Neutron diffraction from superparamagnetic colloidal crystals

Author’s Accepted Manuscript Neutron diffraction colloidal crystals

from

superparamagnetic

M. Ličen, I. Drevenšek-Olenik, L. Čoga, S. Gyergyek, S. Kralj, M. Fally, C. Pruner, P. Geltenbort, U. Gasser, G. Nagy, J. Klepp www.elsevier.com/locate/jpcs

PII: DOI: Reference:

S0022-3697(16)31242-2 http://dx.doi.org/10.1016/j.jpcs.2017.05.002 PCS8052

To appear in: Journal of Physical and Chemistry of Solids Received date: 14 December 2016 Revised date: 24 April 2017 Accepted date: 3 May 2017 Cite this article as: M. Ličen, I. Drevenšek-Olenik, L. Čoga, S. Gyergyek, S. Kralj, M. Fally, C. Pruner, P. Geltenbort, U. Gasser, G. Nagy and J. Klepp, Neutron diffraction from superparamagnetic colloidal crystals, Journal of Physical and Chemistry of Solids, http://dx.doi.org/10.1016/j.jpcs.2017.05.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Neutron diffraction from superparamagnetic colloidal crystals M. Ličena,∗, I. Drevenšek-Olenika,b,∗, L. Čogab , S. Gyergyekc , S. Kraljc,d , M. Fallye , C. Prunerf , P. Geltenbortg , U. Gasserh , G. Nagyh , J. Kleppe a Jožef

Stefan Institute, Department of Complex Matter, Jamova 39, SI-1000 Ljubljana, Slovenia of Ljubljana, Faculty of Mathematics and Physics, SI-1000, Ljubljana, Slovenia c Jožef Stefan Institute, Department for Materials Synthesis, Jamova 39, SI-1000 Ljubljana, Slovenia d Nanos SCI, Nanos Scientificae d.o.o., Teslova 30, 1000 Ljubljana, Slovenia e University of Vienna, Faculty of Physics, A-1090 Vienna, Austria f University of Salzburg, Department Chemistry and Physics of Materials, 5020 Salzburg, Austria g Institut Laue Langevin, CS 20156, F-38042 Grenoble Cedex 9, France h Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, 5232 Villigen, Switzerland b University

Abstract We fabricated a superparamagnetic ordered structure via self-assembly of a colloidal crystal from a suspension of maghemite nanoparticles and polystyrene beads. Such crystals are potential candidates for novel polarizing beamsplitters for cold neutrons, complementing the available methods for polarizing neutrons. Different bead sizes and nanoparticle concentrations were tested to obtain a crystal of reasonable quality. Neutron diffraction experiments in the presence of an external magnetic field were performed on the most promising sample. We demonstrate that the diffraction efficiency of such crystals can be controlled by the magnetic field. Our measurements also indicate that the Bragg diffraction regime can be reached with colloidal crystals. Keywords: colloidal crystals, superparamagnetic nanoparticles, neutron scattering

1. Introduction Spin-polarized neutron beams are required for experiments in fundamental and condensed matter physics [1– 4]. In previous articles we have described holographic gratings functioning as neutron beam-splitters [5–9] and some ideas and preliminary results on using superparamagnetic nanoparticles to construct polarizing beam-splitters [7, 10, 11]. It is known that the total scattering cross-section of nanocrystalline ferromagnets may vary over some orders of magnitude under the influence of magnetic fields [12]. By using a magnetic grating or a non-magnetic grating complemented with magnetic nanoparticles, one can control the diffraction of neutrons by tuning the refractive-index modulation of the grating via an external magnetic field. If the magnetic part of the refractive index modulation exactly cancels the nuclear part for one of the neutron spin states, the grating will only diffract neutrons in the other spin state, thus producing polarized beams. Here, we report on the first neutron diffraction experiment on a periodic structure with superparamagnetic properties, intended to assess the above idea. The structure we used was fabricated by incorporating maghemite (γ − Fe2 O3 ) nanoparticles in a colloidal crystal self-assembled from polystyrene beads. Colloidal crystals are ordered structures that self-assemble from colloidal particles, whose diameters are typically between 100 nm and 2000 nm. Such crystals have lattice constants comparable to the wavelength of visible light and are therefore of particular interest in photonics, either by themselves or as templates for other materials [13, 14]. Various applications of magnetic colloidal crystals have been demonstrated, such as controlling the distance between particles [15–17], controlling the self-assembly process [18–20], and construction of Faraday rotators [21], all focused on modification of optical properties of materials. Because of the submicrometer size of the particles, colloidal crystals are also suitable for fabrication of optical elements for cold neutrons. Neutron scattering studies on magnetic colloidal crystals based on ferromagnetic nickel and cobalt have recently been reported by Grigoriev et al [22] and Grigoryeva et al [23]; in contrast, the present study examines a colloidal crystal with superparamagnetic properties. The main advantage of using superparamagnetic instead of ferromagnetic materials is their very narrow hysteresis, allowing easier control over the magnetisation of the crystal, which is important for our long-term goal. ∗ Corresponding

author Email addresses: [email protected] (M. Ličen), [email protected] (I. Drevenšek-Olenik)

