modified triple-axis spectrometer are in good agreement with those data from the 30 m NG3-SANS instrument located at the National Institute of Standards and Technology (Gaithersburg, MD, USA).

Small angle neutron scattering (SANS) has proven a powerful technique for the study of molecular structures and morphologies with length scales ranging from 10 to 1000Å. Dedicated SANS instruments normally cover a scattering vector range (q range) from 0.001 to 0.6Å1, where q is defined as (4π/λ)sin(θ/2), and where λ and θ are the neutron wavelength and scattering angle, respectively. Measuring the lowest possible q value, qmin, usually requires long wavelength neutrons and a small incident beam. Long wavelength neutrons are produced using cryogenic moderators (e.g., liquid hydrogen), shifting the thermal neutron energy distribution spectrum (Maxwellian) toward lower energies, while a small incident beam is generally produced using either a highly collimated, or focused,1 neutron beam. In the case of a highly collimated beam, the reduced neutron flux on the sample is to some degree compensated by the use of a velocity selector, typically employed in SANS instruments, which increases the incident neutron bandwidth (Δλ/λ).

Presently, at the Canadian Neutron Beam Centre (CNBC) no cold source is available at the 120 MW National Research Universal (NRU) reactor. In order to adapt a triple-axis spectrometer for small angle measurements, the incident beam needs therefore to be highly collimated. Moreover, since a given incident neutron wavelength is selected through the use of a single crystal monochromator (Δλ/λ<1%), instead of a velocity selector (Δλ/λ10%), neutron flux incident on the sample is significantly reduced.

In a SANS experiment, the instrumental q resolution, Δq/q (where Δq is the width of scattering vector distribution) is made up of two contributions:2 (1) the angular resolution which is related to the collimation and (2) the wavelength resolution (Δλ/λ). In order to optimize neutron flux, the full width at half maximum full width at half maximum (FWHM) of λ is usually chosen to lie in the range between 10% and 30%(Δλ/λ), making it comparable to the angular resolution.3 However, as mentioned, single crystal monochromators usually produce neutrons with a Δλ/λ<1%, dramatically reducing the incident neutron flux. Although there are ways to increase Δλ/λ, they usually involve a cost prohibitive redesign of the instrument.4–8 

Another method of increasing incident neutron flux, while not increasing the beam size, is to employ multiple incident beams which converge at a single spot on the detector. This concept of one-dimensional confocal beams was first proposed and tested by Nunes9 and was further developed into two-dimensional (2D) confocal beams by Glinka, et al.10 At CNBC we have designed and implemented a confocal Soller collimator (CSC) for use at the N5 triple-axis spectrometer, making it suitable for SANS measurements. Compared to a single beam of given Δλ/λ and dimension, at a qmin of 0.006Å1 the new CSC increases incident neutron flux at the sample by a factor of 20. This development allows for the ubiquitous triple-axis spectrometer to double, with little cost and effort, as a capable SANS instrument. Moreover, this design is different from the double crystal diffraction technique developed by Bones and Hart.11–14 Due to the slit geometry of the incident beam, an additional horizontal Soller collimator (HSC) is required on the scattered side (detector) in order to reduce the smearing due to vertical divergence. However, in some cases the use of an HSC is also needed on the incident side. In order to validate our data, they were compared to those collected at the 30 m NG3-SANS instrument located at the National Institute of Standards and Technology (NIST). The comparison between the different data sets showed excellent agreement.

Figure 1 shows a schematic of the N5 triple-axis spectometer adapted for SANS measurements (N5-SANS). The source-to-monochromator distance, DSM, is 6.78 m. However the neutrons are collimated at a distance of 0.91 m downstream from the source using an 8.9cm(height)×5.9cm(width) beam channel. This results in a new source-to-monochromator distance, DSM, of 5.87 m.

FIG. 1.

