Opal-like Structures and Inverse Opal-like Structures

Photonic crystals (PCs) with three-dimensional (3D) periodicity of dielectric structures, called artificial opals, or Opal-like Structures, have attracted much attention in the past decade for their ability in light manipulation, which has potential applications in the area of photonics [1]. The inverse opal-like structures (inverse OLS) can be used as eliminators of unwanted heat from the thermal emission sources [2], in the conventional lighting field for increasing efficiency and obtaining improved thermophotovoltaic devices [3], as piezoelectric transducers, solar cells, phosphors, short-wavelength light emitters [4], gas sensors [5] and so on.

Fabrication

Highly ordered artificial opals can be fabricated by using high quality monodisperse spheres made of silica, polymethylmethacrylate, or polystyrene with a procedure based on combination of self-assembly and sol–gel method (sedimentation) [1, 6, 7] (Fig. 1a), self-assembly and pressure (colloidal epitaxy) [8-10] (Fig.1b), self-assembly onto polished conductive substrates by the vertical deposition method 

Figure 1. Methods of fabrication the opal –like structures 

(convective assembly, or controlled drying) [11-16] (Fig.1c), spin coating [17], electrophoresis [18-20].

If the voids of artificial opals used as templates are filled with other materials – polymers [21-23], liquids [24-26], inorganic oxides [27-30], carbon [31], semiconductors [32-35], superconductors [36-38], and metals [39-45] and then the templates is removed (if necessary) we have got an inverse opal-like structures. 

Figure 2. Fabrication (1-3) and SEM image of the inverse OLS. 

On Figure 3 the features of the natural and artificial opals are presented.

Figure 3. The features of the natural (a) and artificial (b) opals. 

Structure

The scanning electron microscopy (SEM) image of the synthesized samples is presented in Fig.1. Typically the vertical deposition method produces a thin OLS consisting of 10 – 40 layers on the substrate. The geometry of the synthesis directly determines the geometry of the future crystal. The direction perpendicular to the

Figure 4. SEM images of the top view of OLS (a) and inverse OLS on the base of Co (b) films.

substrate is the always the [111] axis of the FCC structure. The vertical axis (axis of aqueous suspension drying, or meniscus moving) always corresponds to the [20-2] crystallographic direction. Thus, already on the stage of synthesis one is able to have a clear understanding of the orientation of the crystal. The question remained unsolved is about the structural quality of the obtained crystals which can degrade at each step of the synthesis: 1) synthesis of the template, 2) synthesis of inverse structure, 3) dissolvent of the template.The silica or polystyrene spheres typically pack in a face-centered cubic structure, wherein each sphere contacts 12 others (6 in the same layer, 3 in the layer above and 3 in the layer below) (Fig. 5). Hence, the voids of the artificial opal have quasi-cubic and quasi-tetrahedral forms with concave sides and they are connected by vertices 

Figure 5. Forming of thehard package structure  of the microsphere:

(a)first level (A), (b) second level (B); (b) and (c) third level (C); (d) FCC structure; (e) HCP structure. 

along each of four [111] axes (Fig. 6). It means, that  we can considered inverse OLS as an assembly of small metallic particles duplicating the shape of the voids and connected to each other via thin (several tens of nanometers) and long (several hundreds of nanometers) “legs”.

Studying the internal structure of photonic crystals is inherently difficult: their optical properties exclude the use of microscopy or light scattering techniques for detailed characterization. A similar argument holds for electron microscopy techniques. Using these, information can only be gained about the surface structure of the crystals. X-rays, however, do have the required penetration depth to study the interior of these crystals. By using a specialized X-ray diffraction setup at BM-26 DUBBLE (European Synchrotron Radiation Facility, Grenoble, France) [46, 47] , the internal structure of OLS and inverted crystals was probed. Since the particles are larger than 400 nm in diameter, an extremely high resolution in reciprocal space is required in order to be able to study the crystals using

Figure 6.Schema of the quasi-cubic and quasi-tetrahedral voids of OLS connected by vertices along one of [111] axes.	Figure. 7.Schematic drawing of the diffraction experimentswith the use of synchrotron radiation.

radiation with a wavelength of the order of one Ångström. This is achieved by focusing the beam at the detector using a set of Berylliumcompound refractive lenses positioned next to the sample [48, 49]. The diffraction patterns are recorded at various sample rotation angles of -65^o<w<+65° around the [20-2] crystallographic direction, where w = 0° corresponds to the geometry of the film surface perpendicular to the beam (Fig. 7). It is allowed us to obtain the information about ordering the samples in different crystallographic directions.