Preprint submitted to Journal of Physics and Chemistry of Solids

May 3, 2017

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2. Material and methods

2.1. Sample preparation

Colloidal crystals were prepared using the vertical deposition method, which has been described by Jiang et al [24]. In brief, a substrate is placed vertically into a suspension of colloidal particles, which is then left to slowly evaporate. The evaporation drives a constant flow of water into the meniscus the suspension forms on the substrate, which deposits colloidal particles in an ordered array. As the water level drops, the colloidal crystal is slowly formed over the entire surface of the substrate. Our approach to fabricate a superparamagnetic colloidal crystal was similar to that of Cong et al [25], where magnetite nanoparticles were mixed into the colloidal suspension before self-assembly of the crystal. In order to produce a well-ordered structure, we tested combinations of different sizes of polystyrene beads and concentrations of nanoparticles. Suspensions of spherical polystyrene particles in water (diameters: 202 nm, 503 nm, and 909 nm, with standard deviations 5 nm, 13 nm, and 25 nm, respectively) were purchased from microParticles GmbH and diluted with deionised water so that the particle concentration was 1 mg/mL. Silica-coated maghemite nanoparticles (MNPs) [26] with an average diameter of 12 nm were prepared at Jožef Stefan Institute and added to the colloidal suspension in such concentrations, that the total volume of the nanoparticles Vn was equal to 0.5Vf , Vf , or 2Vf , where Vf is the predicted free volume of the crystal. These concentrations were estimated by taking Vf as the volume of the voids in a perfect FCC crystal formed by all the polystyrene beads in the suspension and then using the density of bulk maghemite to calculate the mass of MNPs needed to fill those voids. To ensure the suspension was well mixed, it was shaken with a vortex mixer and placed in a sonic bath for 15 minutes. For substrates, we used test grade silicon wafers purchased from UniversityWAFER. The wafers were cut into pieces with dimension of approximately 3 cm × 1 cm and placed in piranha solution (volume ratio H2 SO4 : H2 O2 = 7 : 3) at 70 ◦ C for 45 minutes. Afterwards, the substrates were rinsed with deionised water and dried in a stream of nitrogen. The substrate and the suspension were placed in a 5 mL beaker, so that the long edge of the substrate formed an angle of approximately 30◦ with the vertical [27], and were then partially covered with aluminum foil to reduce the evaporation rate. The beaker was then placed in an oven at 60 ◦ C [28] for 72 hours, so that all of the water in the beaker evaporated.

2.2. Determining the concentration of MNPs in the samples

Obtaining the volume fraction of the MNPs in the samples required us to measure the volume of the MNPs inside the crystal as well as the volume of the crystal itself. The former was determined by measuring magnetization curves (Fig. 1a) of smaller pieces (dimensions approximately 3 mm × 3 mm), which were cut from the samples (Fig. 1b). The measurements were made with a Lake Shore 7307 vibrating-sample magnetometer. The magnetisation curves were composed of superparamagnetic contributions of the MNPs and diamagnetic contributions of the rest of the sample. At large fields, the magnetisation of the MNPs is saturated, meaning that only the diamagnetic contributions affect the change in magnetisation of the sample with increasing magnetic field. The slope of a linear fit of the measured magnetisation curves at high fields therefore represents all the diamagnetic contributions, which can then be subtracted to obtain the magnetisation curves shown in Fig. 1a. As seen in these plots, no hysteresis in the curves could be observed within the accuracy of our measurements. Comparing the magnetic moments at saturation with those measured for pure MNPs allowed us to calculate the mass of MNPs in the samples, from which we calculated their total volume by assuming their density is the same as that of bulk maghemite. We calculated the total volume of a colloidal crystal by multiplying its thickness, which was obtained with Jeol’s JSM-7600F scanning electron microscope (SEM), by its area, determined under an optical microscope. We compared the volume of the maghemite nanoparticles to Vf , which was assumed to be approximately 26 % of the total crystal volume, as it would be in a perfect FCC crystal.