Schematic of the N5-SANS adapted from a triple-axis spectrometer to an instrument capable of SANS measurements. The components are as follows: (1) sapphire or Be filter. (2) Monochromator. (3) 23-channel CSC. (4) PG filter/21.6 cm long HSC/open. (5) Sample. (6) 48 cm long HSC. (7) 32-wire position sensitive detector.

FIG. 1.

Schematic of the N5-SANS adapted from a triple-axis spectrometer to an instrument capable of SANS measurements. The components are as follows: (1) sapphire or Be filter. (2) Monochromator. (3) 23-channel CSC. (4) PG filter/21.6 cm long HSC/open. (5) Sample. (6) 48 cm long HSC. (7) 32-wire position sensitive detector.

Close modal

In order to cover an extended q range, different λ’s are used. However, depending on the monochromator crystal planes used to select λ [e.g., pyrolytic graphite (PG) (002) reflection], the incident neutron beam can be contaminated by higher order harmonics of the fundamental neutron wavelength (i.e., λ/2, λ/3, etc.). In the current SANS experimental setup three values of λ (2.37, 4, and 5.23Å) are used. Higher order harmonic neutrons are reduced either through the use of a beryllium (Be) (λ>3.99Å) or PG filter (λ=2.37Å). A sapphire filter is optionally used for reducing the presence of “fast neutrons.”15 Therefore, depending on the chosen wavelength, either a sapphire (λ3.99Å), or Be (λ>3.99Å) filter (component 1 in Fig. 1), cooled to liquid nitrogen temperature is placed upstream of the PG monochromator (component 2 in Fig. 1). Using the (002) crystal plane reflection of a PG monochromator, λ’s of 2.37, 4.00, and 5.23Å are obtained for monochromator angles (θM) of 20.69°, 36.5°, and 51.25°, respectively. The PG monochromator used was of dimensions 5cm(high)×8.9cm(wide)×0.16cm(thick).

Selected neutrons then go through a 66 cm long (the length denoted as LCSC) CSC (component 3 in Figs. 1 and 2) made up of 23 channels, whereby each channel is separated by 0.25 mm spring steel blades coated with Gd2O3. All channels converge on the same spot at the detector. Each individual channel has dimensions of 3.8 cm (high) by 0.13 cm (wide) at the monochromator end and 3.8 cm (high) by 0.10 cm at the end closest to the sample. The nearest distance from the monochromator to the CSC, DMC, is 15 cm. For λ=4 and 2.37Å neutrons, the width of each channel can be increased to twice the original width by removing alternating Sollers.

FIG. 2.

Photograph of the 23-channel CSC.

FIG. 2.

Photograph of the 23-channel CSC.

Close modal

After exiting the CSC, neutrons go through component 4 (Fig. 1), which for 2.37Å neutrons is a PG filter, or in the case of 5.23Å neutrons, a 21.6 cm long HSC with 0.25 cm vertical opening individual channels. In the case of 4Å neutrons, component 4 is removed. At this point, the correct wavelength neutrons interact with the sample (component 5 in Fig. 1), located 86 cm from the nearest point to the CSC (denoted as DCS). The scattered neutrons then go through a 48 cm long HSC containing 0.25 cm high individual channel (component 6 in Fig. 1). A 32-wire H3e position-sensitive detector (component 7 in Fig. 1) is placed after the second HSC with an effective sample-to-detector distance, DSD, of 1.43 m. Each wire is capable of detecting scattered neutrons at the corresponding θ. Prior to experimentation, the efficiency of each detector wire was determined, and was later used to correct the data.

Scattered intensity, Iraw(q), can be obtained from the following equation:

Iraw(q)=IoΔΩηTsam(λ)VdΣdΩ(q)+Ibgd(q),
(1)

where Io, ΔΩ, η, Tsam(λ), V, and Ibgd(q) are incident neutron intensity, sample-to-detector solid angle, detector efficiency, transmission of the sample, scattering volume, and background. (dΣ/dΩ)(q) represents the differential scattering cross section per unit volume and contains all of the pertinent sample information (e.g., shape, interactions, etc.). The goal of a SANS experiment is to obtain (dΣ/dΩ) as a function of q, which is used to determine the morphology of a given system. Therefore, appropriate data reduction has to be performed in order to obtain (dΣ/dΩ)(q) from the measured scattered intensities.