The diffraction patterns of the OLS at rotation angles w = 0^o,19^o, 35^o, and 55^o are presented on Fig.8. The hexagonal arrangement of the Bragg reflections (Fig. 8a)reveals the hexagonal ordering within the planes parallel to the substrate (real space in Figure 9a). The strongest reflections can be understood assuming a FCC structure with the lattice constant of 650 ± 10 nm. However, one can also see a few additional weaker reflections, which are not allowed for an FCC structure. Their origin can be related rather to the finite thickness of

Figure 8. The diffraction patterns of the OLS at rotation angles w = 0^o,19^o, 35^o, and 55^o

the samples than to a random hexagonal-close-packing (RHCP) structure of the OLS. The high fraction of FCC configurations in the studied samples is indeed confirmed by Figure 8d, where the incident beam is at a 55° angle with the substrate and reveals the 4-fold symmetry of the FCC structure seen along the [010] direction (real space in Figure 9c). The surprise is to be found in Figure 8c, measured along the [101] crystallographic direction of FCC. Most peaks do indeed correspond to this, but in addition there are diffuse scattering stripes in the images between 111 and 020 types of reflections. These are the so-called Bragg rods and are indicative of stacking disorder. It is well seen form Figure 9b that the small moving of the colloidal spheres banded by black line from (½,½,1) to (½, ½, ½) positions (along [] direction on Fig.9b) will be result into stacking faults along [111] direction. These findings showed that the line defects, which are usually seen at the crystal surface with scanning electron microscopy (Figure 10), in fact correspond to two-dimensional stacking fault defects terminating at the crystal surface.

Figure 9. Real space OLS orientations

Figure 10. Real space crystal structures. Panel (a) and (b) show SEM pictures of an as-grown crystal and an inverted crystal respectively. The lines of square packing correspond to the stacking faults. In the inverted crystal (b), the same square configuration can be observed in the second layer. Panel (c) is an AFM image, showing the height step associated with the stacking faults.

Except one- and two-dimensional stacking fault defects there are numbers of faults of different nature such as cracks, dislocations, twin planes, point defects. The photonic crystal engineering can use a number of parameters, which can influence the forces involved in the colloid self-assembly process and responsible for the formation of OLS. For example, by adjusting the density mismatch between the particles and the solvent, one can modify the strength of the effective gravity force. Variation of the growth temperature can slightly affect the diffusion and can have a strong effect on the evaporation rate and, therefore, on the convection force. Changing the particle charge can influence the interparticle forces. Still, one may need to have additional means to vary the force balance and, therefore, to fine tune the crystal structure and quality.

Electric field could be an excellent tool to control the crystallization process. Here we present results on application of DC electric field normal to the substrates during vertical deposition of colloidal crystals (Fig.1c). Despite the negative charge of the particles, the crystals are found to form on both positively- and negatively-charged electrodes. It is found that electrostatic attraction between the particles and the substrate increases the crystal thickness while repulsion between them promotes higher crystal quality.

The representative scanning electron micrographs of as-grown colloidal crystals of polystyrene spheres obtained on a cathode and on an anode are shown in Fig. 11. Panels A and B correspond to the top surface and cross section of the crystal deposited at U = 1.5 V on a cathode, C and D – at 3 V on an anode. On the cathode one can see that the particles are neatly arranged into periodic arrays. Still, some defects are visible such as a few vacancies and two-dimensional stacking fault (lines) (Fig. 11a). Fig. 11c illustrates that anode polarization leads to formation of highly defective colloidal crystal structure. In this case the electrostatic attraction between negatively charged particles and the positive electrode is presumably too strong so that the polystyrene spheres have little chance to rearrange their position to find a better place in the crystal. Only top layers of the colloidal crystals formed on are ordered due, probably, to screening of Coulomb interaction by the bottom layers (Fig. 11d).

Figure 11. SEM images of OLS prepared by vertical deposition method in a presence of an external electric field perpendicular to the substrates. Panels A and B correspond to the top surface and cross section of the crystal deposited at U = - 1.5 V, C and D – at U = +3 V.