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Neutron diffraction experiments

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Figure 1: (a) Magnetisation curves measured for samples with beads of three different diameters, after diamagnetic contributions have been subtracted. The vertical line indicates the maximum strength of the magnetic field used in the neutron diffraction experiment described in section 3.2. The inset illustrates the subtraction of diamagnetic contribution from the original data points (dark green) to obtain the final magnetisation curve (light green). (b) Photo of a typical sample. The brown-colored region is where the colloidal crystal formed on the wafer. The white square at the bottom illustrates the size of the samples used for magnetisation measurements.

We also measured the iron content at different depths of the crystals by performing energy-dispersive X-ray spectroscopy (EDS) measurements at several points along each crystal’s cross-section. The measurements were done with the same Jeol JSM-7600F SEM that was used to record the images; the method itself has been described elsewhere (see for example [29]). In brief: electrons from the SEM are used to excite electrons in the atoms present in the sample; upon decaying back into their ground states, the electrons emit X-rays that are characteristic for each atom and can be used for the identification of the chemical composition of the sample. Because our samples are not homogeneous, do not have a flat surface, and are largely composed of relatively light elements, whose mass is difficult to determine accurately with EDS, there is a large uncertainty in the results of the EDS measurements. It is, however, reasonable to assume that these measurement errors are similar throughout the sample, so the values measured with EDS can be used to determine relative concentrations of iron at different depths in a sample. Combining these measurements with those of the total mass of the MNPs obtained by measuring the saturation magnetisation of the samples allowed us to rescale the data points so that the average concentration measured with EDS was in agreement with the average concentration determined through magnetisation measurements.

2.3. Neutron diffraction experiments

Preliminary experiments with empty colloidal crystals, i.e. crystal without incorporated MNPs, were performed at the SANS-II beamline at the Paul Scherrer Institute (PSI) in Villigen, Switzerland. The average neutron wavelength was 1.9 nm, with a bandwidth of ∆λ/λ = 0.1, and a divergence of 3 mrad. The detector at the SANS-II line is circular with a diameter of 64 cm and a pixel size of 4.3 mm × 4.3 mm. The sample-detector distance for our measurement was 6 m. Neutron diffraction experiments on crystals filled with MNPs were performed at the very cold neutron beam of the experimental installation PF2 of the Institut Laue Langevin (ILL) in Grenoble, France. For these experiments, we used an unpolarised beam of neutrons with average wavelength at 5.6 nm, a rather large bandwidth of ∆λ/λ & 0.5, and a divergence of 2 mrad. This divergence was achieved by passing the beam through two square slits of sizes 5 mm × 5 mm and 1 mm × 1 mm that were spaced 2 m apart. The scattered neutrons were detected by a 2D detector with 128 × 128 pixels, where each pixel has a size of 2 mm × 2 mm. The sample-detector distance was 95 cm. To reduce incoherent scattering and absorption of neutrons in air, tubes continuously flushed with helium were placed along the path of the beam. No additional attenuation of the central beam was necessary in either setup due to the low flux of neutrons. Magnetization of the sample was achieved by using an electromagnet to produce an external magnetic field between 0 and 180 mT in the vertical direction, which was perpendicular to the growth direction of the colloidal crystal and the neutron beam (Fig. 2). At 180 mT, the magnetization of the nanoparticles present in the crystal was saturated to about 90 % (see Fig. 1a).

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Figure 2: Illustration of the setup used for the neutron diffraction experiment at the very cold beam position PF2/VCN of the ILL. A section of the helium tube has been cut out in the image to reveal the interior of the tube.

3. Results and discussion 3.1. Optimizing crystal self-assembly We first investigated how the quality of the crystal structure varies with the size of the polystyrene beads. For that purpose, we mixed 202 nm, 503 nm, and 909 nm beads, respectively, with maghemite nanoparticles of total volume Vn equal to Vf . SEM images of the surfaces and cross-sections of the samples revealed that the best quality crystal was formed from 202 nm beads, while the larger beads formed increasingly more disordered samples (Fig. 3). The thicknesses, as measured from crystal cross-sections viewed under SEM, were found to be approximately 13 µm, 9µm, and 12 µm for the crystals made from 202 nm, 503 nm, and 909 nm beads, respectively.

Figure 3: SEM images of surface structures of crystals for Vn = Vf with bead diameters 202 nm (a), 503 nm (b), and 909 nm (c). Insets are Fourier transformations of the main images.