In our experiment, Iraw(q) are collected using different wavelength neutrons (λ=2.37, 4, and 5.23Å) and several detector angles in order to cover the desired q range. The data are normalized by incident neutron flux monitored using a low-efficiency neutron detector located after the CSC. The normalized scattered intensity of the empty cell, Iemt(q) and Ibgd(q) are obtained at the same q values. The reduced intensity, Ired(q), can then be expressed as follows:

Ired(q)=[Iraw(q)Ibgd(q)]Tsam(λ)[Iemp(q)Ibgd(q)]Temp(λ).
(2)

The sample and empty cell transmissions, Tsam(λ) and Temp(λ), respectively, are determined from the straight through beam intensity (measured by the two central detector wires at θ=0°) ratios of the sample-to-open beam and the empty cell-to-open beam. Ired(q) is then put on an absolute scale using a sample with a known (dΣ/dΩ)(q). Finally, the reduced intensities for the various q ranges are merged, yielding a single SANS curve.

The CSC was tested prior to performing SANS measurements. In order to verify the point of beam convergence, the incident beam profiles on the detector at various locations of the CSC along the beam direction axis were measured [shown in Fig. 3(a)]. The data show the optimal DMC—the distance resulting in the highest incident intensity at θ=0° and the narrowest beam width at the detector—to be 15cm, a value consistent with the specified collimator design. Each channel was also scanned with a 0.1 cm slit (slit width is equal to the width of a single CSC channel) across the CSC. Figure 3(b) shows the incident intensity of individual channels, whose intensities remain practically unchanged up to channel 14. The decrease in the neutron flux from channel 15 on, is most likely due to an insufficient monochromator size and/or displacement of the monochromator (no translational capability). Figure 3(c) shows a comparison of the total intensity (all channels opened) with that from individual channels. A Lucite absorber was used for the measurements with all the channels open to avoid saturating the detector. The data shown in Figure 3(c) were corrected by the Lucite’s absorption factor. The neutron beams from individual channels of size of 3.8×0.1cm2 project onto the detector at proximate locations. When fitted with a Gaussian function, the centers of the peak positions vary within ±0.03° from each other, which translates into ±6.3×104Å1 for λ=5.23Å(lowq) and ±1.4×103Å1 for l=2.37Å(highq) in Δq. These values are at least an order of magnitude lower than the calculated resolution functions in shown in Sec. IV B, and do not affect the accuracy of the data. The increased background-to-direct beam ratio and the broad peaks on both sides of the beam when all channels are opened, are presumably the result of low-q scattering from the Lucite attenuator. It is clear that the CSC enhances the incident neutron intensity by a factor of 20, compared to that from each individual channel, without any noticeable effect on the projected beam size (at the detector). Ideally, using a curved monochromator the expected increase in intensity would be 23 times, equal to the number of CSC channels.

FIG. 3.

(a) Characterization of the incident beam width (all channel open) at various DMC. (b) Characterization of the individual CSC channels. (c) Comparison of the incident beam intensity from individual channels (1, 5, 10, 15, 20) and all channels.

FIG. 3.

(a) Characterization of the incident beam width (all channel open) at various DMC. (b) Characterization of the individual CSC channels. (c) Comparison of the incident beam intensity from individual channels (1, 5, 10, 15, 20) and all channels.