The results of the microradian X-ray diffraction are shown in Fig.12. In the diffraction patterns one can clearly identify a large number of Bragg reflections, which can be assigned to the reciprocal lattice of the ideal FCC crystal structure with the cubic cell size of a₀ = 750 nm. It is seen, as well, that diffraction pattern for OLS synthesized at U = -1.5V consists of pointed high order reflections up to four order in compared to artificial opal synthesized at U = +1.5V.

The monotonic improvement of the crystal quality from U = +1.5.V to U = -1.5 V can also be derived from the width of the diffraction spots (Fig.12c). The results obtained for 111 reflection are summarized in Fig. 13b. The full-width at half-maximum (FWHM) of the diffraction maxima in the azimuthal (Δq) and radial (δq) directions characterizes the mosaicity of the colloidal films and the average crystallite size (Λ), respectively. One can see that the mosaicity Δq of OLS decreases from 8º to 4º when the applied voltage changes from +1.5 V to -1.5 V. The peak width in the radial direction is determined from the fit by a Lorenzian accounting for the instrument resolution value (FWHM of the profile of the direct beam). One can see in Fig. 13b that application of the negative potential leads to a significant increase of the average size of crystallites Λ = 2πB/δq, where B is a factor of the order 1.

Figure 12. The diffraction patterns of the OLS at rotation angles w = 0^_o (a) and 35^o (b) for samples synthesized at different U = -1.5, -1, 0, +1, and +1.5 V. (c) The w-dependence of the intensity for (-11-1), and (-1-11) Bragg reflections.

Figure 13. a) The dependence of thickness of a colloidal film on applied voltage U (according to SEM data Fig.13).b) The longitudinal and transfers width of the reflection (111) on the potential applied upon OLS synthesis. 

Thus, increase of a cathode polarization leads to the improvement of crystal quality but, at the same time, the thickness of a film decreases (see Fig. 11b,d). Optimum value of an applied voltage U for the conditions we have used (given concentration of the suspension, pH, charge of colloidal particles, temperature, distance between electrodes, etc.) is around -1.5 V. These conditions allow growing crystals that are 20 layers thick.

Magnetic Structure of OLS on the based of ferromagnetic materials

Due to non-trivial spatial structure, ferromagnetic inverse opals possess unusual magnetic properties. Conventional methodics for magnetic studies like Superconductive Quantum Interference Device (SQUID) magnetometry and Magnetic Force Microscopy (MFM) are not sufficient in this case. MFM allows investigating only the surface of the sample, when IOLS are so interesting due to its complicated 3D magnetic structure. By the way, roughness of the surface (height changing is about hundred nanometers) can lead to significant distortions of obtained patterns or even to cantilever damaging. SQUID-magnetometry allows determine coercivity, remanent magnetization, saturation field and magnetization, which are integrated parameters of the sample, when the magnetization distribution in IOLS remains unstudied.

The only technic, which provides this information, is small-angle neutron scattering (SANS). Since we deal with the ordered object the scattering transforms to diffraction with well defined Bragg reflexes.

SANS measurements were carried out with the instrument SANS-2 at the Geesthacht Neutron Facility (GeNF) [50]. The schematic drawing of the setup is shown in Fig.14. It points out that the instrument equipped with the Polarizer and the Spin Flipper to provide the possibility of studying the polarization dependent neutron cross section.

Figure 14. Schematic drawing of the polarized neutron diffraction experiment.

In our experiments the neutron scattering intensities I⁺(q,+P₀) and I^–(q,-P₀) were measured with the neutron beam polarized parallel and antiparallel to the external magnetic field, respectively. An external magnetic field was applied perpendicular to incident beam and ranged from ‑1.2T to 1.2T.

The cross section of polarized neutrons from a magnetic structure with a large period can be split into three contributions [51]:

I nuclear scattering

(1)

II magnetic scattering

(2)

III interference scattering

(3)

where S(q) — structure factor – a result of scattering from the structure, F(q) – form factor –  a result of scattering from a particle that is the base element of the structure, m is the unit vector of magnetization M, and m_¬q = m – (q×m)q/q². These nuclear and magnetic contributions are determined by the scattering amplitudes A_n and A_m, respectively.

Polarization-independent part of the scattering, which was determined as:

represents the sum of the nuclear and magnetic scattering. The nuclear contribution I(q) to the peak intensity is obtained for nonmagnetized sample ( ‹m›= 0), in that case the magnetic coherent scattering vanishes and the diffuse small angle scattering arises.