To assess the influence of the concentration of MNPs in the starting suspension on the quality of the crystal, we grew two more crystals from 202 nm beads with MNP volume Vn = 0.5Vf and Vn = 2Vf (Fig.4). Inspection of the surface of the samples at several locations revealed that these samples were more ordered than those made from larger beads, but were less ordered than the first crystal made from 202 nm beads with Vn = Vf . In both cases we also observed parts of the structure that were filled exclusively with nanoparticles (Fig. 4c). Mixing less nanoparticles (Vn = 0.5Vf ) with the 503 nm beads improved the quality of the structure (compare Fig. 3b with Fig. 5a), however, the sample was composed of smaller well-ordered domains surrounded by larger disordered areas as seen in Fig. 5b.

Figure 4: SEM images of crystals made from 202 nm beads for Vn = 0.5Vf (a), Vn = 2Vf (b), and cross-section of a crystal showing accumulation of MNPs.

3.2

Neutron diffraction results

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Figure 5: SEM images of a crystal made from 505 nm beads for Vn = 0.5Vf at a smaller scale (a) and a larger scale(b). Insets are Fourier transformations of the main images.

If such colloidal crystals are to be used in neutron optics, it is important that the nanoparticles are evenly distributed throughout the crystal. We therefore measured the iron content at different depths of the crystals as described in section 2.2 - the results are shown in Fig. 6.The error bars represent the uncertainty of the total area under each curve and stem from the uncertainty of the average concentrations of the MNPs used in the normalization. The sample from 909 nm beads had considerably more MNPs at the bottom of the crystal (near the substrate) than at the crystal surface, while the other two samples prepared with the same concentration of MNPs, but with smaller beads, have a much more even distribution, with ratios of MNP volume in the crystal to free volume between 20 % and 40 %. The two samples from 202 nm beads that were made with larger and smaller concentrations of MNPs (Vn = 2Vf and Vn = 0.5Vf ) show a less even distribution throughout the depth of the crystal. The discrepancy between the volume fractions of MNPs inside the crystal and those in the suspensions is not unexpected, because a portion of the polystyrene beads and MNPs is not incorporated in the crystal and is visibly deposited on the bottom and sides of the beaker instead. Note that even with ideal packing, only 74 % of the free volume of the crystal can be filled (assuming spherical MNPs), or probably even less since the shapes of the nanoparticles are irregular. Values higher than 74 % indicate that parts of some samples were composed mainly of MNPs (as seen in Fig. 4c) instead of MNPs only residing in the free volume between beads. The size of the beads seems to have a larger influence on the structural regularity of the crystal than the concentration of the nanoparticles in the suspension. The homogeneity of the nanoparticle concentration in the crystal, however, appears to depend heavily on the concentration of MNPs in the suspension. Additional improvements can be achieved by choosing the optimal concentrations of MNPs, though more research is required to determine the exact relationship between bead size, MNP concentration in the suspension, and quality of the final structure. 260

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3.2. Neutron diffraction results In our initial experiments at PSI, we measured rocking curves (angular sensitivity of the diffraction efficiency) with an empty colloidal crystal self-assembled from 295 nm polystyrene beads, to investigate whether the quality of

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Neutron diffraction results

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the crystals produced by the procedure described in section 2.1 can, in principle, be sufficient to achieve diffraction in the Bragg regime (two-wave coupling regime). This is desirable for the application we have in mind because neutrons should ideally only be diffracted into two spots so that neutrons would not be lost due to diffraction in unwanted directions. Figure 7a shows a diffraction pattern obtained by summing up all the diffraction patterns obtained during the measurement of the rocking curve. The very diffraction spots farther from the  pronounced direct-beam spot in the center correspond to diffraction from the 2¯20 FCC crystal planes. The origin of the less pronounced spots closer to the direct beam is not clear. Their positions suggest reflections from {111} and {200} FCC crystal planes, which do not fulfill the Bragg condition, but could still have been observed because of the relatively large neutron wavelength and imperfections in the crystal [30, 31]. However, the ratio of scattering angles for the outer and the inner spots is 1.76, as opposed to 1.63, as we would expect in case of {111} planes, or 1.41 in the case of {200} planes. The absence of a peak in the rocking curves for the inner spots (not shown) also excludes diffraction from possible HCP stacking sequences in the crystal. Such spots have been observed before in diffraction images of colloidal crystals and were attributed to either stacking faults in the crystal or surface  scattering [32, 33]. Figure 7b shows the rocking curves for the six spots in the diffraction pattern created by 2¯20 planes, which was measured by rotating the sample around a vertical axis going through its center (illustrated in the inset). Diffraction efficiency was calculated by dividing the neutron counts in one spot by the neutron counts in the direct-beam spot as well as all the diffraction spots in the diffraction pattern. Error bars were obtained by assuming that the uncertainty of counts in each pixel is equal to the square root of the counts. The peaks in the rocking curves do not coincide because surface was not completely perpendicular to the neutron beam. The diffraction efficiency for
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Figure 7: (a) Sum of diffraction patterns obtained during the measurement of the rocking curves. Momentum transfers  are marked on the x and y axes, the total neutron counts are represented by the colors. (b) Rocking curves for the reflections from 2¯ 20 planes. The area under one of the curves is shaded to better illustrate the width of the peak.