Close modal

A SANS instrument’s resolution function depends on the collimation used (e.g., pinhole, slit, etc.). In a slit geometry where the x and y dimensions of the slit differ considerably, there is a significant difference between the q variances of the two orthogonal components in the detector plane (qx-qy), σqx2 along the θ direction and σqy2 in the orthogonal direction, resulting in an asymmetric smearing of the data, (i.e., when σqy2σqx2). This effect is demonstrated in Fig. 4, which shows a small angle x-ray scattering (SAXS) result from a 1% phospholipid dispersion [dimyristoyl phosphatidylcholine (DMPC) in water] obtained using an Ultima III diffractometer (Rigaku, Japan). The x-ray diffractometer, with a line source of x-rays, was set up with a 0.5° divergence HSC on the incident side. The two curves show SAXS data with and without a 0.5° divergence HCS on the detector side. A peak (obtained with the HSC on the detector side) corresponding to the lamellar spacing of DMPC is not only smeared, but is also asymmetric in the absence of the HSC on the detector side. Generally, the magnitudes of σqx2 and σqy2 for a slit geometry can be expressed as

(3)
σqx2=(π26λ2)[X12(DCS+DSD)2LCSC2DSD2+X22(LCSC+DCS+DSD)2LCSC2DSD2+(X3DSD)2+(qxq)2θ2(Δλλ)2],
σqy2=(π26λ2)[Y12(DCS+DSD)2LCSC2DSD2+Y22(LCSC+DCS+DSD)2LCSC2DSD2+(Y3DSD)2+(qyq)2θ2(Δλλ)2],
σq2=σqx2+σqy2,
where (X1, Y1), (X2, Y2), and (X3, Y3) are slits for the beam source, the sample, and the detector along qx and qy, respectively.1,2

FIG. 4.

SAXS data of a DMPC sample with (dotted curve) and without (solid curve) a 0.5° divergence HSC after the sample.

FIG. 4.

SAXS data of a DMPC sample with (dotted curve) and without (solid curve) a 0.5° divergence HSC after the sample.

Close modal

To minimize peak asymmetry, as shown in Fig. 4, the dimension of σqy2 should approach that of σqx2. However, since X1, X2, and X3 are highly constrained by the CSC and the width of the individual detector wires (2mm), σqy2 is relaxed, compared to σqx2 (still maintaining a slit geometry), allowing for a sufficient neutron flux. This way, σqy2 dominates σq2. Figure 5 shows a plot of σq/q and σq(σq=σq2) as a function of q. As expected from Eq. (2), for a given λ, σq remains almost constant, and most of the smearing (i.e., σq/q) takes place at the lowest θs. Figure 5 also shows a comparison of this result with that from a pinhole geometry instrument (NG3-SANS) located at the NIST Center for Neutron Research.16 The resolution function of the NG3-SANS is calculated based on a neutron wavelength of 6Å, a Δλ/λof15% and three DSDs (1, 5 and 13.2 m). The magnitude of σq (Fig. 5) increases at higher q values as a result of the poor wavelength resolution (Δλ/λ15% in this case), and eventually becomes comparable to the first three terms [in Eq. (2)] related to distance collimation. However, this increase in σq does not worsen the smearing effect (comparing to lower q values), as σq/q continues to decrease with increasing q. At lowq the instrumental resolution, σq/q of the N5-SANS is worse than the NG3-SANS at q<0.05Å1, but comparable and sometimes even better at q>0.1Å1.

FIG. 5.

Instrumental resolution of the N5- and NG3-SANS instruments. Both σq2/q (red triangles) and σq2 (blue circles) are plotted as a function of q. Hollow and solid symbols represent N5-SANS and NG3-SANS data, respectively.

FIG. 5.

Instrumental resolution of the N5- and NG3-SANS instruments. Both σq2/q (red triangles) and σq2 (blue circles) are plotted as a function of q. Hollow and solid symbols represent N5-SANS and NG3-SANS data, respectively.