The magnetic scattering I_m(q) is proportional to the difference between the magnetic cross-sections of the sample in two principally different states: partially magnetized in the finite field H and fully demagnetized at H ~H_c:

The polarization-dependent part of the scattering is determined as

It is attributed to the nuclear-magnetic interference indicating the correlation between the magnetic and nuclear structures.

The neutron diffraction patterns are shown in Fig.15. Observed reflections correspond to the neutron scattering on the {202} crystallographic planes what is in a good agreement with microradian X-ray diffraction data (Fig.8a). The external magnetic field H was applied along the [-12-1] axis.

By analyzing field dependence of magnetic contribution to the intensity of these reflexes, one can obtain the information about magnetizing of corresponding scattering planes. Thus, such dependencies for different reflexes allow to understand the magnetization distribution in IOLS on the different stages of magnetizing. 

Figure 15. Neutron diffraction patterns for Co IOLS with the magnetic field H = 294 mT along the [-12-1] axis. The Miller indices of the reflections correspond to the fcc structure with the lattice constant of a₀ = 760 ± 10 nm.

Interpretation of experimental data was done by the constructing the model of the magnetization behaviour at the different values of applied external field.

As mentioned above, the IOLS is an array of quasicubes and quasitetrahedra connected by the “legs” – bridges along <111>-type axes of the fcc structure. Magnetic lines go from one cube or tetrahedron (“quasi” is omitted for simplicity) via these “legs”. Neglecting magnetocrystaline anisotropy, one can suppose, that the anisotropy of “legs” forces local magnetization vectors in it to direct along <111>-type axes, being the Izing vectors.

Thus, the tetrahedron is like a crossroad, where four “legs” are meeting. To minimize magnetic energy, flux of magnetization should be equal to zero for each tetrahedron or cube. This requirement looks like the so-called “ice-rule”, which was firstly introduced for conventional ice [52,53].

This rule states, that in tetrahedral cells, constructed by oxygen ions, hydrogens are situated on the line, connecting vertex and central oxygen, so, that two are closed to each oxygen ion, and two are far. (Fig.16a).

Figure 16. Conventional ice structure. Red balls are oxygen ions, green ones are hydrogens (a), Spin ice structure. Blue balls are rare-earth ions, yellow arrows – its magnetic moments (b) Magnetic structure of the IOLS. Arrows are the local magnetization vectors in “legs” (c).

Subsequently, “ice-rule” was applied to new type of magnetic structures – spin ices [54,55]. In vertices of spin ice tetrahedral cells rare-earth ions with high magnetic moment are situated. Herewith, interactions in such systems lead to modification of the “ice-rule”: two magnetic moments direct in tetrahedron and two – out of it. (Fig. 16b). In case of IOLS, such “ice-rule” should be fulfilled for the tetrahedra as well as for cubes. Thus, for the IOLS the “ice-rule” can be formulate commonly: amount of the local magnetization vectors incoming in tetrahedron or cube should be equal to amount of outcoming ones. (Fig. 16c).

In the fully demagnetized state the IOLS is intrinsically frustrated similar to the model of the artificial spin ice. We focus on the IOLS under an applied magnetic field when the frustration and degeneracy is lifted for certain directions of the field by favoring energetically local magnetic moments with a positive projection to the field direction.

Using the ice rule model one can estimate both the total magnetic energy of the IOLS and its average magnetization. Twelve of the 14 vertices present in one unit element are shared with the neighboring elements and, thus, doubly counted. Therefore, for the magnetic structure based on IOLS the unit element is a combination of the four moments of the lower tetrahedron (TD) and the four moments of the upper tetrahedron (TU). The average magnetization is the sum of all eight moments of the unit element and corresponding magnetic energy given by

(7)

where M₀ is the value of magnetic moment in one “leg”, H is the magnetic field, and m_[hkl] is the unit vector along [hkl] direction. E_{ice rule} denotes the energy of the magnetic flux inside the element, which is minimal, when the ice rule is fulfilled for both tetrahedra. The situation when three moments are directed towards each other opposite to the fourth moment at the tetrahedron “crossroads,” or vice versa, is less favorable and the energy E_{ice rule} increases. The most unfavorable configuration arises when all four moments point towards or away from each other at the crossroads.