In the next step, we performed neutron diffraction experiments at ILL on a colloidal crystal that was filled with MNPs. We chose the sample we considered to be of best quality, i.e. the one from 202 nm beads with Vn = Vf . A typical neutron diffraction pattern is displayed in Fig. 8a. The noticeably weaker ¯220 and 02¯2 spots indicate that the beam was not perfectly perpendicular to the surface of the sample. Just as in the PSI measurement, we were unable to attribute the inner spots, which are in this case very close to the direct beam, to diffraction from any planes in an FCC structure. Once the helium tube between the sample and the detector was in place, the outer spots were cut off, so we analyzed the dependency of diffraction efficiency on the magnetic field for the inner spots. The results are presented in Fig. 8b. Plot points represent the diffraction efficiency for segments with an angular width of 20◦ (as illustrated in 8a) and centered at the azimuthal angle ϕ presented on the x-axis. Diffraction efficiency is approximated here as the ratio between the number of neutrons detected in a segment and the number of neutrons detected in the entire analyzed area and the direct beam, without accounting for the reflections that were cut off by the tube. Uncertainties are estimated as described above. Vertical lines are drawn every 60◦ , starting at 30◦ , and match the

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locations of the peaks. The diffraction efficiency for the four spots whose scattering vectors are not parallel to the magnetic field increases with field strength. In contrast, diffraction efficiency remains constant for the two spots with scattering vectors parallel to the magnetic field (indicated by dotted vertical lines). This is consistent with neutron-scattering theory (see for example [34]), from which it follows that the magnetic scattering length bm is proportional to µn · M⊥ (q), where µn is the neutron magnetic dipole moment and M⊥ (q) is the magnetization component perpendicular to the scattering vector q. Therefore, magnetic contributions to neutron scattering are expected only for scattering vectors with components perpendicular to the sample magnetization, i.e. perpendicular to the magnetic field. It can happen that the magnetisation in the outer layers of the nanoparticles is not aligned with external magnetic field [35, 36], which should, in principle, lead to changes in bm for directions that are not perpendicular to B, but this effect was not observed in our experiment. We also performed the same measurement without  the helium tube between the sample and the detector, so that we could observe the diffraction from the 2¯ 20 planes (outer spots). Although the diffraction spots were clearly visible, we were unable to get a statistically significant difference between the measured diffraction efficiencies with and without external magnetic field in this case. We believe that the additional scattering of neutrons in the air between the sample and the detector in our home-made SANS setup produced noise that obscured the rather small effect of the magnetic field. The experiment will be repeated with improved samples and better counting statistics.

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4. Conclusions We have prepared colloidal crystals complemented by superparamagnetic maghemite nanoparticles that fill the voids in the self-assembled crystal structure. Neutron diffraction experiments indicate that the diffraction efficiency can be changed by applying an external magnetic field. The vertical deposition method used for the self-assembly of the crystals investigated in this study was a relatively simple one, without exact control over humidity during the process. If more care is taken to control the self-assembly process, it may be possible to use the same procedure to produce samples of greater thickness, improved order in the crystal, and with a higher concentration of incorporated nanoparticles. This study brings us another step closer to a small and inexpensive polarizing beam-splitter for cold neutrons. At a later stage of development, experiments with deuterated or fluorinated materials to prevent strong incoherent scattering and/or absorption of neutrons will be considered.

5. Acknowledgments The authors gratefully acknowledge the financial support of Slovenian Research Agency (ARRS) in the framework of research programme Light and Matter (grant no. P1-0192), the financial support of the Centre for International Cooperation & Mobility of the Austrian Agency for International Cooperation in Education and Research (grant no. Si 13/2016), and the hospitality of the Paul Scherrer Institute and the Institut Laue Langevin. We thank H. Kabelka and P. Litschauer for providing the electromagnet. This work is partly based on experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland.

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