Close modal

For N5-SANS, the apparent q values, qapp are obtained from (4π/λ)sin(θapp/2), where θapp is tan1(R/DSD), and where R is the distance from the center of the individual detecting wires to the center of the incident beam in the scattering plane. The mean q value, q, is thus different from qapp and can be derived based on the two components of the resolution function (σqx and σqy). We assume a 2D Gaussian distribution of the contributed intensity from various qs (on the qx-qy plane) centered at qapp. Since the scattered intensity along the qy axis is symmetric around the horizontal center line (qy=0) of the detector [i.e., Iraw(qx,qy)=Iraw(qx,qy)], but not symmetric along the qx axis around the vertical center line (qx=0) [i.e., Iraw(qx,qy)Iraw(qx,qy)], different integration boundaries are applied to qx and qy [i.e., (Δqx,max, Δqx,max) for qx and (0, Δqy,max) for qy, where Δqx,max and Δqy,max are calculated from the maximal divergence in the frame of scattering geometry]. Since the values of Δqx,max and Δqy,max are more than seven times of σqx and σqy under all circumstances, the integration of Gaussian function covers more than 99.9% of that over infinity. As a result, an analytic solution q=qapp2+σqy2π can be written as follows:

(4)
q'2=q'x2+q'y2,
qx=qxe(qxqapp)2σqx2dqxe(qxqapp)2σqx2dqxandqy=0qye(qyqapp)2σqy2dqy0e(qyqapp)2σqy2dqy.

Using the N5-SANS, we examine two standard polystyrene microsphere samples with diameters of 24 and 50 nm (PS02N, Bangs Laboratories). The microspheres arrived as 10wt% solutions and were subsequently diluted to 1wt% with D2O (Atomic Energy of Canada Limited, Chalk River, Ontario, Canada). The samples were loaded in rectangular quartz cells having a 5 mm path length. The absolute intensities (i.e., dΣ/dΩ) for both samples are obtained from the NG3-SANS, as shown in Figs. 6(a) and 6(c). To obtain the best-fit structural parameters, NG3-SANS data are fitted using a core-shell-sphere model convoluted with the instrumental resolution. The same model and structural parameters are used to rescale the scattering data of the samples obtained from N5-SANS; however, this time taking into consideration the N5-SANS instrumental resolution [Figs. 6(b) and 6(d)]. The N5-SANS data are rescaled for each q range and then plotted on the same figure. Slight discontinuities at the overlapping regions of the rescaled data are observed, presumably due to different resolution functions of the individual q ranges. We find good agreement between NG3-SANS and N5-SANS data [Figs. 6(b) and 6(d)] (slight discrepancies in slopes of the two curves are the result of different resolution functions and incoherent background subtraction) proving the successful implementation of this SANS design. The total data collection time at the N5-SANS was 4.5h (112h for λ=5.23Å, 1 h for λ=4Å, and 1 h for λ=2.37Å), compared to 40 min at the NG3-SANS. Moreover, the counting statistics of the N5-SANS data are poorer than those obtained at the NG3-SANS data. The reasons for this are twofold: (1) the small detecting area of the 32-wire N5-SANS detector (12×6.5cm2) requires multiple detector locations to cover a given q range (compared to the much larger 65×65cm2 2D detector at NG3). (2) For weakly scattering samples, air scattering dominates at lowq, thus longer collecting times are needed to reduce the errors when subtracting the air scattering from the sample scattering. This latter issue is presently being addressed through the use of evacuated HSCs.

FIG. 6.

SANS data of 1wt% microspheres with a diameter of 24 nm obtained from (a) the NG3-SANS and (b) the N5-SANS, and 1wt% 50 nm diameter microspheres from (c) the NG3-SANS and (d) the N5-SANS. The best fits using a core-shell-sphere model are shown as solid lines. N5-SANS data are rescaled using the same model and structural parameters as the NG3-SANS, but different instrumental resolution. Circles, squares, and triangles in (b) and (d) represent the SANS configurations using λ=5.23, 4, and 2.37Å, respectively. NG3-SANS data (dots) are also plotted in (b) and (d) for comparison purpose.

FIG. 6.