In order to gain insight into the remagnetization process the magnetic states of the IOLS at different magnetic fields have to be considered. These states in the magnetic field applied along the [-12-1] axis are presented in Fig. 17. It is convenient to consider one layer of the (111) plane of the structure. Each layer is connected to the neighboring ones only via “legs” in the [111] direction perpendicular to the layer plane and the magnetic field. The moments along the <111> axes can be divided into four magnetic subsystems, which are represented by arrows in Fig. 17, and connect the central cube via eight vertices with the neighboring tetrahedra. When the magnetic field is applied in the (111) plane, the out-of-plane moments along [111] seem to be degenerate. However, as will be shown below, due to the ice rule this degeneracy is lifted.

H= ‑Hc2	H = 0	H = Hc
H = Hc1	H = Hc2	H > Hc3

Figure 17. Magnetization distribution in IOLS for different stages of the remagnetization process: at  H = ‑H_c2 (a), at H = 0 (b), at  H = H_c (c), at  H = H_c1 (d), at  H = H_c2 (e), and at H > H_c3 (f). The Ising-like magnetic moments (labeled with arrows) are oriented along the <111> axes. Moments in the upper plane are light-colored.

Evolution of magnetic structure during magnetizing occurs via reorientation of magnetic moments in pairs for each tetrahedron or cube. Herewith, each magnetic subsystem reorients at its own value of the field. Due to that, all the process is stepped with some critical fields H_ci.

The most interesting stage at H ~ H_c2 is shown in Fig.17a. I this case, the magnetic moments have positive projections with respect to the field direction and are oriented along the three ([-111], [1-11], and [11-1]) axes. In such a configuration, one magnetic moment points towards the lower tetrahedron, whereas two moments point away from the tetrahedron. According to the ice rule the fourth moment perpendicular to the plane should also point towards the lower tetrahedron (upwards). For the upper tetrahedron the situation is opposite, i.e., two magnetic moments point towards and one moment points away from the tetrahedron. The fourth moment is expected to point away (upwards) similar to the lower tetrahedron. Therefore, the sample has an additional magnetization component, which is perpendicular to the (111) plane pointing upwards and, thus, perpendicular to the applied field.

The average magnetization along the fieldis:

(8)

However, as it was shown, due to the “ice-rule” the component of the magnetization perpendicular to the field and sample plane arises:

(9)

Using the maps of magnetization distribution on each stage of magnetizing (Fig. 17) and Eq. 7 one can obtain both components on these stages. Calculated values are presented in Table 1.

Table 1. Values of the magnetization components parallel and perpendicular to the field at different stages of the reorientation process which correspond to the panels of Fig. 17 (H || [-12-1])

Obviously, that the value of perpendicular component strongly depends on the sample orientation in the field. Going downwards, when the field is applied along [1-21], [11-2], [-211] axes, M_┴ decreases to zero, when the field is applied along [-110], [10-1], [01-1], [-110], [-101], [0-11] axes and going upwards, when the field is along [2-1-1], [-12-1], [-1-12] axes. It changes by the periodical low, with the 120 degrees period, determining by the 3-fold symmetry of the [111] axis of the IOLS. Some more complicated and interesting effects can appear, when the filed vector does not lie in the sample plane.

In the model described above the experimental data can be easily interpreted. The magnetic intensity I_M is proportional to the volume of the scattering element magnetized in the direction [hkl] (V_[hkl]), which is considered equal for the four directions along the <111> axes. It is proportional to the squared magnetization |m_┴Q|² projected to the plane normal to the scattering vector Q (Eq. (5)). We also introduce the proportionality factor a_i(H_c(i)), which is equal to 0, when the subsystem is nonmagnetized, and equal to 1, when it is magnetized. H_c(i) is the threshold field of these subsystems. Thus:

(10)

For two types of the observed reflexes:

The fact that all four moment subsystems are magnetized differently and saturate at different values of the applied magnetic field H_c(1,2,3,4) is observed in the field dependence of intensity I_M(20-2) undergoes another small but abrupt change, while the intensity I_M(02-2) starts to decrease smoothly (Fig. 18).

Figure 18. Field dependence of the magnetic intensity I_M of neutron scattering on Co IOLS with H || [-12-1] (a) at Q_20-2 ⊥ H, (b) at Q_02-2 inclined at 30° with respect to the field H

This decrease of I_M(02-2) is observed up to the highest measured field H = 1.2 T. The intensity I_M(20-2) remains unchanged in the range from H_c3 to 1.2 T. Obviously the theoretical points are in good qualitative agreement with the experimental data, but some differences should be noted. First, the calculated point at H_c1 is lower than both intensities in the experiment. This is due to the fact that our calculations describe only the consequent flipping of two types of magnetic moment pairs, while several different pairs can flip contemporaneously. It means, Secondly, the last theoretical point is too high for I_M(20‑2) (out of plot). This can be explained by the demagnetization occurring inside structural nanoelements in high magnetic fields.

Generally speaking, ferromagnetic inverse opal-like structures, possessing complicated magnetic structure are the interesting objects for studying geometrical frustration in three-dimensional nanostructures. By the way, like in spin ice some unconventional states can arises, at different directions of the magnetic field. For example, when field is along [111] axis, ice rule is not valid, and something like “magnetic monopoles” can appear.

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The results of the investigation artificial opals and inverse opal-like structures are published in:

1. K.S. Napolskii, A. Sinitskii, S.V. Grigoriev, N.A. Grigorieva, H. Eckerlebe, A.A. Eliseev, A.V. Lukashin, Yu.D. Tretyakov. Topology constrained magnetic structure of Ni photonic crystals. // Physica B, 2007, v. 397, pp. 23 - 26.
2. С.В. Григорьев, К.С. Напольский, Н.А. Григорьева, А.А. Елисеев, А.В. Лукашин, Ю.Д. Третьяков, Х. Эккерлебе. Инвертированные магнитные фотонные кристаллы: исследование методом рассеяния поляризованных нейтронов. // Письма в ЖЭТФ, 2008, том 87, вып. 1, с. 15-21. English version: S. V. Grigor’ev, K. S. Napol’ski, N. A. Grigor’eva, A. A. Eliseev, A. V. Lukashin,Yu. D. Tret’yakov, and H. Eckerlebe, «Magnetic Inverted Photonic Crystals:A Polarized Neutron Scattering Study», JETP Letters, 2008, Vol. 87, No. 1, pp. 12–17.
3. V. V. Abramova, A. S. Sinitskii, N. A. Grigor’eva, S. V. Grigor’ev, D. V. Belov, A. V. Petukhov, A. A. Mistonov, A. V. Vasil’eva, and Yu. D. Tret’yakov, «Ultrasmall_Angle X_ray Scattering Analysis of Photonic Crystal Structure» Journal of Experimental and Theoretical Physics, 2009, Vol. 109, No. 1, pp. 29–34.
4. S.V. Grigoriev, K.S. Napolskii, N.A. Grigoryeva, A.V. Vasilieva, A.A. Mistonov, D.Yu. Chernyshov, A. V. Petukhov, D.V. Belov, A.A. Eliseev, A.V. Lukashin, Yu.D. Tretyakov, A.S. Sinitskii, H. Eckerlebe. Structural and magnetic properties of inverse opal photonic crystals studied by x-ray diffraction, scanning electron microscopy, and small-angle neutron scattering // Physical Review B, 2009, v. 79, 045123.
5. J. Hilhorst, V.V. Abramova, A. Sinitskii, N.A. Sapoletova, K.S. Napolskii, A.A. Eliseev, D.V. Byelov, N.A. Grigoryeva, A.V. Vasilieva, W.G. Bouwman, K. Kvashnina, A. Snigirev, S.V. Grigoriev, A.V. Petukhov. Double Stacking Faults in Convectively Assembled Crystals of Colloidal Spheres // Langmuir, 2009, v. 25(17), pp. 10408-10412.
6. А.А.Елисеев, Д.Ф. Горожанкин, К.С. Напольский, А.В. Петухов, Н.А. аполетова, А.В. Васильева, Н.А. Григорьева, А.А. Мистонов, Д.В. Белов, В.Г. Бауман, К.О. Квашнина, Д.Ю. Чернышов, А.А. Босак, С.В. Григорьев, «Определение реальной структуры искусственных и природных опалов на основе трехмерных реконструкций обратного пространства», 2009, Письма в ЖЭТФ, т.90, вып.4, с.297-303.
7. A.V. Vasilieva, S.V. Grigoriev, N.A. Grigoryeva, A.A. Mistonov, K.S. Napolskii, N.A. Sapoletova, A.V. Petukhov, D.V. Belov, A.A. Eliseev, D.Yu. Chernyshov, A.I. Okorokov, Imperfection analysis of opal-like photonic crystals, grown on conductive substrates, Solid State Physics, v.52, 5, p. 1017-1020 (2010)
8. Sapoletova N.A., Martynova N.A., Napolskii K.S., Eliseev A.A., Lukashin A.V., Kolesnik I.V., Petukhov D.I., Kushnir S.E., Vassilieva A.V., Grigoriev S.V., Grigoryeva N.A., Mistonov A.A., Byelov D.V., Tret'yakov Yu.D., «Electric-Field-Assisted Self-Assembly of Colloidal Particles», Physics of the Solid State, v. 53, 6 1126–1130 (2011),
9. N.A. Grigoryeva, A.A. Mistonov, K.S. Napolskii, N.A. Sapoletova, A.A. Eliseev,  A.V. Vasilieva, W. Bouwman, D.V. Byelov, A.V. Petukhov, D. Yu. Chernyshov, H. Eckerlebe, S.V. Grigoriev «Magnetic topology of Co based inverse opal-like structure», Physical Review B, 84, 064405(13), (2011).
10. M. Kostylev, A. A. Stashkevich, Y. Roussign´e, N. A. Grigoryeva, A. A. Mistonov, D. Menzel, N. A. Sapoletova, K. S. Napolskii, A. A. Eliseev, A. V. Lukashin, S. V. Grigoriev, S. N. Samarin, Microwave properties of Ni-based ferromagnetic inverse opals, Phys.Rev.B v. 86, 184431 (2012)
11. A. A. Mistonov, N. A. Grigoryeva, A. V. Chumakova, H. Eckerlebe, N. A. Sapoletova, K. S. Napolskii, A. A. Eliseev, D. Menzel, S. V. Grigoriev, «Three-dimensional artificial spin ice in nanostructured Co on an inverse opal-like lattice», Physical Review B, v. 87, 220408(R) (2013)