SANS data of 1wt% microspheres with a diameter of 24 nm obtained from (a) the NG3-SANS and (b) the N5-SANS, and 1wt% 50 nm diameter microspheres from (c) the NG3-SANS and (d) the N5-SANS. The best fits using a core-shell-sphere model are shown as solid lines. N5-SANS data are rescaled using the same model and structural parameters as the NG3-SANS, but different instrumental resolution. Circles, squares, and triangles in (b) and (d) represent the SANS configurations using λ=5.23, 4, and 2.37Å, respectively. NG3-SANS data (dots) are also plotted in (b) and (d) for comparison purpose.

Close modal

We have reported on adapting a triple-axis spectrometer for use in SANS measurements. Data (from 0.006 to 0.3Å1) obtained from such an instrument (i.e., N5-SANS) agree well with those collected from the well-established 30 m NG3-SANS. Compared to the NG3-SANS, the instrumental resolution is poorer at lowq(q<0.05Å1), but comparable, or even better, at high q(q>0.1Å1). Although the measurements at the N5-SANS compared to the NG3-SANS take longer, this situation can, to some extent, be remedied through the use of evacuated HSCs, which are currently under construction.

This work utilized facilities supported in part by the National Science Foundation under Agreement No. DMR-9986442. M.-P. N. would like to thank Dr. John Barker, Dr. Charles Glinka, and Dr. Boualem Hammouda (NIST) for the helpful discussions.

1.
S. M.
Choi
,
J. G.
Barker
,
C. J.
Glinka
,
Y. T.
Cheng
, and
P. L.
Gammel
,
J. Appl. Crystallogr.
33
,
793
(
2000
).
2.
D. F. R.
Mildner
and
J. M.
Carpenter
,
J. Appl. Crystallogr.
17
,
249
(
1984
).
3.
D. F. R.
Mildner
and
J. M.
Carpenter
,
J. Appl. Crystallogr.
20
,
419
(
1987
).
4.
H. R.
Child
and
S.
Spooner
,
J. Appl. Crystallogr.
13
,
259
(
1980
).
5.
D. F. R.
Mildner
,
R.
Berliner
,
O. A.
Pringle
, and
J. S.
King
,
J. Appl. Crystallogr.
14
,
370
(
1981
).
6.
B. J.
Heuser
,
M.
Popovichi
,
W. B.
Yelon
, and
R.
Berliner
,
Proc. SPIE
1738
,
210
(
1992
).
7.
V. K.
Aswal
and
P. S.
Goyal
,
Curr. Sci.
79
,
947
(
2000
).
8.
V. K.
Aswal
,
J. V.
Joshi
,
P. S.
Goyal
, and
A. V.
Pimpale
,
J. Appl. Crystallogr.
33
,
118
(
2000
).
9.
A. C.
Nunes
,
Nucl. Instrum. Methods
119
,
291
(
1974
).
10.
C. J.
Glinka
,
J. M.
Rowe
, and
J.
LARock
,
J. Appl. Crystallogr.
19
,
427
(
1986
).
11.
U.
Bonse
and
M.
Hart
,
Appl. Phys. Lett.
7
,
238
(
1965
).
12.
U.
Bonse
and
M.
Hart
,
Z. Phys.
189
,
151
(
1966
).
13.
A. R.
Drews
,
J. G.
Barker
,
C. J.
Glinka
, and
M.
Agamalian
,
Physica B (Amsterdam)
241–243
,
189
(
1998
).
14.
F. U.
Ahmed
,
I.
Kamal
,
S. M.
Yunus
,
T. K.
Datta
,
A. K.
Azad
,
A. K. M.
Zakaria
, and
P. S.
Goyal
,
Physica B (Amsterdam)
366
,
11
(
2005
).
15.
H. F.
Nieman
,
D. C.
Tennant
, and
G.
Dolling
,
Rev. Sci. Instrum.
51
,
1299
(
1980
).
16.
C. J.
Glinka
,
J. G.
Barker
,
B.
Hammouda
,
S.
Krueger
,
J. J.
Moyer
, and
W. J.
Orts
,
J. Appl. Crystallogr.
31
,
430
(
1998
).