The results of the investigation artificial opals and inverse opal-like structures were reported on:

1. Kirill S. Napolskii, Sergey V. Grigoriev, Natalia A. Grigorieva, Htlmut Eckerlebe, Andrei A. Eliseev, Alexei V. Lukashin, «Polorized SANS study of the magnetic inverted photonic crystals” ECNS 2007, June 25-29, 2007, Lund, Sweden.
2. Alexander Sinitskii, Vera Abramova, Tatyana V. Laptinskaya, Kirill Napolskii, Sergey O. Klimonsky, Sergei Grigoriev, Natalia Grigorieva, «Neutron, X-rayandlaserdiffractionininverseopalfilms», E-MRSFallMeeting 2007, 17-21 September 2007, Warsaw, Poland.
3. S.V. Grigoriev, K.S. Napolskii, N.A. Grigoryeva, A.V. Vasilieva, A.A. Mistonov, A. Sinitskii, A.A. Eliseev, A.V. Lukashin, D.Yu. Tretyakov, H. Eckerlebe, «Inverse photonic crystals: structural and magnetic properties: from tip to toe», XLII Зимняя Школа ПИЯФ: Физика конденсированного состояния, Санкт-Петербург, 25 февраля – 1 марта 2008, Россия.
4. С.В. Григорьев, Н.А. Григорьева, К.C. Напольский, А.А. Синицкий, А. Петухов, В. Абрамова, А.А. Мистонов, А.В. Васильева, А.А. Елисеев, А.В. Лукашин, «Исследование структуры фотонных кристаллов методом ультрамалоугловой дифракции синхротронного излучения», XLII Зимняя Школа ПИЯФ: Физика конденсированного состояния, Санкт-Петербург, 25 февраля – 1 марта 2008, Россия.
5. N.A. Grigoryeva, S.V. Grigoriev, K.S. Napolskii, A.V. Vasilieva, A.A. Mistonov, A.A. Eliseev, H. Eckerlebe, X-ray and Neutron Small Angle Diffraction on the Co Inverted Photonic Crystal. 7th International Workshop on Polarized Neutrons in Condensed Matter Investigations, Tokai, Japan, September 1^st-5^th, 2008, p. 33.
6. А.В. Васильева, А.А. Мистонов, С.В. Григорьев, Н.А. Григорьева, К.С. Напольский, А.А. Синицкий, H. Eckerlebe, Магнитные свойства инвертированного фотонного кристалла на основе кобальта, XX Совещание РНИКС, 13-18 октября 2008, Гатчина, Россия.